ELEMENTS OF LOGIC;
DESIGNED AS A
MANUAL OF INSTRUCTION.
BY
HENRY COPPEE, A.M.,
PROFESSOR OF ENGLISH LITERATURE IN THE UNIVERSITY OF PENNSYLVANIA; AND
LATE PRINCIPAL-ASSISTANT PROFESSOR OF "ETHICS AND ENGLISH
STUDIES" IN THE UNITED STATES MILITARY ACADEMY
AT WEST POINT.
PHILADELPHIA:
PUBLISHED BY E. H. BUTLER & CO.
1858.




Entered, according to Act of Congress, in the year 1857, by
E. H. BUTLER & CO.,
In the Clerk's Office of t.he District Court of the United States, in and for
the Eastern District of Pennsylvania.




PREFACE.
THE following treatise has been written in the hope
that it may supply, in some degree, a real want. For
several years the author was a teacher of Logic, in
the Military Academy at West Point, where the subject was thoroughly studied by the aid of Archbishop
Whately's text-book.
How much a manual was needed before that work
appeared may be known from the significant fact that,
as soon as it was published as an article in the Encyclopmedia Metropolitana, it was eagerly caught at
by the community of teachers, and used, unaltered,
as a book for college instruction, on both sides of the
Atlantic.
Since the publication of that article many have
attempted the preparation of a manual, which should
have the instruction of classes as its original design;
but the soundness of Whately's views and the con(8)




iv                  PREFACE.
ciseness of his expression, still give to his work the
greatest circulation. Among so many endeavours the
author would venture to express the hope that his little
manual may find its special purpose and mission: it
is short; it is explanative of all the difficult points so
often left to confuse a student; the arrangement is
simple, and much that in a larger treatise would be
of necessity included, is here omitted, so that what
the student learns in the limited time of a college
term, he may learn well, and retain in his memory as
a basis for further investigations. To-some persons
it may seem too much simplified; but let it be remembered that it is a manual for youth; and that its only
aim is to teach them the Elements of Logic, as the
foundation of all reasoning.
The basis of the work is Whately's Logic'; many
of the examples are taken directly from that; so many
indeed, that the acknowledgment is here made for
them all, and for much that is excellent in arrangement and in expression. As the clear expounder of
Aristotle, and the originator of much that is valuable,
Whately must stand at the head of the Logicians of
this age. The author would refer specially also to
the material assistance obtained from, Devey's




PREFACE.                   V
Logic," (Bohn's series), " Aristotle's Post and Prior
Analytics," (Bohn's translation); Neil's Art of Reasoning;" " Blakey's Historical Sketch of Logic;"
" Lord Bacon's New Organon; Arnauld (Logique de
Port Royal);  J. Bentham's "Book of Fallacies."
From Neil a few of the examples have been taken.
Besides these he has consulted a great number of
works, the aid derived from which is so general that
they do not require special mention.
UNIVERSITY OF PENNSYLVANIA, July, 1857.
1*








TABLE OF CONTENTS.
CHAPTER L
PAGE
Section 1. Logic; the meaning of the term and the scope of the
Science.... 13
2. Sources of Error....14
3. Logic and Philosophy....16
4. Objection to Logic as an Art..      19
5. Natural Logic......21
6.. Systematic forms of Error..        22
7. Of Method......... 23
8. Analysis and Synthesis......  26
9. Analysis and Synthesis as applied to Logic...30
Proposed plan of Study: 1. An Analytical View of
Logic. 2. A Synthesis of Formal Logic. 3. A Historical View of Logic..        31-32
(7)




Viii            TABLE OF CONTENTS.
CHAPTER II.
ANALYTICAL VIEW OF LOGIC.
PAGE
Section 10. The reasoning process analyzed.      33
The Dictum of Aristotle..              36
CHAPTER III.
A SYNTHESIS OF LOGIC.
Section 11. Of certain operations and states of the mind in the process of Argument....40
CHAPTER IV.
Section 12. Of Terms.....45
13. Division of Simple Terms..... 47
14. Quantity and Quality of Terms....  49
CHAPTER V.
OF THOSE OPERATIONS IN LOGIC WHICH RELATE TO TERMS.
Section 15. Abstraction and Generalization.      51
16. Species, Genus, and Differentia..... 52
17. Property and Accident...... 53
18. Of the different orders of Genera and Species.. 56
19. Realism and Nominalism.....   58
20. Definition of Terms..                 58
21. Nominal and Real Definitions.....62




TABLE OF CONTENTS.            ix
PAGE
Section 22. Rules for Definition.          63
23. Division...                  68
24. Recapitulation..                 73
CHAPTER VI.
Section 25. Propositions.....           75
26. Propositions divided into Simple and Compound..79
27. Quantity and Quality of Propositions...81
28. Of the Distribution of Terms in Propositions.  85
29. Conversion......88
30. Of Opposition..                  94
31. Of the Matter of Propositions.....  96
32. Of Compound Propositions..        99
33. The Neiw Analytic.....103
CHAPTER VII.
Section 34. Of Arguments.....          106
35. Of the Syllogism.......108
36. Logical Axioms........109
CHAPTER VIII.
OF FIGURE AND MOODS.
Section 37. Figure........ 117
38. Of Mood.....121
39. Of Reduction....                 134




X              TABLE OF CONTENTS.
PAGE
Section 40. Indirect Reduction.......  139
41. Notation of the Syllogism...... 142
CHAPTER IX.
OF IRREGULAR, INFORMAL, AND COMPOUND ARGUMENTS.
Section 42. Of Abridged Syllogisms....      147
43. The Sorites, or Chain Argument..151
44. Of the Epichirema.......  155
45. Of Hypothetical Syllogisms.....   157
CHAPTER X.
FALLACIES.
Section 46. The Meaning and Comprehension of a Fallacy.. 170
47. Of Fallacies in dictione, or Formal Fallacies..172
48. Material, or Informal Fallacies.....  175
49. Verbal Fallacies....... 188
50. The manner of removing Ambiguity in Terms.. 201
51. The Fallacy of Probabilities, or the Calculation of
Chances....202
52. Popular Fallacies...205
CHAPTER XL
Section 53. Of certain modes in which Logic is applied..211




TABLE -OF CONTENTS.                  Xi
CHAPTER XII.
A HISTORICAL SKETCH OF LOGIC.
PAGE
Section 54. Division of the Subject.                220
55. Aristotle.....222
56. The Logic of Christianity...... 236
57. The Logic of Experimental Philosophy... 252
58. Logic in the Eighteenth and Nineteenth Centuries. 266
59. Of Categories and Classification..      268
60. Conclusion....               275








LOGIC.
CHAPTER I.
(l.) Logic: the meaning of the Term and the
scope of the Science.
As of all the Greek words which have been transferred to our English speech, none is vaguer and more
subtle in its meaning than the word logos (^oyos,) so
of all the sciences, none is less understood both as to
its meaning and its scope, than the science of Logic,
the name of which is taken from that word; and, in
consequence, no term is more erroneously applied and
more frequently misapplied than the name itself.
As %oyo5 means a word, some writers have supposed Logic to be simply the science of spoken or
written words, and have thus confounded it with
Rhetoric and even with Grammar: others, considering a word to imply not simply the written
symbol or the spoken sound, but also the expres2                              (13)




14                    LOGIC.
sion of the thouzght, have supposed Logic to be the
science of thought, and have thus confounded it with
Intellectual Philosophy, or the investigation of the
laws of thought and mind: others still, and by far the
greater number, regarding it as a union of language
and thought in the deduction of truth, have claimed
that it had to do with the subject-mdtter of scientific
investigation, and have thus erred more widely than
all by confounding Logic with the labours of physical,
metaphysical, and ethical philosophy.
It seems necessary then, at the beginning of a treatise on this subject, to define the meaning of the word,
and the true scope of the science, before we undertake its study:-to rid ourselves, as it were, of the
mists which surround us, before we can even see
clearly the field in which we are to labour.
(2.) Sources of Error.
Many accurate thinkers have confused the minds
of students by producing books, which, while they
contain a just view of the logical system itself, attempt
at every step to explain the subject-matter upon which
this system is employed, and which forms no part of
it; while many others, adopting strongly the views of
those who have initiated so-called systems of logic,
have, as partisans, carried forward from  period to
period old errors and old perplexities; and, themselves
ignorant of the subtleties which surround them, have




SO{C S- OF ERP.ROR.           15
called their views the true logic, and those of every
other writer false. Others again have endeavoured, in
an amiable but unscientific spirit, to harmonize all the
schemes of the philosophers, and to call the result,
full of error and inexactness, the system of Logic.
There are indeed in the systems of the great philosophers many parts that are mutually dependent, and
true science will be found to harmonize with itself
everywhere. But since there is also error in them all,
no mere greatness of name should exempt from the
scrutiny and exposure of error.
We must take care to distinguish between the different functions of the intellect, so as to call things
by their right names; not including in the name
Logic what belongs to Physics or Metaphysics, but
laying down at the outset the limits and province of
that system, which we wish to designate by the word
Logic. If -we can do this we shall have accomplished
very much at the beginning, and shall find our labour
easy as we proceed.
If we would see how important it is rightly to
understand this fact of the ambiguity which the word
Logic has produced in the minds of men, we need but
look for a moment at the errors into which modern
philosophers have fallen, when speaking of the Logic
of Aristotle as compared with the Logic of Bacon.
If, as we shall endeavour to demonstrate, Logic is
the science which controls the universal and ultimate




16                   LOGIC.
principle of reasoning, given to man, just as speech
was given to him, by a beneficent Creator, then it
is not Aristotle's Logic, nor Bacon's Logic, but a
single, universal Logic, given to man as the rule of
his reason, which must be intelligible and harmonious
wherever and by whomever it is used.
(3.) Logic and Philosophy.
In this consideration another word plays a prominent part. The word which has been pressed into
service, to denote the peculiar progress of great
minds in the domains of Truth, is "Philosophy;"
but even the word 44 Philosopher," adopted by a wise
ancient* as a more modest title than so0os, as the
sages of Greece were called, has been productive of
great confusion. "Philosophy" has been made to
stand for a thousand sciences, and to preside in the
kingdoms of mind, morals, and physics, until to be a
philosopher means to pursue one of many intellectual
pursuits, and Philosophy unqualified means everything or nothing.
And yet this vague and inexact term Philosophy,
is the one which has been most frequently confounded
with Logic, and a want of clear definition and of a just
understanding in the dispute, has led to the production of abominable, distorted, and monstrous systems,
* Pythagoras.




LOGIC AND PHILOSOPHY.           17
both of Philosophy and Logic, which have confused
those desirous of learning, and deterred many from
the difficult and perilous attempt.
Indeed both words, and the errors to which their
use has led, indicate, at once, the yearning and the
weakness of the human mind,-the desire of man to
investigate and systematize truth, combined with the
obscurity and doubt which beset his investigations at
every step.
The acuteness of the Greeks, upon which had been
grafted all the power and attainment of the Oriental
world, could reach no clearer nomenclature, than to
call their studies and their inductions Philosophythe love rather than the attainment of wisdom; and
the art by which they reasoned from truth to truth,
by which they progressed from parallel to parallel in
the sea of doubt and uncertainty, Logic, the art of
words or discourse, the very mention of which suggests a dubious question, and calls up, as it were, two
opponents in considering it.
In avoiding these errors, let us agree to regard
Philosophy as the investigation of truth, as to its
subject-matter, the process of finding materials, and
of classifying and aggregating observations and experiments, and Logic, as the simple reasoning process
by which we pass from truth to truth already found,
and by which we guard against false arguments in
such a passage.
2'-             B




18                  LOGIC.
Having thus seen that the name Logic is in a great
degree arbitrary, and that we should not attain to an
understanding of the subject, if we followed, even
remotely, the etymology of the word, we repeat that
Logic has to do neither with the words themselvesexcept as they are arranged into propositions and
arguments-nor with their meanings, but only with
the process of reasoning, i. e. passing from two kJnown
and acknozwledged judgments to a third which is
derived from their combination.  In general words,
then, we may state a definition of the term. Logic is
the Science and the Art of Reasoning.
Of these two terms, Science and Art, we remark
that Art is in a critical sense more extensive than
Science, since the practice of an Art implies the
application of the principles of Science, while on the
other hand, Science might, indeed does exist in its
theoretic state without being put to practical use.
The Science would be the investigation of the principles upon which the human mind is based in reasoning, and the Art, the application of those principles
to the establishment of practical rules for conducting
the process. Logic may then be more simply defined
the Art of Reasoning, and as such we shall consider
it in these pages: less concerned about the composition of man's reason, than about the practical laws
and methods by which it works.
Before proceeding to explain the system of Logic,




OBJECTION TO LOGIC AS AN ART.       19
which has developed itself since the days of Aristotle,
let us meet at the threshold some plausible objections
which have been brought against the establishment of
any system whatever.
(4.) Objection to Logic as ant Art.
As man has been universally gifted with reason by
means of which he may combine his thoughts and
arrive at just conclusions, and with language in which
to communicate them, it is asserted that every man
carries his own Logic within him, as the immediate
gift of God.
All men reason, it is true, and many men are not
aware of the logical process which they use; and this
has been made, even by men of acute minds, an objection against Logic; for, they say, since men reason,
and reason well, without rules, and without knowing
the process, a system of rules must be unnecessary.
The objection is plausible, and has been fruitful of
evil. But as it is one which may be brought against
many other arts as well as Logic, it may, we think,
be most easily met, and most clearly refuted by illustration. Many children speak with correctness and
precision before they have any knowledge of Grammar;
and there are persons of wonderful powers in arithmetical computation who have never learned Arithmetic;
but Grammar and Arithmetic are not for such reasons
condemned: their rules are an infallible test for pre



20                   LOGIC.
cise speaking, and correct computation, and are tbhus
guides to the weaker and slower intellects,-and these
constitute the immense majority of mankind,-to keep
them from formal error. So, too, in Music and Pailting; great geniuses arise in both Arts, but no one
would contend that hard study, according to the established systems of the great composers, and the great
masters-established upon the true principle of voice
and ear-is not absolutely requisite to excellence
and success.
Many persons of clear perceptive faculties, and
who form and combine their judgments rapidly, may
reason acutely and well without a system of rules;
but, in order to be certain of their correctness, others
must have some invariable test; on the other hand
there are many, of quick but erratic minds, who reason with such dangerous sophistry that the most delicate logical tests alone can expose the fallacy, of
which indeed they may not themselves be entirely
aware. As such delicate tests have not been within
the reach of the multitude, it is thus that men have
become, for want of a popular knowledge of Logic,
at once self-deceivers and deluders of mankind: have
established illogical religious creeds, monstrous social
fallacies, false theories of government, which are immediately made manifest by the simple application of
Logic.
Nay more: since Logic is the one, universal princi



NATURAL LOGIC.               21
pie of Reasoning, applied alike to every branch of
science Exact or Inductive, it seems much more
necessary that we should establish full and unerring
rules for our guidance, and thus be kept, at every
turn, from the manifold errors which arise from systems based upon such objections as those we have
mentioned.
(5.) Natural Logic.
The natural laws which govern the human mind in
its attempts to reason, have been called by the opposers of Logical systems, Natural Logic. We accept
the name, and are ready to allow that this instinct of
reason is in the main right, and originally, perfect in
its kind; but now, in the fallen condition of man, liable
to be biassed by prejudice, distorted by passion, or
ilisidiously tempted into open error. Thus many men,
who reason correctly on most subjects, are swayed,
in one or more, by self-interest, partisanship, fashion,
predominance of the imagination, and such like
causes: and thus men of equally clear minds, in the
main, from the same premises draw different conclusions, or establish the same conclusion by very different premises.  Thus also the same man, at different
periods of his life, or swayed by various circumstances,
will reason differently; and from such causes, it is
evident that each man's natural Logic is not a sufficient guide for his reason.




22                    LOGIC.
Yet still it is from this natural Logic, or rather,
the concurrence of the right reason of many well
ordered minds, that the science of Logic has been
deduced.
By a systematic observation of such minds, as they
reason, taking care to remove all causes of error in
each particular case, we establish rules for the reason,
and are able to detect, by the application of these
rules to other cases, every fallacious argument resulting from such causes of error.
There must have been reason before there could be
a system of laws to govern it, just as we know there
was language before Grammar was formed.     It was
to systematize this reason, to methodize this natural
Logic, and particularly to guard against errors in the
use of the reasoning powers, that a canon was prepared, and that a complete science of Logic has been
formed.
We have spoken in general terms of the confusion
and error which have grown out of the misapprehension of Logic; the more special phases of it are those
resulting from an attempt to systematize these general
erroneous notions.
(6.) Systematic Forms of Error.
By a very common misuse of language, we hear
such phrases as 4 mattlematical reasoning," nmoral
reasoning,"   syllogistic reasoning," and," inductive




OF METHOD.                 23
reasoning;"  which would lead us to suppose that
instead of one there were many kinds of reasoning.
This is a fruitful source of error.
These, so-called, different kinds of reasoning are
only applications of Logic to different subjects, and
different habits of thought: the Logic in each is the
same, the subject-matter alone is different.
It would seem unnecessary to dwell upon this point,
but it has been so commonly misunderstood, and the
error has been so disseminated by professed writers
upon Logic, that it must be plainly stated and carefully remembered.
When we speak, then, of a good mathematician, we
mean one who is able, most surely and rapidly, to
apply Logic to the investigations of numbers and
quantity. When we hear of a great theologian, we
know that he has amassed much theological learning,
and has applied Logic to it successfully. So too with
other sciences.
In general, in which ever of the myriad fields of
Nature and mind, ardent votaries may wander; however various the stores they may amass, they must all
come back with their sheaves to the great measuringcentre of Logic, and apply its dicta before they can
compute or use their gathered gains.
(7.) Of Method.
Method is the order and arrangement of facts to




24                    LOGIC.
produce a certain result; to establish new -truth, to
investigate old, and to explain and teach both. It is
derived from the Greek,to'osov; which denotes the
way through which we arrive at a certain result.
Whatever steps are taken to make knowledge profitable, to reduce theory to practice, and to give clear
and intelligible ideas of science, constitute Method.
The extension of the term Method, it is evident, will
differ according to the subject to which it is applied.
The methods of investigation differ slightly for the
different kinds of science, but may generally be
classified under two heads, Analysis and Synthesis, of
which the former is generally used in the private investigation of truth, and the latter for the purposes
of instruction.
The successive stages in the discovery, progress
and establishment of any science, are three, viz.:
the descriptive, the inductive (also called the experimental), and the deductive or exact stage.
As soon as, by the description of a science, the
statement of its present condition, its wants, its unknown causes, &c., we have a just representation of
it, we proceed to observation and experiment, or induction; and when by induction, or the laboured
collection of many particular facts and examples, we
have established general laws, we may then deduce
from them any particular fact or facts, which it concerns us to know.




ANALYSIS AND SYNTHESIS.           25
These stages of investigation belong equally to the
physical and moral sciences, with the slight difference
in practice, that the vagueness and complexity involved in mental, spiritual, and social phenomena,
which all belong to the moral sciences, require more
delicate and subtle agencies to trace their laws than
those of the natural world around us.
And the sources of experiment are not at all analogous. Here we are surrounded by apparent contradictions.  The world of nature is changeable and
shifting, and yet it is palpable to our senses; the laws
which govern it are mysterious and inscrutable, and
yet they are constant; the moral world which is unchangeable and eternal, is vague and obscure, and
the abstract conclusions to which our inductions lead
us, positive and incontrovertible as they are, are but
few and unsatisfactory.
We shall have occasion to consider the subject of
Method more in detail hereafter, but at present we
design to apply it to the consideration of Logic.
We speak of the Method of a single science, or a
Method which is applied to all-as in that which
leads to the Classification of the sciences. In either
investigation the division of Method into Analysis
and Synthesis, is a just one, as both are used in
either process.
3




26                    LOGIC.
(8.) Analysis and Synthlesis.
To illustrate more clearly the nature of these two
processes, let us take a familiar example.  If we
designed to teach a person how to make and use some
complicated structure, as, for example, a ship, and if
this person had never seen one, the first step in the
process would be to show him the ship completely
built and ready to proceed to sea; fully rigged,
equipped and manned; that he might take in at a
glance its finished appearance, and its ultimate design
and use: in a word, that he might know what he was
to learn to make.  This would be the first lesson in
ship-building.  The next step would be to show it to
him partially dismantled, or in effect, to take it to
pieces before his eyes, that he might see the parts of
which it is composed, and their relative position in
the structure.
The third step would be to show him how each part
was made, and to let him see them all in minute
detail lying together, according to some system, which
should be preparatory to a reconstruction of the
ship.
This process of successive steps is Analysis,* or a
dissolution of anything into its elements.
In the investigation of any science, it is of primary
* nvaX-o-to separate into elements.




ANALYSIS AND SYNTHESIS.            27
importance. Showing us at first the scope and design
of the science, by systematic degrees it decomposes
it into its elements, and prepares us for intelligent
study of its many forms.
This operation shows us also the simplicity of science,
and is evidently derived from the teachings of nature;
for while there are innumerable forms of animal and
vegetable life, the analysis of nature which is constantly going on, shows but few-parts or elements in
all her works, and great simplicity of combination of
the same elements in different proportions, to produce
the most dissimilar forms and results.  So all the
sciences, physical, intellectual, and moral, while they
assume many and varying forms, are in reality composed of a few simple elements of nature or mind, and
this their analysis displays.
The analysis of physical science is of course the
most exact of these processes, in proportion as the
things of sense are easier to comprehend and fix than
those of mind and spirit: in physics, this process of
analysis is carried from the grandest class, such as
kingdoms and high genera, to the observation and use
of atoms and molecules inconceivably small, which
are to constitute the basis-elements of a reconstructing process.  Accurate analysis is a work of patient
labour. Chance experiments have indeed occasionally
produced great results, but this is an argument for,
rather than against, careful analysis. Roger Bacon dis



28                  LOGIC.
covered a fulminating powder when he was not seeking it; but, to be useful, this powder must cease to be
a chance discovery; that is, it must be analyzed into
nitre, charcoal, and brimstone, so that, these constituents once known, we can make our fulminating
powder at will. Science has never proceeded upon
chance; it moves safely only when it moves by invariable but ever-extending laws.
Incomplete analysis has done more to establish and
perpetuate error, than even blind superstition. For
it was in the face of the latter that Copernicus and
Galileo established the true theory of the heliocentric
system; while before their time, the incomplete,
false, and arbitrary analysis of astronomy, and the
belief in stellar influences, which a just analysis would
have destroyed, led all the writers, from the time
of Ptolemy, to build a false system   of celestial
mechanics; and thus to clog the wheels of true
science.
The process of analysis having been completed, we
come naturally to Sy#nthesis.*
Having taken to pieces, we proceed to the other
task of rebuilding: carefully examining each different
element as they all lie before us, until we understand
thoroughly the material of which it is made and its
construction, we proceed to adjust it to its place in
the structure: piece by piece, perhaps slowly and pains vv rir071i-to place together.




ANALYSIS AND SYNTHESIS.           29
fully, we build the ship, until at length it is complete:
nor is the labour yet finished; we launch it upon the
waters, spread its sails to the wind, and see it in
practical and successful movement, and then we may
account ourselves acquainted with the structure, and
able to build its like whenever called upon to do so.
This operation is called Synthesis; it is evident
that it is also continually going on in nature in the
reproduction out of crude materials of the many forms
of complicated existence.
Many writers, in investigating a science, begin with
this latter process, entirely neglecting the former; but
it is so evident that the analysis of a science gives
large and valuable lessons preparatory to its synthesis,
or real study for ourselves, that most modern treatises
on science have adopted and followed this order of
instruction.  It may then be safely stated that in any
science the true synthesis can only be proportional to
a vigorous and just analysis, and there have consequently been rules laid down for proceeding to consider any science or art in pursuance of this method.
The rules for Analysis may be reduced to these:1st. Not to believe any general scientific statement
without proof: that proof determined by the just
principles of evidence.
2d. To divide every scientific dictum into as many
parts or elements as shall be necessary to resolve it.
3d. To make a methodical arrangement of these
3



30                   LOGIC.
elements in order that we may understand them
clearly and the relation which they bear to each other.
Having done this, the corresponding rules for Synthesis are:1st. To use such terms to express the elementary
parts as are free from ambiguity.
2d. In combining these, to assume only such clear
principles or axioms as cannot be contested by any
persons.
3d. To prove, by demonstration, all the conclusions
at which we arrive, in the employment of the terms
and axioms used.
These remarks upon analysis and synthesis, as the
two vital functions of Method in investigation, and as
the two necessary instruments of all scientific study,
are designed for general application. A proper and
constant application of the rules of analysis and synthesis would cause great advancement in our studies,
and would go far to insure us from error, however
rapid that advancement might be. But we have
placed the subject of Method in this place, because
we design to use it in application to the study of Logic
itself; for, as a science to be studied, Logic-comes
under the rules which have been just laid down.
(9.) Analysis and Syntlesis as applied to Logic.
Now, let us employ this method in investigating the
science of Logic.




PROPOSED PLAN OF STUDY.          31
That we may study the subject profitably, making
each step a preliminary to the due understanding of
the successive steps, we propose to divide the entire
subject into the following special considerations:1. AN ANALYTICAL VIEW OF LOGIC.
In this we regard the science in its aim and its
workings, and after thus showing its design and its
scope, we analyze or dissolve it into its different parts,
showing what those parts are which effect by their
combination the purpose designed.
2. A SYNTHESIS OF FORMAL LOGIC.
As Synthesis is the reverse process of Analysis, and
as an Analysis of such a study would be in reality
but a general view of the scope of that science which
Synthesis is to establish, we shall see that while our
analytical view of Logic may be brief and general, our
synthesis must be minute and careful. We must more
particularly examine those parts which our analysis
has given us, in order that we may be able duly to
combine them in their just relations.
In imparting instruction upon subjects which are
known, the synthesis is evidently the more important
process, and hence must be longer and more minute;
while in the investigations of an unknown science the
analysis is the more important and valuable process.




32                   LOGIC.
In the general synthesis of Logic we shall also
devote a chapter to the subject of Fallacies; and
then consider some of the ways in which the syllogism is used, and the technical phrases which express these uses.
3. A HISTORlICAL VIEW OF LOGIC.
This historical view of Logic has been placed after
the study of the formal Logic, rather than before it,
as is usual in most treatises, because we can appreciate
a history only of that which we know, and we shall
understand much better the causes of error and the
obstacles to science which history gives us, when we
are beforehand aware of the true,scope and relations
of the particular science whose history is related.
When we know what Logic is, its history is intelligible
and interesting, and not otherwise.
For Logic is so intermingled or rather entangled
with other kinds of philosophy in almost all of its
principal epochs, that any one who should undertake
to read of its adventures in history without being
able constantly to dissociate it from its companion
sciences, would find it a useless and unprofitable task.




ANALYTICAL VIEW OF LOGIC.           33
CHAPTER II.
ANALYTICAL VIEW OF LOGIC.
(10). The reasoning process analyzed.
To apply the method of analysis to the study of
Logic as an art, we begin with the definition already
laid down that Logic is the Art of Reasoning.
Reasoning consists in the combination of two known
judgments to form a third, which is deduced from
them. Reasoning, when expressed in language, is
called argument.
The ultimate and simple form of argument, logically expressed, is the syllogism.* In a more extended
sense, reasoning covers also the combination and succession of many arguments.
The syllogism is an argument consisting of three
propositions, of which the first is called the major premiss, the second, the minor premiss, and the third,
the conclusion.
Major premiss. All A is B = All men are mortal.
Minor premiss. All C is A = All Hin'doos are men.
Conclusion. Therefore all C is B = All Hindoos are mortal.
e svv and XoytLoiat, more remotely Xeyw.
C




34                   LOGIC.
Each of these propositions consists of two terms,
the subject and the predicate; and the verb uniting
them is called the copula. Men reason to satisfy
their own minds, to convey instruction, or to refute
error, and in so doing, they combine many of these
syllogisms, thus forming compound arguments, which
may always be analyzed into the simple arguments
which compose them. In a simple syllogism, in many
cases, one or other of these premisses conveys a fact
so well known that it may be taken for granted, and
so it is suppressed, and thus is formed an abridged
argument, called an enthymeme. For example:(Minor premiss.) Cesar was a man,
Therefore Csesar was mortal.
This is an enthymeme with the major premiss
suppressed.  This major premiss is, All men are
mortal, which is taken for granted in the conclusion,
where, because 6cesar was a man, it is affirmed that
he was mortal. In every case, however, if the enthymeme appear at all doubtful, the suppressed premiss
may be written out, and the validity or invalidity of
the argument thus determined. Compound arguments, instead of having each syllogism fully expressed, are usually formed of a number of enthymemes
combined.
The groundwork of the syllogism is the dictum of
Aristotle, or his universal test for Argument.
Without in this place entering even very briefly




ARISTOTLE'S DICTUM.            35
into the History of Logic-a history of experiment
and error-it is interesting to know the time of its
first decided manifestation, and the person to whom
we owe it as a definite science. In that magnificent
period when the school of Plato had prepared the
mind of Greece for the coming of Aristotle, and the
energy of Philip had opened the way for the conquests of Alexander, that system of Logic was
formed, which, after having passed through the
fiercest ordeals, has remained almost without change
to our day. It has been indeed covered up, and to
all appearance lost, in the times of European bigotry
and ignorance; schoolmen and churchmen have alike
assailed it; but with the vital principle of truth, it
has remained untouched by the ruinous hand of
Time, amid exploded systems of Ethics, false speculations of Philosophy, and the cunning allegories
of Heathen mythology. The Analytics of Aristotle
form the cyclopmedia of Logic in this age, as in all
former periods.
After many years of patient investigation Aristotle
established the " Dictum de omni et nullo," of which
the first part, de omni, refers to all affirmative reasoning, and the second, de nullo, to all negative reasoning.  Stated by the use of ordinary symbols they
would be written as follows:



36                    LOGIC.
The Dictum of Aristotle.
De omni.                  De nullo.
All A. is B.            No A. is B.
(1)   (2)                   (1)   (2)
All or some  C. is A.       All or some C. is A.
(1)   (2)                     (1)
Therefore all or some C. is B. Therefore no C. is B., or some C.
(2)
is not B.
Or if stated by a geometrical notation, as all syllogisms may be stated: —
n   1),-^           ^    r(2)  A
BD   (   A~
But to explain the dictum practically, it has been
translated thus:
Whatever may be predicated of a whole class, may
also be predicated of all or any of the individuals contained in that class.
To predicate* means to affirm or deny.
Thus in the dictum de omni. In the major premiss
we predicate or affirm B. of the whole class A.
In the minor premiss we assert that all or some C.
is an individual or a number of individuals included
under the class A.:
And in the conclusion we predicate B. of the individuals, as we did in the major premiss of the whole
class to which they belong.
This simple dictum of Aristotle is the groundwork
of the syllogism, and the syllogism is the universal
*Prcedico-are, not pr(dico-ccre.




THE DICTUM OF ARISTOTLE.             37
principle of reasoning. It is sufficient in this place
to state the fact; it will be proven hereafter. The
propositions of which the syllogism is composed are
further analyzed. A proposition consists of two terms
and a copula, of which the first term is called the subject, the last the predicate, and the connexion between
them is the copula.
sibj.  cop.  predic.
(men)  (are) (mortal).
subj.    cop.    pred.
(men)  (are not)  (trees.)
It has been said that the dictum of Aristotle is the
groundwork of the syllogism, and that the syllogism
is the universal principle of reasoning: it must be also
remarked that every valid argument, no matter what
may be its original form, may be put under the form
of the syllogism, and to it in that form the dictum may
be directly applied; and, on the other hand, if any
argument cannot be reduced to this form, it is invalid.
Thus this dictum forms not only the vehicle of correct
reasoning, but is a sure test of error in Logic. We shall
constantly recur, in considering every form of argument, to this test.
The reasons why in mathematical investigation we
use letters, and in arithmetic numbers, are;-first, to
expedite and simplify the work, and secondly, to generalize it. For the same purposes we use symbols in
Logic. If, for example, I write the syllogism
4




38                    LOGIC.
All good men are happy,
John is a good man,
Therefore, John is happy;
I limit my argument entirely to the particular of;Jol7A
being a good man and being happy, whereas,'if I write
All A. is B.,
C. is A.,
Therefore C. is B.;
I propose a general formula which will apply to
many cases according to the subject and the matter
of inquiry. It will be well for the student to frame
particular examples under the general formula, and
thus at once to fix the form in the mind and accustom
himself to the practical applications of the system
of Logic to particular cases.
Besides the dictum of Aristotle, to the form of which
every valid argument may be reduced, there will be
given hereafter a series of rules for detecting fallacy
and for determining the validity of an argument when
it is not exactly in this form, and, by means of these,
the logical student may defend himself against the
subtlest sophistry, holding Aristotle's dictum in reserve as a final test.  Where one who is ignorant of
Logic is obliged to use much effort and circumlocution
to determine the validity or invalidity of an argument, and is in great danger of error in the process,
the logician, at once and without inquiry into the
subject-matter of discourse, applies his tests to the




THE DICTUM OF ARISTOTLE.          39
framework of the reasoning, and indicates infallibly
the defect in the argument. And so deciding as to
the validity or invalidity of the general formula as
expressed by the symbolical letters A., B., C., he has
once for all decided for each particular example which
can fall under that formula.
In concluding this brief analysis of Logic, let us
recapitulate. Logic is the Art of Reasoning: there
is but a single universal principle of Reasoning: its
basis is the dictum of Aristotle, and its simple form
is the syllogism.
The syllogism is composed of two premisses and a
conclusion: each of these is a proposition; and each
proposition consists of three parts, two terms and a
copula. It is now our purpose to examine these constituents of Logical formulae in the inverse order,
beginning with terms.




40                   LOGIC.
CHAPTER III.
A SYNTHESIS OF LOGIC.
(11.) Of certain operations and states of the
mind in the process of Argument.
IN proceeding to the synthesis of the reasoning
process, we must first consider certain operations and
states through which the mind passes in approaching
an argument. Logicians have enumerated many
which are so nearly related to each other, that we
may reduce them to three.
These are: 1st. Apprehension; 2d. Judgment;
3d. Reasoning, or Ratiocination. As a preparation
for these in their order, Attention has been called the
primary state: but this is self-evident. Apprehension
is a pure mental consciousness of the existence of an
object arising from perception; perception being the
process of conveying an impression to the mind,
through the senses. We must first perceive an object
before we can apprehend it.
By the five senses of the body we have a knowledge of the world around us; the first step in obtaining this knowledge, is sensation, or the impression on




A SYNTHESIS OF LOGIC.           41
the organ of sense; sensation is conveyed in a mysterious, inexplicable manner to the mind, to produce
perception; and as soon as we have perceived the
object by this union between the mind and the senses,
apprehension or an intelligent knowledge of it is
produced.
Apprehension is simple or complex.
Simple Apprehension is the notion of one object or
of several which bear no relation to each other; and
this notion is expressed generally by one word, as
John, man, river; or by many connected by conjunction, Tohn and Peter; the man and the boy.
Complex apprehension is the notion we form of
several objects which bear a relation to each other,
as a man walking, a bundle of rods.
When an act of Apprehension is expressed in language, it is called a term.
But, whereas certain words, which express terms;
are equivocal or ambiguous, it must be observed that
Logic deals ~only with general or abstract terms, and
has nothing to do with their distinctness or indistinctness. It only takes for granted that a term is distinct and unambiguous. A Logical term then is a
simple, unequivocal act of apprehension.
2. JUDGMENT.
Judgment is that operation of the mind, by which,
if we have two objects of apprehension or terms, both
known to us, we declare that they agree or disagree
4A



42                   LOGIC.
with each other.  Thus, if I know who c John" is,
and what 4 a hero" is,-I may declare thatJohn.is a hero.
Or that-John is not a hero.
Judgment is therefore of two kinds, affirmative
when the two terms are declared to agree; and negative, when they are declared to disagree.
An act of Judgment when expressed in language,
is called a proposition.
And here, also, it must be observed, that Logic
only takes cognisance of abstract propositions, which
are expressed by logical formulae, and has nothing
to do with their truth or falsity.  It takes for
granted indeed, that, when a proposition is stated, it
is true.
For example, if the proposition be A. is B. it is
assumed by Logic, that A. is in reality B., and thus,
if, when this general formula be translated into a particular proposition, it prove to be false, Logic is not
responsible for the falsehood, nor for the error which
finds its way into an argument by reason of the use of
a false premiss. Much error has arisen through the
mistake of supposing that Logic had to do with Language directly, and with the judgments expressed in
language; but it is just such an error as would lead
us to assign such values to the unknown quantities in
any algebraic formula, such for instance as y2 -  2px
=  0, as would destroy the equation. Algebra pre



OPERATIONS OF THE MIND IN REASONING.     43
supposes the equation to be just, and develops only
such values of x and y as will establish it. The
Logical formula is as abstract and general as this,
and Logical propositions are always assumed as true.
3. RATIOCINATION.
Ratiocination is that act of the mind by which,
having two or more acts of judgment, or propositions,
we pass to another or others founded upon them and
growing out of their combination.
Thus if we have the two propositions
All men are mortal,
Ccesar was a man,
we have, as an inference or fact implied in these two
propositions, and deduced from their combination, the
final proposition, Ccesar was mortal.
An act of ratiocination when expressed in language is called an argument; and an argument when
reduced to its simple logical form is called a syllogism.
That simple logical form demands a certain order in
the premisses and the conclusion.
If now we examine the syllogism
Major premiss. A is B = Men are mortal.
Minor premiss. C is A = Caesar is a man.
Conclusion.  C is B = Csesar is mortal.
we shall perceive that it consists of three propositions,
which are called the major and minor premisses and
the conclusion; and three terms represented by A.,




44                   LOGIC.
*B., and C., each term being used twice in the syllogism. The term which occurs in the major premiss
and the conclusion, (B.) is called the major term; that
which occurs in the minor premiss and the conclusion,
(C.) the minor term, and that which is found in both
premisses (A.) the middle term.
Extended Ratiocination is conducted by the combination of many of these syllogisms, or their conclusions, according to Logical laws.




OF TERMS.                  45
CHAPTER IV.
(12.) Of Terms.
A TERM has been defined an act of apprehension
expressed in language, and may be either simple or
complex.
A simple term is the name of a single object of
apprehension, and is generally expressed by one word,
as man, house, field.
A complex term is the expression of several objects
of apprehension with the relation which they sustain
to each other, as a good boy, a horse running.
It is evident that the name of a term is arbitrary,
and of use only to convey the apprehension to another,
as in different languages the terms which express the
same object of apprehension will be different words;
thus we have the object we call horse, expressed in
French by the word cheval, and in Spanish by the
word cabdllo. Words then, it must be remembered, are
not terms, but are arbitrary signs for conveying and
using terms.
But language, or the use of words, is necessary




46                    LOGIC.
to the form of reasoning, as no reasoning can be applied and tested until it assumes the dress of language.
When a word is capable of being used alone as a
term, it is said to be Categorematic,* and when it needs
the assistance of other words to constitute with it a
term, it is called Syncategorematic. Thus man, horse,
John, are categorematic words: here, gave, and, are
syncategorematic.
By a casual examination of the different parts of
speech we shall find:1st. Of the noun: That it is only categorematic
when in the nominative case; the possessive man's
requires another word denoting the thing possessed,
and the objective a word which governs it.
2d. Of the adjective: That it is syncategorematic;
for, although we say John is good, we understand
man or boy after good.
3d. Of the verb: That it is, so to speak, more than
categorematic, since it contains often the copula and
the predicate: as, the man walks; in this sentence
walks is equivalent to is walking in which is is the
copula, and walking the predicate.
The infinitive mood is often in reality not a verb,
but a noun in the nominative case. Thus the sentence To die for one's country is happiness; means
Death for one's country is happiness; To die being
fully expressed by Death.
Kar7ny6pry7a = something alleged or affirmed.




OF TERMS.                  47
4th. Of the remaining parts of speech we see at a
glance that they are syncategorematic, and are only
used in connexion with other words to constitute
terms.  The word which has the form of the present
participle is sometimes an infinitive, and sometimes a
noun; we might substitute it in the last example
given as a case of either.  Dying for one's country is
happiness, is equivalent to both the forms given.
(13.) Division of Simple Terms.
Simple terms are divided into singular and common.
A singular term is that which expresses a single
individual, and is usually the name of a person, place,
or thing; as John, Philadelphia, the Delaware.
A common term is that which expresses any individual or individuals of a whole class; as a man, the men,
an army. To make a common term singular, we prefix
the demonstrative pronoun this or that, as this man,
that river, which is equivalent to stating the name of
the man or river; as, This man is John; That river is
the Delaware. Common terms stand for classes, and
are sometimes called appellative, as giving name or
appellation to many individuals.
They thus are of great aid to science, in that, when
many common properties have been discovered in a
great number of individuals, and their distinctive
peculiarities have been discarded, they may all be
called by one name, and that name will be a common




48                  LOGIC.
term; when this is in view a common term is called,
according to its comprehension, genus or species.
Common terms are further distinguished according to their matter, into abstract and concrete.
An abstract term is an ideal word, expressing an
abstract property capable of inherence in an object,
and yet without reference to that object. Thus hardness, length, beauty, are abstract terms, which inhere
in many objects, but do not indicate any particular
one.
A concrete term is one which presents to the mind,
at once, the property and the existence of the object
in which it inheres.  Thus hard, long, beautiful, are
concrete terms, implying certain objects which are
hard, long, or beautiful.
Concrete terms are also called denotative and connotative, because they denote the abstract property,
while they connote. or imply in their signification the
body or object to which it belongs.' Thus hardness,
being an abstract term, is also an ideal noun; the
mind rests upon the vague idea, because it indicates
nothing farther  but when hard is mentioned we feel
the right to ask, what is hard? the answer is-stone.
Thus the concrete term hard has denoted the quality
of hardness, and connoted stone as the object in which
that quality inheres.




01 TERMS.                 49
(14.) Quality and Quantity of Terms.
Terms are further divided according to their quantity and quality.
The quality of a term is the mode or manner in
which it expresses an act of apprehension.
Terms are said to be synonymous under this division, when they express the same act of apprehension;
but by common usage this exact meaning is departed
from, and synonymous terms now mean those which
express different shades of meaning; thus happiness
and felicity are synonymous terms, and yet their etymology teaches us a difference in their meanings;
the former attributing pleasure to luck or fortune,
and the latter simply asserting a state of unalloyed
pleasure.
Incompatible terms are those which cannot be used
as predicates of the same subject at the same time:
thus hot and cold; asleep and awake.
Positive terms are those which state the real existence of the objects they stand for. The opposite of
these are negative terms, or those which deny the
existence, or assert the absence of certain objects or
attributes.
There is a class of terms called Privative, which
are often confounded with negative terms; but there
is a real and important difference between them. A
privative term expresses, that some quality or attribute usually belonging to the class, is wanting in some
5                  D




50                   LOGIC.
individuals of that class: thus dumb, idiotic, are privative terms, since their very names call to the mind
the fact that man generally is gifted with speech and
reason.
Terms are divided according to their quantity into
many distinct classes, according to their number and
dimensions.
Thus we have the common division of numeral and
ordinal, as twenty, a hundred, two; positive (in its
grammatical sense), comparative and superlative terms,
as good, better, best; and that which is more truly a
logical division into distributed and undistributed:
a distributed term being one the whole of which is
considered, and an undistributed term one in which
only a part is taken, this part being usually an indefinite part, expressed by such words as some, few,
several, &c. All men is a distributed term, some men,
an undistributed term.




OF TERMS.                  51
CHAPTER V.
OF THOSE OPERATIONS IN LOGIC WHICH RELATE TO
TERMS.
(15.) Abstraction and Generalization.
ABSTRACTION consists in drawing off and considering one or more of the properties of an object to the
exclusion of the rest.  Thus we use abstraction when
we observe the colour and odour of the rose, disregarding its other characteristics.  If we abstract the
colour and odour of one rose, then of another, and so
of many, and finding these alike for all, call them all
by one common name Rose, we are said to generalize.
GENERALIZATION then consists in disregarding the
differences between many objects which are alike in
certain properties, and calling. them  by a common
name, by reason of their resemblance or identity in
these properties.
We may abstract, it is evident, without performing
the other process of generalizing, but we cannot
generalize without first abstracting: in the general
case, however, we abstract for the purpose of generalizing. It is by these two processes that we obtain
common terms, or the names of classes.   All these




52                    LOGIC.
common terms are the result of higher or lower processes of generalization.  Thus, by a low generalization, we obtain tea-rose, by a higher, rose, by a higher
still, flower, and by one step farther, vegetable, &c.
But common terms, as classes, are further distinguished into species and genera; and, as expressive
of certain things belonging to the species and genus,
they are also divided into the differentia, property,
and accident.  Some writers, in considering the substance of a term, have called the object for which it
stands, the essential part or the essence.
(16.) Species, Genus, and Differentia.
A  species is a class obtained by generalization,
which includes only individuals or subordinate classes,
and is itself included in a genus: as an Arabian horse
is a species of horse; horse is a species of quadruped;
quadruped is a species of animal.  A genus is a class
obtained by a higher generalization, which comprehends under it two or more species; as animal is the
genus alike of quadruped and biped, quadruped is the
genus of horse, cow, deer, &c., and biped the genus of
man, &c.
It is evident that in one sense the species implies
more than the genus; as, for instance, if quadruped
be the genus and horse the species, horse will contain
all the signification of quadruped, and also the dis



OPERATIONS WHICH RELATE TO TERMS.       53
tinctive signification of horse as to shape, size, habits,
uses, &c.; which latter does not belong to quadruped.
For this reason the species is said to express the
whole essence of the object, while the genus expresses
only a part of the essence, and that the material part.
Thus, man expresses the whole or complete essence
of the animal so called, while animal expresses only
the comprehensive or material part of the essence
which only limits him to an animate existence.
The differentia of an object is the formal or distinguishing part of that object, and divides it from a
class to which it does not belong; and, when united
with the genus or material part, forms with it the
species or whole essence. Thus, if man be the species,
and animal the genus, rational would be the difer(species)  (dif erentia)  (genus)
entia, and we should have man = rational animal.
By which it appears that although the genus comprehends this species and many others, the species really
implies, although in a different sense, more than the
genus, viz., the genus and differentia.
(17.) Property and Accident.
Thus, having shown the relations between the genus,
or the whole essence, the species, and the differentia,parts of the essence,-each of which is expressed by
a common term, we come to consider those things
which are or may be joined to the species or essence.
They are divided as follows:5,




54                    LOGIC.
I. Property, which is joined universally to the
essence, and thus must be asserted as belonging to
every individual of the species; and 2d. Accident,
which is joined only contingently, that is, to one individual or certain individuals of the species, and not to
the whole species.
Property is of two kinds. 1st. That which is universal, or belonging to every individual of the species,
but not peculiar to the species, as respiration, which,
although it belongs to all men, is not confined to the
species man. 2d. That which is universal and peculiar, as the power of intelligent speech, which, while
man, as a species, possesses it, is peculiar to man.
Some writers have erred in enumerating a third kind,
viz.: peculiar but not universal, as, for example, to
be able to be a poet. But this violates our definition,
since, if it belong to some individuals and not to the
species, it ceases to be a property, and becomes an
accident.
II. Accident is something joined contingently to the
species, or belonging only to certain individuals of it.
Accident is of two kinds: separable and inseparable.
A separable accident is a circumstance which may be
detached from the individual, without affecting his
identity or altering our general conception of him; as
John is walking, or is lying down; in which examples
the accidental circumstance of walking or lying dozwn
is not a necessary part of the individual, but may be




OPERATIONS WHICH RELATE TO TERMS.        55
detached from him, so that we may still conceive of
him as doing neither.
An inseparable accident is one which cannot be
detached from the individual; as, born in Philadelphia; born in 1800.
It is by means of such inseparable accidents that
a man is described or his history written; but it must
be remarked that this phraseology is rather convenient than exact, for, as soon as the event which we
call a separable accident occurs in the life of an individual, it really becomes inseparable.  Thus, if John
walked to the city on a certain day, or, being unwell
afterwards, was lying down in consequence, we can
no more detach these facts from his history, than we
can the event of his being born in a certain place, and
at a certain time.
Having now illustrated the meanings of genus, species, essence, differentia, property, and accident, let
us, for convenience and clearness of illustration, write
out a sentence embodying all these uses of common
terms, as a model, by which the student will easily
frame other examples for himself. This sentence will
also embody the different processes of generalization.
(property, universal
(Individual)  (species)  (differentia)  (genus)  but not peculiar)
John is a Man, -  a rational animal, who breathes,
(property universal and peculiar)  (separable accident)
has the faculty of speech, is lying on the sofa, and was
(inseparable accident)
born in Philadelphia.




56                    LOGIC.
The logical name given to every common term representing a genus, species, differentia, property, accident, is predicable; viz., something which may be predicated: no other terms than these are predicable.
(18.) Of the different orders of Genera and
Species.
A summum genus or highest genus is the highest
class of all, and has no genus above it.
A term which expresses at once a genus and a species
is called a subaltern genus and species. For example,
quadruped is a genus of horse and a species of animal.
In the descending scale from the summum genus, the
successive or inferior genus is called a subaltern genus.
In the ascending scale from the lowest species, it is
called the subaltern species.
When a genus is divided into its species they are
called  co-ordinate or cognate species, to indicate
that they are not subordinate to each other.  Thus
if quadruped be divided into horse, cow, lion, as representing the equine, feline, and vaccine races, these
would be cognate species.
A species which contains beneath it no other species,
but only individuals, is called an infima or lowest species. In any scientific investigation, however, ranging
between any two limits although not absolutely the
highest and lowest, it is usual for convenience to call
the highest limit named, summum genus, and the lowest, infima species; as though we should say " Let




OPERATIONS WHICH RELATE TO TERMS.        57
A be the summum genus, and C the infima species,
during this investigation." There are also in common
use the phrases proximum genus and remote genus,
the first of which means the genus next above, and the
second, a genus farther removed from, the species in
question.  Thus quadruped is the proximum, and
animal the remote genus of horse.  It is necessary
that the proximum genus should be the genus next
above the species in question; but the remote genus may
be any one farther removed, and not necessarily the
summum genus, which is of course the most remote.
It must be observed that the use of a common term,
as either species, genus, differentia, property, or accident, is a relative use; and because it is used with one
of these significations in one sentence, this does not
deter us from using it with quite another meaning, on
another occasion.  Thus if we take the word red, we
shall find we can make it serve as each, in turn.
The colour Red is a genus under which as species
are ranged pink, scarlet, crimson, vermillion, &c., the
different kinds of Red.
Red is a species of the genus colour, and ranges
with white, blue, yellow, &c., as cognate species.
Red is a differentia of the " Red rose," which distinguishes it from other roses.  Red is a property of
blood; and an accident of a house, separable if it be
painted red, inseparable if it be built of Red stone.
And thus in analyzing any sentence we must be care



58                    LOGIC.
ful to ascertain the real value of the common terms
employed.
(19.) Realism and Nominalism.
While upon the subject of common terms, it is well
to refer to the long-standing controversy between the
Realists and the Nominalists, which, although it became
strangely intermixed with theology and church polity,
had its origin in the significance of a common term.
It will be referred to more at length in the historical
view. The Realists contended that every common term
was the name of something really existing; that a
genus and a species were real things, while the Nominalists believed that we obtained common terms merely
to express a certain inadequate undefined notion of
one individual, which we apply to many.
It would seem to be a trivial subject for controversy,
but the more we examine it, the more difficult and
subtle it appears. Like many subtle controversies, it
seems to be of little consequence in which way it could
be decided; but it had, to the disputatious Greeks,
and the more disputatious Schoolmen, a charm on
account of its subtlety, which its value could not
secure to it.
(20.) Definition of Terms.
Definition* is applied to terms in their logical use,
and means describing them in such a manner as to
distinguish them from all and any other terms.
*de and finio, more remotely finis.




OPERATIONS WHICH RELATE TO TERMS.         59
As much error arises from the indistinctness of
terms, and the fact that different persons employ them
in different meanings, just definitions which may bind
both parties in a controversy are very important.
A definition is usually put in the form of a categorical proposition, of which the subject is the term to
he defined, and the predicate is the description or distinct explanation.  Thus in the example a Mlan is a
rational animal," the whole sentence is called the definition.  This is not, however, strictly speaking, correct; as the predicate alone ( rational animal" defines
" man," as if in answer to the question " what is the
definition of man?
The first division of definition is into two kinds,
Essential and accidental; Essential definitions are
further divided into physical and logical.
The second division of definition is into nominal
and real.  Before explaining the meaning of these
divisions, we shall arrange them, for the sake of convenient reference, into a tabular statement.
DEFINITION.
1st division  (divided into)  2d division
Essential  Accidental  Nominal       Real
(div. into)
Physical   Logical
An essential definition is one which presents to us




60                    LOGIC.
the principal parts of the essence of the thing defined;
thus, a steamboat is " something consisting of hull,
engine, wheel-houses, smoke-pipe, &c.;" or, again, it
is "La vessel for water transportation propelled by
steam."   In each case the form of our essential definition would be induced by the character of the person asking the definition, and according to the information he desired, but always in terms of the essential
parts of the object for which the term stands. But
it must be particularly observed that these principal
or essential parts are of two kinds widely different
from each other: physical parts or parts which are
actually separable by the hand, and Logical parts, or
those which are only divisible by the mind.  To explain, a physical essential definition of a ship would
be 4 an object which consists of hull, masts, cordage,
&c.," being the parts into which it may be physically
divided; while the logical parts which would constitute a logical essential definition would be the genus,
viz., " ocean vessel;" and dfferentia, viz., " of peculiar build;" which, as we have seen, when combined
make up the species ship.
(species)    (genus)      (differentia)
A ship is an ocean-vessel of peculiar build.
A logical essential definition then, in every case,
consists of the genus and differentia. Logic is concerned with logical definitions alone, but examines
the others to distinguish between them and logical




OPERATIONS WITICH RELATE TO TERMS.       61
definitions. And it is likewise true that the physical
and logical definitions sometimes coincide, but this is
of rare occurrence.
An accidental definition, or description, as it has
been technically called, consists in presenting the circumstances belonging to an object, and these are its
property or accident; as these are generally more descriptive of an animal or object than the material part
which is the genus, or the differentia which distinguishes the species in question only from its co-ordinate species.
From what has been said before, it will appear that
in describing a species we can only use properties, as
accidents attach alone to individuals, while properties
belong to every individual of a whole species: we
should use, besides, properties which are universal and
peculiar, since, as they belong to every individual of
the species, and to none out of it, we thus find its own
characteristics; whereas if we used the properties
which were universal but not peculiar, we should only
know characteristics which marked that species in
common with others, and thus not define it. Thus if
we should describe man as " a being who lived and
breathed," this would not define or describe him justly.
So, too, in describing an individual, as for instance
in biographical notices, we should not use separable
accidents which are not a permanent and necessary
part of the object, but inseparable accidents which
6




62                   LOGIC.
belong necessarily and permanently to it. For example, if we say " William was the Duke of Normandy
who conquered England in 1066," we describe him by
means of the inseparable accidents, viz., that he was
Duke of Normandy, and that he conquered England.
(21.) Nominal and Real Definitions.
We come now to the second division of definitions,
into nominal and real.
A nominal definition is one which gives the meaning of the term which is used as the name of the
thing. In brief, it defines the name. Thus, " a telescope is an instrument for viewing distant bodies."
"4 The photograph is a painting made by light on sensitive plates."  4 The decalogue is the table of the
ten commandments."
A real definition analyzes and explains, not the
name of the thing, but the thing itself; enumerating,
besides, all its important characteristics and properties; thus, a real definition for a telescope would be
a treatise on the construction, powers, and uses of the
instrument, and a real definition of the decalogue
would be given only by reciting all its commandments.
In the investigations of science it is evident that
the aim is to obtain real definitions, and the fuller
and more complete they are the greater their value;
but since in Logic we have only to do with the names
of things, and not with their subject-matter, or the conceptions which they convey to us, it is evident that




OPERATIONS WIIICH RELATE TO TERMS.      63
we only need nominal definitions and not real; and
indeed, with regard to matters of general information,
a nominal definition will be sufficient to settle the
grounds of a controversy; for while it is the name
that indicates the individual or the class, the definition
explains the name.
We may even, sometimes, provided both parties to
an argument agree to do so, consider as a definition
something which is purely hypothetical, but which still
partakes of the nature of a definition; thus, for example, in an astronomical problem we say, " let C be
the sun's place in the heavens;" or in any case for
purposes of illustration, (- let so and so be so and so."
This form of definition is purely relative; for although,
in reality, C is not the sun's place, it is so relatively
to the other points on the diagram.
It must also be observed that it is not necessary to
the justness of a definition that it should refer to real
things, as, for example, we define an unicorn to be " a
fabled animal, having but one horn;" and a phoenix to
be c a bird fabled to live without a mate and to rise
from its own ashes."
(22.) Rules for Definition.
So important has the subject of definition been
considered, that Logicians have laid down three rules
for it, to which, if we adhere, we shall insure just and
adequate definitions.
1st. The definition must give to the mind a clearer




64                   LOGIC.
conception than the name of the thing defined, or it
will be useless.
In most of the arts and sciences this consists in
putting a technicality into plain language, for those
who are uninitiated; but if I am asked to define cow,
a word understood by every one, and say that cow is
a ruminant quadruped, I violate the rule. In the nomenclature of science many technical terms give, in one
word, what it would require much circumlocution to express in common words. Accompanying this rule there
is the caution that the character of the definition should
depend upon the subject and the persons addressed.
2d. The definition must be adequate; that is, neither
include other things than those necessary to define, nor
exclude any necessary explanation of the thing defined.
Thus, if I define bird to be "c an animal that moves
in the air by means of wings," I am too extensive in
my definition; as that would include other animals
than birds, as bats, flying fish, &c.; and if I define
it to be " a feathered animal that sings," that would be
too narrow, as some birds do not sing.
3d. The third rule is rather a caution which grows
out of the other two than a rule like them. It is, that
the words used in a definition should be sufficient and
of the proper kind to define the thing.
If we use too many words, we confuse the meaning
and are liable to tautology; if too few, we are liable to
obscurity. Thus, to say that " a square is afour-sided




OPERATIONS WHICH RELATE TO TERMS.      65
figure with equal sides," would be true but not definite,
as there may be drawn other parallelograms not rightangled, with equal sides. If we say ", a parallelogram
is a four-sided figure whose opposite sides are equal and
parallel;" we use too many words, as the equality of
the sides implies the parallelism, and vice versa.
In the first case we err, because we do not exclude,
in our definition of the square, all other figures: in
the second, because we allow it to be supposed that
there are four-sided figures whose opposite sides are
equal and not parallel.
The examples taken are broader and more apparent
than those in which faulty definitions are generally
used, but they render the error more obvious, and indicate to us the character of the danger to be avoided.
If we would see the practical necessity of definitions, we need but consider a few of the vague and
inexact terms which we use in our ordinary speech,
and which it seems a prevailing fashion to distort in
their meanings. We shall recur to this subject under
the general title of "Verbal Fallacies," but may now
give a few illustrations of the value of exact definitions. Take for example such words as Necessity
and Necessary, which may mean either an accordance
with the invariable law of God, or an obedience to
the blind decree of fate, according to the belief or
scepticism of him who uses them. In its political sense,
the adjective necessary has been said to be capable of
6*              E




66                    LOGIC.
certain degrees of comparison, as in the argument urged
in favour of the Bank of the United States,* in speaking of the means necessary for carrying out the provisions of the Constitution, it was asserted that they may
be classed under the three categories of necessary, very
necessary, and absolutely and indispensably necessary.
So also in religion, certain things are said to be generally necessary to salvation, while others are said to bo
absolutely necessary. Thus the technical sense of the
word is entirely lost; as that refers to an absolute
condition, which cannot but be, or cannot be otherwise,
and therefore does not admit of comparison. Or if we
would see a strange, conglomerate example of indefinite and erroneous terms, demanding a clear definition,
take the war-cry of the French revolutionists,
" Liberty,.Equality, Fraternity;" no one word of
which can express to the people a distinct idea, or
will bear the test of a clear definition.
It has been a custom in nominal definitions to define one term by means of its synonym, borrowed
from another language. Although our language is, in
its structure and the great majority of its words,
Anglo-Saxon, still the large number of French and
Latin words which have been brought into it, have
formed terms synonymous with the original Saxon:
but, when they had become naturalized, as we had
no use for two words exactly synonymous, wisdom
* Kent's Commentaries, vol. i., Lect. 12.




OPERATIONS WHIICH RELATE TO TERMS.     67
suggested that they should exhibit shades of difference
in meaning, which did not originally belong to them;
so that few if any words are justly defined by their
synonyms. Besides, as a similar idea among any two
people would have its differences drawn from their own
peculiarities of clime, and race, and manner of life and
government, the synonyms when brought into the language would often express great differences at once, and
without any effort on our part to cause them to do so.
As a remarkable instance of this, let us see how very
wrong it would be to define our English word freedom,
by its synonym liberty, which comes to us from the
Latin; and yet, how many confound the two. Indeed
these are historic words, and give us an insight into
the times of their birth, wonderfully illustrative of
the people and countries from which they came.
Freedom is the personal, individual independence and
right of every man, his free doom, i. e. free province or
jurisdiction from his birth. Coming as it does from
the Teutonic element in our language, it tells us of
the free and independent Germans, who by their own
valour, overturned the great fabric of the Roman
empire. They were men of the forest and mountain,
inhabiting no cities-there were none in Germany till
after the eighth century —but only roving where were
the lordliest spoils, and claiming them as the reward
of their personal freedom..On the other hand, liberty
tells us of the Roman cities, of the sway of the Roman




68                  LOGIC.
empire, and of Roman licentiousness; of a form of
manumission, implying slavery; individuality merged
in citizenship; to be a Roman citizen to have attained
the post of honour, open to all advancement in diplomacy and war. Nor is the spirit belonging to these
words yet lost. While we cling like good citizens to
our liberty, vouchsafed to us by the constitution of
the country, as Americans, we much more desire to
keep well guarded that freedom of opinion, of speech,
of action, which is our indefeasible right as men.
In view of the importance of just definitions, let us
undertake no controversy, or expression of opinion involving a vague and indistinct term, without demanding a definition, and agreeing to use it during the
discussion.
(23.) Division.
It is of great importance in the consideration of
common terms which stand for classes, that we should
be able to divide them into all their several parts or
significates.  An individual, as its name indicates,*
is incapable of logical division. It is only a species
or genus, i. e. a class, in more general language,
which can be so divided.
Division is of two kinds, physical and logical; to
these some writers add, improperly, numerical division.
* in and dividuus, from divido, to divide.




OPERATIONS WHICH RELATE TO TERMS.      69
Physical division is the actual separation of the
physical parts of which a thing is composed. It is
evident that an individual is capable of physical division; thus, an individual tree, as a certain oak, may
be divided into trunk, branches, and these further subdivided into bark, heart, leaves, &c.; an individual
man, as John, may be physically divided into head,
arms, trunk, legs, &c. With this kind of division
Logic has directly nothing to do.
Logical division, which cannot be applied to individuals, but only to classes, consists in separating a
genus into its different species; and a species into the
individuals composing it: and this in regular order
from the summum genus to the infima species. Thus,
the genus tree would be logically divided into oak,
maple, hemlock, fir, pine, elm, &c.; and the species
oak, into red oak, white oak, live oak, scrub oak, &c.;
and each of these again into the individual trees comprising its kind.
It will be evident that in a just division, each one of
the parts-denoting a species-will be less than the
whole number which make up the genus; or any one
of the parts-denoting an individual-will be less than
the whole number which make up the species; or, as
a test of the correctnesss of the division, we must be
able to predicate the summum genus of any one of
the parts.
If, for example, we have assumed tree to be the




70                     LOGIC.
summum genus, we must be able to predicate tree of
oak, or live-oak, or any individual live-oak.
It is evident that the same term may be logically
divided, according to race, into Caucasians, Malays,
&c.; according to creeds, into Buddhists, Jews, Mcahomedans, Christians, &c.; according to nation, into
Americans, English, French, &c.     These cross-divisions must not be mingled or confounded; for example, to divide man into Caucasians, Mahomedans,
Americans, &c., would be false and useless division.
The principle of division is best illustrated by a,
scheme, or inverted tree, in which is arranged clearly,
symmetrically, and without arbitrariness, the different
parts of the division.
SCIIEME OF DIVISION.-SUMMUM GENUS.
TREE.
Oak.                   Maple.    Pine, &c.
r-' —-— " — r-"                  "~ —-------
Live-Oak, White-Oak, Red-Oak, &c.  Sugar-Maple, Common-Maple.
Individual Trees.       Individual Trees.
It may be well to observe particularly an auxiliary
phrase, according to, which we use to keep us from a
simple but dangerous error.   Man is divided not into
races, creeds, nations, &c., but according to these,
into various parts; thus:SUMMUM GENUS.-MANKIND DIVIDED ACCORDING TO.
Race.            Creed.              Nation.
Caucasian, Malay, &c.  Jews, Christians, Mahomedans.  English, French, German, &c.




DIVISION.                 71
It is evident that all the co-ordinate species must
be on the same line or platform, that is, they must
hold the same relative position to the summum genus.
We must be careful to omit no subaltern genus; and
we must place each subaltern genus in its own relative grade. Thus, if we should place oak properly, in
the division of tree, but should pass immediately from
the genus tree to the species sugar maple, thus leaving
out the species majle, co-ordinate to oak, we should
make an unequal and undue division. This would
be placing one of the co-ordinate species on the same
level with one subordinate to it.
From what has been said, it will perceived that the
process of Division is exactly the opposite of Generalization.
As in Generalization, we disregarded the differences between many individuals, or between many
species, and considered only the properties they
had in common, that we might constitute them respectively species and genus, calling them by a common
name; so in Division, we take the genus thus obtained
and add to it the several differences which we had removed in Generalization, and which distinguish its
parts, that we may call the parts thus enumerated by
separate names.
The two inverse processes of generalization and
division may be plainly illustrated by a scheme or




72                       LOGIC.
double tree; and this may be made as full as we
please: thus, from individual trees we may generalize
to the genus tree; or, from trees and shrubs and other
kinds of vegetation, we may generalize to the summum   genus vegetable.    The division will be of the
exact species, &c., but in the inverse order.
SCHEME OF GENERALIZATION AND DIVISION.
Individual Trees.   Individual Trees.    Individual Trees.
Live-Oak, Red-Oak, &c.  Sugar-Maple, Birdseye-Maple, &c.  White-Pine, Yellow-Pine, &c.
Oak.               Maple.                Pine.
TREE.
f- --- - ---------                  -
Oak.              Maple.                Pine.
Live-Oak, Red-Oak, &c.  Sugar-Maple, Birdseye-Maple, &c.  White-Pine, Yellow-Pine, &c
Individual Trees.   Individual Trees.    lndivideual Trees.
What has been called mathematical or numerical
division is in reality but a form of physical division;
thus, I divide a loaf into slices, or an apple into pieces,
physically, with or without regard to the equality of
the pieces, or their sizes relatively to each other. If
this equality or relation be observed, it may be called
numerical division, but it is only an exact form of
physical division; as a half, a third, ten times as
great, &c., &c.




RECAPITULATION.               73
By a comparison of the subjects of Division and
Definition, it will be seen that division is, after all,
but a systematic and practical kind of definition, since
there can be no better way to illustrate the meaning
of tree, than logically to divide it, before our eyes, into
all its species down to individual trees.
It will be readily seen that the nature of the logical
division of terms will depend much upon the science
in which they are used, and the principle according to
which they are to be classified. Thus an ethnologist
would divide mankind according to races; a theologian
according to creeds; and a statesman according to
nation.  The principle of all the divisions would be
the same, while the resulting cross-divisions, as we
have seen, will be widely different.
(24.) Recapitulation.
It will be well to recapitulate briefly what has been
said upon the subject of terms, and the various operations which concern them.  We have shown,
1st. That a term is the expression of an object of
apprehension, and have explained the different kinds
of terms, according to a regular division.
2d. That common terms are obtained by the processes of Abstraction and Generalization.
3d. The distinction between genera, species, and
individuals, Ge.
7




74          -        LOGIC.
4th. The Definition of terms, and just rules for
definition.
5th. Division of terms, with the difference between
physical and logical division, and special consideration of the latter.
The next step will be to combine these terms into
propositions: that is, from our knowledge of two of
them to assert their agreement or disagreement.




PROPOSITIONS.                 75
CHAPTER VI.
(25.) Propositions.
A proposition* is an act of judgment expressed in
language, and consists of three parts, a subject, a
predicate, and a copula: the subject and the predicate are called the terms or extremes of the proposition.
The subject, in the due order, is placed first, and is
that of which something is predicated, i. e. affirmed
or denied.
The predicate is that which is affirmed or denied of
the subject.
The copula is the uniting word which expresses
the agreement or disagreement between the subject
and predicate; and is always some part of the verb
to be.  When the copula is affirmative, agreement is
expressed, when negative, disagreement.
sub. cop. pred.   sub.  cop.  pred.
A   is  B     (Caesar) is (a tyrant.)
sub.  cop. pred.      sub.    cop.     pred.
A   (is not) B  =  (Csar) (is not) (a tyrant.)
* Frompropono-something proposed or set forth for our acceptance.




~~76            ~LOGIC.
The negative particle, it must be observed, is always
a part of the copula.
What appear, in our ordinary speech, to be simple
propositions, are sometimes inverted or elliptical forms
of expression, which must be put into simple logical
form before they can be considered as propositions.
Thus we say,, I hope to see you," "c I desire to remain;" and in these cases the subject is really placed
last; the true meaning being
subj.   cop.           pred.
(To see you) is (the thing which I hope, or my
hope.)
As an example of another form of inversion, we
have that which springs from the constant use of the
neuter pronoun it. Thus, in ordinary language, we
say " It is true that I think so." The true logical
form may be given thus:subj.     cop.     pred.
(That I think so) is (a true thing).
Many writers have denied that there is such a thing
as a negative judgment; and, consequently, that any
negation attaches to the copula: for they say that
the proposition John is not happy is equivalent to
John is unhappy, which indicates a positive sensation
or frame of mind, as well as the other; but this is a
quibble about words, as there are propositions in which
the negation cannot be thus destroyed, and such is
the case with far the greater number. The positive




PROPOSITIONS.               77
term is generally limited and intelligible; the negative unlimited and indefinite; thus man, is a term
which we can grasp, but not man, includes all the
universe beside.
Of the Copula.-The copula may be always reduced
to the present tense of the indicative mood of the
verb to be, and consequently expresses neither past
nor future time. Thus,," Csesar was the conqueror of
Gaul," is equivalent to, Caesar is the historic personage who conquered Gaul.", I shall be glad to see
you;" is the same as ", I am the person who will be glad
to see you," &c.; but as this reduction is in general unnecessary, we agree to call those propositions which are
expressed in time other than the present. Very often
the copula and predicate are expressed together in
one word, as c" The sun shines;" here the word shines
may be resolved into is shining, in which is is the
copula, and shining the predicate. And sometimes,
in other languages, as the Latin or Greek, a proposition is conveyed in one single word, as amo, I love or
I am loving, t7e)L, I am striking; but in every case,
a proposition may easily be placed in such a form that
the subject, predicate, and copula are distinctly stated.
But this definition of a proposition, as a sentence
consisting of a subject, predicate, and copula, is evidently a physical definition, and is not sufficient for
our purpose. The logical definition of a proposition
is "' a sentence which affirms or denies;" here propo7*




78                    LOGIC.
sition is the species, sentence the genus, and which
affirms or denies is the differentia, or statement of
the difference between this kind of sentence and all
others.  The word proposition not having in its etymology this strict meaning, it is very loosely used to
express almost every kind of sentence. We must be
careful, in Logic, to limit it to the definition just
given. Hence, we should say that a categorical proposition, in its grammatical sense, implies the indicative mood, since absolute affirmation or denial is expressed only by that mood. Thus are excluded, the
imperative mood or all commands, the subjunctive
mood or all hypothesis, the infinitive mood, which, as
its name indicates, is not a finite, uniting verb, but
only a verbal noun.
If we examine these moods a little more in detail
we shall find, first, that even in the indicative mood,
questions, or the interrogative form of that mood are
excluded, for the use of a question implies that one
of the parts of the proposition is wanting, and that
we depend upon the answer to supply it. Thus the
first and simplest form of the question is
Is A B? -- Is man mortal?
if the answer be affirmative, then we have a right to
the copula is, which before was wanting, and may write
A is B -   Man is mortal.
Another form of the question is," what is A?" or
" what is B?" the answer to which will supply us with




PROPOSITIONS.                79
the predicate and subject respectively. With regard
to the subjunctive mood there are, it must be observed,
propositions which assume that form and which are
called hypothetical, and they come under the class of
compound propositions, as
If A is B, C is D.
In almost every case the hypothesis is stated in the
indicative rather than the subjunctive mood; thus
If A is B, C is D; rather than in the form:If A be B, C will be D.
Of the infinitive mood it may be observed that there
are various forms thus, to ride is pleasant, may be
rendered by riding is pleasant; horseback exercise is
pleasant; plainly showing that with the verbal form
there is a substantive value.
(26.) Propositions divided into Simple and
Compound.
If now, we proceed to consider first the substance
of propositions, we shall find them divided according
to their substance into simple and compound.
A simple proposition is one which has but one subject and predicate, united by the copula is or is not.
Simple propositions are also called categorical, that is
there is simply affirmed or denied an agreement
between the subject and predicate.
A compound proposition is one which has more than
one subject or more than one predicate, and may be
resolved into two or more simple propositions; as




80                    LOGIC.
7Te.Delaware and the Schuylkill are rivers in Pennsylvania.  Compound propositions are further divided
according to their substance into categorical, conditional, causal, and disjunctive.
A compound categorical proposition, like a simple
categorical, affirms or denies the predicate simply and
certainly of the subject; thus:Alexander, Ccesar, and Napoleon were ambitious
of military glory.
A conditional proposition consists of two simple
categoricals united by the conjunction if; thus:If A is B, (:is ID.
It is usual, for convenience, to place the conjunction first; the first categorical-A is B-is then called
the antecedent, and the other-C is D-the consequent.
A causal proposition is one in which the reason of
the truth of a simple proposition is stated thus:
Because A is B, CD is D.
A Disjuenctive proposition is one in which one of
two simple propositions is asserted to be true; thus,
either A is B, or C is D.  This is done by the use
of the conjunctions either and or.
Propositions are still further divided according to
two of Aristotle's categories which will be considered
hereafter, i. e., according to their quantity and quality.  In simple language Quantity considers of how
much of the subject the predicate is affirmed or
denied; as, some or all A is B.




PROPOSITIONS.               81
And Quality regards the kind or manner of that
predication, i. e. whether it be affirmative or negative:
whether A. is or is not B.
(27.) Quantity and Quality of Propositions.
The quantity of a proposition is determined by the
comprehension of its subject.  If we assert that the
predicate agrees or disagrees with the whole subject,
that is, all the significates which come under the
term, the proposition is said to be universal, thus,
All men are mortal, No men are trees:.
are universal propositions, because the whole of the
subject is considered. But if we assert the predicate
to agree or to disagree with only a part of the subject, the proposition is called particular.
Some men are brave; fezw men are good;. many
men are not prudent; are examples of particular propositions.
The quality of propositions we shall find also to be
of two kinds; the quality of the subject-matter, and
the quality of the expression. Propositions are divided according to the quality of the subject-matter into
true and false, and, according to the form of expression, into afirmative and negative.
It is evident that with the quality of the subjectmatter, Logic has directly nothing to do; for since the
logical form of a proposition is A is B, it is taken
for granted, as we have already seen, that this stateF




82                     LOGIC.
ment is true, and that, from the very form it assumes.
With the subtleties of statements Logic is not concerned: taking for granted the truth of a proposition,
it makes use of it properly; whatever falsity lies in
it will pervade the argument, but this will not be the
fault of Logic. In Logic the Quality of the subjectmatter is accidental and not essential.
The essential quality of propositions in Logic is
then the quality of the expression: and this quality
is made, as before shown, to depend upon the copula.
If the copula is affirmative, the proposition is called
affirmative; as
All A is B.
Some A is B.
If the copula is negative, the proposition is said to be
negative; as
No A is B.
Some A is not B.
To mark these divisions according to quantity and
quality, and to simplify the future operations in which
they are used to frame arguments, we employ letters
as symbols. Since every proposition must be universal or particular, and at the same time affirmative or
negative, there are four and only four classes of simple categorical propositions, which we represent by
the following symbols:Universal affirmative: as All X is Y, by  A.
Universal negative; as No X is Y, by  P.
Particular affirmative; as Some X is Y, by  I.
Particular negative; as Some,X is not Y, by 0.




PROPOSITIONS.               83
The sign of a universal proposition is the same as
that of a distributed term; i. e., the prefix All or
Every for the universal affirmative, and No for a universal negative:
And here it must be particularly observed that the
universal negative is only correctly written when in
the form No A is B. It might at first sight seem
that this is equivalent to All A is not B; but it is
not so, although often meant to be so: Thus all
soldiers are not cruel, has a very different meaning
from no soldiers are cruel. The first is not indeed a
universal proposition as it appears to be, but a particular, implying that some soldiers are cruel, while
some are not.
The translators of our English Bible have, in a few
instances, made use of this form improperly to express
a universal.  Thus, the Hebrew text of the Psalms
expresses with regard to the wicked: —" All his
thoughts are' there is no God;' " while the translators
have it c God is not in all his thoughts;" the meaning of this is evidently God is not in any of his
thoughts.
The sign of a particular proposition is the same as
that of an undistributed term,-i. e. the prefix some,
few, several, many, and like words, indicating a part
only of a whole, for particular affirmative propositions;
and the same prefix, with a negative copula, for particular negative.




84                    LOGIC.
But it constantly happens that a proposition has no
prefix, and we are then thrown upon our knowledge
of the subject-matter of the proposition to determine
whether it be universal or particular. Such propositions as have no prefix to denote their quantity are
called indefinite propositions, which Logic alone will
not enable us to understand.  We must then look to
their meaning, and thus find out what prefix is their
due. For example,-Men are artists.
By examining the matter of this, we find that only
some men are artists, and then making the proper
prefix we declare the proposition to be particular.
Birds fly. This is true of birds universally, and
we have the right to prefix the sign all, which denotes it a universal proposition.
A singular proposition is one which has for its subject a singular term; as
Alexander was a conqueror.
Coesar was ambitious.
It would seem at a first consideration of the quantity of these propositions, that they were particular,
but this is erroneous; they are evidently universal;
since when I assert that Alexander was a conqueror,
I mean the whole of Alexander, or Alexander taken
in his.fullest extension.
As a general rule, then, singular propositions are
universal. There are many other divisions of propositions which are curious rather than useful dis



PROPOSITIONS.                85
tinctions. The above are all those necessary to a
comprehension of the logical processes which follow.
(28.) Of the Distribution of Terms in Propositions.
Having treated of the quantity and quality of prositions, and observing that, as we have already seen,
these propositions are to be hereafter used in the
framing of syllogisms, we come to consider the distribution of terms in propositions, and to establish
rules for this distribution. If we examine the four
categorical propositions, with their geometrical notations,Affirm. A  All Xis Y.   e.   f No X is Y.
ffiSrm.  omeXisY.   Ng 0. j Some X is not Y.
(A)         (I)          (E)           (0)
first with reference to their subjects, it will be evident
that in A and BE the whole of the subject being considered, the subject is distributed, as is also indicated
by the prefixes All and No. It will be equally evident
that in I and 0 the subject is undistributed, a portion
only being taken, as is indicated by the prefix Some.
The rule deduced then, as far as the subjects are
concerned, is very simple; it is, that
All universal propositions distribute the subject.
No particulars distribute the subject.




86                   LOGIC.
But since the predicates in these propositions have
no such prefixes, how are we to determine whether
they are distributed or undistributed? By an examination of the relation existing between the subject
and predicate in each case, we shall see that the distribution of the subject by no means implies that of
the predicate.
If we assert, 1st that All X is Y, we do not assert
that other things likewise may not be contained in
Y; for though all X is Y, All W may be Y, All Z
may be Y, &c.; or, to illustrate by a geometrical
figure, we have
Q\\
(    Y
and still space enough for other things to be contained
in Y. Hence, it is evident that the whole of Y is
not considered in the proposition all X is Y, or that
Y, the predicate, is not distributed in a universal
affirmative proposition.
Again, if we take the proposition some X is Y, the
same reasoning will apply, since many other things
may be Y, besides this some X; as is illustrated in
the figure




PROPOSITIONS.               87
Likewise then we see that the whole of Y is not
taken in this case, or that the predicate of a particular affirmative proposition is not distributed.
Thus far, then, we have found it true of affirmative
propositions, whether they be universal or particular,
that they do not distribute the predicate.
If now, we consider the universal negative, no X
is Y, we shall find that we must consider the whole
of X and the whole of Y, before we can assert that
no part of one belongs to any part of the other:thus
We have already seen that the subject X is distributed, and it thus appears that in a universal negative
proposition the predicate also is distributed.  The
whole of the subject is brought in contact with'the
whole of the predicate, or we could not entirely deny
their agreement. It remains now to consider only
the predicate of a particular negative, some X is not
Y. The same reasoning applies here as in the last
case; or we must know and consider the whole of Y,
before we can assert that no part of it belongs to the
some X in question.
(Y




88                       LOGIC.
It therefore appears that the predicate of a particular
negative proposition is distributed.
If we collect together these four results, we shall
thus establish two rules:
1st. The subjects of universal propositions, and
not of particulars, are distributed.
2d. The predicates of negative propositions, and
not of affirmatives, are distributed.
It may be well, for the sake of convenient reference, to arrange the quantity and quality of propositions, and the distribution of the terms, in a tabular
form, so that it may be referred to until it be fixed in
the mind of the student.
Four classes of Categorical
Ptropositions.    Sbject.      Predicate.  Simpleb Form.
A. Universal affirmative.  Distributed.  Undistributed. All X is Y.
E. Universal negative.  Distributed.  Distributed.  No X is ~.
I. Particular affirmative.  Undistributed.  Undistributed. Some X is Y.
O. Particular negative.  Undistributed.  Distributed.  Some X is not Y.
There is a logical process which is passed upon propositions and upon propositions only, and this process
has in view the use which we make of propositions in
the framing of arguments.       It is called Conversion.
We cannot convert a term, nor is it proper to speak
technically, as some writers have done, of the conversion of arguments.
(29.) Conversion.
Conversion consists in transposing the terms of a
proposition in such a manner as to place the subject




CONVERSION.                  89
for the predicate, and the predicate for the subject.
Thus, having the proposition A is B, we convert it
into B is A. When no other change than this is
made, the conversion is called simple conversion: but
by an examination of the four forms of categorical
propositions, it will be evident that they cannot all be
simply converted, and retain in the converted proposition or converse the truth of the original proposition
or exposita. As a simple example of this; having
the proposition
All men are mortal;
we cannot write the converse,
All mortals are men.
No other conversion is allowed in Logic than that
which is called illative,* or that in which we may infer
the truth of the converse from the truth of the exposita.
To simplify this, let us convert each of these propositions in turn.
1st. (A.) All X is Y = All men are mortals.
It is evident, as we have already seen, that we
cannot convert this proposition simply, for we cannot read
All Y is X = All mortals are men,
since Y (or mortals) includes many other races besides
men.
We, therefore, limit the quantity of the proposi-': in and fero, (latum).
8



90                    LOGIC.
tion from universal to particular, so that Y, which was
undistributed in the original proposition, may remain
so in the converse. Expressing then this non-distribution of Y by the prefix some, we shall have as the
converse
Some Y is X = Some mortals are men.
From the nature of the process, this form of illative
conversion is called conversion by limitation.*
From this we see that the converse of a universal
affirmative is a particular affirmative, or A becomes,
when converted, I. If we examine the universal
negative,
2. (E.) No Xis Y= No men are trees,
we shall see that as X and Yare taken in their whole
extension, or are distributed, we may here convert
simply, and read
No Y is X = No trees are men.
The converse of a universal negative is a universal
negative.
So, likewise, in the particular affirmative
3. (I.) Some X is Y = Some men are cruel,
we shall find that neither subject nor predicate is taken
in its full extent or distributed, and that we may,
therefore, convert simply:
Some Y is X = Some cruel (beings) are men.
*The Latin name employed by logicians, for this kind of conversion, is conversio per accidens.




CONVERSION.                    91
The converse of a particular affirmative remains a
particular affirmative.  There remains only the particular negative to be considered.
4. (0.) Some X is not Y = Some quadrupeds are not horses.
This proposition presents a special difficulty.  We
cannot convert it simply as in the cases of E and I;
for we should then have Y, which is distributed in the
exposita, undistributed in the converse; thus we would
have the absurdity
Some Y is not X == Some horses are not quadrupeds.
Nor can we invert the process of conversion by limitation as in the case of A (1.,) and pass back from
particular to universal, as
All Y is not X = All horses are not quadr2upeds.
To overcome this difficulty we detach the negative
particle not in the original proposition from the copula,
and attach it to the predicate; thus, instead of the
open form some X is not Y, we read,
Some AX is (not Y) = Some quadrupeds are (not horses).
and then it is evident that for all logical purposes,
the proposition ceases to be 0 or particular negative,
and becomes I or particular affirmative, since for (not
Y) we might place any other symbol, as Z, and convert
by simple conversion. But without this trouble, if we
convert we shall have
Some (not Y) is X = Some (not horses) are queadrupeds,
or in our ordinary language, to complete the sense:
Some (beings which are) not horses are quadrupeds.




92                     LOGIC.
This is called conversion by contraposition or by negation.
We arrive by this process at a rule for illative conversion-which is, that No term must be distributed in
the converse which was undistributed in the exposita.
By arranging the different kinds of illative conversion in tabular form, we shall simplify them for reference.   Taking the letter p to indicate conversion by
limitation or per accidens; s, simple conversion; and
I, conversion by negation, we shall have the following
table.
ILLATIVE CONVERSION.
Original Propositions. Methods of Converting. Converted Propositions.
(A.) All X is Y.    p.       Some Y is X.  (I.)
(E.) No X is Y.     s.        No Y is X.  (E.)
(I.) Some X is Y.   s.       Some Y is X.  (I.)
(0.) Some X is not Y.  7c.   Some (not Y) is X. (I.)
The above are the regular forms of conversion, but
there are certain Additional conversions to be noticed.
It must be remarked that the universal affirmative,
All X is Y - All men are mortals,
is sometimes converted in another manner, i. e. by
putting immediately before both subject and predicate
the negative particle not, and then converting, thus
All (not) Y is (not) XY = All (not) mortals are (not) men.
i. e., All (who are not) mortals are not men; or in
common phrase, None but Y can be X      =   none but
mortals can be men.
Again, (E), which is converted simply, may be like



CONVERSION.                 93
wise converted by limitation, since, if having the universal form
No A is B = No men are trees,
we can say
No B is A -= No trees are men,
we can also say, what is less than this,
Some B is not A - Some trees are not men.
It may happen that for some purpose of logical
technicality it will be better to use the particular when
we have a right to use the universal, but from the existence of the universal we infer that of the particular, which is only a part of it.
There remains only one remark to be made upon
the subject of conversion; it is that there are a few
propositions which bear the form of A or universal
affirmative, which are capable of simple conversion.
The terms of such a proposition are said to be convertible terms, or the predicate and subject are either
exactly equivalent or exactly co-extensive: for example in the proposition All common salt is chloride of
sodium, we have a right to assert that all chloride of
sodium is common salt. From the proposition A II the
good are saved, we have a right to infer that All (who
are) saved are good. Many just definitions come
under this class. Besides such propositions as these,
there are many mathematical propositions which seem
to be single propositions with convertible terms, when
in reality they contain two distinct propositions, each




94                  LOGIC.
of which requires distinct proof. Thus, All equilateral triangles are equi-angular.  The apparent converse that All equi-angular triangles are equilateral,
is indeed true, but this is not inferred from the original proposition, it is proved separately by geometricians; so that instead of being the converse of the
proposition stated it is, in reality, a distinct proposition.
The processes of conversion have been applied
above only to the forms of simple categorical propositions; they may likewise be applied, however, to
compound propositions, and when we come to consider these, we shall show how they may be converted;
but it may be here observed, that as all compound
propositions may be readily reduced to the simple
categorical form, having shown how to convert these,
we have in reality shown how to convert them all.
The next process of importance in considering propositions, is the manner and character of their opposition to each other, and this, like the process of
conversion, becomes of special value when we are
joining propositions together to frame arguments.
(30.) Of Opposition.
Two propositions are said to be opposed to each
other, when, having the same subject and predicate,
the one denies either entirely or in part what the other




OPPOSITION.                     95
affirms, or affirms either entirely or in part what the
other denies; as, for instance, the proposition
(A.) All men are mortal, is opposed by both Noe men are tmodal.  (0.)
Somie mnen are not mortal. (O.)
and (E.) No angels are men, is opposed by both ( All angels are nen,  (A.)
(Some angdels are men.  (I.)
Again, two propositions are said to be opposed
when, having the same subject and predicate, the one
affirms in whole what the other affirms in part, or denies in whole what the other denies in part,   Thus:
(A.) All men are mortal, (0pp.) Some men are mortal.  (I.)
(E.) No men are trees,  (Opp.) Some men are not trees. (0.)
It will appear, then, that the opposition in propositions is both in quantity and in quality, and as there
are four forms of categorical propositions, and any
two may be thus opposed, we shall have four kinds
of opposition, which will best be illustrated by the
following figure:A   contraries  E,2         s,  CD
I  sub-contraries  0
In which the two universal propositions A and E are
called contraries and differ only in quality, being respectively affirmative and negative; the two particulars I and 0 are called sub-contraries, differing
likewise in quality only; the two affirmatives and the
two negatives are called respectively subalterns, differ



96                   LOGIC.
ing in quantity only; the universal affirmative and
particular negative, and the universal negative and
particular affirmative, are respectively called contradietories, and differ both in quantity and quality.
If we desire, as in applying Logic we may do, to
determine the relative truth and falsity of these respective propositions, we must look for a moment at
the matter which they may contain.
(31.) Of the Matter of Propositions.
The matter of a proposition is the nature of the
union between the terms of the proposition, or in ordinary language, the exact meaning of the proposition.
By considering the nature of this connexion between the terms, we shall see that it can be of only
three kinds: necessary, which is expressed by an
affirmative proposition; impossible, expressed by a
negative proposition, and contingent, which is expressed by a particular proposition.
To illustrate: if wie have given to us the two terms,
men and mortal, and are told to connect them by a
copula, we ask ourselves, what is the nature of the
connexion between these two. The answer is, it is
necessary, and we express that necessity by using an
affirmative copula, and prefixing the sign All:
All men are mortal.
Again if we have given to us the two terms men and




OPPOSITION.                    97
trees, to perform  an analogous operation, we shall
assert the nature of the connexion between them to
be impossible, and express that impossibility by the
use of the prefix noNo men are trees.
If again, we have the terms men and handsome, we
assert the nature of the connexion to be contingent,
as some men are and some are not handsome, and thus
to express contingent matter we write the proposition
with the prefix some;
Some men are handsome.
Some men are not handsome.
If, now, we examine the matter of these propositions
we shall see that
In necessary matter all affirmatives are true, and
negatives false.
Necessary Matter.
True.                        False.
(A) All men are mortal.    (E) No men are mortal.
(I) Some men are mortal.   (0) Some men are not mortal.
In impossible matter all negatives are true and affirmatives false.
Impossible Matter.
True.                            False.
(E) No men are trees.         (A) All men are trees.
(0) Some men are not trees.   (I) Some men are trees.
In contingent matter all particulars are true and
universals false.
9                   o




98                      LOGIC.
Contingent Matter.
True.                           False.
(I) Some men are handsome.    (A) All men are handsome.
(0) Some men are not handsome.  (E) No men are handsome.
From this examination we perceive that if one contrary is true the other must be false, but if one is
false the other may be false also: if one sub-contrary
is false the other must be true, but if one is true the
other may be true also.   But in the case of contradictories, if one is either true or false, the other must
be just the opposite, i. e., false or true.
It remains to consider the subalterns, which differ
in quantity. If the universal (A or E) be true, the
particular I or 0 will be true also; as
(A) All men are mortal,  (E) No men are trees,
implies                 implies
(I) Some men are mortal. (0) Some men are not trees.
If the particular I or 0 be true, the universal A
or E is not necessarily true.
(I) Some islands are fertile, does not permit us to
infer (A), All islands are fertile.
(0) Some islands are not fertile, does not permit us
to imply (E) No islands are fertile.
But if the particular be false, the universal must
of necessity be false also. Thus the false particular
Some men are trees, would give us also All men are
trees as a false universal.
By summing up these inferences we may state the




COMPOUND PROPOSITIONS.           99
following rules, which must be kept in the memory as
we approach the subject of Reduction.
I. Contraries may both be false, but never both be
true.
II. Sub-contraries may both be true, but never
both false.
III. Of Contradictories, if one be false the other
must be true, and vice versa.
IV. In Subalterns we reason from the affirmation
only of the universal to the affirmation of the particular; but from the denial of the particular to the
denial of the universal.
With the remark that opposition may be also illustrated in compound propositions or those not directly
in the simple categorical form; or that such propositions may be reduced to this simple form, by an easy
process still to be explained; we pass to the subject
of compound propositions.
(32.) Of Compound Propositions.
A compound proposition consists of two or more
simple propositions, united together either by a simple
copulate, expressed or understood, or by a conjunction denoting an hypothesis.
Compound propositions are consequently divided
into two classes, categorical and hypothetical.
Conmpound categorical propositions are of two kinds,
copulative and discretive.




100                    LOGIC.
A copulative proposition consists of two or more
subjects united with the same predicate, or with two
or more predicates, by the use of the copulative conjunction, as
Men, horses, and birds are animals.
A discretive proposition consists of two simple propositions, which are contrasted on account of an apparent inconsistency, as
Fox, though dissolute, was a patriot.
Many compound propositions are tacit or implied,
and thus have the form of simple propositions.
A hypothetical proposition consists of two or more
simple propositions united by a conjunction which
expresses hypothesis. This conjunction is usually
placed at the beginning of the proposition.
fHypotheticals are divided into conditional, disjunctive and causal, and take these names from the conjunctions which express the condition of the hypothesis.
A conditional proposition expresses the condition
by the conjunction if; as
If A is B, C is D = If John return, Harry will go.
A disjunctive proposition is formed with the conjunctions either and or; as
Either A is B, or C is D == Either the day will be fine or cloudy.
A causal proposition unites its parts by the conjunction because; as
A is B, because C is D.
John is well because he is prudent.




COMPOUND PROPOSITIONS.          101
It is evident in the case of categorical propositions,
that they may be at once resolved into the simple
propositions of which they are composed: thus we
may divide the copulative proposition given into three
distinct propositions; viz.,
Men are animals,
Horses are animals,
Birds are animals,
and the discretive may be divided into two; thus:Fox was dissolute.
Fox was a patriot.
Unlike the compound categorical propositions, the
hypotheticals contain within themselves the germ of an
argument, and only require that the hypothesis shall
be established or fail of establishment, to arrive at
a conclusion. Thus, having the proposition,
If A is B, C is D,
we need only know whether A is B, in order to
state the argument and arrive at the conclusion that
C is D.
Conditional propositions, however, may be, in every
case, reduced to a categorical form, by regarding them
as universal affirmative categorical propositions, of
which the antecedent is the subject, and the consequent
the predicate. We then rid ourselves of the condition,
by the use of the words, c" the case of;" thus, instead
of the form, If A is B, C is D, we shall have
(The case of) A being B, is (the case of) C being D,
which is purely categorical in form.
9 -




102                   LOGIC.
Disjunctive propositions may be reduced to conditionals; thus:
Either A is B, or C is D, is equivalent to If A is not B, C is D,
or we may place it at once in a categorical form without this double process, by reading it thus:
Thze two possible cases in this matter are that A is B, and that C is D.
It is more usual to reduce the disjunctive however
to a conditional form, into which it very naturally
falls.
The causal proposition,
Because A is B, C is D,
becomes either at once categorical, when we establish
the truth of because, and thus we have
A is B, therefore C is D,
as an enthymeme, to which, having the subject-matter,
we might supply the wanting premiss; or the causal
proposition becomes simply conditional, if the causeexpressed by the first proposition A is B-be doubtful, and then we read,
If A is B, C is D,
which must be treated like the conditional above.
As it seems, then, that all these are reducible to
the conditional form, we need only show how the process or conversion is applied to conditionals, in order
virtually to apply it to them all. From what has
been said, it will appear that conditionals are con



THE NEW ANALYTIC.              103
verted by negation only; thus, to convert the proposition,
If John has the smallpox he is sick;
we may readIf John is not sick he has not the smallpox,
or, the conversion rests upon the fact that the denial
of the consequent leads to the denial of the antecedent.
We cannot convert without this negation, for we
could not reason from the affirmation of the consequent to the affirmation of the antecedent; thus,
If John is sick he has the smallpox,
since that consequent (sickness), may have sprung from
some other antecedent than the smallpox.
(33.) The New Analytic.
And here it becomes necessary, before closing the
subject of propositions, to refer briefly to the effort
of certain late writers to quantify the predicate; that
is, to place prefixes before it similar to those placed
before the subjects of propositions to determine at a
glance its distribution or non-distribution, and to form
thus a new set or class of categorical propositions.
Thus, instead of the form all men are animals, they
would write all men are some animals, and claim
thereby not only a greater precision in the logical
statement, but in some instances the establishment
of a distinct proposition; as, for example,
All A is (all) B.
It may be admitted that sometimes a new idea is
suggested by such a quantification of the predicate,




104                  LOGIC.
but it is only suggested, not contained in the proposition thus rendered. Thus if we say
All men are sinners,
we mean, by our rule, some sinners; now the question
as to the comprehension of this word sinners may
arise, when we place such a prefix; whether angels
and devils may or may not be included in it; and
whether the ill-conduct of brutes is excluded from it.
Whereas, if we could write,
All men are (all) sinners,
we should exclude at once all other beings from the
category. Hence, the quantification of the predicate,
which in the old system is implied, does when expressed,
suggest new thoughts or judgments, but those new judgments rest upon their own basis, and have really
nothing to do with the original proposition. There
seems really, therefore, nothing gained in the extension of the proposition by this attempt to quantify the
predicate, but rather a confusion of judgment and a
complication of logical forms.
It is not intended to give, in detail, the applications
of the "new analytic," nor to deny that results,
totally out of the province of Logic, are attained by
it. It is evident that if we quantify the predicate, in
categorical propositions, we shall have four additional
forms, viz.:
Established Forms.   New Forms.
A.       All A is B.      All A is all B.  X.
E.       No A is B.       No A is some B.   Y.
I.       Some A is B     Some A is all B.  U.
0        Some A is not B.  Some A is not some B. Z.




THE NEW   ANALYTIC.              105
Now of these new forms we have already considered
X, as in the case
All equilateral triangles are (all) equi-angular,
and in the cases of exact definitions, as
All common salt is (all) chloride of sodiumn,
In the first we have seen that there are two distinct
propositions, and in the second that there are but two
names for the same object.
As for Y, U, and Z, they are so clearly contained
in the old forms that they need but little elucidation.
Y.    Some trees are all oaks,
when converted gives us
All oaks are trees,       or A.
U.    No heroes are some men,
Conv. Some men are not heroes.     0.
Z.     Some quadrupeds are not some horses,
by which we determine that the quadrupeds referred
to may belong to other species, or may be included in
the species horse, apart from the some horses mentioned.                 Hoses
Quadrupeds
It was attempted, in the new analytic, to simplify the
subject of conversion, but, it seems, with inadequate
results.
And here we leave the subject of quantifying the
predicate so far as it relates to propositions alone.
If carried out in the syllogism, it would much enlarge
the domain of Figure, and give much fruitless labour
to the logician.




106                     LOGIC.
CHAPTER VII.
(34.)  Of Arguments.
AN argument is an act of reasoning or ratiocination.  It consists of two parts; that to be proven,
and that by which it is proven.
The part to be proven is embodied in the conclusion,
and that by which it is proven is embodied in the
premisses.   When these are inverted from the usual
logical order, so that the conclusion is stated first, it
is called the question; and the premisses which are
joined to it by the word because, are then called the
reason; thus,
(Question) Why are all Americans mortal?
or All Americans are mortal,
Because They are men.
But in logical form and order the premisses are stated
first, and the conclusion is connected with them by
the illative conjunction therefore; thus
Premisses f All men are mortal,
A All Americans are men,
Therefore  All Americans are mortal.




ARGUMENTS.                 107
These two forms must be distinguished from what is
expressed by the words inference and proof, which
have not to do with the order of the parts in an argument, but with the special design of the person who
uses the argument, i. e., whether from known facts or
premisses, he seeks to establish a conclusion; or has
adopted a conclusion, and is simply seeking for premisses by which to substantiate it.
Logic teaches us to draw from known proofs only
a just inference, or to maintain a given inference only
by just proofs.  We may more clearly illustrate by
observing how, in the various professions, these
different methods are used; thus, a naturalist gets
together many observations and makes many experiments, forming a strong store of proofs, before he
may justly infer a conclusion; while an advocate at
law, assumes the innocence of his client or the guilt
of the prisoner, as a foregone conclusion, and then
uses every means for obtaining proofs and thus establishing premisses by which to substantiate his conclusion.
It has been observed that the logical form of an
argument is a syllogism, which consists of three propositions, i. e. two premisses and a conclusion.
After fully explaining the syllogism, we shall consider all forms of irregular and abridged arguments,
and show, as has been asserted, that they may all be




108                   LOGIC.
reduced to this simple form, so that the logical tests
may be at once applied to them.
(35.) Of the Syllogism.
In the analysis of Logic, the dictum of Aristotle
was distinctly laid down and illustrated. Its form
was:
No. 1.              No. 2.
All A is B.        No A is B.
All or some C is A.  All or some C is A.
All or some C is B.  No C is B, or some C is not B.
The principle of the dictum is, that whatever (B)
we predicate (in the major premiss), of the whole class
(All A); under which class we assert (in the mna'or
premiss), certain individuals (All or some C) to be
ranged; we may also predicate (in the conclusion) of
those individuals.
Thus, B is predicated of (All A), C is an individual
of the class A, therefore we have a right to predicate
B of C.
But, as few arguments, in the ordinary uses of language, are placed in this exact form (although all
valid arguments may be), there have been laid down
two logical axioms and several important rules for
determining the validity of syllogisms, without the
labour of bringing them to this form.
It must be constantly remembered that it is a condition of every syllogism that it contains three and
only three terms: the major term, the minor term, and




THE SYLLOGISM.              109
the middle term.  The first two of these terms must
not be confounded with the premisses which bear the
same name, and which are propositions. Thus in the
example,
mid.   maj.      mid.   maj.
Maj. prem.  A  is B    All men are mortal.
min.   mid.        minor.   mid.
Min. prem.  C  is A -  All Americans are men.
min.   maj.        minor.   major.
Concl.    C  is B   -  All Americans are mortal,
B is the major term, and it is in the major premiss;
C is the minor term, and it is found in the minor premiss; A is the middle term, because it is the medium
of comparison between the other two. In the major
premiss, the middle term is compared with the major;
in the minor premiss it is compared with the minor,
and in the conclusion, the minor and major terms,
having been thus found to agree with the same middle
term, are asserted to agree with each other.
The minor term is always the subject of the conclusion, and the major term the predicate.
This simple process of comparison leads us to the
statement of those axioms which determine the conditions of agreement and disagreement between the
major and minor terms, and to note some important
consequences following from them.
(36.) Logical Axioms.
1st. If two terms agree with one and the same third
term, they will agree with each other.
10




110                  LOGIC.
2d. If of two terms, the one agree and the other
disagree with one and the same third term, they will
disagree with each other.
Rules.
I. From the first of these axioms we observe that
if both premisses of a syllogism are affirmative, thus
expressing the agreement of the major and minor
terms with the middle, the conclusion must likewise
be affirmative, or express the agreement between these
two terms; thus, B being the major term, C the minor,
and A the middle, we have
A is (or agrees with) B,
C is (or agrees with) A,
and we must consequently state the
conclusion
C is (or agrees with) B.
II. Again, from the second axiom, we see that if
one of the premisses (as the major) be affirmative, and
thus express the agreement between the major term
and the middle, and the other be negative and thus
express a disagreement between the minor term and
the middle, we must have a negative conclusion to
express the disagreement between the major and the
minor, which we have thus shown, the. one to agree
and the other to disagree in the premisses with one
and the same third (the middle).
Thus if, A is not (or disagrees with) B,




THE SYLLOGISM.              111
And if, C is (or agrees with) A,
we must have, C is not (or disagrees with) B.
III. It is further evident that if both premisses be
negative, we can draw no conclusion; because in these
premisses the middle term, simply disagreeing with
both the major and minor terms, is no longer a
medium of comparison between them. For example,
state the premisses,
No A is B - No men are trees,
No C is A -= No horses are men;we have established no relation whatever between C
and B, or between horses and trees, so that, although
we might truthfully write
No horses are trees,
it would be an accidental statement, and not spring
from the premisses stated.
In the conclusion is stated the relation between the
major and minor term, which was established in the
premisses by the medium of the middle term. The
minor term is the true subject of the conclusion, and
the major term the true predicate.  Sometimes in an
inverted or elliptical conclusion these terms may
appear *ansposed, but when properly written out
they will take the places indicated.
The middle term, which occurs twice in the premisses, is the medium of comparison between the two




112                    LOGIC.
other terms, and is generally the name of a class, of
which in one premiss something is predicated, or to
which some quality is attributed, as
1. Jian is a rational animal,
in which man is the name of a class, and rationality
a predicate or attribute: under which in the other
premiss we range an individual or individuals belonging to the class, as
2. John is a man,
and by means of which we have a right to predicate
or attribute this same thing rationality to the individual; thus,
3. John is a rational animal.
IV. Ambiguous middle.
It is scarcely necessary to state that the middle
term  must be univocal, i. e., must have the same
meaning in both premisses. If it be ambiguous, or
possess one meaning in the major premiss and a different one in the minor, we shall violate the first principle in the construction of a syllogism, and have four
terms instead of the three, and only three, required.
Most languages have many such ambiguous words,
and the English particularly is full of theme thus
1. A bank is a financial institution,
2. The margin of a stream is a bank,
3. The margin of a stream is a financial institution.




THE SYLLOGISM.             113
Many such glaring examples will occur at once to the
student; but it must be remembered that the sophist
who would construct his artful fallacies to deceive,
does not employ such manifestly ambiguous words,
but those whose double meanings are much more
nearly the same.
Thus, in their philosophic meanings, the words
church and faith have given rise to sharp controversy
and violent partisanships. As ambiguous terms play
a very prominent part in the subject of Fallacies, we
shall recur to them under that head.
When the argument is written out in symbols, the
ambiguity either disappears entirely, that is, when we
represent the term in both premisses by the same
letter, thus
A is B,
C is A,
C is B,
or it becomes at once manifest, when we represent the
term in the major premiss, by one symbol, as A, and
that in the minor, having a different meaning, by another, as D, thus
A is B,
C is D,
in which premisses there are four terms, and the error
distinctly appears.
V. Undistributed middle.
The middle term must be distributed, i. e., taken in
10               H




114.                  lO(GIC.
its whole comprehension, at least in one of the premisses, for it will otherwise occur that we may compare the major term with one part of the middle, and
the minor with another part, and thus it would fail to
be a just medium of comparison. It might happen,
by chance, that these two parts should be the same,
but it would be only by chance; in the general case
they would be different parts, and if we choose to
regard each part as a distinct term, we should again
run into the error of having four terms instead of
three; thus
Some quadrupeds are cows,
Some quadrupeds are sheep,
Therefore Some sheep are cows.
White is a colour,
Black is a colour,
Therefore Black is white.
But if one of the extremes be compared with the
whole of the middle term, and the other be compared
only with a part, which part is necessarily contained
in the whole, they may then be compared with each
other.
VI. Illicit process.
Again, in order to distribute either the major or
minor term in the conclusion: it must have been previously distributed in the premiss in which it occurs;
because, we only have a right to compare that part
of the term with the other, in the conclusion, which




THE SYLLOGISM.                 115
we have already compared with the middle in the
premiss, thus
All men are animals,
No dogs are men,
Therefore No dogs are animals.
The technical name for this logical fallacy is the illicit
process.  In the example, the major term, animals,
which is not distributed in the premiss (as it is
the predicate of an affirmative proposition) is distributed in the conclusion (as the predicate of a negative proposition); this is called an illicit process of the
major term: if it be the minor term thus treated, it
is called an illicit process of the minor term.
The following is an example of illicit process of
the minor.
1. All men are rational beings,
2. All men are animals,
3. All animals are rational beings.
In this example the minor term animals, which is undistributed in the minor premiss-as the predicate of
an affirmative proposition,-is distributed in the conclusion, being there the subject of a universal.
Let it be remembered that this is called an illicit
process of the major or minor term, not of the major
or minor premiss.
VII. If both premisses in a syllogism be particular
propositions, we can draw no conclusion; thus:
1. Some men are wise,
2. Some men are foolish,




116                   LOGIC.
leads us to no conclusion. Nor are we benefited if
we make one of the premisses particular negative;
thus:
1. Some men are wise,
2. Some men are not brave,
we are as before without any medium of comparison.
The fact is as stated; the causes are various, and
will be fully explained in the chapter on Figure.
It is sufficient, now, for the student to know that
the cause is in every case, either an undistributed
middle, or an illicit process of one of the other terms.
By the foregoing axioms and rules, we extend the
range of syllogistic forms, and are able to see the
validity or invalidity of an argument without reducing
it to the invariable formula of Aristotle's dictum.
We proceed now to show how many of these forms
there may be, and the relation they sustain to the
dictum itself; and this brings us to the subject of.Figure and Moods.




FIGURE AND MOODS.             117
CHAPTER VIII.
OF FIGURE AND MOODS.
(37.) Figure.
fFigure is the technical name employed to designate
the classification of syllogisms according to the position of the middle term with reference to the two extremes in the premises.  Now, it is evident that the
middle term can have only four variations of position,
and hence we say there are four figures.
1st. The middle term may be the subject of the
m.ajor premiss, and the predicate of the minor, and
this designates the 1st figure.
2d. It may be the predicate of both premisses, and
thus the 2d figure is designated.
3d. In the 3d figure it is the subject of both premisses; and
4th. In the 4th figure (which is the reverse of the
1st), it is the predicate of the major premiss and the
subject of the minor.
If we designate the major term by P (as it is
always the predicate of the conclusion), the minor




118                   LOGIC.
term by S (being the subject of the conclusion), and
the middle term by M, and merely state these various
positions of the middle term, without considering or
denoting the quantity or quality of the propositions in
the syllogism, we shall have the abstract syllogisms,
I.        II.        III.       IV.
M is P.    P is M.    M is P.   Pis M.
S is M.    S is M.    M is S.   M is S.
S is P.    S is P.    S is P.   S is P.
These are called the four figures; and to the syllogisms which occur in them, the axioms and rules
already laid down directly apply.
If now we proceed to examine these figures in order,
we shall find that the first figure is but the symbolical
representation of Aristotle's dictum, the simplest form
of the syllogism. There will be four variations of
it; viz.:1.         2.           3.         4.
All M is P.  All M is P.  No M is P.  No M is P.
All S is M.  Some S is M.  All S is M.  Some S is M.
All S is P.  Some S is P.  No M is P.  Some S is not P.
We have simply supplied the quantity and quality
required.
Since, in the major premiss, then, of Aristotle's
dictum, we assert or deny the predicate of the whole
class which is the subject (All M), it is evident that in
the first figure, the major premiss is always universal.
If, then, with this relative position of the middle term,
i. e. in the first figure, we find a syllogism, the major




FIGURE.                 119
premiss of which is particular, we may at once declare
it to be invalid.
Again, since the province of the minor premiss in
the dictum is always to assert that certain individuals
belong to the given class (and in no case to deny it),
it appears that in the first figure the minor premiss
must always be afirmative, so that if we find a syllogism in this figure with a negative minor premiss, we
may at once declare it invalid.
Thus, in stating the four forms of the dictum, we
have stated the only four forms which the first figure
can cover.
But the other figures, which are not directly in the
form which the dictum assumes, instead of being explained by it, are to be considered in the light of the
axioms and rules for determining the validity of syllogisms when the dictum does not directly apply. By
examining the second figure,
P is M,
S is M,
S is P,
we shall find that there are several forms which it
will assume when we supply the quantity and quality
to the propositions. We observe at once that the
conclusion must, in every case, be negative, because
1st. The middle term is the predicate of both premisses;
2d. The middle term must be distributed at least
once in the syllogism;:




120                   LOGIC.
3d. In order that the predicate of a proposition
shall be distributed, the proposition must be negative;
4th. This will give us one negative premiss, and by
the second axiom, if we have a negative premiss the
conclusion must be negative (universal or particular).
Third Figure.
M is P,
M is S,
S is P.
By the supplying of quantity and quality this
figure assumes a greater variety of forms than any
other.
By considering the position of the terms here, it
will appear that we can only draw particular conclusions.  For if both premisses be affirmative, and we
draw a universal conclusion, or All S is P, then S
(the minor term) which was undistributed in the minor
premiss (being the predicate of an affirmative proposition), will be distributed in the conclusion, as the
subject of a universal; or we shall have an illicit process of the minor.
If the major premiss be negative, and we draw a
universal conclusion, it is easily shown that the same
error-an illicit process of the minor-obtains; and
if the minor premiss be negative, we shall have an
illicit process of the major.




MOOD.                   121
Fourth Figure.
P is M,
M is S,
S is P.
The fourth figure, which was not proposed by Aristotle with the other three, and only recently adopted
by logicians, is an inversion of the first. and an unnatural and unnecessary form of the syllogism. By
a similar examination of all the terms we shall find,
that we may draw, as conclusions, in this figure all the
categorical propositions except A, which, as has been
shown, can only be drawn in the first figure. It is
the prerogative of Aristotle's dictum alone, to draw
from  certain premisses a universal affirmative conclusion.
The various forms of the syllogism due to the different quantity and quality of the propositions composing them, are arranged, in the different figures, in
what are called moods, or a concise manner of expressing a syllogism by symbols.
(38.) Of uMood.
If, having any syllogisms, as the followingAll A isB, (A.)       No A isB.     (E.)
1. All C is A, (A.)  2. Some C is A.  (I.)
All C is B, (A.)    Some C is not B. (0.)
we write together the symbols characterizing each
proposition which composes them, we are said to deter11




122                  LOGIC.
mine the mood of the syllogism; thus the symbol of
the major premiss in the first syllogism is
A, or universal affirmative;
that of the minor,
A, or universal affirmative;
and that of the conclusion likewise
A, or universal affirmative.
Hence we say that A A A is the mood of the syllogism.
In the second syllogism we shall find by a similar
process that the mood is E I 0.
Now, it is evident that the number of moods we
can have will depend upon, 1st, the number of propositions in the syllogism, viz., three; and 2d, upon the
number of categorical propositions which we can enumerate, viz., four, A, E, I, 0; it becomes then a
simple algebraic arrangement of four letters A, E, I,
0, in three columns in every possible combination. The
number of these possible combinations will be sixtyfour. For each of the propositions A, E, I, and 0,
may be a major premiss; and each of these may have
each in turn as a minor premiss; thus,
Maj. prem. Maj. prem. IMaj. prem.  Mcj. prem.
A        E         I         0
may have asmi- AEI    A E I    A E I     AE I 
nor premisses, )
Again, each of these sets (sixteen in all) may have
four different conclusions, i. e. each of the categori



MOOD.                  123
cals as a conclusion. Taking the first set, for example,
and supposing the operation performed for the rest,
FIRST SET.
laj. prem. A.
I.1          1           1
lin. prem. A         E          I           0
I          I I! i  I  I  I  I  I  I  i  I  I  t  I
Conc. A E I O   A    I 0    A E I 0    A      I O
This same process may be performed for E, I, and 0.
There will evidently be sixty-four moods, of which,
however, it is at once evident that very many will
violate the axioms and rules already laid down, and
must be for this reason discarded.
Thus, all the combinations of affirmative premisses
having negative conclusions, as A A E, A I 0, &c.,
&c., must be thrown aside, because they violate the
first axiom.
All the sets of negative premisses, with whatever
conclusions, are useless, as E E, 0 0, E 0, 0 E, &c.
All the sets of particular premisses, with whatever
conclusions, must be neglected, such as I I, 0, 0 I,
I 0, &c.
If all these eliminations be performed, and simple
as they are, the student is advised to go carefully
through them once for himself, we shall find twentyeight moods excluded on account of negative and particular premisses: eighteen by the condition that the
conclusion follows the inferior part, and we shall see




124                  LOGIC.
that one-I E O-is rejected for an illicit process of
the major term, in every figure, and finally that of
the sixty-four arrangements which we call moods, only
eleven represent valid arguments, or
FOUR AFFIRMATIVES and SEVEN NEGATIVES.
A A A             E A E
AI I              AEE
A A I             E A 
IAI               A O0
0 A 
E I 0
AE 0
If now we apply these moods to each figure, in
detail, it would seem, since there are four figures, that
we should have 4 X 11 = 44 moods in all the figures,
but in this application we find that many moods which
are valid in one figure, are not in others; as, for example, the mood I A I, which is allowable in the third
figure, would be in the first figure a case of undistributed middle, and would further violate the principle of Aristotle's dictum, which requires that the
major premiss should be a universal proposition.
A E E is a valid mood in the second figure, while, in
the first, it would have an illicit process of the major
term, and would further violate that principle of the
dictum which requires the minor premiss to be always
affirmative.
By applying these eleven moods to the four figures,
we find that there would be six in each figure, or




MOOD.                   125
twenty-four in all; but even of these, five are omitted
as useless; for example, the mood A A I, in the first
figure, because it is implied and contained in the
mood A A A. Since, if the universal conclusion A
be true, the particular I is necessarily true. By an
application of each of these moods to every figure,
we shall have left, finally, nineteen moods in all; or,
FOUR in the first figure, FOUR in the second, six in the
third, and FIVE in the fourth.
The moods of the first figure are called perfect
moods; those in the other figures, imperfect moods.
As it has been asserted that all arguments may be
put in the form of Aristotle's dictum, that is, that
all the imperfect moods may be made perfect, we proceed to fulfil this assertion, by the process of reduction,
i. e. the reducing of moods in the 2d, 3d, and 4th
figures to the 1st figure, which is the form of the
dictum.
In order to facilitate this process, as well as to retain easily in the memory the different moods and
their value, the following verses, Latin in sound and
scansion, but without intrinsic meaning in the words,
has been formed:FIG. I.-BArbArA, CEIArEnt, DArII, FErIO, dato primce.
FIG. II.-CEsArE, CAmEstrEs, FEstlno, FAkOrO, secundce.
Fr. III.  Tertia DArAptI, dIsAmIs, dAtIsI, FElAptOn,
DOkAmO, fErIso, habet; quarta insuper addit
FIG. IV.-BrAmAntlP, cAmEnEs, dImArls, fEsApO, frEsIsOn.
11 *




126                  LOGIC.
There are variations in these lines, made by various
writers; we have adopted the above as the form which
will indicate to us in the simplest manner the processes of Reduction.
Before explaining these lines, which the student
must memorize in order to make them useful, that he
may have the moods, and their places in the figures,
at his tongue's end, it will be observed that there are
a few words used in these verses which are of no use
except to make out the hexameter lines; of these are
dato primce in the first, secundce in the second, tertia
habet in the third, and quarta insuper addit, which
states-moreover the fourth adds, &c. Leaving these
out of the consideration, in the lines themselves the
vowels in each word represent the moods; thus, barbara is the mood A A A; Cesare, the mood E A E,
&c., &c.
The following consonants indicate what changes
are to be made in the given imperfect mood to reduce
it to a perfect mood of the first figure, s, that the proposition indicated by the vowel immediately preceding it is to be converted simply; thus in Camestres, the
first s indicates the simple conversion of the first E,
or the minor premiss, and the last s the simple. conversion of the second B, or the conclusion. In similar relations p and k stand respectively for conversion by limitation and conversion by negation; m,




MOOD.                  127
wherever it occurs, expresses that the premisses must
be transposed; the other consonants have no meaning, and are only employed to frame the words. P,
in the mood Bramantip of the fourth figure, denotes
that the transposed premisses, indicated by M, will
warrant a universal conclusion instead of a particular.
The initial letters B, C, D, F, of the words which
contain the moods, are so arranged throughout the
figures as to indicate the mood in the first figure to
which any imperfect mood will be reduced; thus
Darapti of the third figure will, when reduced,
become Darii of the first, Camestres will become
C(elarent, &c.
It must be observed that this arrangement is only
for the sake of convenience, as the process of reduction is invariable, and the mood Darapti would become
when reduced the mood A I I of the first figure, whether
it were called Darii or by some other name. Students are apt to be misled with reference to these initial letters, and to suppose that they will aid them in
the process of reduction; it is on this account that
they are cautioned that this is only a convenient and
not an auxiliary arrangement. Before proceeding to
explain the system of reduction, let us give an example of each mood, in all the figures; putting the
logical frame-work to its legitimate use, and showing
every form which the syllogism can assume. We shall




128                    LOGIC.
make the examples very simple, leaving it to the student, with these before him, to frame longer and more
complex ones for himself; a practical exercise which
will be found very useful. The middle term is placed
in italics in each example.
Examples.
FIGURE I.
Barbara.
A. Every desire to gain by another's loss is covetousness.
A. All gaming is a desire to gain by another's loss.
A. All gaming is covetousness.
Celarent.
E. No one who is enslaved by his appetites is free.
A. Every sensualist is one who is enslaved by his
appetites.
E. No sensualist is free.
Darii.
A. All pure patriots deserve the rewards of their
country.
I. Some warriors are pure patriots.
I. Some warriors deserve the rewards of their
country.




EXAMPLES IN THE FOUR FIGURES.        129
Ferio.
E. Nothing which impedes commerce is beneficial
to the revenue.
I. Some taxes impede commerce (or are things which
impede commerce).
O. Some taxes are not beneficial to the revenue.
FIGURE II.
C'esare.
E. No vicious conduct is praiseworthy.
A. All truly heroic conduct is praiseworthy.
E. No truly heroic conduct is (or can be) vicious.
Camestres.
A. Every true philosopher accounts virtue a good
in itself.
E. No advocate of pleasure accounts virtue a good
in itself.
E. No advocate of pleasure is a true philosopher.
The true middle term   here would be (one who)
accounts virtue a good in itself.
Festino.
E. No righteous acts will produce ultimate evil to
the actor.
I. Some kinds of association will produce ultimate evil to the actor.
I




130                  LOGIC.
0. Some kinds of association are not righteous
acts.
Faakoro.
A. All true patriots arefriends to religion.
0. Some great statesmen are notfriends to religion.
0. Some great statesmen are not true patriots.
FIGURE III.
Darapti.
A. All wits are dreaded.
A. All wits are admired.
I. Some admired (persons) are dreaded.
Disamis.
I. Some lawful things are inexpedient.
A. All lawful things are what we have a right
to do.
I. Some things which we have a right to do are
inexpedient.
Datisi.
A. All that wisdom dictates is right.
I. Something that wisdom dictates is amusement.
I. Some amusement is right.
Felapton.
E. No science is capable of perfection.
A. All science is worthy of culture.




EXAMPLES.                 131
O. Something worthy of culture is not capable of
perfection.
Dokamo.
O. Some noble characters are not philosophers.
A. All noble characters are worthy of admiration.
O. Some (who are )worthy of admiration are not
philosophers
Feriso.
E. No false theories exist in a perfect state of
being.
I. Some false theories are harmless things.
0. Some harmless things do not exist in a perfect
state of being.
FIGURE IV.
Bramantip.
A. All oaks are trees.
A. All trees are vegetables.
I. Some vegetables are oaks.
Camenes.
A. All miracles are things of rare occurrence.
E. No things of rare occurrence make a slight impression on the mind.
E. No (things which) make a slight impression on
the mind are miracles.




132                   LOGIC.
Dimaris.
I. Some taxes are oppressive.
A. All (that is) oppressive should be repealed.
I. Some things which should be repealed are taxes.
Fesapo.
E. No immoral acts are proper amusements.
A. All proper amusements are designed to give
pleasure.
O. Some (things) designed to give pleasure are not
immoral acts.
Fresison.
E. No acts of injustice are proper means of selfadvancement.
I. Some proper means of self-advancement are unsuccessful.
O. Some unsuccessful (efforts) are not acts of injustice.
It will be observed that the conclusions in the fourth
figure are indirectly stated, and that it would seem as
if in tracing the major term back from its place as
predicate of the conclusion, it is in reality predicated
by means of the other terms of itself; thus: in the
conclusion it is predicated of the minor, which in the
minor premiss is predicated of the middle, which in
the major premiss is predicated of the major. The
fourth figure, therefore, is not often used, and is




MOOD.                    133
rather accidentally stumbled into than employed intentionally.
The exact accordancy of the first figure with the
dictum of Aristotle has been already stated. Of the
second figure, it may be remarked that it is commonly
used to disprove something that has been maintained,
or is likely to be believed, although not true. As an
illustration, suppose it had been asserted that
All great statesmen are true patriots.
Then our example just given of Fakoro would be a
refutation of this, and the argument would naturally
take that form.
Of the third figure, it will appear that it will be
useful where we have singular terms, which can only
be subjects of propositions, i. e. never predicates; and
also where our purpose is to offer and sustain an objection to our opponent's premiss, which is particular
when the argument requires it to be universal.
There are very many inverted and curious forms
of arguments growing out of the elliptical and inverted forms of propositions, which we have already
considered.  Two common examples of these are
added by way of illustration.
1.
None but whites are civilized.
The Hindoos are not whites.
The Hindoos are not civilized.
The phrase none but whites, may be rendered, other
12




134                    LOGIC.
than whites; and this being the true middle term, we
shall haveNo other than whites are civilized.
All Hindoos are other than whites.
No Hindoos are civilized.
Which is evidently a syllogism in Celarent, of the first
figure.
2.
No one is rich who has not enough.
No miser has enough.
No miser is rich.
The major and minor premisses must be put in the
form of categorical propositions, and we shall have
No one who has not enough is rich.
Every miser is one who has not enough.
No miser is rich.
Which is likewise in the mood Celarent. In both these
examples the minor premiss, which appears to be a
negative proposition, is in reality affirmative.
(39.) Of Reduction.
If we have any imperfect mood, i. e., a mood in
the second, third, or fourth figure, and we desire to
prove the same conclusion in the first figure, so that
the dictum of Aristotle may immediately be applied
to it; the process by which this is done is called
Reduction.
Reduction is of two kinds, direct and indirect.
Direct reduction consists in proving in a perfect mood
either the same conclusion, or one which, being illatively converted, will give us the same conclusion which




REDUCTION.                135
we had in the imperfect mood. Indirect reduction consists in proving, not that the original conclusion is
true, but that its contradictory is false, from whichby the scheme of opposition (30)-we know that the
original conclusion must be true.
Of direct reduction.
It has been shown that we have a right to convert
any of the propositions of the syllogism illatively;
and it is also evident that we may transpose the premisses without affecting the truth of the propositions
or the validity of the argument. If, then, we apply
the processes indicated by the letters in the mnemonic
lines, we shall see that they will give us the forms of
direct reduction.
Taking for example Cesare, the mood EAE in
the second figure; to write it out we remember in the
first place that the position of the middle term in the
second figure is predicate of both premisses, and we
observe that the major premiss is E, universal negative,
the minor premiss A, universal affirmative, and the
conclusion E, universal negative: we have, then, X
being the major, Z the minor, and Y the middle term,
Cesare. Fig. II.
E.   No X is Y - No men are trees.
A.   All Z is Y -= All oaks are trees.
E.   No Z is X - No oaks are men.
The only consonant in the word CEsArE which indicates a process of reduction is s, which tells us that




136                    LOGIC.
the major premiss, expressed by the first E, is to be
simply converted; performing this operation we shall
have
Celrent. FIG. I.
E. No Y is X = No trees are men.
A. All Z is Y = All oaks are trees.
E. No Z is X — = No oaks are men.
This syllogism is in the first figure, since the middle term  Y or trees, has become the subject of the
major and the predicate of the minor premiss; again,
Fakoro. FIG. II.
A. All X is Y    = All good men are virtuous.
O. Some Z is not Y = Some clergymen are not virtuous.
O. Some Z is not X = Some clergymen are not good men.
The k expresses that the major premiss (A) is to be
converted by negation; performing this operation,
(there is no other indicated), we shall have
Ferio. FIG. I.
E. All (not Y) is not X = All (not virtuous) are not good men.
I.  Some Z is (not Y) = Some clergymen are (not virtuous).
O. Some Z is not X  = Some clergymen are not good men.
This process, in effect, changes our middle term
from  Yor virtuous to (not Y) or (not virtuous), while
we have the same conclusion as before in the mood
Ferio, of the first figure.
The reduction of the other moods of the second
figure will be analogous to those already performed,
and the student will find no difficulty in reducing
them for himself.   Passing then to the third figure,




DIRECT REDUCTION.              137
and remembering that in this figure the middle
term is the subject of both premisses, let us reduce
the mood
Disamis. FIG. III.
I. Some Y is X = Some men are heroes.
A. All Y is Z  = All men are mortal.
I. Some Z is X = Some mortals are heroes.
The two letters which indicate changes in the process of reducing this mood are s (twice employed) and
m: s indicates the simple conversion of the major
premiss and the conclusion, and m, the transposition
of the premisses; performing these operations, we have
Darii. FIG. I.
A. All Y is Z - All men are mortal.
I. Some X is Y = Some heroes are men.
I. Some X is Z - Some heroes are mortal.
which conclusion is the simple converse of the original
conclusion, as was indicated by the final s.
Fesapo. FIG. IV.
E. No X is Y       No quadrupeds are men.
A. All Y is Z    - All men are animals.
0. Some Z is not X = Some animals are not quadrupeds.
Converting the major premiss simply, and the minor
premiss by limitation, as indicated by the s and p, we
shall have
F'erio. FIG. I.
E. No Y is X     = No men are quadrupeds.
I. Some Z is Y   = Some animals are men.
O. Some Z is not X = Some animals are not quadrupeds.
It will be well for the student to reduce every im12




138                          LOGIC.
perfect mood, forming for himself particular examples under each.
Although we have made the subject of Reduction
plain  by the    examples already       given, we append a
table of the manner of reducing each mood for reference, until the student is familiar with them.             It is
but a recapitulation in tabular form of what has been
already explained.
____-  -.   ezPl   Will reMood to be reduced.  duce to.     Process of reduction.
( Cesare.   Celarent. (s) Convert major premiss simply.
(m) Transpose the premisses. (s & s)
I Camestres. Celarent.  Convert the minor premiss and conFIG.:  -                       celusion simply.
Festino.   Ferio.   (s) Convert the major premiss simply.
Faloro.    Ferio.   (k) Convert the major premiss by negation.
Darapti.     Darii.  (p) Convert the minor premiss by
limitation.
tj{ ~   ~       (m) Transpose the premisses. (s & s)
Disamis.   Darii.      Convert the minor premiss and conclusion simply.
IG III.  Datisi.   Darii.   (s) Convert the minor premiss simply.
Felapton.  Ferio.   (p) Convert the minor premiss by
limitation.
aDol-r> m  Drl.  (k) Convert the major premiss by neDokamo.    Dar.       gation. (m) Transpose the premisses.
I Feriso.   Ferio.    (s) Convert the minor premiss simply.
Ba. (m) Transpose the premisses. (p) Con(Bramantip. Barbara.   vert the conclusion by limitation.
Camenes.   Ce,      (m) Transpose the premises. (s) Con-.   Celarent.   vert the conclusion simply.
im ris.    Darii.  (m) Transpose the premisses. (s) ConIG. I. IV.  marls.   D          vert the conclusion simply.
jl~~             (~(s) Convert the major premiss simply.
Fesapo.    Ferio.     (p) Convert the minor premiss by
limitation.
Frion.  (s & s) Convert the major and minor
LFresison.  Ferio.    premisses simply.




INDIRECT REDUCTION.              139
(40.) Indirect Reduction.
This process, called by the old logicians Reductio
ad impossibile, is analogous to the reductio ad absurdum of geometry. It consists in proving that the
given conclusion cannot be false, by proving, in the
firstfigure, that its contradictory is false.
The symbols used to indicate the processes of
direct reduction, do not guide us in the indirect reduction, but we must deduce rules for this apart from
the other.
To illustrate, let us take the mood
Fakcoro. FIG. II.
A. All X is Y   = All good men are virtuous.
0. Some Z is not Y = Some clergymen are not virtuous.
O. Some Z is not X = Some clergymen are not good.
If this conclusion be not true, its contradictory All Z
is X=   All clergymen are good, must be true. Assuming this as true, and taking it in the place of the
minor premiss in the syllogism, we shall have a new
syllogism, as follows:A. All X is Y = All good men are virtuous.
A. All Z is X  All clergymen are good men.
from which premisses by.our rules we draw the conclusion
A. All Z is Y = All clergymen are virtuous.
But this conclusion must be false, because it is the
contradictory of the original minor premiss,-and the




140                   LOGIC.
premisses were assumed to be true,-hence one of
these last premisses from which this conclusion is
derived must be false; but it is not the major, for
that was one of the originally assumed premisses; it
must, therefore, be the minor, which we know to be
the contradictory of our original conclusion; and the
original conclusion must therefore be true: this, it
will be observed, is proven in the first figure, in the
mood Barbara. To take another example, let us reduce the mood
Darapti. FIG. III.
A. All Y is X   All gold is precious.
A. All Y is Z  - All gold is a mineral.
I. Some Z is X = Some mineral is precious.
If this conclusion be not true, then must its contradictory
No Z is X - No mineral is precious,
be so. Substituting this as the major premiss in the
syllogism, we have
No Z is X = No mineral is precious.
All Y is Z = All gold is a mineral.
From which we draw the new conclusion
No Y is X = No gold is precious.
But this conclusion is false, because it is the contrary
of the original major premiss, which we assume to be
true; one of the premisses from which it was derived
must be therefore false: it cannot be the minor, which
was also assumed to be true; it must, therefore, be




INDIRECT REDUCTION.            141.
the major, which is the contradictory of the original
conclusion; hence, the original conclusion must be
true.
It will occur, in reducing many of the moods by
this process, as in the last example, that we shall find
the conclusion false because it is the contrary and not
the contradictory of one of the original premisses.
By referring to the subject of Opposition (30), we see
that if one contrary is true the other must be false.
Without presenting a greater number of examples
of this kind of reduction, which the student may
multiply for himself, we lay down the following rules
for reducing the various inperfect moods.
Rules for Indirect Reduction.
1st. In the second figure, substitute the contradictory of the conclusion for the minor premiss, and proceed as above in the mood Fakoro.
2d. In the third figure, substitute the contradictory
of the conclusion for the major premiss, and proceed
as with the mood Darapti.
3d. In thefourth figure, substitute the contradictory
of the conclusion for the minor premiss, and proceed
as before.
As reference is always easier to a tabular form, we
annex one showing in what perfect mood the indirect
reduction of each imperfect mood will take place:



142                    LOGIC.
Fig. II.         Fig. III.         Fig. IV.
Cesare to Ferio.  Darapti to Celarent. Bramantip to Celarent.
Camestres to Darii. Disamis to Celarent. Camenes to Darii.
Festino to Barbara. Felapton to Barbara. Dimares to Celarent.
Datisi to Ferio.  Fesapo to Celarent.
Dokamo to Barbara. Fresison to Celarent.
Feriso to Darii.
Before proceeding to consider the irregular, informal, and compound syllogisms, we pause to show the
method of geometrical notation, already referred to,
by which the pure syllogism may be expressed.
(41.) Notation qf thie Syllogism.
As there subsists in the mathematics such a relation of analysis to geometry, as that most analysis
is capable of geometrical construction, and every form
of geometry may be stated analytically in terms of
its equation; so mathematical logicians have attempted
to make for the analysis.or symbolic form of the syllogism such a geometrical notation as shall at a glance
represent to the eye, in areas of limited space, what
the symbols do to the mind. Indeed, the idea is so
simple that we have already illustrated the dictum of
Aristotle through its agency. Many writers, however,
have been inclined to go too far in its use.
The schemes of notation best known are those of
Euler, Ploucquet and Lambert, and the more complete one of Sir William Hamilton. This latter, however, passing beyond our needs, is suited to such




NOTATION.                143
changes as would result from the introduction of the
new analytic, and, as we have advisedly declined to
place that system in our text-book, it is sufficient to
mention Sir W. Hamilton's scheme without explaining it. In a more extended historical treatise it
would demand a special consideration. We can here
only explain what we mean to use.
Euler's scheme of notation is altogether the one
best suited to our purpose, and we shall limit ourselves to the explanation of that. It is essentially an
arrangement of three circles, to represent the three
terms of a syllogism, and, by their combination, the
three propositions. Thus if we have the judgment
All men are mortal,
we know that under this class, all men, are included
many species and individuals; as, for example, all
Americans. Representing then the sphere of the
conception mortal, by a circle; placing within this
circle a smaller one, wholly contained in it, as the
sphere of all men, and yet a smaller one wholly contained in this latter, as the sphere of all Americans,
we shall have
/OFA L
M EN
AMERIC 




144                  LOGIC.
which is the notation of a syllogism in BArbArA.
By similarity of process, we shall represent the syllogism in CE1ArEnt
No A is B,
All C is A,
No C is B.
DArII, will be thus expressed: —
B...
a,/ f^~^\'~  \ All A is B,
(A  C) C )     Some C is A,
\  /  i  Some C is B.
Here it is evident that it is only that some C which is
contained in A that we have a right to assert is also
contained in B, although other portions of C may by
chance be also contained in B.
FErIO:No A is B,
^  ~(1)_     Some C is A,
X / *.....'Some C is not B.
t~~~j~~,~ ~     (2)
B       A~~~~~~i~)




NOTATION.                 145
Here two cases are presented; where no C is B, and
whore some C is B; neither of which affects the truth
of the conclusion that some C is not B.  We have
only applied this scheme to the first figure, but by
this simple notation of Euler every syllogism in the
other figures may be represented to the eye, and made
clear to those who are much quicker at geometry than
at analytical work.  Take for example Darapti of
the third figure:All A is B,
All A is C,         B    A     
Some C is B.
But besides this representation of valid syllogisms,
this system exposes at once fallacious arguments and
acts as a test upon a test of their unsoundness. Take
for example the case of illicit process of the major
term:All quadrupeds are animals,
Nu/~,~^\ MA bird is not a quadruped,
A bird is not an animal.
Quadrupeds Birds
In which the figure denies the conclusion by allowing
the premisses, and yet showing that birds are contained
18                  K




1 4G                  LOGIC.
under the genus animal.  Or if we take the case of
negative premisses: -
No A is B,
No C is A,
the figure shows us that there is no relation whatever
established between or among the terms which would
entitle us to a conclusion.
The student will find it easy and pleasant to write
out all the moods and the logical fallacies by this circular method of notation; and, as two modes of coming
at facts make the memory more tenacious of them,
this practice will fix clearly in his mind the moods
and figures of the syllogism.
This system also illustrates the categorical propositions as to the distribution of their terms, very satisfactorily:
All A is B,
No Ais B,                )
Some A is B,       A(  B
A i
Some A is not B.  (A   B)'-'.-*x^ ^



ABRIDGED SYLLOGISMS.          147
CHAPTER IX.
OF IRREGULAR, INFORMAL, AND COMPOUND ARGUMENTS.
(42.) Of Abridged Syllogisms.
WE have thus far considered only those arguments
which appear directly and without analysis in the
form of a simple syllogism; and have explained those
processes which we perform upon known and acknowledged facts, stated as premisses and conclusion; but
the mind of man sometimes passes intuitively over
certain steps of these processes without stopping to
express them, which gives rise to abridged arguments;
or it halts in doubt and uncertainty, being not sure
of its facts, but frequently balancing between two,
one of which must be true, because of the truth or
falsity of the other.  This produces hypothetical
syllogisms.
A11 these in the present chapter will be treated of
as informal syllogisms, or arguments which are not




148                    LOGIC.
syllogisms in form, but which, if they be valid, must
be capable of being put into the syllogistic form.
The first of the abridged arguments to be considered, because the one in most common use, is
The Enthymeme.*
The enthymeme is a syllogism with one premiss suppressed; it matters not which; thus, having the syllogism,
All men are mortal,
Coesar is a man,
Cwesar is mortal,
we may suppress the major premiss and write the
enthyemem,Caesar is a man.
Therefore Caesar is mortal.
Or suppressing the minor premiss, we have,
All men are mortal,
Therefore Caesar is mortal,
either of which is a satisfactory expression, because
all three terms of the syllogism are expressed in either
form of the enthymeme, and we can at once reconstruct the syllogism; thus, taking the latter form,
with the minor premiss suppressed, we see by examining the conclusion, in which the major and minor
terms are always contained, that Ocesar is the minor,
being the subject of the conclusion, and mortal the
major, being the predicate.  Men, then, must be the
f evrOvqEoyaz, to conceive in the mind.




THE ENTHYMEME.               149
middle term, and we at once compare it with the
minor term to form the suppressed premiss; thus:
Caesar is a man.
By a similar process we may reconstruct the syllogism when the major premiss is suppressed.
It is worthy of observation that in ordinary discourse men suppress the major premiss habitually, as
that to which the mind most readily yields assent,
although if the proof of its truth be required, the
task would be more difficult than to establish the truth
of the minor. Thus, in the example given above, we
would take for granted as a fact that
All men are mortal;
whereas, without the declarations of the Bible-and
Logic, as a science, moves independently of any extraordinary or supernatural dicta-this proposition is
incapable of proof; for, although all men have died
thus far in the world's history, the process of induction cannot be finished until the end of man as a race.
But this seems like a cavil. The major premiss,
although thus incapable of mathematical proof, is the
one which most surely demands belief; and so, when
in the enthymeme we speak of the suppressed premiss, we mean the major premiss, unless it be otherwise explained.
As a simple rule for reconstructing the syllogism
from the enthymeme, we observe that,
13-e




150                  LOGIC.
If the subject of the conclusion be found in the
expressed premiss, that premiss is the minor. If the
predicate of the conclusion be found in the expressed
premiss, it is the major.
Sometimes it becomes necessary to put the enthymeme into logical form before proceeding to reconstruct it. Thus, the example given above might be,
and most commonly is, thus spoken or written:Caesar is mortal,
Because Cesar is a man.
which is evidently a transposed form of the enthymeme.   Whenever the causal conjunction because
unites the propositions of an enthymeme, we may invert the propositions and unite them with the illative
conjunction therefore, and then proceed to reconstruct
the syllogism, thus:
Caesar is a man,
Therefore He is mortal.
Many abridged arguments which appear in a hypothetical form, are in reality simple enthymemes, thus:
If murder is a crime,
The murderer should suffer.
In which there is really no hypothesis or condition in
the premiss, because all allow that murder is a crime;
and are consequently ready to declare that
The murderer should suffer.
When the enthymeme has been reconstructed into a




THE SORITES.                   151
syllogism in any one of the figures, we shall be able
to put it directly into the first figure, and can then
apply to it the test of Aristotle's dictum.
(43.) The Sorites,* or Chain Argument.The Sorites is an abridged argument consisting of
a series of propositions in which the predicate of the
first is the subject of the second; the predicate of
the second the subject of the third, and so on until
we combine the subject of the first and the predicate
of the last to form a conclusion. Thus: —
A is B  The mind is a thinking substance.
B is C = A thinking substance is a spirit.
C is D = A spirit has no composition of parts.
D is E = (That which has) no composition of parts is indissoluble.
E is F - (That which is) indissoluble is immortal.
Concl. A is F  The mind is immortal.
Now, if we try to put this collection of abridged
arguments into the syllogistic form, in order to apply
the dictum of Aristotle to them, we shall see that the
Sorites is an abridgment of a series of syllogisms in
the first figure; that the terms B, C, D, and E, which
are used twice, are middle terms, and that we may
construct as many syllogisms as we have middle terms.
Taking then the second proposition of the sorites, B
is C, as the major premiss of the first syllogism; and
cCopetrrls = a heap, or collection.
t Called by the Germans, more significantly, Kettenschluss, or chain
argument.
T This example is borrowed from Hedge's Logic, as it is one of the
best for illustration;




152                    LOGIC.
the first A is B, as the minor, we shall have as a conclusion A is C, which we use as the minor premiss of
a second syllogism, using the third proposition of
the sorites as a major premiss; and so on, as long as
the middle terms last, thus:1st.        2d.       3d.        4th.
B is C,    C is D,    D is, E, is F,
A is B,    A is C,    A is D,    A is E,
A    is CA     is. A     is E.  A   is F.
A thinking substance is a spirit.
1st.  The mind is a thinking substance.
The mind is a spirit.
A spirit has no composition of parts.
2d.   The mind is a spirit.
The mind has no composition of parts.
That which has no composition of parts is indissoluble.
3d.  The mind has no composition of parts.
The mind is indissoluble.
That which is indissoluble is immortal.
4th.  The mind is indissoluble.
The mind is immortal.
These are all in the first figure, and consequently are
forms to which the dictum will directly apply.
It must be observed that in the sorites the first proposition, A is B, is the only one which may be particular, because it is the only minor premiss expressed,
every other being used as a major, and we have
already seen that in the first figure the major premiss
must be universal.




THE SORITES.              153
So, again, the last proposition, E is F, is the only
one that may be negative, for, if any other be negative, we should have in one of the syllogisms a negative conclusion which is to be in turn the minor premiss of the succeeding syllogism, and we have already
shown that in the first figure the minor premiss must
be affrmative. But the conclusion deduced from the
last syllogism does not become a minor premiss, and
so the last conclusion may be negative; it would then
read thus:
No E is F.
All A is E.
No A is yF.
Or the chain of the sorites would be broken in whatever place the negative proposition should occur.
The sorites is a very simple and conclusive abridged
form of argument; for the mind, taking the only expressed minor term A, which is expressed in the
chain, links it by jumping from middle term to middle
term, B, C, D, E, to the final major term or F, as
surely and more easily, than in the syllogisms into
which it is elaborated.
By its aid we easily establish the points in any
great argument, either as recapitulating the process
of the argument, or as stating them preparatory to a
comprehensive discussion. Thus, to establish the
effect of a republican government, we shall have,




154                     LOGIC.
The Americans make their own laws.
Those who make their own laws are free.
Those who are free are contented.
Those who are contented are happy.
Therefore The Americans are happy.
It is evident that the sorites may be properly stated
in the inverse order; thus:
D is E,  C is D,  B is C,  A isB,
Therefore A is E.
Here the sorites starts from its widest terms, D
and E, to include the narrower and more limited
terms, C, B, and finally, A.
This form is called the Goclenian Sorites, from the
name of its originator.  It serves, perhaps, better to
illustrate the fact stated that only the most extensive
proposition, which in the ordinary form is the last, and
in this, the first, may be negative; which, as we have
seen, will give us a negative conclusion; thus:
D is not E,  C is D,  B is C,  A is B,
Therefore A is not E.
lHypothetical Sorites.
If we have a string of conditional propositions,
such that the consequent of each becomes the antecedent of the succeeding one, the argument is called
a hypothetical sorites, and the conclusion is obtained
either by affirming the first antecedent with the last




THE EPICHIREMA.                    155
consequent, or by denying the last consequent with
the first antecedent; thus:
1. If AisB, C isD; If C isD, EisF;
But A is B,      Therefore E is F.
2. If A is B, Cis D; If C is D, E is F;
But E is not F,  Therefore A is not B.
Examples.
1.
If the Bible is from God it should be taught;
If it should be taught, men should be set apart to teach;
If men should be set apart to teach, they should be supported;
But the Bible is from God, therefore its teachers should be supported.
2.
If the Bible is false, it deceives the world;
If it deceives the world it should be destroyed;
But it should not be destroyed, therefore it is not false.
To the hypothetical sorites it is evident that the
Goclenian form will also apply.      Indeed this is illustrated in the last case mentioned, where we reason
back from the denial of the last consequent to the
denial of the first antecedent.
(44.)  Of the Jipichirema.*
Most arguments employed in ordinary conversation
and writing consist of simple syllogisms, abridged
into enthymemes, linked together in a compound form;
-' The Greeks seem to have considered this a great logical weapon,
as the name they gave it signifies a violent onset, or laying of hands
Upon. ear, and Xip.




156                       LOGIC.
but in many cases the form of the syllogism is observed where the premisses are arguments in themselves. When the premisses are thus separately
established, before the conclusion is deduced, the
argument is called an Epichirema; thus:
The victors are injured by war; because it hardens their hearts;
The French were victors at Jlarengo, for they retained the field;
The French were injured by their victory.
The major premiss is an enthymeme, which may be
expanded into a syllogism; the same is true of the
minor; hence we have two distinct arguments within
the one which originally appeared. To apply the
tests to their validity, they need only be written out
in syllogistic form. In most apparently simple syllogisms, there is in reality implied the epichirema. As
for example, in the one given to illustrate the mood
Faakoro, of the second figure,
All true patriots are friends to religion,
Some great statesmen are not friends to religion,
Some great statesmen are not true patriots,
the   major   premiss   demands    in  itself a   reason.
Thus:
All true patriots are friends to religion, because religion is the basis
of national prosperity and advancement.
So also does the minor,
Some great statesmen are not friends to religion, because their own
lives are not in accordance. with its precepts.
Each of the premisses given is an enthymeme; of




HYPOTHETICAL SYLLOGISMS.              157
which the clause because, 5c., is the premiss, and the
first statement, all true patriots, sc., is the conclusion.
Now, this premiss to the premiss is called the prosyllogism.
Sometimes the establishment of the final conclusion will warrant us in drawing other conclusions
also; thus:
A is B,
C is A,
Therefore C is B.
Therefore X is Y, &c.
This conclusion from a conclusion (X is Y) is called
the epi-syllogism.
To take the example before quoted, we shall have
All true patriots are friends to religion.
Some great statesmen are not friends to religion.
Some great statesmen are not true patriots.
Therefore They deceive their countrymen,
and Deserve no rewards from their country, pc.
(45.) Of Hypothetical Syllogi mS.
Corresponding to the various forms of hypothetical
propositions, viz., conditional, causal, disjunctive, &c.,
we have conditional, disjunctive and causal syllogisms.
They are all of so simple a nature that the mind
finds no difficulty in the ratiocination which they express; but as we have asserted that, if valid, they
may be reduced to the form of a categorical syllogism
14




158                    LOGIC.
in the first figure, we proceed to show how this may
be done.
Conditional Syllogisms.
If we examine a conditional proposition we shall
see at once that the affirmation of the consequent will
follow from the affirmation of the antecedent; thus:
If A is B, C is D == If he has a fever, he is sick.
But if we deny the antecedent, we may not therefore
deny the consequent, since this consequent might
spring from some other antecedent as well as from
the one given. Thus:
If A is not B, if he has not a fever,
we cannot say,
C is not D  - he is not sick.
since
C might be D = he might be sick,
from some other cause than
A being B, or his not having a fever.
For similar reasons we may pass from the denial of
the consequent to the denial of the antecedent, but
not from the affirmation of the consequent to the
affirmation of the antecedent.  When we pass from
the affirmation of the antecedent to the affirmation
of the consequent, the reasoning is called constructive;
and when we pass from the denial of the consequent
to the denial of the antecedent, it is called destructive.
We may form, then, two, and only two, forms of
conditional syllogisms, constructive and destructive.
To form the first we take the whole conditional pro



CONDITIONAL SYLLOGISMS.           159
position as the major premiss; the affirmation of the
antecedent for the minor, from which premisses we
shall draw the affirmation of the consequent as the
conclusion; thus:
MaI. prem. If A is B, C is D = If he has a fever, he is sick.
Min. prem. A is B      = He has a fever.
Conclusion. C is D     - He is sick.
To frame the destructive conditional syllogism, we
take the whole proposition as before for a major premiss; the denial of the consequent for a minor, and
we deduce as a conclusion the denial of the antecedent; thus:Maj. prem. If A is B, C is I) = If he has a fever, he is sick.
Min. prem. C is notD   = He is not sick.
Conclusion. A is not B  — He has not a fever.
As these are the only possible forms of conditional
syllogisms, and as we have shown that all other forms
of hypothetical propositions, disjunctive, causal, &c.,
may be easily reduced to conditional propositions; we
have only to show how these conditional syllogisms
may be reduced to the form of simple categorical syllogisms, and we shall, in effect, have shown it for all.
Considering first, the constructive form, and remembering that the form of condition may be removed by
the phrases " the case of," and " the present case;"
and that the proposition assumes the form of a categorical proposition, of which the antecedent becomes
the subject, and the consequent becomes a predicate, we
shall have for the constructiveform,




160                     LOGIC.
X                        Y
r____..... ~      t, _ —----         -_
Maj. prem. The case of A being B  is  the case of C being D.
Z                        X
Min. prem.  The present case   is the case of A being B.
Z                        Y
Concl.      The present case   is  the case of C being D.
or,        All X is Y. (A.)
All Z is X.  (A.)
All Z is Y.  (A.)
which, X  being the middle term, is evidently in the
first figure, and the dictum may be at once applied.
Using the same phraseology, and thus translating the
destructive form, we have,
X                        Y
The case of A being B  is  the case of C being D.
Z                          Y
f              x          f' — L ---'     x
The present case  is not  the case of C being D.
Z                          X
The present case  is not  the case of A being B.
or, All X is Y. (A.)
No Z is Y. (E.)
No Z is X. (E.)
which, Y being the middle term,-is in the second
figure, and in the mood Camestres, which must be reduced to the first figure, or the form of the dictum.
If, now, we perform the operations indicated to reduce this mood (m, s, s), we simply convert the minor




CONDITIONAL SYLLOGISMS.              161
premiss, and then transpose the premisses, and simply
convert the conclusion: we shall have,
Y                          Z
The case of C being D  is not  the present case.
X                         Y
The case of A being B  is  the case of C being D.
X                         Z
The case of A being B is not  the present case.
or simply converting the conclusion,
Z                          X
The present case  is not the case of A being B.
No Y isZ. (E.)
AllXisY. (A.)
No X isZ. (E.)
or,   No Z is X.
which is the form of Celarent in the first figure.
The logical form of the conditional does not depend
upon the subject-matter of the propositions composing
it. There may be, for example, two apparently independent propositions, that is, propositions in which
the terms are entirely distinct, thus conjoined, or there
may be a term the same in each; which will cause no
difference in the logical form: thus we may have
If A is B, C is D - If John remain, James will go; or,
If A is B, A is C = If the Bible is true, it (the Bible) deserves our
attention.
14                L




162                       LOGIC.
To explain this apparent difference, it will be remembered that A, B, C, &c., although terms in the
proposition, are not the terms of the syllogism     when
it is put in a categorical form; but that the antecedent and consequent become the true terms, and therefore it matters not whether there be three or four
independent terms in the conditional proposition
before its change of form.
A few examples of conditional syllogisms are given
to accustom the student to the form, and to guard
him against the improper use of it.
Examples.
1.
If the fourth commandment is obligatory upon us, we are bound
to set apart one day in seven.
But the fourth commandment is obligatory upon us.
Therefore we are bound to set apart, &c.
2.
If any theory could be framed to explain the establishment of
Christianity, by human causes, such a theory would have been
proposed before now.
But none has been proposed.
Therefore, no such can be framed.
3.
If the eclipses of Jupiter's moons occur sixteen minutes later,
when the earth is farthest from Jupiter than when she is nearest
to Jupiter, light must travel ninety-five millions of miles in eight
minutes.
But these eclipses do occur so much later in the given position.
Therefore light travels at the rate stated; -   or, two hundred
thousand miles in a second.
4.
If taste is uniform, all men will admire the same objects.




DISJUNCTIVE SYLLOGISMS.                163
But all men do not admire the same objects-(one sees beauty
where another only finds deformity).
Therefore, taste is not uniform.
Disjunctive Syllogisms.
A  disjunctive syllogism   is one, the major premiss
of which is a disjunctive Proposition (26), and the
minor a categorical.
Brutus was either a parricide or a patriot = Either A is B, or it is C.
He was not a parricide              - A is not B.
He was a patriot                    = A is C.
Here, when the major premiss consists of two
members only, the minor asserts the one and the conclusion denies the other; or the minor denies the one
and   the conclusion asserts the other.       Or we may
have, instead of two alternatives, three or more;
thus:The angle A must be equal to, or greater or less than the angle B.
But it is neither equal to or less than it.
Therefore it is equal to it.
It is evident that the disjunctive syllogism may be at
once stated in a categorical form by any simple phraseology which will rid us of the disjunctive form; thus:
Brutus could not be at the same time a parricide and a patriot
(but must be one of the two).
-le was a patriot.
Therefore he was not a parricide.
or, He was not a parricide,
Therefore he was a patriot.




164                      LOGIC.
Examples of Disjunctive Syllogisms.
1.
It is either true that knowledge is useful, or that ignorance is so.
But it is not true that ignorance is useful.
Therefore knowledge is so.
2.
Mahomet was either an enthusiast or an impostor.
He was an enthusiast.
Therefore he was not an impostor.
This is Gibbon's argument, but it is faulty in point
of fact, for a man may be both enthusiast and impostor,-and some men have a great enthusiasm          for
imposture.
3.
A government either licenses a free press, or it is oppressive.
The French government does not license a free press.
Therefore it is oppressive.
4.
A wise lawgiver must either recognise future rewards and punishments, or must appeal to an extraordinary Providence.
Moses did not do the former.
Therefore he must have done the latter.
Of the Dilemma, Trilemma, ce.
A dilemma is a compound argument composed of
conditional propositions, upon which we reason disjunctively. When two conditional syllogisms are combined with a disjunctive minor premiss, the argument
is called a dilemma. When three, four, &c., are so combined, they constitute a trilemma, tessaralemma, &c.
The generic name Dilemma, however, is technically
given to them all.    Dilemmas are divided into four




THE DILEMMA.                165
kinds, according to their being simple or complex,
constructive or destructive.
A simple dilemma is one in which we have as a
major premiss, several antecedents, with a single consequent, thus:
[ But either
f                                A is B
I If A is B,                      or
IMaj. prem.  If C is D, then X is Y. Min. prem.  C is )
If E is F,                       or
EisF
Conclusion. Therefore X is Y.
A complex dilemma is one in which we have several
antecedents, and each has its own consequent, thus:
Fi AisB
If A is B, G is H.               o
Maj. prem. I If C is D, I is K.  Min. prem.  C is r
If E is F, L is M.               or
E is F
Either
Gis H
Conclusion. Therefore  is 
I is K
or
L is M
Now, if in the simple dilemma, instead of reasoning
as we have done constructively from the disjunctive
affirmation of the antecedents to the disjunctive affirmation of the consequent, we reason destructively, that
is, deny the single consequent; then all the antecedents
fall to the ground; there is no longer the condition
of the dilemma; for we have a simple conditional




166                     LOGIC.
syllogism. Or if we have one antecedent and several
consequents, and reason destructively, it is as though
we had but one consequent, since the denial of any
one requires the denial of the one antecedent; thus, in
the argument,
C is D,
If A is B,   G is H,
L is M,
it matters not whether we deny one or all the consequents, the denial of the antecedent follows.  Hence,
properly speaking, there is no such thing as a simple
destructive dilemma.   It difers in no wise from     a
simple destructive conditional syllogism.
The destructive dilemma proper, then, consists of
several antecedents, each with its own consequent, in
which we disjunctively deny the consequents, that is,
deny any one of them or all in turn, and we may
disjunctively deny the antecedents.
If A is B, C is D.        But either C is not D,
ca?. prem.                 ti. Mi. prem.
IfGisH, LisM.               or   L isnotM.
&c.    &c.
Conclusion. Therefore either A is not B,
or G is not H.
To apply this abstract form to a particular example;
let us take the argument of Antisthenes:-.    If we conduct the affairs of state well, we offend men.
If we conduct them ill, we offend the gods.
If now we reason constructively we shall add,
But, we.must either conduct them well,
Miin. prem.
or conduct them ill.
Conclusion. Therefore we must either offend men,
or offend the gods.




THE DILEMMA.                 167
If we reason destructively, we add-as a minor
premiss,
But we must either not offend men, or not offend the gods.
and as a conclusion,
Therefore, we must either not conduct them well, or not conduct
them ill.
To rid themselves of the perplexities of the dilemma,
the old logicians always established from their premisses an undue, because not a logical conclusion, but
a moral and material one, a passage of the mind to a
purpose which had been suggested by the matter of
the argument; thus, the conclusion of Antisthenes
from the perplexity of the dilemma was, that we had
better not meddle with the ffairs of state at all. Take
another illustration:If a wife is beautiful, she excites jealousy;
If she is ugly, she gives disgust;
and the illogical, but common conclusion is,
It is best not to marry.
Most logicians have erred at the very outset, by
supposing that, because there is an alternative expressed in the dilemma, it is a disjunctive instead of
a conditional syllogism, and thus have rendered it a
vehicle of fallacy which it would be impossible foi
Logic to arrest; thus, they would read the last example,
Either a wife excites jealousy by her beauty,
Or disgust by her ugliness;
Hence it is better not to marry.




168                    LOGIC.
In any such case, if we first put the dilemma in its
true conditional form, and then (leaving the province
of Logic which presumes all given propositions to be
true) examine the subject-matter of the propositions
themselves, we shall find the falsity which causes perplexity: thus, it is not true universally, nor commonly,
as is implied in the example, that if a wife is beautiful, she excites jealousy.  It is even less true, that is
in a fewer number of cases, that if she be ugly, she
causes disgust; hence the conclusion, that it is best
not to marry is less true, i. e., applies to a fewer number of cases than either of the foregoing assertions,
i. e. the falsehood is increased by the number of false
statements preceding the conclusion.
It is evident that the dilemma may be resolved into
as many conditional syllogisms as the greatest number of antecedents or consequents; and that these
may be reduced according to the rules for the reduction of conditional syllogisms.
Any dilemma may also be stated in a categorical
form. Thus,
The case of A being B, is the case of G being H.
The case of C being D, is the case of E being F.
and we may then proceed as in conditional syllogisms.
Examples of the Dilemma.
1.
If Eschines joined in the public rejoicings, he was inconsistent.
If he did not, he was unpatriotic.
But either he did join, or he did not:Therefore, he was either inconsistent, or unpatriotic.




THE DILEMMA.                     169
The following dilemma was formed to confute the
doctrine of Pyrrho, the sceptic, which was, that because everything has its contradictory, everything is
false; or, that no one could know anything certainly.
2.
If what you say is true, then there is something which is not
false (i. e. your system is wrong).
If what you say is false, then it has no value as an argument (i. e.
your system is wrong).
But what you say must be either true or false.
Therefore, in either case your system is wrong.
There are two kinds of things which we ought not to fret about:
what we can help, and what we cannot.
(The student will put this in the form of a dilemma.)
Having explained the various forms of argument,
simple and compound, our next subject of investigation is of the erroneous use of these forms; to this
has been given the generic title of Fallacies.
15




170                  LOGIC.
CHAPTER X.
FALLACIES.
(46.) The Meaning and Comprehension of a
Fallacy.
DIFFERENT terms are used to express the errors
which are found in terms, propositions, or arguments,
in Logic. Thus, we say of a term, when it is not univocal, i. e. when it has not one meaning, and only one,
that it is equivocal or ambiguous, i. e. has more than one
meaning; of a proposition, if it be not true, that it is
false, which expresses in other words, that the predicate and subject have no proper connexion; of an
argument we say, when it violates the dictum of Aristotle or any of the rules given, that it is invalid, and
sometimes of an invalid argument, we say that it is
fallacious.
A fallacy, then, is an invalid argument, which appears at first sight to be valid.  If it be used with the
intention to deceive, the fallacy is called a sophism. An




FALLACIES.                 171
argument manifestly and foolishly invalid, would then
be neither a sophism nor a fallacy.
The subject of fallacies is one of the most important in the study of Logic, for not only is Logic designed to teach us to reason correctly, but also it
should teach us to perceive and detect all errors in
reasoning; hence we find the earliest writers on Logic
giving rules and cautions for avoiding and detecting
fallacies.
The first division of fallacies which they have made
is into fallacies in dictione, and extra dictionem. As
dictio means the form of words and not the meaning
of the words, or what is expressed in our word
diction, the class in dictione, or fallacies- in form,
will evidently come within the province of Logic,
while those extra dictionem, not being in the form,
but in the subject-matter, with which Logic is only indirectly concerned, will really not fall within the
scope of our study.
But since the line between the two, although easy
to be drawn, is continually mistaken in practical argument or controversy unless it be thus drawn, it becomes necessary to explain both classes with care,
that we may always distinguish between the truly
Logical and the non-Logical or material fallacies.
One class of these material fallacies, which arises
from the ambiguity in words, and is therefore called




172                   LOGIC.
verbal fallacies, needs but a slight change, as we shall
see, to become formal or logical fallacies.
(47.)   Of Fallacies in dictione, or Formal
Fallacies.
These are the fallacies, about which Logic is particularly concerned.
Under this class are included all violations of the
dictum of Aristotle, and of the axioms and rules
laid down for determining the validity of an argument. The fallacy in all cases under this head is
apparent in the form of the expression; hence the
name, formal fallacies.  Of this kind are
1. Undistributed middle terms.
2. Illicit process of either term.
3. Negative premisses.
4. Affirmative conclusion from a negative premiss,
and vice versa.
5. More than three terms in the argument.
Of these, repeated examples have been already
given, in syllogistic form: it is only by putting them
in this form that the fallacy is at once and easily
detected.
But it should be borne in mind that in practice,
such fallacies are not stated in the syllogistic form,
in which they are thus easily to be detected, but are
stated in the form of an enthymeme, or other abridged




FALLACIES.                17 3
argument, and so covered with words that the effect
is produced without the mind being convinced; the
conclusion allowed, because the mind cannot see
the false steps which have been used, although it has
not certified itself that the true have been taken.
Let the student then take the trouble, in each such
case, to write out the argument in syllogistic form,
and, for greater clearness, to use symbols, and the invalidity will be apparent.
Thus, we are told that "i a certain man was a good
father, because he attended to the physical necessities
of his children"; food and clothing, and shelter,
being the criterion of a good father. Let us apply
the test of Logic to such an argument:X                     Y
Ma, pe.  All good fathers  provide for the physical wants of
Myj, prem. A   g fa            t   er
their children.
Z         Y
Min. prem. A B  did thus provide.
Z           X
Therefore A B  was a good father.
Or, using symbols,
All X is Y,
Z is Y,
Z is X.
That is,-Y, which is the middle term, is undistributed,
being the predicate in two affirmative premisses.
Again, it is asserted that 44 brutes are not responsible
15 *




174                    LOGIC.
beings, because they are not accountable"; which involves a fallacy of illicit process. Thus,
x                   Y
JMaj. prem. All responsible beings  are  accountable.
Z                    X
Min. prem. Brutes  are not  responsible beings.
Z                 Y
Therefore Brutes  are not accountable,
All X is Y,
No Z is X,
No Z is Y.
In which Y, which is distributed in the conclusion,being the predicate of a negative proposition,-is undistributed in the major premiss: an illicit process of
the major term.
It will be observed in this latter instance, that the
conclusion is, we believe, a true one, but it is not
reached by such premisses; and thus indeed it constantly happens, that men adopt a conclusion on internal grounds which they cannot explain, and then seek
in every direction for premisses by which to substantiate it: and so, on the other hand, many a just
statement loses credence, from the fact that weak and
empirical men undertake to prove it by false premisses
or fallacious reasoning.
It is further to be remarked, that men who are
guilty of fallacy in argument, either through design




MATERIAL FALLACIES.            175
to deceive, or weakness of reasoning power, are apt
to combine many single arguments into a compound
argument. If, then, one of these be faulty in its
ratiocination, every ulterior conclusion is endangered,
and the whole chain of argument is fallacious. To
detect the error. therefore, requires that the whole
chain be exposed link by link, and that the proper
tests be applied to each argument. We have given
examples of the fallacy of undistributed middle, and
illicit process; the student will not need illustrations
of the other formal fallacies mentioned.
(48.)  Material, or Informal Fallacies.
It will be allowed that in every fallacious argument
the conclusion does or does not follow from the premisses.  If it do not follow from the premisses, then
when written out by symbols the fallacy is apparent,
coming under one of the heads of formal fallacies
which we have just enumerated. The fault here is
evidently in the reasoning; but when the conclusion
does follow from the premisses; when, written out by
symbols, the fallacy is not apparent, the fault will
not lie in the reasoning, but either in the premisses or
in the conclusion, i. e. as to their truth or falsity, or
as to the ambiguous meaning of words used in both.
Such fallacies, with which Logic is not directly concerned, are called Material Fallacies.
It has been remarked before, that Logic indeed




176                  LOGIC.
takes for granted that the propositidns composing its
syllogisms are true; and that when we write the
general proposition A is B, no meanings shall be
given to A and B which shall violate the truth of the
proposition.  If then we put for A, Learning, and
for B, useless, and thus write,
Learning is useless,
or, by a change of words, the doctrine of the Stoics,
Pain is (a lesser sort of) pleasure,
we shall reason to false conclusions, the matter of
the propositions forming the syllogism being false,
while the logic of the argument may be correct. It must
be allowed that material fallacies are more numerous,
and more fruitful causes of error, than the logical, and
as such deserve a special consideration, although indirectly allied to our subject.
We shall, therefore, endeavour briefly to give the
principal forms or titles of material fallacies, and to
illustrate them by examples, observing at the outset,
that they assume many and varied forms under these
titles, all of which we cannot take the time to consider.
The simplest division of them is one which grows
out of the consideration of
1. Errors in the premisses.
2. Errors in the conclusion.
Of Errors in the Premisses.
Logicians have adopted technical names for the




MATERIAL FALLACIES.             177
fallacies of this kind; viz.:-the petitio principii, or
begging the question; Arguing in a circle; Non causa
(pro causa, or the assignment of a false or undue
cause. These branch out into various minor divisions.
As all these grow out of a false or utndue assumption of premisses, they are akin to each other, and
in many cases are not easily to be distinguished.
Especially is this true of the first two.
I. Petitio principii. This consists in using as a
premiss to support an adopted conclusion or assertion,
the same fact in other words.  Thus we are told that
" if the heart be touched death ensues, because it is
a vital part," or that " morphia produces sleep because
it is an anodyne."
Now what is it to say, but that death ensues, when
the heart is touched, because death does ensue; or
that morphia produces sleep, because it produces sleep.
Our language, which has so many synonyms from
the Anglo-Saxon and the Latin, gives full play to
this sort of fallacy, and many a wordy man is guilty
of it without knowing his own error. And besides,
this fallacy is the just recompense of those who endeavour to prove axioms, or who seek to penetrate into
the ultimate facts for which God assigns no cause but
the fiat of his own will.
II. Arguing in a circle.  This fallacy depends
upon finding a premiss to prove an asserted conclusion,
and then, when asked for the proof of the truth of
M




178                     LOGIC.
that premlss, endeavoring to make the conclusion
prove the premiss; or, as this would be easy of detection, to make the circle still larger, i. e., proving
the truth of the premiss by a third proposition which
depends upon the conclusion, and then playing upon
these three, like the juggler's balls of which one is
always in the air, but which-it is very difficult
to tell.  In case of the simplest form, writing out
the syllogism will detect it; and in the latter and
more complex case, the sorites, or its syllogisms
written out, will find it out.
Thus; many men, not content with the everywhere
shining proof within and without that there is a God,
and mistaking the relations which the Holy Scriptures bear to him, would prove the existence of a
God from the truth of the Scriptures, and then prove
the inspiration of the Scriptures from the fact that
they came from God.
As the Scriptures are the word of God, what they declare must be true.
The Scriptures declare that God exists.
Therefore That God exists is true.
Or again;
The word of God must be true.
The Scriptures are the word of God.
The Scriptures are true.
III. Non Causa pro causa.     This fallacy, which
indeed may stand for the general title of unduly assumed premisses, consists technically in assigning as a
reason or cause in the premisses, one which has nothing




MATERIAL FALLACIES.          179
to do with the conclusion, or one which is not itself
proven, and is not therefore a sufficient cause. The
first of these errors is called the fallacy of a non tali
causa pro tali, or the assignment of a cause as though
it were a cause, when it is not; and the second is the
a non vera pro vera, in which the assumed premiss
cannot be proven to be true as a cause, and may
therefore be considered false.
Of the latter of these, the a non vera, we find a
striking example, and an excellent logical retort, in
the reported dialogue between Charles II. and Milton,
after the poet had become blind. "c Think you not,"
said the king, ", that the crime which you committed
against my father must have been very great, seeing
that Heaven has seen fit to punish it by such a severe
loss as that which you have sustained?" " Nay, sire,"
Milton replied, 4 if my crime on that account be adjudged great, how much greater must have been the
criminality of your father, seeing that I have only
lost my eyes, but he his head." Another and common example of this is the following:The natives of barbarous countries regard an eclipse
as portentous of war and famine, and should they come
together, they would assign it as the cause of their
trouble. We know that it is not; but they only note
to the conjunction of the two as satisfactory proof that
it is. Either of these may be easily written out in
the syllogistic form, in which the propositions can be




180                   LOGIC.
scrutinized as to their subject-matter, and the falsity
detected.  Of the a non tali, the following example
will serve as an illustration; viz.:All poisons should be avoided.
Brandy and wine are poisons.
Therefore They should be avoided.
That is, they are poisons only when taken in certain
amounts and under certain circumstances. This is an
invalid argument used by many good persons. The
true reason for avoiding brandy and wine being the
danger of acquiring a habit of using them to such an
extent that they will be poisons.
Errors in the Conclusion.
We come now to the second division of material
fallacies, those in which the error lies in the conclusion;
they are all included under the general head of Ignoratio elenchi, or irrelevant conclusion.
The word elenchus, as used in the early writers,
meant the contradictory of your opponent's assertion,
and thus implies, what indeed was a feature in earlier
Logic, the existence of an opponent. Dialectics were
almost always in the form    of dialogue, and the
Socratic mode of questions and answers was adopted
as the acutest method of argument.
The disputatious spirit of the Greeks was as much
concerned about the victory in logomachy or wordwar, as about the discovery of truth, and hence arose
many of their errors and paradoxes. This spirit of




MATERIAL FALLACIES.              181
controversy, and the constant keeping in sight of the
elenchus has pervaded the methods of Logic to a very
late period.
The ignoratio elenchi is the ignorance of the contradictory of our opponent's assertion, which we display
when, instead of establishing the elenchus, i. e. proving
the contradictory, and thus proving his conclusion or
assertion false, we attempt to establish something resembling the contradictory.
As it is not our purpose to reproduce the Grecian
technicalities and method, let us get rid of this name
and form, and call the fallacy, as it has been called
by modern writers, the fallacy of irrelevant conclusion.
Those who employ it, and this, it may be remarked,
is the most common and practical of all the material
fallacies, generally state the conclusion as a fact, and
when asked for the premisses or proof, are compelled
to present such as display the irrelevancy of the conclusion. Thus, one asserts the fact that c" Alfred the
great was a scholar," and when asked for proof, says,
" because he founded the University of Oxford."
Now, there may be distinct proofs that he was a
scholar, but this certainly is not conclusive. Let us
state the syllogism:Those who found universities are patrons of learning;
Alfred the great founded the University of Oxford;
Therefore, he was a scholar.
16




182                    LOGIC.
The conclusion is irrelevant; the true conclusion
being, from these premisses, that
ile was a patron of learning.
If polemical writings, and especially those which
partake of the nature of popular and heated controversy, be analyzed, this will be found to be the standing fallacy, as often self-deceiving as deceiving others,
and responsible for much of the wide-spread error in
speculative science.
So varied is its nature, that it has been from the
early times known under various names, and presents
its insidious temptations to all kinds of persons.
Perhaps that form which is of most universal application is the argumentum. ad hominem, the unfair
appeal to personal opinions, or to one's vanity or prejudice. After exhausting all the arts to prove a
thing wrong which is not so, the argument closes with
" Well, you would not do so!"  Even in matters of
religion we are triumphed over by the adversary by
a reference to ourselves and our own imperfect
actions, when the question concerns the abstract
truths of God's holy law. This form of the fallacy
needs, then, a special watch as the most insidious.
Next in enumeration is the argumentum  ad populum, which is the former fallacy extended from one
individual to many, from personal opinion to popular
prejudice,




MATERIAL FALLACIES.           183
Unprincipled demagogues use this fallacy continually; and where the sophistry would be apparent
to any single mind gifted with common sense, the
enthusiasm and thoughtless spirit of a mob, moved
by a fiery harangue, is blind to its unreasonableness.
This may be called the logic of revolutions.
A third kind of irrelevant conclusion is the argumentum ad verecundiam, or appeal to the modesty of
our opponent, hoping that he will not presume to
attack respected authorities and time-honoured customs. Although healthful progress may have demonstrated their errors, and provided us with better
methods, the cry is of recreancy to our fathers' memories, to old associations, to History; and thus the
world has been trammelled and clogged by what professes to be the genius of conservatism, but what is
in reality the genius of obstinate error.
Besides these forms of irrelevant conclusion, there
are many which have been proposed in pleasantry,
such as the argumentum ad baculinum, and others
which Sterne humorously refers to in cTristram
Shandy."
There are, however, it must be particularly observed,
many cases in which these very arguments are not fallacies; in which, indeed, they may with great propriety
be used, clothed with all the graces of rhetoric and
imbued with all the fire of enthusiasm.
The argumentum ad hominem is not a fallacy when




184                  LOGIC.
the design is to teach pure truth, and when no unholy
passion or emotion of man is appealed, to. In this
application it was used by our Saviour himself to the
Jews on many occasions, with great force and beauty.
His touching, and yet searching, appeal to them for
the woman taken in adultery, sent them out one by
one before its power. Each one felt the argument
and admitted the conclusion.
His arguments in favour of healing on the Sabbath,
and searching the Scriptures, that they might find
every page luminous with Him whom they denied,
were examples of the unfallacious and powerful use
of this form of reasoning.
So, too, an appeal (ad populum), not to the prejudices, but to the conscientious scruples and feelings of
a multitude, is without fallacy, and is productive of
the best results.
Many customs, long honoured, and dear to every
heart; customs national, civic, professional, domestic,
unmingled with error, unopposed to progress, make
the argumentum ad verecundiam a most proper and
effective appeal.
But such is the waywardness of man that the temptation to fallacy in their use is exceedingly strong,
and must be carefully guarded.
Argumentum ad rem and ad judicium.
Opposed to all these, when used as fallacies, are two
forms of valid argument: the first expresses a con



FALLACY, OF OBJECTIONS.        185
Centration solely upon the reason of the thing itself,
and is therefore called the argumentum ad rem; the
second is when the appeal is made to the unbiassed
exercise of the individual judgment: this argument
is called argumentum ad judicium.  Many writers
have increased the number of these fallacious argumenta to a much greater extent; but those given are
the principal ones, and will sufficiently indicate the
process by which they are coined when needed.
Changing the point in dispute.
Another form of the " irrelevant conclusion" is the
fallacy of changing the point in dispute, in which one
of the parties in a long and difficult controversy, after
having tried in vain to establish his irrelevant conclusion, dexterously shifts his ground from the point in
dispute to some other, and pertinaciously claims that
to be true which has not been disputed, while the true
matter of contention is left, without an honest confession of his inability to prove his assertion. For example, a person undertakes to prove that the people in
general are not educated; i. e., he first denies that they
are; but failing of this, he really proves, what no one
denies, viz.: that all the people should be educated.
Fallacy of Objections.
It has been remarked, that Ignorance may state in
a few words objections against Science, which wise men
could not refute in whole volumes. The truth of this
16 w




186                  LOGIC.,
is manifest.  The error of reasoning from the statement or existence of these objections, to the falsity
of the science, is one of the forms of irrelevant conclusion which has been called the Fallacy of Objections. It consists in asserting that, since there are
objections against a Science, that Science is false;
whereas the judgment demands that the claims of the
Science as well as the objections be duly stated: and
that the turning of the scale decide whether truth or
error predominate.
If it be a complicated system, it will be found to
contain portions of both; if an abstract theory, it will
stand or fall by such a test. This fallacy has been industriously aimed by sceptics against the mysteries of the
Christian faith, but it soon loses its point in such an
encounter. From the consideration of the various species of the fallacy of irrelevant conclusion which have
been mentioned, and the examples given, it will be seen
that it is in all its forms the standing sophism in houses
of legislative convocation; that it is the demon of debate. Few subjects of debate are so abstract and unitlike but what dull minds will find room to wander about,
one losing the very point in question, another concerned about a crowd of details which have little or
no bearing upon it, a third mistaking the fine and
delicate points of the logical argument; some, becoming heated in the controversy, will lose their temper
and reasoning powers together, and overpowered by




FALLACY OF OBJECTIONS.               187
the truth and Logic of their opponents, will have recourse to appeals to the prejudices and interests of
their audience; and others, more shrewd than just, will
seek to bring by similar means the cause and persons
of their adversaries into disrepute, by the light arrows
of ridicule, or the more ponderous weapons of insult.
It is amidst such scenes, and under such circumstances, that the master mind shows itself as it rises over
the storm of the debate, and brings them back first
to the consideration of the subject in dispute, in its
true and abstract form.    Perhaps the most striking
illustration of this is found in our own Congressional
history. After Mr. Webster's first speech on,, Foote's
resolution," many senators had delivered their views,
and much sectional excitement was aroused. Mr.
Webster began his famous second speech, with just
such a master-effort to come back to the true merits
of the controversy:"Mr. President,-When the mariner has been tossed for many
days in thick weather and on an unknown sea, he naturally avails
himself of the first pause in the storm, the earliest glance of the
sun, to take his latitude, and ascertain how far the elements have
driven him from his true course. Let us imitate this prudence, and
before we float farther on the waves of this debate, refer to the
point from which we departed, that we may at least be able to conjecture where we now are. I ask for the reading of the resolution
before the Senate."
The resolution was read; the Senate found their
true position, end Mr. Webster's speech is as masterly for its logic as for its oratory.




188                    LOGIC.
(49.) Verbal Fallacies.
There is still a most important class of invalid
arguments to be considered; it is that growing out
of the ambiguous or equivocal meanings of words;
many words being identically the same, and yet bearing widely different meanings. Thus, the simple word
line, when used in different connexions, means many
distinct things; for example:-a cord used in fishing;
a few words in a letter; an arrangement of troops or
ships in battle arrcay; and when we see the word
porter, we are in doubt which of three meanings is
intended,-a gate or door-keeper, a, man who bears
burdens, or a kind of malt drink.
In most such cases, however, there is a single root
to which we may trace all these secondary meanings;
thus all the meanings of a line refer to the mathematical definition that it is length, without breadth or
thickness, and all the uses of porter refer to the Latin
word which signifies to bear.
It is true that there are examples of words spelt
alike which have different etymologies; but these are
few: host, from hostis, and host from hostia in the
sacrifice of the mass, are examples of this; so also
league from ligare to bind, and league from the Latin
locus or distance between places, contracted in French
to lieue, as the word focus is into feu;-are examples
of such words.  With these few illustrations of am



VERBAL FALLACIES.              189
biguous terms, let us see how they are used in argument.
The ambiguous word is sometimes the middle term,
and sometimes it is the major or minor;.in most cases,
however, it assumes the former place, so that the
general name given to this form of verbal fallacy, is
" the Ambiguous middle."
X                      Y
The church  is the company of faithful people.
This stone building  is the church.
Therefore This stone building is the company, &c.
Now, if this glaring and absurd fallacy be stated
by symbols, we shall have
X is Y,
Z is X,
Z is Y,
which is the form of a, valid argument in the first
figure; so that the fault lies in the matter of the
propositions which compose the argument, and not in
the form, which is correct; the fallacy then must be
classed, with such an investigation, among the material, and not among the formal fallacies.  But let us
go a step farther; since "the church" in the major
premiss means something entirely different from," the
church" in the minor, they are in reality different
terms; let us symbolize them by different letters, and




190                   LOGIC.
calling the first X, let us call the second P; we shall
have, writing by symbols, as before,
X is Y,
Z is P,
Z is Y,
a formal fallacy, in which there are, contrary to the
rules laid down, four terms instead of three; and
this comes within the province of Logic. The fallacy
of Ambiguous middle has very justly, then, been called
by logicians, a semi-logical fallacy; before we discern the ambiguity it is a material fallacy, with which
Logic is not concerned; but as soon as we discover
the ambiguity, it discloses four terms, which make it a
formal or logical fallacy.  It is because of this peculiarity, and because it is so very much used in common life, that we treat of it under the distinct head
of verbal fallacies.  But we have said that it is not
only in the middle term that this ambiguity occurs;
it also happens in the major and minor terms; and is
quite as sophistic when it lurks there as in the middle
term.  We have therefore discarded the title "4 Ambiguous middle," as applied to the general class, preferring  Verbal fallacies," as more truly illustrative
of the error in any of the terms.
There are many ways in which words are used
ambiguously, and we shall give a few of them with
illustrations; and first, we place the influence of
Etymology.




ETYMOLOGY.                  191
Etymology,
A word which originally meant one thing, now means
quite another, and the fallacy consists in using it in
the two senses, in two propositions of the syllogism.
Thus, taking the first meaning of pagan to be a villager (paganus*), and its present meaning to be a believer in some other religion than that of Christ, we
have,
A pagan is a disbeliever in Christ;
very villager is a pagan;
Every villager is a disbeliever in Christ.
Akin to this, and indeed ranging under the general
subject of etymology, is the use of paronyms, or paronymous words.
Paronymous words, are the noun substantive, adjective, verb, &c., belonging to each other and springing from the same root.    To project, project, projection, projector, &c., are paronyms, springing from
the Latin compound of pro and jaeeo.   So presume
(in its two senses), presumption, presumptive, presumptuous, &c., are paronyms growing from the root
presumo.
Take the following example, in which the ambiguity will lie in the middle term:Presumption is impertinence;
That the sun shines, Ipresume (or, is my presumption);
Therefore I am impertinent.' From pagus, a village.




192                   LOGIC.
It will be remembered that the true logical form of
the minor premiss, which is usually written, "I presume that the sun shines," is
subj.              pred.
That the sun shines  is  presumed by me.
Again:
To propose a railroad is a project (or a projector's work.)
This man proposed a railroad.
Therefore He is a projector.
in which the ambiguity lies in the major term. Now,
no one can work advisedly, without making projects,
whereas one of the meanings of projector, is a scheming and visionary man, who ought not to be relied
upon.
Fallacy of Interrogations.
This is a use of two or more terms in a question,
making thus in reality two questions, requiring two
distinct answers, and the ambiguity lies in the single
answer given to both. It is common for those who
use this fallacy to express but one question, while the
other is implied. Thus, if a man who has always
been temperate is asked, " when he gave up drinking?"
the implied question is, " did he ever drink?" and
then, if so, when did he cease? or, in the celebrated
inquiry of King Charles II., cu zwhy a dead fish does
not add to the weight of a vessel of water?" the implied question being " does a dead fish add, &c.?" and




FALLACY OF INTERROGATIONS.        193
if so, "rwhy, &c." This fallacy, which is called by
the writers, Fallacia plurimum interrogationum, is
made more subtle by the number, and closeness of
resemblance, of the points included in the questions.
Amphibolous Sentences.
Sometimes the ambiguity, instead of residing in the
words which compose the argument, lies in the construction, and thus, by different punctuations, we
have double and opposite meanings. This passes
from the ambiguous words to amphibolous sentences.
Among the most celebrated of these is the response
of the Delphic oracle to Pyrrhus when he went to
encounter the Romans:
Aio te (Eacida Romanos vincere posse,
Ibis redibis nunquam in bello peribis.
In the first line, either accusative may be taken
with the infinitive, thus making either c( Pyrrhus," or
"s the Romans," able to conquer; and in the second,
nunquam may qualify either redibis or peribis.
So also in the Nicene Creed, we have, in reference
to our Saviour, the words —" being of one substance
with the Father, by whom all things were made."
The latter clause, so manifestly introduced by the
Council, to declare the creative power and Godhead
of Christ, in reality by strict rhetoric'applies to
" the Father."
The name given to this fallacy is the fallacy of
17             N




194                  LOGIC.
amphibolous * sentences, i. e., tossed from  one to
another, with a doubtful meaning.
Causes of Ambiguity.
Having mentioned the various kinds of ambiguity
in words, we come to consider why words have two or
more meanings.
We have already seen that many words expressing
simple primitive ideas grow by usage to have other
meanings, in which, however, the primitive idea is to
some extent retained: thus, line, in all its meanings,
adheres to the mathematical notion of extension in
length.
Now, without being able to trace the exact process
in all cases, by which a word is thus gradually changed,
we find that it ranges itself under one of these heads:
1. Resemblance; 2. Analogy; 3. Association; 4. Ellipsis; 5. Accident.
1. Resemblance. Many things bear the same name,
from their actual similarity in appearance. Thus, in
carpentry, a dove-tailed joint is so called from its
similarity to a dove's tail, or a spear of grass from
its resemblance to the military weapon, a spear. So
in the military art, a "p priest-cap," or cc swallow-tail"
is a redoubt so named from its actual resemblance to
these two things, and a "c crow's foot" takes its name
from the form of a bird's talons.
- a/btl and jaXXco.




ASSOCIATION.               195
2. Analogy. Our ordinary speech is full of the use
of this figure of speech, and this fact has contributed
to the ambiguity in many words. As resemblance is
a similarity in appearance, analogy is a similarity in
use, purpose, or relation. Thus, we speak of the arm
of a chair, because it holds the relation to the chair
which the arm does to the human body: and thus an
arm-chair is a chair which has arms.
We speak equally of a sweet food, or a sweet sound,
because there is a similarity between the relations of
the food to the palate, and the sound to the ear. So
a sour lemon and a sour individual, create relatively
similar effects upon the taste and upon the mind.
Ambiguity of resemblance and of analogy are both
produced and perpetuated by the use of metaphor
and comparison, in our ordinary discourse, and a wayward fancy, expressing itself in the social exaggerations of the day, is robbing some of our best words
of their true shades of meaning: for example, sweet,
lovely, horrid, agony, wretch, are deflected from their
original neanings entirely.
3. Association. By this we mean the connexion
of pares in the same structure or institution, or to produce a single result. Thus, a door is the opening in
the wall, or the swinging shutter that closes it. Faith
is belief, and," the Faith" is the system of Christianity. Shot is the leaden pellet: a good shot is
either the person who shoots, or the effect of the shot.




196                  LOGIC.
It is by the association of ideas, which, unlike our
examples, are subtle and difficult to fix and determine,
that fallacies have grown out of this ambiguity; and
such is the want of correctness in the language of
the great number of people, that the tendency to this
fallacy of words, expressing associated ideas, is particularly strong and dangerous.
4. Ellipsis.  Another habit into which men naturally fall, in trying to avoid the use of many words,
and words conveying thoughts which the mind will
readily supply without their being expressed, is the
use of elliptical language. While in most cases this
is harmless and even profitable, in some it leads to
error. Thus, we speak constantly of Scott, Byron,
&c., when we mean their works or their persons. We
use the form  to my father's," "4 at Mrs. Smith's," when
we mean the houses or "c parties" of these persons, and
such ellipsis is always understood; but many persons
are deceived in their business relations by such
ellipsis as the statement of another's wealth at so
many thousands of dollars, when in reality, although
it may produce the interest on such a sum, it cannot
be made available for anything like the amount of
the principal sum mentioned.
5. Accident. It seems in certain cases as though a
word had assumed two meanings in a manner inexplicable and accidental. Such, for example, is the
word light, which is equally opposed to heavy and




ACCIDENT.                 197
dark: and which in conduct means the opposite of
serious or dignified. But even in such a case we
shall find one idea, however subtle, pervading them
all, and that is the removal of a covering of some
sort; thus, light removes the pall or covering of
darkness; the incumbent weight of something heavy;
the just restraints of dignity and sobriety. In strict
truth, then, there is no accidental ambiguity, for,
although there may be words in the double meanings
of which we can discover no relation to a single idea,
that relation undoubtedly exists, and by a profound
research the number of such words would be very
much diminished.
Many words are forced into a double meaning by
a popular or political use, which may be called accidental, but which in reality is designed by one party
as an equivoque, or stratagem, in the way of retort
upon the other. It was thus with the use made of the
word Pretender, by the English Jacobites. When it
became treasonable in any way to maintain the claims
of James Stuart, the son of James II., who was called
" the Pretender," they toasted him in the well-known
verses:God bless the king; God bless the Faith's Defender;
God bless-no harm in blessing-the Pretender.
But which is the Pretender; which the king?
God bless us all,-that's quite a different thing.
It is evident that such a use of the word would deceive no one; nor was it indeed so designed, but rather
17 *




198                    LOGIC.
to violate the spirit and yet adhere to the letter of
the law. The true argument used by the adherents
of the new dynasty, wasThose who aid a pretender to the English throne, deserve punishment.
James Stuart is a pretender.
Those who aid James Stuart, deserve punishment.
It must be understood that pretender in both premisses has the same meaning, i. e., false claimant.
But there is still another form of ambiguity which
leads to fallacious arguments; it is where the ambiguity lies not in words but in the context; or where
our assertion means one thing when taken in a general
sense, and quite another if considered in a special
sense.  Of these fallacies, arising from ambiguity in
the context, there are two kinds.
1. The fallacy of accidents.
2. The fallacy of division and composition.
Under the first head are included the Fallacia accidentis, and the Fallacia a dicto secundum    quid ad
dictum simpliciter. These are the converse of each
other.
Fallacia accidentis.
This is where, in one premiss, we assert something
of a subject in a general sense, and, in the other, place
upon that subject some accidental peculiarity, which
will lead us to error in the conclusion; thus,
Things bought in market we eat.
Raw meat is a thing bought in market.
Therefore, Raw meat is what we eat.




FALLACY OF DIVISION AND COMPOSITION. 199
Here the middle term is things bought in market, and
it is considered in the major premiss as to its essence;
viz.: that these things are in market for general use as
food; in the minor we lose sight of its essence, and only
regard some accident of it, viz.: that the meat bought
in market is raw. Thus, in reality, the error is thrown
upon the middle term, which is shown to be not one,
but two distinct terms, and the fallacy is thus exposed.
The other form of this, which for shortness is
called the Fallacy of Quid, may be translated reasoning from the broad sense of a term (secundum quid),
to its special reference or application (ad dictum  sirpliciter).  Thus:A horse drinks on all fours and out of a trough.
This man drinks like a horse.
He drinks on all fours, &c.
Fallacy of Division and Composition.
In this fallacy the middle term is used in its collective or additive sense in one premiss, and in its distributive sense in the other.  When the middle term
is used collectively in the major premiss, and distributively in the minor, the fallacy is of "Division";
when the reverse takes place, it is a fallacy of
" Composition."   The following are examples:Fallacy of Division.
The Christians were persecuted at Rome.
Constantine was a Christian.
Therefore lHe was persecuted at Rome.




200                     LOGIC.
Fallacy of Composition.
Three and two are two numbers (distributively).
Five is three and two (additively).
Five is two numbers.
Positive and Negative Intention.
Akin to these fallacies are those absurd conclusions
reached by a play upon certain negative words, such
as nothing, and no, when used as an adjective; thus:
Nothing is better than Heaven.
A shilling is better than nothing.
Therefore A shilling is better than Heaven.
No cat has two tails.
Every cat has one tail more than no cat.
Every cat has three tails.
In these examples the middle terms nothing and
no cat, are taken in a positive sense in the major
premiss, as though they expressed living or existing
things, while in reality they mean non-existence. In
the minor premiss they are taken in their true negative sense.
The best method of refuting them is to deny the
major premiss, or to demand that it be put in other
words, thus:It is not true of anything that it is better than Heaven:
which will foil the one who wishes to draw the absurd
conclusion.   It should be observed that such arguments are really used only in sport, but it is well to
detect and understand the error which they contain.




REMOVING AMBIGUITY IN TERMS.         201
(50.) The Manner of removing Ambiguity in
Terms.
The true method of ridding ourselves of this ambiguity of terms in argument, is to demand a definition, in each case, and to keep our terms distinct when
thus defined. It will not, in most cases, be necessary to give a real definition, as a nominal one will
answer every purpose.    The ambiguity is usually
such that by giving the true, limited and exact name
(which is the province of a nominal definition), we
shall detect and remove it.
In many cases where the fallacies consist of a number of arguments and many ambiguous terms, the
first thing to be done is to disentangle the web of
sophistry, by writing them out in full, and in due
order, and then after detecting the terms in which the
ambiguity lies, to demand a definition in a few but
plain and conclusive words, in every case.
The equivocal nature of the word becomes apparent, if we change the language, as in the translation
of the familiar example, into Latin:Light is contrary to darkness.
Feathers are light.
Therefore, Feathers are contrary to darkness.
we shall have,
Lux est contraria tenebris.
Plumse sunt leves.
PlumSe sunt contrarime tenebris.*
Latham's Logic, p. 221.




202                   LOGIC.
This change of language, it will be seen, is of the
nature of a definition.
(51.) The Fallacy of Probabilities, or the Calculation of Chances.
This consists in stating two probable premisses, and
then drawing a certain conclusion, as though the
number of probabilities combined amount to certainty, whereas, in most cases, the conclusion will be
less probable than either; thus:Those who have the plague probably die;
This man probably has the plague;
Therefore He will (certainly) die.
Whereas, suppose ten out of twelve of those who
have the plague die, then, if we express certainty by
the number 1, that probability is expressed by the
fraction 10 or 6, and if it is an even chance whether
or not he has the plague, that probability will be expressed by 1.   The probability of the conclusion,
therefore, will be  X ~ -= 2, or as I is the expression
for perfect doubt, i. e., an even chance of his living
or dying, he is less likely to die than to live, his chances
of dying being 5 out of 12, and of living, 7 out of 12.
This fallacy is practically used in times of sickness
and mortality, when fear of evil, excited by nervousness, affection, &c., place an anticipated conclusion
for the true one.
When instead of one syllogism, or enthymeme,




FALLACY OF PROBABILITIES.         203
many are combined to make a compound argument,
and the errors of probability are thus multiplied, the
result will be at once farther from the truth, and
more difficult to detect.
Let us deduce then a simple rule for the calculation
of probabilities.  The subject has been called " the
doctrine of chances."
When we speak of chance, we really mean probable
results of God's laws, and in the use of either word,
we express our ignorance of the connexion between
natural causes and effects. Now, as that ignorance
may be partial or entire, the probability ranges between the two extremes, certainty and impossibility.
We do not pretend to assert by this that man may divine
the results of God's doings in the future; but that
according to the action of natural laws, and the sequence of an established order, we may approximate
to the truth without assuring ourselves of it.
Thus, in throwing dice, we cannot be sure that any
single face or combination of faces will appear; but
if, in very many throws, some particular face has not
appeared, the chances of its coming up are stronger
and stronger, until they approach very near to certainty.  It must come; and as each throw is made
and it fails to appear, the certainty of its coming
draws nearer and nearer.
The probability of a single event depends upon the
number of chances, of which it is one; thus, if A. is




204                 LOGIC.
in a single action where 10 men are killed, his company numbering 50, the chance which each man
stands of being killed, and consequently that of A,
is a or 5.  If we subtract 5 from 1, or certainty, we
shall have 4 for his chance of being saved. The calculation of probabilities becomes more complicated
where the events are combined. Thus, if in a second
action 10 men more are killed, his chance of being
killed in this last action, is as 10 to 40, or 4: and that
of his being saved 4. If now we would determine his
chance of being saved, after both actions, we must multiply the two chances together: 4 X  =  2 =,
which is as it should be, since 20 men are lost of the
original 50, and 30 remain, his chance of being among
the latter should be as 30 to 50, or -.
It is upon this principle of calculating chances that
insurance companies are founded; and it finds a benevolent issue and scope particularly in those Life-assurance companies, which, demanding but a small percentage, making a large aggregate, are thus enabled
to pay to widows and orphans an honourable support:
snatching out of the jaws of death the means of life
and social comfort.
It is, however, upon a false study or rather in an ignorant and fatal reliance upon this principle, that those
who frequent gaming-houses throw away their means,
reputation, and life; for the true gainers are not the
frequenters of the gaming-table, but the keepers, who




POPULAR FALLACIES.           205
are acting upon this very doctrine of chances. By a
calculation of chances it is found that in the long run,
the keeper of a gaming house must win, in almost every
kind of game played; while only an occasional player,
with what is called a marvellous run of luck, chances
to win largely.
The subject of probabilities, which in its right use
is not fallacious, but is reduced to arithmetical accuracy, has been placed under the general head of Fallacies, because of its being so liable to fallacious use,
and so much employed thus. Mingling as it does with
the superstition in our nature, we deem those things
more probable than they are, which we desire or fear.
The wish is father to the thought, for pleasant
hopes: and presentiments of evil are taken for its
probable coming, in our gloomy periods. We give a
rule by the use of which all this may be avoided.
Rzule.
The probability of any event is expressed by a fraction, of which the numerator is the number of chances
in its favour, and the denominator is the sum of all
the chances.
(52.) Popular Fallacies.
It will be well, before closing the chapter on Fallacies, to show their practical use, especially in a popular illustration. A community, a state, a nation, will
18




206                  LOGIC.
unite upon a fallacy, from which it will be a sort of
social treason to dissent; an age will be tinctured by
error, pervading all classes, which only the innovation of a succeeding age can remove; a false principle
will cling to human nature, in the mass, during many
centuries, which the philosophic mind can only deplore in secret.
It will be our purpose then to put forth some of
the simplest forms of popular fallacy, beginning with
the most general.  Some of these have been already
mentioned in their logical places, as the different
forms of irrelevant conclusion, &c.
I. The fallacy which is expressed by the adage,Nil de mortuis nisi bonurm. There is a just meaning
to this indeed; it is that the tongue of private enmity
should be silenced; that we should consider Death
as having adjusted all difficulties a.s between man and
man, and awed our mortal infirmities into a silence
and forgetfulness of the evil which existed in him
who is now dead.   So far the adage is good: but,
when it becomes a principle in public morals; when
it tinctures the historian and the historical biographer,
who should deal with the dead as with living defendants, arraigned for trial, its evil nature is apparent.
When it eulogizes the dead at the expense of the
living, and runs riot in obsequious praises and flattering epitaphs, it assumes its most sophistic form.




POPULAR FALLACIES.           207
" The same man," says Jeremy Bentham, 4who bepraises you when dead, would have plagued you without mercy when living." The reason of this is apparent. A  dead man cannot be a rival; he incurs
nobody's envy, and is removed from all the results of
malice.
II. Not unlike the preceding is the fallacy conveyed in the trite saying-De gustibus non est disputandum. This is used fallaciously to put a stop to
controversy; the assertion implying that as God gave
man, each his own taste, one taste is as good as
another. But all our systems of education teach us
that this is not true; that there is, on every subject
which comes under the dictum of taste, a true standard, which can and ought to be used. It certainly
is better to put an end to controversy by saying that
it is better to differ than to become excited and
quarrel, than falsely to state that there can be no
dispute about tastes.
III. There is a fallacy which particularly assails
patriotism: it is the fallacy of asserting that any one
form or system of Government is abstractly the best.
The Russian deems that men cannot be controlled in
masses, without single autocratic power; the Englishman defies the world to pick a flaw in his limited
monarchy and superb aristocracy; while the American
boldly declares that the best government is the democratic, representative form. Where such men as




208                 LOGIC.
Milton and Locke have "c astonished the world by
signal absurdities" in their models of government, we
might be sure that its theory must be difficult;-but
the truth is, there is no abstract theory of human
governm ent.
Asiatic barbarians, when they leave their patriarchal,
wandering life, as in Russia, and come into the first
corruptions of a half-civilized life, must be governed
by despotic power; they cannot be republican: while
on the other hand, it is only where education is general among the people-that they may know their wants,
and how to supply them, and where individual honesty
and virtue are everywhere felt, that no undue means
may be taken to bring about such an end,-that a
democratic government is the right one. Then, in this
freest form there is a reciprocal influence between the
government and that upon which it is founded. A free
government enlightens and purifies the people; while
the enlightenment and purity of the people strengthen
and insure the government under which they live.
IV. There is a popular fallacy, which may be called
Swzeeping classifications. It consists in ascribing to
an individual something really belonging to another
individual, only because the two happen to be of the
same class; thus, during the French Revolution, when
the fate of Louis XVI. seemed to hang upon a thread,
one pamphlet was issued with the title c The Crimes
of Kings." Now, as there had been many bad kings




POPULAR FALLACIES.            209
in Europe, and not a few in France, Louis XVI., the
best of them, was put into the category of condemnation, simply because he was a king.
In times of religious revolution this has been very
common; as, when we hear the cry, " the cruelties of
the Roman Catholics," uttered at a time when a bill
for their relief was before Parliament.  Former cruelties in far distant countries all being thrown upon
the shoulders of the disabled and harmless Roman
Catholics of that day. Such, too, was the cry among
Roman Catholics themselves in the time of James II.,
and the after Jacobite struggles, of c Protestant intolerance."  As a further example, we refer to the
stories circulated about the Jews, in the fourteenth
and fifteenth centuries; that they crucified Christian
babes, and were guilty of secret crimes of great
enormity.
V. Space would fail in which to enumerate the
current and manifest popular fallacies, most of which
are used in legislatures and councils, and are considered in the light of shrewd and dexterous diplomacy.
There is the," no precedent argument."  It is stated
thus:-" The plan proposed is entirely new.  This is
certainly the first time such an idea has been broached
in this honourable house; and therefore, the secret
hope is, that this house will not now entertain it."
Next, we have personalities introduced, laudatory
18*             0




210                  LOGIC.
or abusive, by which to turn the current of the argument.
Another form is the assertion with regard to any
measure, that as ", no complaint has ever been brought
against it before, it must be a good one."
But perhaps the most insinuating form of popular
fallacy is that by which a man is required to join one
or the other party in every question; thus causing the
young ignorantly and prematurely to commit themselves to views and measures which later experience
teaches them to be wrong; if then they change they
are traitors or turncoats, if it be a national or political
question; and fickle and unreliable, if it be of a less
general nature. It is lamentable to see party guides
bringing those under their control forward to swell the
ranks of their party; and those thus introduced,
glorying in their new distinction, when self-interest
and not truth has been the motive on both sides.




APPLICATION OF LOGIC.          211
CHAPTER XI.
(53.) Of certain modes in which Logic is applied.
IT is not within the scope of this work to enter
upon the subject of applied Logic; this would require an investigation of all the sciences, or at least
of a very numerous classification. But it is designed
to explain the meanings of certain phrases which
refer to the general applications of Logic.
We have the phrase moral reasoning, and it is
often used as if conveying an opposite or contrary
meaning to demonstrative reasoning.
This has reference, not, as we have clearly shown,
to the kind of reasoning-as there is but one-but to
the nature of the evidence employed-the meaning
of evidence being, that testimony which sets forth the
truth of a proposition. Then, moral reasoning is
the use of evidence in moral subjects, and demonstrative reasoning its use in mathematical subjects.
Now, evidence may be of three kinds, that is as to




212                  LOGIC.
the manner in which we obtain it; it may be intuitive,
inductive or deductive.
Of Intuition, Induction and Deduction.
We come now to consider the means of discovering
truth, which are most useful, but which have been
strangely confounded with Logic. They are processes
as much bound by logical laws as all other movements
of the reason are.
It is evident, that in order to the Logical process,
we must have premisses; now, these premisses are
obtained evidently by the three methods just mentioned-Intuition, deduction, and induction or experiment.
By intuition, we mean the absolute knowledge
which, without any apparent effort, we find implanted
in us. Such for example, is the aspiration of man's
soul after a Deity, as exemplified in the religious
systems of all people even the most barbarous, and
such as the existence of certain affections, and notions
of moral conduct.
The truth of axioms is determined by intuitive
evidence or intuition; and in brief, consciousness in
most of its forms, and the testimony of our external
senses, are said to be sources of intuition.
But most of our knowledge is derived from what
we possess already in another form, as where we
deduce certain inferences from acknowledged pre



INTUITION, INDUCTION AND DEDUCTION.    213
misses, or from observation and experiment, and
generally, many observations or experiments are
necessary before we can determine a general law;
thus, it required centuries of observation to determine
the Copernican theory of our solar system; and
almost all the developments in natural science are
the fruit of many observations and experiments
aggregated in each case to form one general law.
It is an effort of man by a close study of the
phenomena -(Tavosvac) or appearances of nature, to
arrive at some degree of acquaintance with the
noumena (vooviva) or essences of its objects.
To unite these was the aim even of the heathen
philosophers, and with their obscure lights they worked
ardently in the labour; it remained for a doubter
(Sextus Empiricus), two centuries after the coming of
Christianity, to connect them for another purpose,
and that was to arrive at a suspension of all judgment on objects whose nature is obscure, and thus to
acquire a certain repose of mind (atapafio), and perfect
equanimity of disposition (,Erptwoita0o). But the inductions of Sextus were never really performed; he
theorized to his scepticism, and his theories will not
bear the rude hand of physical practice.
In order to illustrate the difference between induction and deduction, let us suppose a law already
determined, which we state in the proposition A is B.
Let any number of particular examples, as x, y, z,




214                   LOGIC.
range under this law, thus, x is A, y is A, z is A,
and we can manifestly reach the conclusion that x,
y, and z, are all and severally B.
But suppose the general law unknown, and that it
be approximated to in proportion to the number of
particular examples; we shall thus have x is B, y is
B, z is B, &c.; but x, y, z, &c., as we increase the
number of the examples, represent the class A; hence
we may state the law A is B: the truth of which
will depend upon the number and extent of the experiments performed and particular instances observed.
Or, to recapitulate in syllogistic form:Deduection.             Induction.
(Law)  A is B.          (Part. examples)  x, y, z, &c., are B.
(Part. examples)  x, y, z, &c., are A.  A is the class to which x, y, z, &c. belong.
(Conclusion)  x, y, z, &c., are B.  (Law)  A is (likely to be) B.
Now there are certain sciences in which, from the
nature of things, we can never state more certain results from induction than this likelihood; but this
likelihood, it must be observed, becomes greater and
greater, and at length touches absolute certainty,
when we examine many particular instances and find
none of them failing to range itself under the law
which we call likely. So that at the last we write it
to all intents and purposes as a categorical proposition,
A is B. In some sciences we may exhaust all the
particular examples and finish our induction by a
certain law.  This induction has led, as the other
could not, to certainty.




INTUITION, INDUCTION AND DEDUCTION.      215
There are two kinds of induction, material and
formal; and it is by a want of proper distinction between them that the error has arisen of comparing
induction improperly with the syllogism, and asserting
that while induction is one kind of reasoning, the syllogism is another, i. e. deduction.
Hence Lord Bacon and his followers, finding that
deduction generally moved from what was contained in
known premisses to lower classes or individuals contained in them, threw aside the syllogism as useless,
and inaugurated induction as the new Logic of experimental philosophy. A simple examination of material
and formal induction will set us right.  Material induction is the process of experiment and observation;
the laborious investigation of facts, as to their discovery and their combination; but formal induction
is obtained by the use of the syllogism itself: not
confined, as some writers have attempted to show, to
the third figure, but in most examples capable of being
at once written out in the first figure, the form in
which they may be immediately tested by the dictum
of Aristotle; as in the example:Iaf. poem. rWhatever is true of the cow, goat, deer, &c., is likely
to be true of all horned animals;
Min. prem. Rumination is true of the cow, the deer, &c.;
Concl. (Law). Rumination is likely to be true of all horned animals.
The naturalist receives this as the only just conclusion from the formal induction to which the syllogism has helped him; but, having as yet found no




216                   LOGIC.
exception to the rule, he writes it out boldly and
without fear of contradiction,
All horned animals are ruminant.
Of certain modes of using Syllogisms.
Argument d priori.-This is the mode of passing
from known antecedents, to necessary consequents;
or, in the sciences, from cause to effect. Thus, if we
consider the being of a God and of his attributes to
be independently known, as by intuition, then we reason a priori to the existence of his works, the universality of his providence, and the gracious designs of
his redemption; this reasoning is most plainly stated
in the form of the constructive conditional syllogism;
the affirmation of the antecedent-orn cause-helping
us to the affirmation of the consequent-or effect.
Arglument d posteriori.-This is reasoning from
efect to cause. If, by an inverse process, we first study
natural religion, and experiment upon the wonders
of the human mind, and then pass back from these
works around us to the establishment of the existence
of a first great cause, who must have made them all,
we are'said to reason d posteriori, or from results to
their causes.
Of the two modes of reasoning, both are useful
and effective, but the reasoning d priori is the most
certain, and analogous to deductive inference, while
the reasoning d posteriori must always have some un



MODES OF USING SYLLOGISMS.        217
certainty akin to the processes of induction. For if
the argument be placed in the conditional form, as
before, we have really no right to pass from the affirmation of the consequent, to the affirmation of the antecedent. It is usual, therefore, to limit the conditional in
reasoning a posteriori, so that the consequent in question must be considered to spring from that antecedent, and no other.
History uses both forms, and combines them with
great success: taking, for example, on the one han(
the early elements of a nation's life; its people, its
geography, its tendencies of government-history
seeks to trace these to their legitimate results among
the changing scenes of national existence; while on
the other, looking around at the present condition and
conduct of anation, she takes these results, and tracing
them back, in careful combination, with each step removed from the present, she seeks for their early and
prime causes, in the classic times of the country's
origin.
There are, it must also be observed, certain results
of a spiritual kind, both in natural and revealed religion, which may be justly reasoned upon a posteriori,
to their certain causes and source.  Such, if we mistake not, is our Saviour's teaching, when he declares,
"by their fruits ye shall know them:" asserting the
exact analogy between the fruits of the Spirit and the
19




218                   LOGIC.
fruits of vegetable life.  Since certain events of which
we are aware, while yet their causes are unknown to
us, may have sprung from any one of several causes,
we must be careful upon what subjects and to what
extent we use the d posteriori mode of reasoning, for
even when it seems most applicable, it may fail us.
Thus, if in time of yellow fever we should see a man
suddenly sick, and should assert,
This man is sick,
Therefore, He has the fever;
it might prove an exceptional case; he might be sick
of something else. This is a very open and familiar
illustration, but serves to indicate the dangers to which
it is liable. Almost all the processes of discovery in
natural religion are by means of the reasoning 8
posteriori.
Argument dfortiori.-This is a method by which
we establish a stronger conclusion even than ordinary
premisses need to warrant us. Thus,
A is greater than B.
B is greater than C.
A is greater than C.
That this conclusion is just there can be no doubt;
and that the form of it is not exactly that of the regular
syllogism, is equally apparent.
Hence, some writers have denied that it is a syllogism, or can be put at once into syllogistic form.




MODES OF USING SYLLOGISMS.         219
Easily to demonstrate the error of such, let us transpose the apparent premisses, thus:B is greater than C.
A is greater than B.
A is greater than C.
And replacing (greater than C) by X, we shall have
B is X.
A is B (because it is greater than B).
A is X.
This conclusion is a comparative proposition which can
be at once shown by replacing X, by its value, (greater
than C).
This reasoning a fortiori is very effective and
proper; and was used by our Saviour in his invectives
upon   Chorazin, Bethsaida and Capernaum, with
thrilling effect. So also is it forcibly used by the
apostle, to the Hebrews (x. 28), in the words:
c He who despised Moses' law, died without mercy
under two or three witnesses: of how much sorer
punishment shall he be thought guilty, who hath
trodden under foot the Son of God," &c.




220                  LOGIC.
CHAPTER XII.
A HISTORICAL SKETCH OF LOGIC.
(51.) Division of the Subject.
HAVING completed, in general outline, the study of
the formal Logic, in its present condition of exactness
and practical use, we are ready to go back to its
feeble beginnings, and trace it in its slow and trammelled movements from the days of the early Greek
Philosophy, through the applications of Roman
Science, the enlightening process of Christianity, the
darkness of the scholastic subtleties, the dawn and
advance of Experimental philosophy and the metaphysics of the eighteenth century, down to the controversies of our own day.
Nor are we yet to regard the science of Logic as
established beyond dispute, and fairly stationed among
its sister sciences; it is yet an arena of dispute, and
the most distinguished philosophers disagree, as has
been seen, even as to what it is, and as to what is its
scope.




HISTORY OF LOGIC.           221
It would be of great interest and profit to take
such a historical view in detail; but the limits of this
work will not permit it, and, besides, for all practical
purposes, the periods of the history naturally divide
themselves into four.  These so much transcend all
others in interest and value, and so absorb the events
which just precede or immediately follow them respectively, that they form the plainest and most convenient method in which to present the History of Logic.
They may be marked by the titles1. Aristotle.
2. Christianity and Logic.
3. Bacon, and the rise of Inductive Science.
4. The present system.
1. Under the first may be classed all the efforts of
the human mind in the arrangement of a canon of
reasoning, in that early time when knowledge, preceding method, was only seeking in darkness and obscurity that system of laws and principles by which
alone knowledge may be made available. Around
Aristotle, too, cluster the great expansions of science
which were due to the conquests of Alexander, and
the great kingdoms of his successors.
2. In the coming of Christianity, Logic found not
a rival, but a guide, and in the early'church it was
the weapon of their spiritual warfare.  To the church,
as the representative of Christianity, is due much of
the error as well as the good of scholasticism.




222                  LOGIC.
3. Logic was the servant, the ill-used servant of
Inductive philosophy, and owes much of its long bondage and oppression to the illustrious founder of the
system of Experimental philosophy.
From these considerations, it has been assumed that
we are better able to look into this history now that we
are acquainted with the scope of the science; otherwise
we might fall into the same error, by reason of the
honourable company in which we should find ourselves.
4. Since the time of Lord Bacon, and perhaps by
reason of his example in condemning the syllogism,
Logic has been degraded from its position as the controller of the reason on all subjects, and has been so
intermixed with Mental philosophy as quite to lose its
identity, and be miscalled by its own name. This was
its condition during the eighteenth century. In the
nineteenth there have sprung up many champions of
Aristotle and the syllogism, among whom first in distinction is Archbishop Whately. The universal principle of reasoning has been rescued by him from oblivion and degradation; and Logical science, although
still maligned and fiercely attacked, seems ready to
take its permanent place among the great Elementary sciences of human investigation and instruction.
(55.) Aristotle.
It must be considered that the progress of such a
science as Logic was necessarily gradual and slow;
that from the beginning, men had been contemplating




ARISTOTLE.               223
the operations of the reason, or were making vain but
progressive efforts to distinguish the exact functions
of the reason, among the mazy elements of the human
intellect. Many men had collected much material,
which lay floating in a chaotic state upon the great
deep of the human mind.
The logical doctrines of conception as expressed
in terms, of judgments as formed in propositions, were
known to Socrates and Plato. Indeed, Zeno the
Eleatic, who is mentioned as the inventor of Dialectic,
had invented logical puzzles which required an investigation of the laws of thought, and that caused a
race of so-called teachers of Dialectic to spring up
in Greece.
So the first movements in Logic were trammelled
by the ignorance and empiricism of those who called
themselves teachers.
The experience of our own age has taught us that
true science is more impeded and injured in this than
in any other way. A whole class of speculative logicians in the early times went by the name of Sophists.
We are accustomed to hear the Sophists spoken of
in terms of contempt, and sophistry has come to mean
Fallacy. But we should err very greatly, as many
in all ages have erred, if we regarded them as wholly
evil. The most enlightened writers of modern times
have demonstrated, that much of the odium which




224                  LOGIC.
attaches to the name, belongs really to the abuse of
their art; they were paid teachers,-among whom
are enumerated Protagoras and Gorgias,-whose duty
was to train up young men for the duties and pursuits
of public life. The character of the Greeks, who
were fond of riddles and disputes, and the errors of
the age, led to their real sophistry, and their abuse of
the rhetorical art to make " the worse appear the
better reason;" after that, their efforts were not for
the purpose of widening the range of knowledge
and truth, but really served to check these, and thus
give a free course to fallacious reasoning.
The Logic of Euclid consisted in negative proofs;
his design was, in encountering an opponent in controversy, not to attack his premisses, but his conclusion.
Chief among the early logicians, as he is distinguished among the sages of the world, was Socrates.
Much interest and sympathy attach to the virtuous
and heroic life, and the tragical fate, of this wise and
good man; but it is principally by his philosophy and
logic that he has been useful to the world. Keeping
in view always before his numerous scholars, the
dignity of Logic as a science, and the loftiness of the
reasoning powers, he guided the logical processes by
what is now called "6 common sense.",a This is implied
in Cicero's declaration, that Socrates brought philo



ARISTOTLE.               225
sophy from Heaven to earth. Xenophon, likewise, tells
us in his'Memorabilia,' that when he wished to
form a decision on any subject, his reasonings always
proceeded from propositions generally assented to or
understood."* Condemning the errors into which the
Sophists had been led, he claimed Truth as the real
aim of reasoning, and established in all his arguments
a high principle of moral responsibility. The analytic
process was that mainly employed by Socrates; and
thus, when Plato appeared, he found the science of
Logic, and the art of Dialectics, presented by detached and isolated views, as the result of previous
investigations. The analysis had only prepared for
the synthesis.
The plan adopted by Plato was the Synthetic
method, and by this he worked out many great results.
Perhaps the best feature in the Logic of Plato was
that on approaching the science, he tells us to keep
the mind free from all preoccupations and preconceptions: he declared, as an axiom, that," Ignorance is
the true start point for Science." Disputing the assertion of the earlier philosophers that sensation was the
foundation of truth, he proved it to be one of the
instruments by which truth is arrived at. Without
stopping to give a sketch of his system, we may state
that his Logic and theology are so intimately connected, that we may judge of the vigour of the one
* Blakey's Historical Sketch of Logic, p. 24.
P




226                  LOGIC.
by the developments of the other. He proved the
existence of a Deity, who was the measure of all
knowledge, the centre of all truth; and in mysterious
language he declares that this centre is c the beginning, middle, and end of all things." But Plato was
to be eclipsed by a greater mind; in fact one of the
greatest minds the world has ever seen.
When much material was thus collected, when
many vague theories had thus been started, and when
crowds of ignorant pretenders had arisen to be converted or silenced, Aristotle came to create a new
system-to enlighten, to harmonize, and to sweep away
all the errors of the Dialecticians and the Sophists.
He, who was to. correct the characteristic errors of
the Greek philosophy, was himself a Greek. The
Greek mind was eminently a curious one. All the
speculations of philosophy, all the systems of Ethics,
were directed apparently and nominally indeed to the
discovery of truth; but if they reached, by specious
arguments, a pleasant conclusion, it mattered little
for pure truth. They contented themselves with the
fruits of their system, once that system was established.
The Athenians were characterized by the apostle
as "s spending their time in nothing else" but the pursuit of novelty; and they were but the types and
representatives of the other states and cities of




ARISTOTLE.                227
Greece. There are in the early Greek authors many
corroborations of the apostle's assertion.
Aristotle, building upon the combined foundations
of Socrates and Plato, discovered many new principles and established new rules, until he had elaborated
the system of Logic which we have at this day.
His Logical works, published in full under the title
of ",Aristotle's Organon," comprise the following
works: 1. The Book of the Categories; 2. Of Interpretation; 3. The Prior Analytics; 4. The Post
Analytics; 5. Topics; 6. Of Sophisms.
Of these, the most important are " The Book of the
Categories," and both c4Analytics."  We shall proceed directly to explain their meaning.
He drew the true and somewhat nice distinction
between Logic and Rhetoric, and established the fact
(a fact not yet learned by many who call themselves
logicians) that Logic is not concerned with the truth
of propositions, but only with the reasoning upon
such propositions as are given into its charge. If
the premisses be true, then Logic will give a true
conclusion; but if the premisses be false, Logic gives
a false conclusion; but in this latter case the Logic
is as good, the argument as valid, as in the former.
In establishing his dictum, which we have assumed
to be the universal principle of reasoning, he laid
down the general law of Logic, a law which has been




228                  LOGIC.
misunderstood and misinterpreted, for this dictum
was not a model for common arguments, but simply a
test for all.
As the Greeks looked for truth and found that
Logic did not impart it; that before Logic could be
used th6y must be possessed of premisses, which premisses were given them  either by intuition or by
observation, i. e., induction,-they either abused Logic
for not doing what it could not propose to do, or else
injured it much more than their abuse could do, by
using it as a vehicle for false philosophy and mythic
religion. They took, to save themselves the trouble
of laborious induction in search of premisses, the
vagaries of their own quick, joyous and disputatious
minds, and thus produced monstrous and absurd conclusions, which, since their Logic was valid, they felt
satisfied to consider as true.
The union of this Grecian spirit with the equally
vague and fantastic imagination of the Orientals, with
whom by conquest they became acquainted, further
corrupted their intellects, and robbed Logic of its
true character and mission; leaving the whole domain
of Philosophy without the true guide of Reasoning.
Let us now look in turn at the logical works comprising the Organon.
The Categories.
We ar.e in the habit of using the word category, for




ARISTOTLE.               229
example, we speak of a person or thing being but in
this or that category; the word and its use we owe to
Aristotle. His categories are ten in number. They are
not all now considered of importance in classification,
but are still worth an explanation, as the original system, from which, by careful elimination, we have produced our own later classifications.  The categories
were supposed to imply answers to all possible questions concerning a term, expressing an act of apprehension: i. e., all of which we can have any knowledge.
1st, Substance. 2d, Quantity. 3d, Quality. 4th,
Relation.  5th, Action.  6th, Passion.  7th, The
Where. 8th, The When. 9th, Position, in space.
10th, Possession.
The categories may   be thus more fully explained:1. SUBSTANCE may be defined that which is in itself,
which may be conceived as existing by itself. This
is divided into spiritual and temporal; and subdivided
according to classes, genera, species, &c.
2. QUANTITY may be translated how much, or
how great, and by implication, as to time, how long.
Thus, under the head of Quantity, we have the three
special considerations of Number, Magnitude and
Time (as to duration). Number, we know, is either
abstract or concrete, as when we speak of a number
disconnected with any objects, or, of a number of
20




230                  LOGIC.
objects or things. Thus, quantity, as a category, covers
the science of arithmetic. Magnitude is either linear,
superficial or solid; and thus its genus quantity covers, likewise, the science of geometry. Time is either
permanent or successive, and is used to indicate the
movements or conjunctions of Number and Magnitude.
3. QUALITY describes the kind or sort of which a
thing is; and is subdivided into tlabit, or a quality
induced by frequent repetition of the same act, as
virtue, vice, &c.; Inherent nature, as man's reason:
From these grow the many subdivisions of colour,
sound, hardness and shape.
4. RELATION is the consideration of two or more ideas
with reference to each other. The first idea of two,
is called the relative, the second the correlative, as
prince and subject. master and servant.
5. ACTION has a double meaning: it is at once the
exertion of power by one body on another, and the
effect produced by such an exertion.
6. PASSION is the endurance of another's action.
7. THE WHERE includes the three meanings which
we express by the words where, whence and whither:
as in Philadelphia, from New York, to London.
8. THE WHEN has reference to the exact period
of time, and not its duration, which, as we have seen,
belongs more properly to quantity.  The When may




ARISTOTLE.                231
be expressed by the phrases to-day, to-morrow, a hundred years ago.
9. POSITION has reference, not to the place where,
but to the posture in which a body is found, as lying
dozn, standing up, kneeling, &c. The question then
is, how did you find it? not where?
10. POSSESSION has reference to something belonging to the object, or placed upon and clothing it; and
as a category, covers all questions concerning the
rights of property.
Of these categories, it will appear that substance
stands apart from the rest, in that it is sensibly existent, and they are all attributes of such an existence;
It will further appear, upon examination, that Quantity and Quality are essential attributes, i. e., belong
to the essence of the object necessarily; while ]Relation, Action, Passion, The Where, The When, Position, and Possession, are accidental circumstances
which may be dissociated from it.
To render this clearer, for facility of reference, we
state it in a tabular form. In this table we place all
the explanatory parts as by the rules of division before given, but number the categories, that the eye
may at once rest upon them.




232                     LOGIC.
The object or existence expressed by a term.
Attributes belonging                     1. Substance.
to the substance.
Circumstantial.                   Essential.
4. Relation.         2. Quantity.       3. Quality.
Number.   Magnitude.     Time.
r.. —-. —---------             %
Habit.   Inherent nature.  Shape, &c.
5.Acion. Passion.  TheWhere. 8. Thehen Position. 0.ossession.
5. Action. 6. Passion. 7. The Where. 8. The When. 9. Position. 10. Possession.
Aristotle asserted, that everything which could be
said of any subject is included in one, some, or all of
these categories, and his own illustration of their use
is one of the simplest which can be found. It was as
follows: —    Substance, man; Quantity, one; Quality, white; Relation, greater; The Where, in the Forum; The When, yesterday; Position, sitting; Action, whatever he may be doing; Passion, whatever
may be being done to him."
It is under this first attempt at method, that the
sciences began to range themselves in classes, and by
this all other systems of classification seem to have been
suggested. Thus: Substance is the foundation of all
Physical and Historical investigation: Quantity, the
subject of Mathematics; Quality, of Medicine; Relation, of Ethics; Action and Quantity, of Astronomy,
Music and Mechanics: Passion and Action, of Elec



ARISTOTLE.                23o
tricity; the Where, of Geography; the When, of
Chronology; Position and Quality, of Sculpture;
]fabit and Position, of Painting: and so each art and
science would be found to range under one of these
singly, or more than one, when combined.
The books of ct Prior and Post Analytics" originate
and develop his system, of the doctrines and use of the
Syllogism.  They have been the resort of all writers
on formal Logic since his time, and there has been but
little alteration in his method. Aristotle established
but three figures of the syllogism, the fourth being
afterwards added by Galen.
In his book of Topics, he discusses the subject of
Predicables, or Classes, and establishes the expression
of a predicable to be in four ways, i. e., by genus,
differentia, property, and accident: in these he implies the species, since we have seen that if we add
the differentia to the genus, we obtain the species.
In his book of Sophisms he states thirteen Fallacies,
as including all those which can bear a syllogistic
form.  Six of these refer to the words used, and are
called Fallacies in dictione, and seven consist in the
matter of the propositions, and are called Fallacies
extra dictionem.
The logical works of Aristotle seem to have been
providentially preserved. Transmitted by his disciples from hand to hand, they were at length concealed in a vault during one hundred and thirty years,
20 




234                  LOGIC.
until they had mouldered into an almost illegible condition. Restored from this condition, they came by
the fortune of war into the hands of a Roman general, and thus were given a second time to the world.
We cannot pause to notice all the changes attempted
in Logic and Philosophy from this time until the Christian era. After the Peripatetics, came Pyrrho of Elis
and his Sceptics, who seem to have employed Logic to
deny the possible attainment of pure truth. They
embodied their system in Ten Tropes, or logical rules
for the government of mind in the search of truth.
Their doubt led to what they termed a suspension of
judgment, rather than a positive denial.
Of the Epicureans and Stoics, it may be said that
they aimed at the establishment of no Logical system,
but rather a few tenets in the shape of propositions;
by these, as doctrines, they guided their course.
The tenets of Epicurus may be comprised in the
assertion that," whatever is useful, pleasant and delightful, is true." This is to assert that man's senses
and bodily appetites are the only test of truth. These
have been called his "c emotional criteria."
The Stoics rejected the categories of Aristotle and
adopted four of their own: and attained the conclusion
that " pain is no evil:" a philosophic stretch of the
imagination which has given its name to an unshrinking endurance of pain and evil.
Very little transpires concerning Roman systems




ARISTOTLE.               235
of Logic. Although Cicero, Maximus of Tyre, and
Galen lay claim to the title of logicians, the logical
system of Aristotle was adopted by them all:
Rhetoric became the more valued and important
study.
The history of Logic, then, from the time of Aristotle to the coming of Christ, is not a history of
change; but the logic however unchanged of Aristotle
had been most unworthily used. No longer the guide
and test of just reasoning, it became the vehicle of
ingenious falsehood, was made to support any theory,
and gave power to its possessor c" to argue on both
sides of any question."  To satisfy curiosity it established any paradox, and one being made the premiss
to another, the error was multiplied 4 in infinite progression undefined." It was not the logical system,
but the mind of man, which needed purification: not
abstract propositions, but the matter they contained,
which demanded scrutiny.
We shall see also that the misconception of the
sphere of Logic was equally fruitful of error long
after the establishment of Christianity, and that it
has remained for the nineteenth century, notwithstanding the utmost resistance of many learned but
dogmatic philosophers, to give to Aristotle and his
system their true place in the domain of science: an
instauration, not by one man; a new Organon, not
the product of one teeming brain, but the tribute of




236                 LOGIC.
Philosophy, inductive and deductive, to Aristotle,
the great founder and framer of that system which
alone controls the unbridled reason, and sends pure
truth into the channels of usefulness and practice.
But, meanwhile, the coming of Christianity was to
produce great marvels in the domains both of Logic
and Philosophy.
(56.) The Logic of Christianity.
The Logic of the Grecian schools had been the
guide of man's Reason, but now it was itself to be
brought into companionship with a higher human
attribute, Faith. Premisses were no longer to be
sought by the ordinary means of evidence, but to be
supplied in a new and marvellous manner. Christianity combined this new element with Philosophy,
and taking the art of Logic as the vehicle of its
great truths, used it in a manner at once beneficial
and practical; putting an end, as it seemed, to the
controvertsies and paradoxes which had beguiled and
engaged the Greek and Roman mind.
By this new tutelage of human reason, Christianity
produced an immediate and startling change in Philosophy, by opening the Finite upon which man may
use his reason, as well as indicating the Mysterious
and Infinite to his faith.
As much as we may despise the Greek systems of




LOGIC OF'CTRISTIANITY.        237
speculative Ethics, upon which they employed their
nobler Logic, we must remember that they were the
gropings of men in the dark, pursuing a faint glimmer
of light in the hope that it would lead them into the
full sunshine and free air of Truth. They had no
revelation of intelligible fact or of mystery. The
efforts of Plato to attain to different degrees of knowledge which he calls —t the absolute, the probable,
the imperfect," the Politics and Ethics of Aristotle;
the bold dicta and quiet endurance of the Stoics;
the c" emotional criteria of Truth," propounded by
Epicurus, and so much abused by his disciples,-were
all vain attempts to arrive at that knowledge which
could come to man only by miraculous revelation.
God vouchsafed no such revelation to them; it is no
cause of wonder that they erred greatly without it.
This, then, was the crowning glory of Christianity,
that it gave to man pure Truth, and furnished him
with a world of new facts upon which to reason, of
glorious propositions upon which to try the powers of
his Logic. The language of God to man, was, first,
c" Come, now let us reason together," and thus the
whole system is based upon reason; and afterwards, as
if thus founded surely and safely, " Believe, and ye
shall be saved."
Unlike the Greeks, the Jews had always possessed
this revelation, in a ceremonial and progressive form.
Their own Scriptures had disclosed to them not only




238                  LOGIC.
the true story of man's origin and fall, but of God's
supremacy, and his gracious design of restoration,
and their prophets had told them with a heavenly
Logic of Type and Symbol; premiss upon premiss in
glorious abundance, of that certain conclusion, the
advent of the Messiah.
The c" fulness of time" came, and the event fulfilled
the prophecies, the conclusion completed the premisses.  Christianity brought philosophic as well as
religious light.
By a strange infatuation, they who had thus awaited
His coming, refused Him when IHe came; and since
He could not be the glory of His earthly "people
Israel," tIe was, in a truly philosophic sense, " a light
to lighten the Gentiles."
In three centuries, He had been eagerly embraced
by Heathen Rome, and the Logic of Aristotle, freed
from its vile and improper uses, and used as the
propounder of a full and pure creed, was applied with
great power to the spread of the Christian religion.
Where false premisses had been ignorantly used, leading to a false conclusion, or where false conclusions
had been improperly deduced from true premisses,
everything for a time was changed. Truth was everywhere triumphant, and its reign seemed to be eternal.
Such was the first influence of Christianity upon
Logic.  Containing in itself nothing repugnant to
reason, it gave a host of new and glorious truths,




LOGIC OF CHRISTIANITY.         239
fresh from the mouth of God; it simply threw away
the vague speculations, the unsound paradoxes, which
had been heretofore used as premisses, and took these
new truths to reason upon. In the teachings of our
Saviour and the apostles, it need scarcely be remarked,
not only that every statement is true, but that every
argument is valid.
On the other hand, Logic, turning gladly away
from the subtleties and absurdities of mythical philosophy, pressed forward with ardour in the task of
systematizing and promulgating the new doctrines of
Christianity.
In this manner arose the logical systems of the early
Christian writers and apologists, known as c the
fathers." There is, indeed, error to be found in their
uninspired writings, such as we should expect in all
human productions, but from Justin Martyr to St.
Augustine, one object of their writings seems to have
been the harmonizing of Christian doctrine with the
Logic of Aristotle, and thus while they preached the
truth, to show at once the union and true relation of
Reason' and Faith. How well they succeeded as a
class, may be seen at the present day from the growing interest in their writings which is manifested by
all who are interested in Religion or Philosophy.
Never forgetting that they were surrounded by enemies
and error, one part of their works was fiercely controversial, always keeping in view the elenchus, and




240                  LOGIC.
warily observing an opponent, or rather the many opponents who were scrutinizing their deeds and words.
Where, in the old system of Philosophy, Sensation
was the starting point, and man must evolve philosophy from within himself-they established Revelation
as the centre and starting point, and would draw, by
the same logical formulhe, all true philosophy from
God. From this time, Logic was inseparably connected with theology: the Church ruled the world.
The Christian Church had, in its union with the
Roman empire, a strength and stability from which
great philosophic results must have sprung; but just
when they were framing this glorious system at once
of Religion and Philosophy, the Roman empire of the
west fell under the ruthless attacks of the Northern
barbarians, and the Church was temporarily paralyzed
by the shock. For centuries after, the great efforts
of the Church were directed to the attainment of a
firm social basis, and political power.
We have already stated the connexion between
Logic and Philosophy. They may be dissociated, but
are both then useless. Thus, indirectly, Philosophy
has exerted such an influence upon the uses of Logic
that it is important to trace the systems with which
Logic was combined, and to promulgate which it was
used after the establishment of Christianity. Most
of the Christian writers investigated the subject of
the human reason, and studied the Logic of Aristotle.




LOGIC oF CIRISTIANITY.          241
As might be expected, so magical a transformer as
Christianity was not without fierce philosophic opposition.  With equal steps Scepticism and Heresy advanced.  Those who were doubters before where only,Science was concerned, were doubly doubters when
told of Christian mysteries.
The representative of the new sceptics was Sextus
Empiricus, who lived in the beginning of the third
century, and who was but a new incarnation of Pyrrho
of Elis. Unwilling to receive, on primc facie evidence, the truth of the new revelation, they had
fallen back upon the old material, and had worked to
the same results as the Greek philosophers; they
turned their backs on the light,-which admits of no
better proof than the physical light of day,-and
walked into the cave of darkness, of doubt, and, in a
religious view, of despair.
The scepticism of Pyrrho, three hundred years
before Christ, was consistent, and well deduced when
compared with this, and yet the Greek academicians,
we know, had convicted him of absurdity.   " Because everything is contradictory, everything is false."
Now, if this be true, the axiom itself is false, and so
the sceptic, thrown upon the horns of a dilemma, must
grope again, in vain, for new proofs of falsehood, and
new certainties of doubt.
Of the Neo-Platonic   Eclectic or Alexandrian
21               Q




242                  LOGIC.
school, the object seems to have been to unite the
Greek philosophy and Oriental dogmatism into one
system; but it was a false and feeble combination,
fated to a speedy and ridiculous end.
Its metaphysics, as prepared by Plotinus, was the
attempt by the combination of heathen obscurities to
attain to Christian light; its theology, as reduced by
lamblichus, was a strange retrogradation from the
Scriptures, which revealed the person and word of
God, to the ridiculous deities of the Pantheon; and
its Logic, of which the great Porphyry was the applier, was an attempt, by the use of the Aristotelian
system, to establish all these errors, at the expense
of the fair fame and even of the existence of Logic.
Nor in the singular applications of Christianity to
Logic must the Gnostics be forgotten. Their name
indicated their creed; yvro5,, knowledge, as opposed to
faith: Naked Logic, stripped of its armour, was made
again to do duty in the ranks of the Prince of Darkness. Gnosticism ", took such portions of the Gospel
as suited its views or struck its fancy; but these rays
of light they mingled with such a chaos of absurdity,
that the apostles would hardly have recognised their
own doctrines."*
The greatest, perhaps, of the indirect evidences of
* Burton's "Heresies of the Apostolic Age,"' p. 15, quoted by
Neil.




LOGIC OF CHRISTIANITY.          243
the truth of the Christian religion is, that in spite of
the false systems which sprang up to oppose it, it has
steadily and mightily prevailed; in its progress it has
purified human philosophy, and unfettered Logic;
but it did not accomplish this without fierce contests;'it was to come upon dark days, in which it was the
only glimmer of light; days in which the misuses of
Logic were no longer to be confined to profane systems-or heretical creeds. Unfortunately, they are
constantly found in the career of the Christian Church
herself. As an institution designed to convey Christian truth to all generations, it would be supposed
she could have little to do with the conflicts of the
world around her. Not so. As soon as the Church
was struck with the ambition for power, the lust for
empire, she began to pervert facts and degrade Logic.
The days of the truthful and zealous Fathers had
given way to that of ambitious prelates, and greedy
ecclesiastics of every degree.  It was the dark age
of Logical Philosophy.  As long as she was weak,
and feared lest the brute force of kings and barons
should crush her power, and check her increasing
influence, she asserted the difference and distinction
between the secular and spiritual; and thus maintained herself as the spiritually strong; but as soon
as she had acquired strength and control, in her spiritual capacity, she claimed a share in temporalities,




244                  LOGIC.
and put her strong hand upon all the kingdoms of the
world: she usurped the power and province of her
divine Master, and said,,, By me do kings reign, and
princes decree justice."
Claiming infallibility at first, only in doctrine; at
length, in general opinion; she trammelled science,
expurgated literature; controlled, or attempted to
control, the thoughts of men, and placed the gauntleted hand of despotism upon philosophy, demanding
that it should speak only at her will and by her
dictum. It was an evil day for the Logic of Aristotle,
when this corrupt Church claimed it as the framework of her ethical system, because she used it only
to draw from false premisses, false conclusions. It
was a happy thing for the Church that Logic did not
look beyond the form of the expression, or her machinations would have been more thoroughly exposed.
Assuming premisses slightly false, the Church reasoned to conclusions monstrously false. From probable
premisses, it arrived at certain conclusions: and not
unfrequently was it guilty of Logical fallacies, as
well as Zicaterial. A slight and cursory examination of the sophistries of the Church in the Middle
Ages, would show us how Logic was degraded and
misused; but we shall content ourselves with a few
words upon the rise and progress of Scholasticism,
the form which seems, in its changes, to present at
once the Philosophy and the Logic of Christian




LOGIC OF CHRISTIANITY.         245
Europ in the Middle Ages. That the Church should
have espoused the formal Logic of, Aristotle was not
entirely without good: for as the Church espoused
it, it became a popular science in the new schools
which arose wherever the Church went. Thus arose
in the foundations of Charlemagne, the Schoolmen,
whose object was to connect or harmonize the elements
of all truth which remained to man after the fearful
convulsions in the Western Empire; a restoration
in Philosophy similar to that of Charlemagne in donzinion.
The duty of the Schoolmen seems to have been to
determine what was Philosophy, and how much it had
to do with Religion. In such a question Philosophy
would surely hide its diminished head. Distinguished
Popes, like Gregory the Great, were for proscribing
all secular studies, and making theology the only study
of the world:-in order to effect this purpose, we
know that he destroyed valuable manuscripts. A host
of mad enthusiasts, called Saracens, had destroyed a
wealth of history and science in the library of
Alexandria; but the very darkness of the times was
significant of the coming dawn.
The first era of Scholasticism was the adoption
of Logic as the form and vehicle for Religion, and
thus far they were in the right path.
The second phase was the attempt to unite Religion
21.




246                  LOGIC.
and Philosophy, and this produced new champions of
Realism.
The third phase was an opposition: Religion and
Philosophy were rudely dissevered, and this produced
Nominalism.
If, now, we separately consider these three phases
of the Scholastic philosophy, we shall perceive that
the first was the just and true one, and that the succeeding ones were learning which had to be unlearned.
That part of the Greek system which could be
made theform and vehicle of religion, as it is of all
correct reasoning, was only the Logic. To apply that
to the service of Faith, was just the first design of
Christianity towards Logic, and thus far the Schoolmen were right; indeed, it would seem ignorantly
right; for while using the forms which constitute Logic, they still persisted in calling many other parts of
the Greek philosophy by the name'of Logic, and
thus making Logic bear the blame which truly belonged to the errors, obscurities, and absurdities of
exploded systems of metaphysics, theology, and
morals.
This is apparent in the works of Alcuin, the contemporary and friend of Charlemagne, and especially
in his dialogues on G Grammar, Rhetoric, and Logic."
So, too, Erigena lays down the logical rules of Division, Definition, Analysis, and Demonstration, and
asserts, that by the use of these man may attain te




LOGIC OF CHRISTIANITY.         247
truth, manifestly begging the question, and asserting
that man attains to truth by arriving at truth. There
must have been a great superiority of intellect about
this man, however, as we know that he was regarded
by the Church as dangerous, and his works afterwards
placed in the " Index Expurgatorius."  More lofty
was the simple distinction of St. Anselm, that there
are but two modes of Cognition-Faith and Science;
and grander yet the idea, "c that Science begins where
Faith ends,"-in the bosom of God!
But let us consider the second and third phases.
Nominalism and Realism were but the reproduction
in the ninth century of the old Platonian controversy,
already referred to. Nominal and real were the abstractions of what we call respectively universal and particular.
When I speak of a single man, and point him out,
I designate a real existent individual; when I speak
of man, as a common term, is there a real entity corresponding to the word?  The realists said Yes! the
nominalists said No! it is but a name to indicate numbers. This had been the origin of the controversy.
Plato, with his divine but vague philosophy, had
asserted that there was a real existence, an archetype
in the bosom of God corresponding to the name of a
class, as man, angel; Aristotle, that they were only
generalized names from many individual abstractions.
And thus these great parents of Logical Philosophy




248                  LOGIC.
set the example of wrangling to their myriad children
of the schools.  It is curious to see how such a dispute first connected itself with religion. It was thus 
the question seemed to involve another and a more
important one, viz.: s what is the foundation of
human knowledge?" Roscellinus of Compeigne, who
lived in the eleventh century, was the originator of
the new controversy in the Middle Ages between the
realists and the nominalists.  He was a fierce nominalist, and as this led to supposed heresies, he was an
object of persecution on this account. As warmly
was the cause of realism espoused by William  of
Champeaux; and throughout the schools there was a
word-war of great fierceness on this subject.
Passing over the quarrels of the schoolmen until
we reach the time of Roger Bacon, and thus neglecting many great names in the history of Logical Philosophy, we are struck with the power of his experiments
and analysis, and the manifest fact that he deserves
the name of the founder of Inductive Philosophy; that
his "4 Opus Jlajus" may justly be considered the
precursor of the," Novum  Organum" of his more
illustrious namesake, Francis Bacon.
Disgusted with the categories of Aristotle as trammelling an ardent physical scholar, who must establish
categories for himself by experience, he considers
experiment, based upon constant observation; the only
rule for philosophy, and in his works in the labora



LOGIC OF CHRISTIANITY.         249
tory and with his pen we discern the first dawning of
the day of Induction.
For awhile, as was very natural, formal Logic fell
into disrepute, and gave way to experiment in physics;
and from that day down to our own times, there has
been but little appreciation or understanding of the
art of reasoning, although it has been constantly used,
and constantly ignored. Like savages, who breathe
the invisible air around them and are not aware of
its existence, so minds of all kinds and calibres have
used the Logic which they found established as the
vehicle of thought, without knowing where to make
their acknowledgments.
At length the Logic of Aristotle received a shock
ruder than any which it had yet experienced.
Long used by the powerful Church, and long
subtly applied to many sophistries by that Church;
it had been accused also of becoming corrupt; errors
and crimes, not its own, were imputed to it; it was
contaminated by the theology, stained by the practices, monopolized by the avarice of the Church; and
was conseqently to go through two distinct phases;
first, to be punished with that Church;-and, secondly,
to be disefithralled and separated from it.  The first
took place at the Reformation, of which premonitory
symptoms had been seen by Roger Bacon in England,
in the 13th century, and distinct signs by Wiclif in
thne 14th. In this, both Bacon and Wiclif were. etfi



250                  LOGIC.
cient instruments.  Still, the battle cries were, nominalismr and realism.  Realism suited the blind belief
of the Church, and nominalism the unmasking dogmatism of the reformers.
Peter Ramus, in the early part of the 16th century, having published a thesis, controverting some
of the chief tenets of Aristotle, and disparaging his
entire system, which system it will be remembered
had been adopted by the Church, the Pope condemned
him and his book as "s rash, impudent and ignorant;"
whereupon Boileau put forth a satire in the form of
an humble petition, craving c an interdict against
Reason and Experience, because they would not
submit to the laws of Aristotle."  This satire and
ridicule gained the day; and when the shock came
paralyzing the Church, there were weightier questions
of concernment than those of the schools. It is a
most interesting inquiry to examine the logical views
of the Reformers. As a matter of course, they condemned in the m'ost sweeping manner, the logical
system of Aristotle, endorsed by the Church, and all
", scholastic dialectics." Perhaps the views of Luther
are the fairest illustration of their system, if it may
so be called; and Luther was not ignorant of Logic,
that being one of his branches when a professor.
But in a fervour of enthusiasm, he seems to ignore
rather than disprove the doctrines of Aristotle and
the schoolmen; asserting with a certain unanswerable




LOGIC OF CHRISTIANITY.          251
air: —, In divine things, the Father is the Grammar,
for he imparts words; the Son is Logic, and suggests
order, arrangement and sequence of ideas; the Holy
Ghost is Rhetoric, who persuades and presses home."
And so charging the schoolmen with having given
up the substance for silly trifles, he goes on to say
that, ", the Decalogue is the doctrine of doctrines; the
Creed the history of histories; the Lord's Prayer the
prayer of prayers; and the Sacrament the ceremonies
of ceremonies." In short, his purpose, and that of the
other Reformers, seems to have been to find everything in the Bible, and to seek for nothing out of it.
This is not to be wondered at; it was the period of
enlightenment; first, the dark places must be illuminated, before the errors could be made manifest;
and the Reformers were right in their views for the
times and to effect the purpose desired.
The light which was thus produced, soon began to
shine with great power and brilliancy, and its effects
were no less to be observed in philosophy than in
religion and morals. The kingdom of Nature lay
exposed to its searching beams, and invited the
Naturalist to examine and comprehend her works;
the Mind, disenthralled and opened, was no less a
subject of most interesting study; the reformation in
religion was but the precursor of the birth of Experimental Philosophy, and the Reformers were heralds of
Lord Bacon as its interpreter.




252                 LOGIC.
(57.) The Logic of Experimental Philosophy.
In order clearly to understand the origin of Experimental Philosophy, we must remember that the
union of Christianity and philosophy had been fairly
tried and had proved unsuccessful; scholasticism,
fulfilling its true purpose, but not that designed by
its founders, in gradually emancipating man's reason
from the thraldom  of the schools of theology, by
manifesting its own imbecility, had failed in its first
design,' that of intellectual progress.  Now, an element seems to have been introduced into philosophy,
which till then had been considered unimportant;
and that was observation and experiment; or, to use
the term by which we have expressed the methodical
and successive observations of such phenomena in
nature as will lead us to general laws,-Induction.
Aristotle himself had stated the value of induction
for the discovery of new truth; and men, in all ages,
had used it as an exercise of common sense in their
ordinary conduct; so that it must not be supposed
that in any sense, Bacon is its inventor. Ie only
applied it by system to natural science.
Logic, which is the vehicle of truth in its intellectual passage from premiss to conclusion, had only
reasoned upon the known and conceded:-mainly
from some general law to a particular example; now
its premisses were to be new truths aggregated aby




LOGIC OF EXPERIMENTAL PHILOSOPHY.    253
experiment; it was to reason from many particular
examples to the establishment of a general law.
This, then, let it be borne in mind, was the only new
duty which Logic was called upon to perform; and
this, had it been desired, she had always been ready
and able to do.
She had been the fearful servant of ecclesiastical
authority and-theocratic reverence; to argue without
permission of the Church, or otherwise than by
priestly dictation, was worse than vicious; it was
heretical.
But when the reformation in Europe had thrown
contempt on the authority of the Church, the intellectual bonds of Europe also were burst, and the
childhood of experimental philosophy began. The
unchangeable principle of reasoning was simply
applied to new subjects and investigations.
There were two great realms to be emancipated, or
rather released from prison and darkness: the realms
of Nature and Thought, or as they are ordinarily
called, matter and mind. The founders of the new
system adopted the same method for both, Analysis:
constant experiment and observation upon the phenomena of the outer world, and upon those of the consciousness within.
Bacon was the early interpreter of Nature; Descartes the analyzer of Thought. To each is due an
illustrious share of the developments in philosophy.
22




254                  LOGIC.
But Bacon is the more distinguished, because his investigations were made in every domain of nature;
and his system is at once more intelligible and popular
on that account.
The starting point of Bacon's philosophy was the
assertion that the universe is a great store-house of
facts; and that it is man's duty and interest, and it
ought to be his pleasure, to explore, discover and
understand these facts, not only in their isolated characters, but in their relations to each other and to the
universe itself. His experiments and his use of the
experiments of others, was to enable him to arrive at
general laws of the universe. Now, corresponding
with the world around us, that is, the world of Nature,
there is a world within us,-the world of Thought.
Let either be impaired or cease to exist, and in just
such a proportion is the other impaired or does it
cease to exist.
To unite them we have sensation and perception,
and the union is lost if sensation and perception fail.
The happy union, then, of Thought and Nature
would lead man to Truth, and to attain to Truth is
his highest aim. It will at once be seen that this
was the establishment, not of a logical, but of a
philosophical system.  But to proceed: the various
forms which truth assumes to inspire the faculties and
entice the pursuits of men, are called sciences, and
by an examination of multitudes of these phenomenal




LOGIC OF EXPERIMENTAL PHILOSOi HY.     255
fiacts, the true definitions of the sciences might be
made, their true relation determined, and a plan of
classification formed for practical purposes.
Such then, very briefly, was the aim of the new
experimental philosophy, a great restoration which was
proposed by Bacon in his Instauratio MIagna. With
it directly, Logic had but little to do; but that little
led men of science into errors, which remain to the
present day.
Without attempting to enter into the details of the
4" Great Restoration," it will be well to consider some
of the steps proposed by Bacon, as preliminary to it.
Finding, in his inquiries about facts, or phenomena,
that they greatly differ in importance; that some
are simple, others complex; some are easy of interpretation, others very difficult; he proposed a classication of the instances in which any phenomenon or
fact occurred, and this should be a sort of value scale
of the instances in which a special phenomenon
occurred.  These he calls prerogative instances, or
those cases of most importance to us in interpreting
a fact or a series of facts. He has stated twentyseven of these, from which we shall choose four,
as better illustrating their own meaning than it can
be done in other words.  Our purpose is not to use
these, but merely to indicate their nature and design.
I. Solitary instances, or those in which two or
more objects agree or differ in all qualities save one.




256                  LOGIC.
II. Forth-slzowing instances.  Under this head,
range those facts or instruments which show forth the
quality in question in the highest degree,; as a galvanic battery, in electricity, and a barometer in pneumatics.
III. Analogous instances. Those in which are found
objects bearing a resemblance of purpose or relation,
however unlike the objects themselves may be. Thus,
a camera obscura is analogous to the eye, and a system of waterworks to the heart.
IV. Crucial instances. There arie two probable meanings to the word crucial, as here used. It may be
the putting nature to the torture-crucifying her-to
wring from her her secrets, or it may have reference
to the way-side crosses, which at the parting of the
roads indicate the true direction to the traveller.
Franklin's electric kite might be called a crucial instance, in the first sense. Such also, in the second,
was Newton's law of gravitation, a finger-board for
ever to point to the true direction of investigation
and belief, concerning our solar system.
The other instances, which we cannot stop to mention, are designed to exhaust the classification of
experiments on facts, and to lead to induction; and
here began the danger and difficulty: it was here,
also, that the syllogism, which Bacon despised and
misunderstood, was, and always is, the only safe guide
of Philosophy.  For, suppose the facts ranging under




LOGIC OF EXPERIMENTAL PHILOSOPHY.      257
these instances to be established, how many of them
will give us the right to the establishment of a general
law, or a distinct science?  We have seen that, in
most sciences, we only attain to likelihood.  On account of human ignorance, the process has been this:
-we first establish a few facts: we then adopt a hypothesis or theory based upon them, i. e., jump at the
general law, simply in order to make a nidus for our
accumulating facts; and thus proceed to verify-if
the new facts will verify-our proposed theory. The
tendency of man's mind is so great, however, to repose
upon a darling theory, even if it be unsound, and
rather to seek-like an advocate-for such facts and
statements as will support it, than to look for just
proof, and in the absence of such to discard it,-that
induction has often led to grievous error. Many a
student has learned one theory of some part of Natural Science, and when he had just mastered it, has
been obliged to discard it for another.
In the consideration of Judgment, Bacon has given
special attention to the Fallacies which assail the
mind of man. These he calls idols of the intellect,
and in almost every case, since they are contained in
false judgments, they belong to the class of material
fallacies. But all these idols occasionally assume the
garb of logical fallacies.
These idols, or E&G&8C,, which Bacon calls " the deepest
fallacies of the human mind," are the sources of error
22*              R




258                  LOGIC.
which assail men in their investigations in Philosophy,
and which "must be renounced, and the intellect
wholly freed and purified therefrom," before we can
hope for healthful progress.  By the word idol,
Bacon means the prejudice which stands in our way
of receiving truth, and the bias of the mind from
which such prejudices arise.
But these idola will most clearly explain themselves: they are of four classes. Idola Tribus, Idola
Specus, Icola Fori, Idola Theatri; and with reference
to these, an author of his own time remarks: " The
temple which he purified was not that of nature itself, but the temple of the Mind; in its innermost
sanctuary were all the idols which he overthrew."
1. The idols of the Tribe are those which are imposed upon the understanding by the general nature
of mankind: in other words, they belong to the human
tribe, in its universal comprehension. Thus, he asserts
that men-as men-are quicker to be moved by cffirmative and active events than by negative and jprivative,
though in justice they should be moved by both. To
illustrate this, he tells the story of the Greek, who
was shown, in Neptune's temple, the votive pictures
of those who had escaped shipwreck, and when asked
if he did not now acknowledge his divinity, said," show me first where those are painted who paid their
vows and were then shipwrecked."
2. The idols of the den or cave spring from the nature




LOGIC OF EXPERIMENTAL PHILOSOPHY.    259
of each particular man, and grow out of his peculiar
nature both of mind and body;-these may also be
fostered or developed by education, custom or accident. The name is suggested by fancying the confusion and error of a man being brought out of a
dark den or cave into the full light and glory of
Nature. This finds its counterpart in the world of
philosophy, where men only emerge from the den of
their minds to find confusion and disorder in the
beautiful universe of God.
3. The idols of the markcet are errors which grow
out of words and communication, such as are the
pass-words and common coin of conversation and
intercourse in the market-place; and they imply, like
the idols of the tribe, a social organization, but on a
much more limited scale.  Instead of being universal
with men, they are errors which belong to a small
circle, like a crowd in a market-place, moved at the
sound of an orator's words, by a common impulsion
of prejudice, passion or other emotion.  These idols
are causes of the greatest disturbance, as they are
immediately connected with the naming of things,
" for words are generally given according to vulgar
conception, and divide things by such differences as
the common people are capable of; but when a more
acute understanding or a more careful observation
would distinguish things, better words murmur
against it."




260                   LOaIC.
Thus, many words in our every day use convey no
definite meaning to the mind; but have, in their very
indefiniteness, so many shades of meaning that they
are a constant cause of verbal fallacy. As special
reference has been made to such words in the chapter
on Fallacies (X.), it will only be necessary to mention
a few such to illustrate the idols of the market-place:
such is the word republic, which we have been apt to
confound with democracy; Liberty means either freedom or license, as its champions wish-and taste and
beauty have as many forms as there are eyes to see
or imaginations to indulge.
The last of the sources of error enumerated among
the idols of Bacon, are the idols of the theatre.
These he distinguishes from the others, as perhaps of
more social power and influence. Of these, he says,," they are superinduced by false theories or philosophies, and the perverted laws of demonstration."
They are comprehended under three heads:-Partisanship, Fashion and Authority.
Partisanship is the generic name under which are
found factions in politics and in religion-and under
whose influence wars of creed and caste have so often
desolated the world.
1Fashion is a kind of partisanship, which, however,
has few opponents, and no great rivalries; but which
pervades society from high to low. We do not refer
to its simple sway in dress, equipage and social life 




LOGIC OF EXPERIMENTAL PHILOSOPHY.     261
but to its more comprehensive dominion, over all the
works and thoughts of man, over art, science, religion. Great masses of men are herded like cattle,
and driven willingly in the train of this all-swaying
Fashion; resting their happiness here, and their hopes
in an eternal future, upon the dictum of Fashion.
As Fashion partakes of the nature of Partisanship,
so is Authority strengthened by an alliance with
both. This consists in blind obedience to an existing
control, and reliance upon it, without the use of our
own judgment.
As God, who has given man Reason, has made
some things higher than that reason, but nothing
repugnant to it, every theory of authority in Church,
in state, or in general philosophy is, of right, to be
examined by our reason, before we can accord to it
our belief. Reliance upon authority, without a due
understanding of its claims, is to treat our own moral
constitution with injustice, and to stop the wheels of
healthful progress, both of individuals and societies.
It was an increasing distrust of authority that
brought about the Reformation in the Church; that
exploded the scholastic philosophy and the superstitious practices of the Middle Ages; and that destroyed
the divine right of kings, with a host of evils which
appertained to it.  To examine the claims of asserted
authority is to investigate nature and mind-and to




262                   LOGIC.
do this, is to move forward to new and glorious victories in the domains of both.
In reviewing these error-sources, it is scarcely
necessary to remark that it is the abuse and not the
use of our words and associations which lead to them.
Thus, the idols of the tribe, would not be false and
deceitful, if man should concur universally and everywhere in just and truthful opinions; nor would the
den darken men's minds to the true light, if they
were capable of carrying into their meditation the
true elements of combination and just views of the
objects in the universe around them.  Heraclitus has
told us " that men seek the sciences in their own
narrow worlds, and not in the wide one."  Such is
the influence, but not the necessary consequence of
the den.
So it is easy to avoid the errors which grow out of
ambiguous words, such as those which mark the idols
of the market; by demanding just definitions, and
when such cannot be given, either agreeingfor argument sake upon one which is not just; or, declining
to argue at all where the very question is involved in
obscurity.
We may observe, concerning the idols of the
theatre, that partisanship has its good as well as its
evil character; and that to championize the right is
noble and just; it is, however, even in such a cause
that its tendency is to extremes.




LOGIC OF EXPERIMENTAL PHILOSOPHY.      263
So fashion, crowds of whose votaries are miserable
and self-tortured, is incident to man's social character,
and is productive to those who use it aright, of method
and comfort, and success. Although fashion has
done much evil, it could not be spared in our social
or intellectual systems. Nor must Authority, however formidable the name, be accounted of slight
importance; for under just authority are ranged
obedience, order and wholesome discipline; without it
government would be anarchy, and education would
be a curse instead of a blessing. It is the timehonoured abuse of it, which demands our dislike and
resistance.
Beyond a few, and very erroneous allusions to the
Logic of Aristotle, Bacon and his immediate successors did very little for it as a science.
Hobbes seems to have had just views of the syllogism, as,, the instrument of demonstration," but
carried his investigations-his written ones at leastvery little beyond such a statement.
Resting upon the basis of the Baconian philosophy,
the thinkers of the seventeenth and eighteenth centuries seem to have neglected the art of reasoning for
the subject-matter about which we reason, and thus to
have entirely confounded Logic with the art of thinking. For this they had the authority of their great
master, Bacon, who, in his c" Advancement of Learning," has divided the Art of Judgment into Induction




264                  LOGIC.
and the Syllogism; and has classified as four kinds of
demonstration: 1. That by immediate consent and
common notions; 2. By Induction; 3. By Syllogism;
and 4. By Congruity. The error of this classification
is at once apparent to us.
Indeed it may justly be said, that in everything
pertaining to Logic, in its proper meaning, Lord Bacon
is entirely at fault; while in everything which bears
upon Experimental Philosophy, he is great beyond
any competitors; he is the inventor of Induction,
and as a few words have shown that all induction
must be brought to the syllogism to verify and test
the laws at which we arrive, his philosophy can be
easily disconnected from his Logic, and the faults of
the latter exert no evil influence over the excellencies
of the former.
Many logicians in England, France and Germany,
followed in the steps of Bacon in the seventeenth
century, attempting to unite Logic and Experimental
Philosophy in a manner which was injurious to the
former.
Locke, misunderstanding the syllogism as Lord
Bacon had done, discards it from his system, and
bases his views of the understanding on two sources
by which ideas enter the mind, viz.: Sensation and
Reflection.  But to show how so great a thinker
erred, by his false notions of the syllogism, he states
reasoning to consist of four parts:-1st. Finding




LOGIC OF EXPERIMENTAL PHILOSOPHY.    265
proofs; 2d. Arranging them; 3d. Showing their connexion; and 4th. Employing them correctly.
Now, what is all this, but, 1st. Finding middle
terms by which to establish premisses; 2d. Stating
syllogisms; and 4th. Combining arguments. As for
the 3d, that is included in the 2d, for they cannot be
arranged without their connexion being manifest.
Leibnitz, in Germany, seems to have thrown light
upon the theories of Descartes, and to have elucidated
also many things in Locke.
Milton has been called the most learned man of his
age; he vindicated this opinion by writing upon
almost every subject within the range of knowledge,
and in most cases, writing well. We are not, therefore, astonished to find that he has written a work on
Logic. It is in Latin, and seems to be very little
known. In that he adheres to much of the Aristotelian doctrine, and specially championizes Peter
Ramus, the logical Martyr. He divides Logic, which
he calls the chief of Arts, into two kinds-Natural,
i. e., the faculty of reason in the human mind; and
Artificial, i. e., rules for directing the operations of
that faculty. But even Milton erred in stating that
" it belongs to Logic to lead us from universals to
particulars," which would limit the Syllogism to
Deductive reasoning.
In this state of confusion, Logic existed until the
new rise of Philosophy in the 18th century, the
23




266                  LOGIC.
source of which was the continent of Europe rather
than England.
(58.) Logic in the Eighteenth and Nineteenth
Centuries.
But little remains to be said, in order to complete
this brief sketch of the History of Logic. Even to
mention the names of the principal writers who have
sprung up under the impulse of the Baconian philosophy, from that time to the present, would occupy
more space than we can give; and to discuss their
metaphysical works would in this connexion be difficult and improbable.
The logicians of the eighteenth century seem to
have bent their energies to the task of classifying the
science; of making such a logical arrangement as
would make much labour unnecessary, and find for
each its true niche in the temple of Truth.
In England, Doctor Isaac Watts published a trea-,tise on," Logic, or Right Use of the Reason," which
is a compound of Logic and Philosophy alike injurious
to both. Selecting a few tenets from Aristotle, from
Lord Bacon, and from the Schoolmen, he has endeavoured to harmonize them. In another of his volumes,
"( The Improvement of the Mind," he has moved upon
surer ground and with much better success.
Bishop Berkeley wrote the 4 Principles of Human




EIGHTEENTH AND NINETEENTH CENTURIES. 267
Knowledge," a work of profound thought and excellent reasoning; and Bishop Butler has exemplified
the correct use and application of Logic, in his famous
treatise on the ", Analogy of Religion."
France has also produced in the eighteenth century
many fine logical minds, who have devoted themselves
to science specially in attempts at classification;
among these were D'Alembert, Diderot, and their
coadjutors, known as the Encyclopoedists, who, in the
eighteenth century, startled the world not less by
their methodical arrangement of the sciences, than
by the scepticism which their studies induced, and
the atheism or denial of God's existence, which took
the place of doubt.
It would be improper in a treatise of this kind to
do more than simply refer to the present writers on
Logic, and the present condition of the science.
Archbishop Whately has renewed the Logic of
Aristotle in its pristine vigour; and placed it in its
true position as the only sure guide or Art of Reasoning. Many English writers have differed from him;
some, in his conception of the meaning and scope of
Logic itself, and others as to the extent to which the
Aristotelian system may be carried.
Of the first, may be mentioned Mr. J. S. Mill,
whose work, according to the view we have taken,
may fitlier be called ", an encyclopedia of philosophic




268                  LOGIC.
tenets connected with, or resulting from, the Science
of Logic." *
Of the second, are Sir William Hamilton, and
Mr. Augustus de Morgan, who would develop more
than four categorical propositions, and establish what
we have called the "c New Analytic."
The most important changes, however, in the applications of Logic to science are to be found, as has
been said, in the subject of Categories and Classification; and to this, in illustration of the later movements of the science, we shall now give a few words.
It will be at once perceived, that the object is to
reach a summum genus under which all the sciences
may range, and then by a logical tree of division, to
place all the lower classes and their co-ordinate
species, in their proper places. In any less general
classification it is evident that the principle of classification will be changed for the different sciences.
(59.)  Of Categories and Classification.
This is a part of the duty of Method.
The Categories of Aristotle which have already
been explained, may be considered the basis of the
classification of the sciences. For although there
has been, in former times, much dispute concerning
* Neil's Art of Reasoning, p. 234.




OF CATEGORIES AND CLASSIFICATION.      269
their true reference, that is, whether it be to words,
or things, or conceptions, it is now allow-ed that,
imperfect as they are, they are designed to apply to
the summa genera, under which all things which are
named may range themselves.  This establishment of
proper summa genera, then, is the true start point of
classification.
Many writers have simplified these categories mainly
by reducing the number. The schools of Pythagoras,
Plato, and Epictetus had each its corresponding list
or table; Locke wrote three, viz.: Physica, Practica
and Semeiotica, or, as they have been translated,,
Substance, Modes and Relations; Hume, two, viz.:
Ideas and Impressions.   But these are manifestly
none of them of that practical form and character
which is desirable for useful reference, and hence it.
has been the aim of later writers, especially upon
Metaphysics and Logic, to write out tables of classification which should comprise and methodize all
forms of human science. To classify palpable, tangible objects, is to arrange them in groups according
to a certain method, and that method will usually be
based first upon the great division of kingdoms, and
afterwards upon the relation of species to genus.
If we reflect for a moment upon the innumerable
forms of life and existence in the three great kingdoms, Animal, Vegetable, and Mineral, we shall at:
once be struck with the difficulty and labour of a just
23 -:



270                   LOGIC.
and adequate classification; and yet, strange as it may
seem, true progress in any of these branches has but
kept pace with such a classification; the naming and
placing of a minute species in its proper place being
the necessary way of fixing it there for ever.
It has already been said that the basis of physical
classification is the establishment of the summum genus, and that the rules of Logical division must determine all the subaltern genera and species.  This must
serve us for the classification of the known and determined; but in the world of Theory, another mode may
with propriety be adopted: it is the classification by
series, investigated by Comte.  It consists in selecting some particular phenomenon, the laws of which are
to be investigated, and then ranging the various objects which sustain a relation to it, in a nearness proportional to that relation.
With this subject of classification, scientific nomenclature is immediately connected, and'it will appear
how important this must be regarded, when we consider that the value of the classification will depend
upon the names of the different classes, as to their
precision or total want of ambiguity, their completeness, or expressing the whole of the class specified, and
their expressiveness, in denoting the properties of the
object, and the reason of its classification.  Thus, in
chemistry, a law of nomenclature has been formed,
based, indeed, upon some unfortunate beginnings,




OF CATEGORIES AND CLASSIFICATION.    271
which have been allowed to remain, but very systematic, and universal in its reception.
But the high aim of metaphysical philosophers, to
smooth the paths of Logic, has been, not the classification of one science, but the analysis and classification of universal Science, the establishment of a
complete table, in which all human investigation
should find its place, and link itself to the great mind
of all ages in its study of all topics within its sensual
or intellectual range.
It will not be attempted to give a history of classification, nor to prepare or copy a complete table of
any previous author, but rather to indicate the manner
in which it has been done, with a general reflection
upon the results attained.  Classification, to be logical and just, must be made after certain investigations,
which are necessary to determine the true class of
the object in question.  This will be done in Physics
by formal analysis, such as the organic analysis in
chemistry, and in the exact sciences by the application of the principles of demonstrative proof.
Passing by, only because our limits do not permit
their consideration, the system of Bacon, which was
adopted by the French Encyclopedists of the last
century as the basis of their great work, " L'Encyclopedie Methodique," and the details of the system
of Locke, we come down to our own times before we
find any definite attempt to supply the want. An




272                  LOGIC.
eminent Scotch writer, as he reviewed the efforts of
previous philosophers to classify human knowledge,
asserted that it was an impossible task, and so, from
its magnitude, it would fairly seem.
Nothing daunted by such an assertion, Coleridge
suggested the plan of classification, which was adopted
in the arrangement of the English,, Encyclopcdia
Metropolitana," but which he found to require, after
he had exhausted his categories, an additional category of "4Miscellaneous" species; the unfortunate
subalterns which had no summum genus under which
to range themselves.
Among the curious but highly philosophic remains
of Jeremy Bentham, is a proposed system of scientific
classification; but, like his other works, it is only a
store-house of theory from which less gifted but more
practical men draw capital for constant use.
All the more modern writers agree in considering
the system of Ampere the most correct and useful.
It is based upon the two categories of mind and
matter, and under these it expands into a very great
number of subordinate sciences, many of which, it
must be said, are created, i. e., in name to fill up
gaps which would spoil the symmetry of his table.
It is not our purpose to write out his table in full;
it would be out of place in a text book, as it could
only be examined, not studied; but we will form a




OP CATEGORIES AND CLASSIFICATION.       273
tree of one or two of his subjects, to illustrate his
plan, and indicate its truthfulness and use.
His First Table contains:
(Kingdoms).
( Cosmological sciences,      ( Noological sciences,
i i. e., pertaining to matter.  i. e., pertaining to mind. 
Cosmologics proper.  Physiologics.  Noologics  Social sciences.
I ~*!  ~I             proper.
Mathematics. Physics. Nat. sciences. Med. sciences. Philosophies, &c. Ethnology,
I               1       I        I         &c.
Geometry, &c.       &c.     &c.      &c.        i
I                                          &c.
Elementary geometry, &c.
I
Synthetical and analytical geometry,
&-c.
Of these there are several tables and more than a
hundred branches.    In thus indicating rather than
writing out in full the tables of Ampere, we spare
the student the reading, in place, of many names
unknown to our ordinary scientific studies, such as
-Dialegmatics -  Eleutheroteclhnics -  TecAnesthetics,
while we present to him what is alone our present
purpose, the theory and principle of classification.
The chief merit of his tables, which he spent his
life in constructing, seems to be that there are no
cross divisions-that no subordinate science lies out
of its own class or laps over into another-errors
which rendered Bacon's system worthless, and which
caused Bentham to abandon his great idea and leave
it in its inchoate form.
Auguste Comte, who has given to the world, in his
S




274                  LOGIC.
Oours de la Philosophie Pqsitive, his views of philosophy, did not attempt so much to classify science as
to determine the true relation between general science
and positive science: to make positive science more
general in its application, and general science more
practical and positive.  This has been his life-work.'There is much of his work which bears indirectly
but dangerously upon religious belief, and there is
an elaborate description of the historical progress of
positive science-through what he calls the mystical
and metap,.hysical eras, to the positive.
To explain more clearly his view of this positive
er, it is that in which the mysticism or mythology of
ancient and early times, as well as the crude metaphysical notions of the Middle Ages, which found their
issue in astrology and magic, are swept away, by the
light of modern free thought and investigation, and
in their place are substituted the laws of creation, laws
which regulate its origin, its progress and its destiny.
There are six positive sciences, which include every
thing that can be known.   These are Mathematics,
Astronomy, Physics, Chemistry, Biology, and Sociology.
But it is not within our scope to explain his philosophy; we have only to do with its Logic, and this
is found in his classification.
The subject of classification is yet open, and will
beomne, without doubt, clearer and more practical as




OF CATEGORIES AND CLASSIFICATION.      275
science advances to the discovery of the proximate
laws of creation.
(60.) Conclusion.
From the foregoing investigation of the art of Reasoning, we may pause a moment at the end to reflect
upon its real value and importance. If Logic is really
the art which controls and guides the reason in its
workings, and without which we can attain to no truth
upon which the reason is exercised, it is surely worthy
of a high place in the catalogue of elementary studies,
and the statement and adoption of its laws must be
considered of the first importance.
And, above all, should it be placed upon its own
foundation, and dissociated from any other sciences
which either rob it of its own identity, or use it without acknowledging its office.
THE END.
IEARS & DUSENBERY, STEREOTYPERS.  C. SHERMAN & SON, PRINTERS.








ERRATA.
Page 50, 6th line from top, for according to read expressing.
" 53, 6th line from bottom, for genus read species, and 5th line
from bottom, for species read genus.
91, 7th and 8th lines from top, for Y read X: for distributed
read undistributed, and for undistributed read distributed.
105, 11th line from top, for Yread U; and 14th line from top,
for U read Y.
"163, 10th line from bottom, for equal to it, read greater than it.
199, 11th and 12th lines from top, for broad read restricted, and
for special reference or, read broad or unrestricted. And,
for the example following, substitute:
This man is innocent (of a certain crime),
But the innocent (entirely) are sure of Heaven;
Therefore This man is sure of Heaven.








VHILADELPHkia,
No. 67 SOUTH FOURTH STRAHT.
STANDARD BOOKS
PUBLISHED BY
E. H. BUTLER & CO., PHILADELPHIA.
t <e the e foltowing wilt be forvarded  by mail, post-paid, for a remittance of t(e price nao
against the work or works ordered.
GOODRICH'S SCHOOL HISTORIES.
GOODRICH'S PICTORIAL HISTORY OF THE UNITED STATES.
A Pictorial History of the United States, with Notices of other Portions of
America. For the use of Schools. By SAMUEL G. GOODRICH. 1 voL
12mo. 360 pages.
GOODRICH'S PICTORIAL HISTORY OF ENGLAND.
A Pictorial History of England, Scotland, and Ireland. For the use of
Schools. By SAMUEL G. GOODRICH. 1 vol. 12mo. 444 pagea.
GOODRICH'S PICTORIAL HISTORY OF ROME.
A Pictorial History of Ancient Rome, with a Sketch of the History of
Modern Italy. For the use of Schools. By SAMUEL G. GOODRIcW
I vol. 12mo. 333 pages.
GOODRICH'S PICTORIAL HISTORY OF GREECE.
A Pictorial History of Greece, Ancient and Modern. For the use of
Schools. By SAMUEL G. GOODRICH. 1 vol. 12mo. 371 pages.
GGODRICH'S PICTORIAL HISTORY OF FRANCE.
A Pijtorial History of France. For the use of Schools. By SAMNBL,.
GooDn caH. 1 vol. 12mo. 347 pages.
1




PAHLEY'S (GOODRICl'S) COMMON SCHOOL HISTORY.
& Brief Compend of Universal History.    For the use of Schools. By
SAMUEL G. GOODRICH. I vol. 12mo. 309 pages. Price, 75 cents.
- These works are written in a lively and pleasing style, abounding in illu;iytn
tire anecdotes, incidents, and descriptions, the histories, in all cases, being based oe
Geography, illustrated by maps. The manners and customs of each country and age
are constantly kept in view. The works are freely supplied with engravings, giving
correct ideas of manners and customs, views of cities, monuments, battles, &c. They
nave been got up with great care and expense, and are published in a superior style.
It is believed that therp is no series of familiar histories, in America or Europe, that
may challenge comparison with these, either in interest, accuracy, or beauty of mechanical execution. The publishers are able to add that they have received the approLation of leading men, and are introduced into the principal seminaries throughout
the United States. They are uniform in size and price.
MANN & CHASE'S NEW ARITHMETICAL
SERIES.
IN TIREE PARTS.
MANN & CHASE'S PRIMARY ARITHMETIC, Part 1.
The Primary School Arithmetic: designed for Beginners. Containing
copious Mental Exercises, together with a large number of Examples
for the Slate.  By HORACE MANN, LL.D., and PLINY E. CHASE,
A. M., Authors of "Arithmetic Practically Applied."   1 vol. 18mo.
Price, 25 cents.
MANN & CHASE'S ARITHMETIC, Part 2.
The Grammar-School Arithmetic: containing much valuable Commercial
Information; together with a system of Iltegral, Decisral, and Practical Arithmetic, so arranged as to dispense with many of the ordinary
rules. By IORbAC MANN, and PLINY E. CHASE, Authors of "Primary
Arithmetic." 1 vol. duodecimo. Price, 63 cents.
MANN &      CHASE'S ARITHMETIC, Part 3.
Arithmetic Practically Applied: for Advanced Pupils, and for Private
Reference, designed as a Sequel to any of the ordinary Text Books ( n
the subject. By HORACE MANN, LL.D., the First Secretary of the
Massachusetts Boartl of Education, and PLINY E. CHASE, A. M. 1 YvL
duodecimo. Price, $1.00                                    2




ANGELL'S READING BOOKS.
This is a series of Spelling and Reading Books, in Six Numbers; comiilea
by OLIVER ANGELL, A. M., Principal of the Franklin High School,
Providence.   Th,. Numbers composing the series may be briefly de.
scribed as follows:
ANGELL'S READER, NO. 1.
72 pages 18mo.    Price, 8 cents.
The arrangement of the lessons in this book is such, that the child commencee
reading as soon as he commences putting the letters together into syllables, the exer.
cise of spelling and reading being simultaneous. The same syllables and words which
form the Spelling lessons, are arranged as Reading Lessons directly opposite, or immediately under the Spelling columns.
ANGELL'S READER, NO. 2.
136 pages 1nmo. Price, 14 cents.
This is a continuation of the First Number, containing Easy Reading Lessons, most
of which are pleasing stories, designed to interest the mind of Zte learner, and afford
nstruction. Spelling Lessons, consisting of words from the Reading Lessons, precede
every Reading Lessecl.
ANGELL'S READER, NO. 3.
206 pages lSmo. Price, 17 cents.
This is a gradual advance from the Second Number, having the Reading and Spell
ing Lessons arranged on the same plan. The Lessons, in each of the Numbers, are
followed by a set of Questions, to exercise the reader on what he has read.
ANGELL'S READER, NO. 4.
252 pages 12L;io. Price, 30 cents.
Also designed as a Reading and Spelling Book, and containing a variety of other
useful matter.
ANGELL'S READER, NO. 5.
296 pages 12mo. Price, 50 cents.
A Reading Book for the higher classes in Common Schools, with Spelling Lessons
and definitions adapted to each reading section; with Tables, Mental Arithmetic, &0.
ANGELL'S READER, NO. 6.
504 pages 12mo. Price, 75 cents.
IBeing a selection of pieces in prose and verse; designed as a Reading Bost for the
highest classes in Academies and Schools.
These six volumes, compiled by OiVER ANGoL, comprise a series which Is'a,
3




ANO ELL'S READING BOOKS-continued.
douhtedly more suitable for the purpose for which they are designed, than snfy P,.
vious publications; and they are more popular among those who have the dire..of education than any ever prepared in this country. There is a decided advaizage
in possessing sets of elementary books by the same author, who has pursued a similar
plan with each, rising step by step, and who, it is presuomu., would be better able to
preserve the proper gradation of style and matter, than several individuals would.
This nill be found to be the case in the present series.
RICIARDSON'S ENGLISH          DICTIONARY.
A New Dictionary of the English Language, by CHARLES RICHARDSON.
2 volumes quarto, 2295 pages. Price, $22.50.
RICHARDSON'S ENGLISH DICTIONARY is acknowledged to be the great Thesaurus of English Philology and Lexicography. Its character as a work of standard
authority is so well established, that few scholars or professional men will deem their
libraries complete without it.
FLEMING & TIBBINS' FRENCH            DICTIONARY.
An entirely New and Complete French and English, and English and
French Dictionary, adapted to the present state of the two Languages.
By Prof. FLEMING, Prof. of English in the College of Louis-le-Grand,
and Prof. TIBBINS, author of several lexicographical works: with important additions, by CHARLES PICOT, Esq., Professor of French in the
University of Pennsylvania, and JnDAH DOBSON, Esq., Member of the
American Philosophical Society, of the Academy of Natural Sciences,
&c., &c. 1400 pages royal 8vo. Price, $4.
FLEMING & TIBBINS' FRENCH DICTIONARY, ABRIDGED.
1 vol. 12mo. 724 pages. Price, $1.25.
NUGENT'S FRENCH AND ENGLISH DICTIONARY.
& Pocket Dictionary of the two Languages. In two Parts. 1. French an
English. 2. English and French. By TuoMAs   NUGENT, LL. D. 45
pages square 12mo. Price, 63 cents.                      4




DONNEGAN'S GREEK LEXICON.
A New Greek and English Lexicon, on the Plan of the Greek and Geimnal
Lexicon of Schneider; the words alphabetically arranged,-disrin.
guishing such as are poetical, of dialectic variety, or peculiar to certain writers and classes of writers; with Examples, literally translated,
selected from the classical writers. By JAMES DONNEGAN, M. D., of
London. Revised and Enlarged by ROBERT B. PATTON, Professor of
Ancient Languages in the College of New Jersey; with the assistance
of J. ADDISON ALEXANDER, D. D., of the Theological Seminary at
Princeton. 1422 pages, royal 8vo. Price, $4.' The auick sale of so many large editions of this Lexicon, is the best evidene2
the publishers could desire of its acceptableness to scholars generally.
WALKER'S PRONOUNCING DICTIONARY.
A Critical Pronouncing Dictionary and Expositor of the English Lan,
guage. To which is annexed a Key to the Classical Pronunciation
of Greek, Latin, and Scripture Proper Names, Ac. By JOHN WALKER.
Octavo, 782 pages. Price, $1.12~.
ITURD'S GRAMMATICAL CORRECTOR.
A Grammatical Corrector, or Vocabulary of the Common Errors of Speech A
being a collection of nearly two thousand barbarisms, cant phrases,
colloquialisms, quaint expressions, provincialisms, false pronunciations, perversions, misapplication of terms, and other kindred errors
of the English Language, peculiar to the different States of the Union.
The whole explained, corrected, and conveniently arranged, for the
use of Sch ols and Private Individuals. By SETH T. HURD. 124
pages 12mo. Price, 34 cents.
MrITH'S GRAMMAR.
nglish Grammar on the Productive System: a Method of Instr"ultion
recently adopted in Germany and Switzerland; designed for Schools
and Academies. By ROSWELL C. SMITH, author of Introductory Arilh;
metie, &c. 192 pages 12mo. Price, 25 cents.
5




HrA RT'S ENGLISH GRAMMAR.
An Exposition of the Principles and Usages of the English Language. By
JOHN S. HART, LL.D., Principal of the Philadelphia High SchooL
192 pages 12mo. Price, 34 cents.
HART'S CLASS BOOK OF PROSE;
AN)
HART'S CLASS BOOK OF POETRY;
Each 384 pages 12mo. Consisting of Selections from distinguished English and American Authors, from Chaucer to the present day; the
whole arranged in Chronological Order, with Biographical and Critical
Remarks. By JOHN S. HART, LL.D., Principal of the Philadelphia
High School. These volumes are sold separately. Price, 75 cents for
either work.
HART'S CONSTITUTION OF THE UNITED STATES.
A Brief Exposition of the Constitution of the United States, in the form
of Questions and Answers. For the use of Schools and Colleges. By
JOHN S. HART, LL. D., Principal of the Philadelphia High School,
and Professor of Moral, Mental, and Political Science, in the same.
100 pages 12mo. Price, 30 cents.
COMSTOCK'S ELOCUTION.
A System of Elocution, with special reference to Gesture and Defective
Articulation. With numerous Diagrams and engraved Figures, illustrating the subject.  By ANDREW COMSTOCK, M. D. 1 vol. 12mo.
Price, $1.00.
FRlOST'S COMPOSITION.
Easy Exercises in Composition, designed for the use of Beginners  Ry
Jong FROST, LL. D. 120 pages 12mo. Price, 25 cents.
6




COATES'S SCHOOL PHYSIOLOGY.
First Lines of Physiology: being an Intrduction to the Science of Life,
written in popular language, designed for the use of Common Schools,
Academies, and General Readers.   By REYNELL COATES, M. D.,
author of First Lines of Natural Philosophy. Sixth edition, revised,
with an Appendix. 340 pages 12mo. Price, $1.00.
COATES'S NATURAL PHILOSOPHY.
First Lines of Natural Philosophy, divested of Mathematical Formulae;
being a practical and lucid Introduction to the study of the Science;
designed for the use of Schools and Academies, and for readers generally, who have not been trained to the study of the Exact Sciences,
and for those who wish to enter understandingly upon the study of
the Mixed Sciences. By REYNELL COATES, M. D., author of Physiology for Schools. Illustrated with 264 Cuts. 402 pages 12mo. Price,
75 cents.
BOOTH'S PHONOGRAPHIC INSTRUCTOR.
New Edition-nearly ready. Being an Introduction to the Compounding
Style of Phonography. With engraved Illustrations and Key. By
JAMEs C. BoOTI.
KENDALL'S URANOGRAPHY.
Uranography, or a Description of the Starry Heavens: designed for the
use of Schools and Academies; accompanied by an Atlas of the
Heavens, showing the places of the Principal Stars, Clusters, and
Nebulae. By E. OTIS KENDALL, Professor of Mathematics and Astronomy in the Central High School of Philadelphia, and Member of
the American Philosophical Society. The Uranography contains 365
pages 12mo., with nine fine Engravings. The Atlas is in 4to., and
contains eighteen large Maps. Price of the Uranography and Atlas
$1.50.
MI'CARTNEY'S DIFFERENTIAL AND INTEGRAL CALCULUS.
Fhe Principles of the Differential and Integral Calculus, and their applicntion to Geometry. By WASHINGTON M'CARTNEY, Professor of Mathenmati-s in Lafayette College. 1 vol. 8vc. Price, $1,25.?




GREEN'S GRADATIONS IN ALGEBRA.
Gradations in Algebra, with the First Principles of Analysis; explained bi
ductively, for the use of Primary and Common Schools. By RlCHABIt
W. GREEN, A. M. 1 vol. 12mo. Price, 63 cents.
GREEN'S KEY TO GREEN'S ALGEBRA.
1 vol. 12mo. Price, $1.00.
COLEMAN'S HISTORICAL GEOGRAPHY OF THE BIBLE.
Historical Geography of the Bible. Nearly 500 pages. By Rev. LYMAI
COLEMAN, D. D. Illustrated with new and beautiful Maps of various
Countries mentioned in the Scriptures. 1 vol. 12mo. Price, $1.25.
By this work the reader is assisted to study in connexion, the History and Geography of the Bible: both of which are, by these means, made more interesting and
instructive. This is indeed the only way to interest the young in the study of Sacred
Geography. It is a book for Sunday Schools, Bible Classes, High Schools, Academies,
and Colleges, as well as for parents and instructors, and all who would read with
intelligent interest the Sacred Scriptures.
PHILOSOPHIE PROVERBIALE:
Par MARTIN F. TUPPER, Docteur en Droit, et Membre de la Socifte Royale.
Traduite en Francais d'apres la dixieme edition. Recommended and
approved as a French Reader for schools. 1 vol. 12mo. Price, 75 cents.
CHURCH's FRENCH SPOKEN.
A New System of teaching French. By EDWARD CHURCH. 302 pages small
quarto. Price, $1.00.
DtxoN & KERR'S ORNAMENTAL AND DOMESTIC POULTRY
& Treatise on the History and Management of Ornamental and Domestic
Poultry. By Rev. E. S. DIXON, A. M., with large additions by J. J.
KERR, M. D. ("Asa Rugg.")     Embellished with sixty-five original
Portraits from life, drawn and engraved expressly for this work. Price,
$1 00. In gilt, with all the plates, coluuoi....2.50.
8