OUTLINES OF LOGIC : 
 
 AN ENGLISH TRANSLATION 
 
 OF 
 
 TRENDELENBURG'S 
 
 ELEMENTA LOGICES AEISTOTELEiE. 
 
 Second Edition. 
 WITH ENGLISH NOTES, 
 
 BY 
 
 R BBOUGHTON, M.A., 
 
 , HERTFORD COLLEGE. 
 
 ^rranptJ for Bitterleatiing; tottb t&e QLttL 
 
 xfortr: 
 
 A. THOS. SHRIMPTOX & SON, 23 & 24, BROAD STREET. 
 
 LONDON: SIMPKIN, MARSHALL, HAMILTON, KENT, & Co., Ltd. 
 
 1898. 
 
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OUTLINES OF LOGIC. 
 
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 OUTLINES OF LOGIC. 
 
 1. Wherever we have truth or falsehood we must 
 first have concepts compounded as if they were one ; for 
 it is with the compounding and dividing of concepts that 
 truth and falsehood are concerned. Now simple names and 
 verbs resemble the concept where no process of compound- 
 ing or dividing has taken place, e.g., the concepts man or 
 white, where nothing is added to them. As yet we have 
 neither truth nor falsehood, as we see by the fact that 
 the concept Goat-stag has indeed a meaning, but as yet 
 we cannot call the meaning either true or false, unless there 
 be added the conception of Being or Not-being with or 
 without a notion of time. He, therefore, judges rightly 
 who thinks of that which is divided as divided, and of 
 that which is in composition as compounded ; and he falsely, 
 who holds an opposite opinion to that which the facts of 
 the case warrant. 
 
 2. Every sentence is significant, but only that of which 
 truth or falsehood carf be predicated is declaratory. These 
 cannot be predicated of all sentences, as, for instance, 
 prayer takes the form of a sentence, but is neither true 
 nor false. Dismissing, then, all other kinds as fitter sub- 
 jects for investigation by Poetry or Ehetoric, our present 
 study concerns itself with the Sentence declaratory. 
 
 3. 1 Of terms when not used in combination, each sig- 
 nifies either Substance, Quantity, Quality, Relation, Place, 
 Time, Position, State, Action, or Passion. As examples 
 
2 OUTLINES OF LOGIC. 5 
 
 of Substance we may take man, horse ; of Quantity, of two 
 cubits, of three cubits ; of Quality, white, literary ; of Rela- 
 tion, double, half, greater ; of Place, in the Lyceum, in the 
 market ; of Time, yesterday, last year ; of Position, is reclin- 
 ing, is sitting ; of State, is shod, is armed ; of Action, cuts, 
 burns ; of Passion, is being cut, is being burnt. 
 
 4. A declaratory sentence is (1) affirmative, (2) nega- 
 tive. Affirmation is declaration of a relation between this 
 and that; Negation is a declaration of non-relation. The 
 statements are true according as they agree with the facts 
 of the case. 
 
 5. The phrase Not-man is not a name ; nor is there 
 any existing name by which we can call it, for it is neither 
 a sentence nor a negation. Let it pass as an Indefinite 
 name, for it can be ranked equally well under either Being 
 or Not-being. Every affirmation or negation will be made 
 up of a name and a verb, or of an indefinite name and a 
 verb : for without a verb there can be neither affirmation 
 nor negation. 
 
 6. Of terms, some are General, others Singular. By 
 the former I mean such as can be predicated of many sub- 
 jects ; by the latter, such as cannot; e.g., we place man 
 among general terms, Kallias among singular. 
 
 A Proposition is a sentence affirming or denying one thing 
 of another. It may be either Universal, Particular, or 
 2 Indefinite. 3 By Universal, I mean a proposition which 
 asserts something of all or none of its subject; by Par- 
 ticular, one which asserts or denies something of some 
 or not all of the subject; by Indefinite, one which makes 
 an assertion without specifying whether it is universal or 
 particular, as were one to say that the same science deals 
 with opposites, or that pleasure is not a good. 
 
6 OUTLINES OF LOGIC. 3 
 
 It is very evident that the universal proposition is supe- 
 rior to the particular; for of the two propositions, when 
 we know the former, we are acquainted with the latter also, 
 and know it virtually, or in potentiality. As, for instance, 
 if a man knows that every triangle contains angles equal to 
 two right-angles, he may be said to know that the angles 
 of an isosceles triangle are equal to two right-angles, even if 
 he does not know the isosceles as a form of triangle. On 
 the other hand, a man acquainted with the particular pro- 
 position has no knowledge whatever of the universal, either 
 virtually or actually. Again, the universal proposition is 
 cognised by the reason, the particular by the senses. 
 
 4 7. Every proposition is of predicability, either unquali- 
 fied, necessary, or contingent. 
 
 8. Of the whole number of existing terms, some are 
 such as not to be truly predicable universally of any other 
 terms; as, for instance, the terms Kleon, Kallias, and all 
 other individual things and objects of sense-perception. On 
 the other hand, these may have other things predicated of 
 them; Kallias and Kleon, for instance, may be called men 
 and animals. 5 Another class of terms are predicable of 
 others, but cannot first have others predicated of them. A 
 third class can be both predicated and "predicated of, as, for 
 instance, we may use man as a predicate of Kallias, and 
 animal as a predicate of man. It is plain, then, that of 
 existing terms some are naturally unfit for being used as 
 predicates ; for every object of sense-perception is of such a 
 nature as to be predicable of nothing. 
 
 Genera can be predicated of their species, but species 
 cannot conversely be predicated of their genera. 
 
 9. It is impossible for the same thing to be at once 
 predicable and not-predicable of the same thing, and in the 
 same respect. This is the most certain of all principles, 
 for it is impossible for any one to conceive the same thing 
 both as being and as not-being. Accordingly, in all demon- 
 strations this is appealed to as an ultimate principle. 
 
4 OUTLINES OF LOGIC. 7 
 
 6 Truth must always, and in all points, be consistent with 
 itself ; for with truth all the facts of the case agree, but with 
 falsehood they quickly disagree. 
 
 10. Inasmuch as it is possible to deny predicability 
 where it exists, and to affirm it where it does not exist, 
 to deny it where it does not exist, and to affirm it where it 
 does, and in the same way with respect to 7 other times than 
 the present it will be possible to deny every affirmation and 
 to affirm every negation. Plainly, therefore, to every affirm- 
 ation a negation stands opposed, and to every negation 
 an affirmation. Let this, then, be called Contradiction, 
 affirmation and negation being the opposites. By Oppo- 
 sition I mean the affirmation and negation of the pre- 
 dicability of the same predicate, of the same subject, but 
 8 not in the same sense. 
 
 9 Contradiction is an opposition admitting of no interme- 
 diate. One part of a Contradiction is the affirmation of 
 predicability, the other part is the negation of it. 
 
 In every case of affirmation and negation, whether the 
 subject exist or no, one assertion will be false, and the other 
 true. For in the case of the assertions, Socrates is ill, 
 Socrates is not ill, if Socrates exist it is plain that one of 
 them must be true or false. In like manner if he do not 
 exist; for to say that he is ill when he does not exist is 
 false, and to say that he is not ill true. So that of these 
 propositions alone, which are opposed to each other as 
 affirmative and negative, will it be a property that one must 
 be either true or false (and the other the reverse). 
 
 11. Of members of the same genus, those which stand 
 most widely apart from one another we define as con- 
 traries. 
 
 Contradiction admits of no intermediate, contraries do 
 admit of an intermediate. 
 
8 OUTLINES OF LOGIC. 5 
 
 12. An affirmation and negation are opposed as con- 
 tradictories, when the one enunciates a universal propo- 
 sition, and the other maintains that the predicate cannot 
 be universally affirmed of the given subject. 
 
 E.g. (i.) All men are white. 
 Contradict. Some men are not white. 
 
 (ii.) No man is white. 
 Contradict. Such and such a man is white. 
 
 Contrary opposition, on the other hand, consists in the 
 affirmation and negation of the same universal proposition. 
 
 E.g. (i.) All men are white. (ii.) All men are just. - 
 Contraries. No men are white. No men are just. 
 
 Such affirmation and negation, therefore, cannot both be 
 true at the same time. 
 
 13. Verbally, propositions may be opposed in four 
 ways, thus : 
 
 (i.) Universal affirmative to universal negative, 
 
 (ii.) Universal affirmative to particular negative, 
 
 (iii.) Particular affirmative to universal negative, 
 
 (iv.) Particular affirmative to particular negative ; 
 but in reality in only three, 10 for the particular affirmative 
 is only verbally opposed to the particular negative. Of 
 these Opposites, the universals, the affirmative to the nega- 
 tive, are contraries (e.g. the proposition, All science is good, 
 to the proposition, No science is good), while the other two 
 are contradictories. 
 
 1 4. n As we have seen, every proposition asserts predica- 
 bility, either unqualified, necessary, or contingent; and of 
 propositions in each mode, some are affirmative and some 
 negative ; and again, of affirmative and negative propo- 
 sitions, some are universal, others particular, others in- 
 definite. The universal negative necessarily has its terms 
 convertible : if no pleasure is a good, it follows that 
 no good is a pleasure. The universal affirmative also is 
 necessarily convertible, but only by becoming particular 
 instead of universal : if all pleasure is a good, some good 
 is a pleasure. Of the particular propositions the affirmative 
 is necessarily convertible : if some pleasure is a good, then 
 also some good will be a pleasure ; but this is not the case 
 with the negative, for it does not follow that if some animals 
 are not men, therefore some men are not animals. 
 
6 OUTLINES OF LOGIC. 9 
 
 15. The range of enquiry is co-extensive with the range 
 of knowledge ; we enquire as to four points : 12 the Fact, the 
 Keason, the Existence, the Essence. When, after enumerat- 
 ing every possible case, we enquire as to whether this or 
 that is true e.g., as to whether the sun is or is not in 
 eclipse we are investigating a question of fact. Herein 
 lies the proof : as soon as we have ascertained the fact of 
 the eclipse we stop ; and if we start from the assumption 
 that the sun is in eclipse, we do not investigate whether it 
 is so or not. When we are assured of the fact, we proceed 
 to enquire into the reason (or the How and the Why) of it ; 
 as, for instance, when we know that the sun is in eclipse, or 
 that there is an earthquake, we investigate the causes of 
 these occurrences. So much for this class of questions. 
 There is another class which we investigate differently from 
 these ; such, for instance, is the question, Does or does not 
 a Centaur or a God exist? (Here I am speaking simply of 
 the fact of existence, and not, for instance, as to whether 
 it is white or not.) Finally, when we have ascertained the 
 fact of existence, we enquire as to its nature or essence ; 
 as, for instance, What is the nature of a God, or of a man % 
 
 16. It is not the same thing to know the fact and the 
 reason of it : the knowledge of the latter is referred to the 
 first cause. The perfection of knowledge is the contempla- 
 tion of the reason of things. 13 
 
 17. We believe that we possess an absolute knowledge f 
 of anything when we believe ourselves to know the cause 
 through which the thing is as its cause, and not only that, 
 but as its invariable cause. 
 
 18. All teaching and all learning, by the operation of 
 the intellect, proceed from pre-existing knowledge. On a 
 comprehensive examination this will be plain : it is thus 
 {for example) that the mathematical sciences are attained, 
 and similarly also all the arts. 
 
 1 9. Things are prior and better known in two ways. For 
 the same thing is not naturally prior and prior in relation to 
 us, nor naturally better known and better known in relation 
 to us. By "prior and better known in relation to us," I 
 mean things which are more accessible to sense-perception ; 
 a 2 
 
 / 
 
10 OUTLINES OF LOGIC. 7 
 
 by "absolutely prior and better known," those that are less 
 accessible : of the latter class are universals, of the former 
 particulars. 
 
 20. All belief comes either from syllogistic reasoning, 
 or from induction. Knowledge is acquired either by induc- 
 tion or by demonstration : demonstration starting from 
 universals, induction from particulars. 
 
 21. A syllogism is a form of reasoning in which, certain 
 premisses being granted, a conclusion differing from these 
 necessarily results by virtue of their existence. By this 
 phrase I mean that the result is produced by means of the 
 premisses ; and when I say " by their means," I assert that 
 there is no need of any fresh term for the conclusion to be 
 a necessity. 
 
 22. By Terms I mean the parts into which the propo- 
 sition may be analysed, i.e., the predicate, and the subject 
 which is predicated of. 
 
 23. 14 Whatever is asserted of the predicate will be 
 equally asserted of the subject also. 
 
 24. Whenever three terms are so related to one another,, 
 that the last (or minor) term is included in the middle as a 
 whole, and the middle is or is not included in the first (or 
 major)' term as a whole, there must necessarily be a perfect 
 conclusion of the extreme terms. 
 
 By the Middle Term I mean one which is itself included 
 in another, and has another included in it. In position 
 also it holds the middle place. The extreme terms are such 
 that the same thing may be ranked under one, and have the 
 other ranked under it. 
 
 Example. A is a predicate of all B (all B is A). 
 B is a predicate of all C (all C is B). 
 
 Necessarily A is a predicate of all C (all C is A). 
 
 A figure like this I call the First. 
 
8 OUTLINES OF LOGIC. 11 
 
 25. Whenever the same thing is predicated of all of 
 one subject and none of another, or of all or none of either 
 of them, such a figure as this I call the Second, and in it 
 I call that the middle term which is predicate in both pre- 
 misses. In this figure the middle is placed outside the 
 extreme terms, and comes 15 first. There will be a valid 
 syllogism, whether the terms are universal or not.* If 
 they are universal, we shall have a conclusion when- 
 ever the middle can be predicated of all the major 
 and none of the minor, or vice versa; it making no 
 difference which of the terms is 2nd Fig. 1st Fig. 
 negative. For let M be the predi- No N is M No M is N 
 cate of no X and of all X, since All X is M All X is M 
 a negative proposition is converti- ' 
 
 ble, X will be predicable of no M No X is N 
 
 but M was given as the predicate of all X, so that X is the 
 predicate of no X. For this was proved before (in the first 
 figure). Again, if M is a predicate 2nd Fig. 1st Fig. 
 of all X but of no X, then X is a pre- ^11 N is M Y No M is X 
 dicate of no X. For if M is a pre- No X is M A All N is M 
 dicate of no X, X is a predicate of . *. No X is N .-. No N is X 
 no M. But M was given as a pre- .\ NoXisN 
 
 dicate of all X : .'.X will be a predicate of no X ; for again 
 we have got to the first figure. And since negative propo- 
 sitions are convertible, X will be a predicate of no X, so 
 that there will be the same conclusion. 
 
 Xo affirmative conclusion can be reached by this figure \ 
 but both the universals and the particulars are all negative. 
 
 26. The case in which one predicate may be asserted 
 and another denied universally of the same subject, or in 
 which both may be either asserted or denied universally of 
 it, I call the Third Figure ; and in it I call that term the 
 middle which is subject of both predicates, while the major 
 and minor terms are the predicates. The middle term is 
 placed outside the major and minor, and comes 16 after them. 
 There will be a valid conclusion, whether the terms are 
 applied universally to the middle or not.f 
 
 * N.B. Of course, at least one of them must be, or there would 
 be an undistributed middle. 
 
 f i.e., whether both are or only one, one must be. 
 
12 OUTLINES OF LOGIC. 9 
 
 If they are both applied universally, whenever both P 
 and E can be predicated of all S, P will necessarily be 
 predicable of some E. For since ^rd Yig. 1st Fig. 
 an affirmative proposition is con- ^11 S is P All S is P 
 vertible, S will be predicable of All S is R Some R is S 
 some E ; and P is predicable of all 
 S: therefore P is necessarily pre- Some R is P 
 
 dicable of some E ; for we have arrived at our conclusion 
 by the first figure. It will not be possible to obtain a uni- 
 versal conclusion, either negative or affirmative, by means of 
 this figure. 
 
 27. It is clear that in all demonstration there will be 
 three terms, and no more. This being plain, it is clear also 
 that it must proceed from two premisses, and no more. For 
 the three terms make up two premisses. 
 
 28. In all the figures the middle term must necessarily 
 occur in both the premisses. Where the middle term is 
 both predicated and predicated of, or where the same term 
 is predicated and has another term denied of it, we shall 
 have the first figure ; where it is both predicated of one 
 thing and denied of another, the second figure ; where other 
 terms are predicated of it, or one is denied and the other 
 predicated, the third. 
 
 29. In every figure also there must be one term affirm- 
 ative and one universal predication. For unless there be 
 one universal predication, either there will be no conclusion 
 at all, or it will have nothing to do with the question ; or, 
 again, the original question will be begged. 
 
 For let the question be, that pleasure derived from 
 "Music" is good. If, then, one should lay down that 
 "Pleasure is good," without prefixing the "all," there will 
 be no conclusion. If we say, " Some pleasure is good " ; if 
 the pleasure meant is other than that derived from music, 
 it is beside the question ; if it has to do with music the 
 original question is begged. 
 
 30. It is only through the first figure that we can 
 search for the knowledge of a thing's essence. In the 
 second figure we can obtain no affirmative conclusion, 
 
10 OUTLINES OF LOGIC. 13 
 
 while the knowledge of a thing's essence belongs to affirm- 
 ation. In the last figure we can, indeed, obtain an affirm- 
 ative conclusion, only not a universal one ; but the essence 
 belongs to universals. 
 
 31. It is clear that whoever tries to reason from pre- 
 misses less sure than the conclusion, reasons badly. 
 
 32. It is impossible to obtain a false conclusion from 
 true premisses, but a true conclusion may be obtained from 
 false ones ; 17 only, however, concerning the fact, not the 
 reason of it. 
 
 It is plain, then, that if the conclusion be false, either 
 some or all of the premisses must be false ; but when the 
 conclusion is true the premisses are not necessarily true, 
 neither all nor any of them. It is quite possible, with no 
 true premiss in the Syllogism, for the conclusion all the 
 same to be true j only not necessarily so. The reason of 
 this is, that when two things are so related that the 
 existence of the first necessitates the existence of the 
 second ; if the second does not exist, neither does the first 
 either ; but if the second exist, the first does not of neces- 
 sity exist also. 
 
 33. A demonstrative syllogism is called a ^tXocroc^rjfxa ; 
 an argumentative syllogism an E7rt^etp^/xa ; a captious syllo- 
 gism a 26<io-/za ; and an argumentative syllogism, involving 
 a contradiction, an 'Airop-qfjia. 
 
 We speak of demonstration when the conclusion of a 
 syllogism proceeds from true and primary premisses, or 
 from premisses which owe their origin to true and primary 
 principles of the particular science. An argumentative 
 syllogism, on the other hand, is one which reasons from 
 probable matters. 
 
 One form of false argument is that which seems to reach 
 a conclusion, while in reality it does not. We call this the 
 Captious Syllogism. 
 
 ^p: libra, 
 
14 OUTLINES OF LOGIC. 11 
 
 Captious arguments are those which reach, or pretend to 
 reach, a conclusion from premisses which seem to be but are 
 not probable. 
 
 Doubt would seem to be produced by the balancing of 
 opposite arguments. 
 
 34. Induction is the process from particulars to uni- 
 versal. For instance, if the pilot who is instructed in his 
 work is the best, and so also with the driver, we may con- 
 clude generally that the instructed man is in each case the 
 best. Induction is a more persuasive and clearer process, 
 and is more easily known by sense-perception, and more ac- 
 cessible to ordinary men. The syllogism, on the other hand, 
 is a more cogent process, and a more powerful weapon, 
 against opponents. 
 
 35. Induction and the inductive syllogism is the prov- 
 ing by means of the minor that the major may be pred- 
 icated of the middle* ; e.g., if B be the middle term, A and 
 C the extremes, it proves by means of C that A is predicable 
 of B. It is thus we make our inductions. 18 Of (the minor 
 term) C, which is made up of the sum of the particulars, we 
 must have immediate knowledge ; for induction proceeds 
 by means of the sum of the particulars. 
 
 36. Induction is in a way opposed to the syllogism : 
 the latter, by means of the middle, proving the major term 
 predicable of the minor, while the former, by means of the 
 minor, proves the major predicable of the middle. Natu- 
 rally, therefore, the conclusion reached through the middle 
 term is prior and more knowable, but relatively to us that 
 gained by induction is clearer. 
 
 37. Eikos, or probable judgment, is not the same as 
 ^jLtetov, or judgment based upon marks. The first is 
 a proposition founded upon common opinion. For that 
 which, as a general rule, we know as occurring or not 
 occurring, being or not being, this we call probable, as 
 that " those who envy, hate," or " the objects of love 
 feel affection." 19 The judgment based on marks, on the 
 other hand, is to be taken as a demonstrative pro- 
 position, either necessary, or founded on opinion : 
 
 * N.B. The middle term in induction, and in the first figure of 
 the syllogism, is that which quantitatively is between the other two. 
 
12 OUTLINES OF LOGIC. 15 
 
 for when the existence or occurrence of another phenom- 
 enon is either preceded or followed by the phenomenon in 
 question, it is a mark of its occurrence or existence. A 
 conclusion obtained from premisses based either on prob- 
 abilities or marks, we called an Enthymeme. 
 
 38. 20 When the major term is proved to be predicable 
 of the middle, by means of a term like the minor, we call 
 the process TLapdSeiyfjLa, or Example. In this we must 
 know that the middle is predicable of the minor, and the 
 major of the parallel term. For instance, let A be "evil" ; 
 B the making war on neighbours ; instances of this, C by the 
 Athenians against the Thebans, D by the Thebans against the 
 Phocians. If then we wish to prove that it is an evil to 
 make war on the Thebans, we must first obtain the premiss 
 that it is an evil to make war on neighbours. This we be- 
 lieve from parallel cases, such as the Theban war against 
 the Phocians. Making war, therefore, on neighbours being 
 an evil, and the war against the Thebans being against 
 neighbours, it is plain that to make war on the Thebans 
 is an evil. Plainly, therefore, B is predicable of C and D 
 {both being cases of making war on neighbours), and A of 
 D (for the war against the Phocians did not profit the 
 Thebans). That A is predicable of B will be shown through 
 D. The method is the same when the parallel cases, which 
 make us believe in the connection of the middle and major 
 terms, are more in number. 
 
 Plainly, then, Example does not stand in the relation 
 of part to whole, nor of whole to part, but of part to part ; 
 both cases coming under the same head, and one of them 
 being known. Moreover, it differs from induction, inas- 
 much as the latter, by means of all the individuals, showed 
 the major to be predicable of the middle, without applying 
 the syllogistic process to the major; while example makes 
 this application, and its proof is not from the sum of the 
 individuals. 
 
 39. Both the syllogistic and the inductive proof make 
 their demonstration by means of premisses previously 
 known : the first taking the premisses on authority, the 
 second proving the universal by means of the obviousness 
 of the particular. 
 
16 OUTLINES OF LOGIC. 13 
 
 Khetorical persuasion proceeds on the same methods, 
 either by way of examples when it comes under induction, 
 or of enthymemes when it comes under the syllogism. 
 
 40. "EAeyxo?, or Disproof, is the proof of a contra- 
 diction. 
 
 41. "Evcrrao-Ls, or Objection, is a proposition opposed to 
 a proposition. It differs from the proposition (used as 
 premiss) inasmuch as the objection may be particular, while 
 the premiss either cannot be so at all, or, at least, not in 
 universal syllogisms. 
 
 42. Some propositions being knowable immediately, 
 others mediately (for first principles are known imme- 
 diately, all that come under these mediately), when we try 
 to prove immediately that which is not so knowable, we beg 
 the original question. 
 
 Of begging the question there seem to be five ways. 
 The most glaring, and the one we shall notice first, is to 
 assume the very proposition to be proved. It is not easy 
 for this to pass unnoticed, if we look at the thing itself ; 
 but it is easier in the case of synonyms, and in all 
 cases where the name and the description have the same 
 meaning. 
 
 The second way is, having to prove a particular, to 
 assume the corresponding universal, e.g., in trying to prove 
 that there is one and the same science for contraries, to 
 assume generally that there is one and the same for all 
 opposites. Plainly, the proposition which should have been 
 proved is here assumed along with many others. 
 
 The third way is, having to prove the universal to assume 
 a particular, e.g., having to prove that there is the same 
 science for all contraries, to assume it for any particular 
 pair. In this case also, it is plain that the proposition 
 which should have been proved with many others, is 
 assumed separately by itself. 
 
 The fourth way is, to beg the question by dividing it, 
 e.g., having to prove that the art of medicine deals with 
 both health and sickness, to assume each part of the propo- 
 sition separately. 
 
14 OUTLINES OF LOGIC. 17 
 
 The last way is, of two propositions that follow neces- 
 sarily on each other, to assume one, e.g., having to prove 
 the diameter incommensurable in terms of the side, to 
 assume that the side is incommensurable in terms of the 
 diameter. 
 
 43. An affirmative proposition is prior, and better 
 known than a negative : for it is only through affirmation 
 that negation is knowable ; and affirmation is the prior, on 
 the same principle as Being is prior to Not-being. More- 
 over, demonstrative proof has the more primordial char- 
 acter, for without the demonstrative there can be no 
 negative. 
 
 44. All who employ the proof per impossibile, ob- 
 tain a false conclusion and thus, by means of an hypo- 
 thesis, prove their original proposition, by showing that 
 the supposition of its contradictory involves an impos- 
 sible result. 
 
 The method of proof per reductionem ad impossibile is as 
 follows : Having to show that A is not predicable of B, we 
 assume that it is predicable, and also that B is predicable 
 of C, with the result that A is predicable of C. But this 
 is known and acknowledged as impossible. It is impossible, 
 therefore, for A to be predicable of B. We have shown 
 that affirmative proof is better than negative : it is now 
 plain also that it is better than proof per reductionem ad 
 impossibile. 
 
 45. Knowledge and the thing known differ from opinion 
 and the thing opined, inasmuch as knowledge is of uni- 
 versal, and rests on necessary grounds ; and the necessary 
 does not admit of being otherwise. But opinion is an 
 uncertain thing. 
 
 46. It is impossible to make an induction without 
 having sense-perception : for individuals are the objects 
 of sense-perception. 
 
 On the other hand, we cannot arrive at knowledge by means 
 of sense -perception only. Even if this has cognisance of 
 quality, and not merely of this or that particular object, 
 
18 OUTLINES OF LOGIC. 15 
 
 yet it is necessarily the particular object, and under 
 particular conditions of place and time, that the senses 
 perceive. Of the Universal and the Always it is impossible 
 to have sense-perception. This is not subject to conditions 
 of particular existence and particular time ; if it were, it 
 would not be universal. It is only that which is always 
 and everywhere that we call universal. Thus, if we were 
 on the moon, and saw the interception of the earth, we 
 might still be ignorant of the cause of the eclipse, for our 
 senses would only perceive the fact of the present eclipse, 
 and not the general cause of it ; for, as we said, our senses 
 cannot perceive the universal. 
 
 47. An universal Attribute is an attribute which may 
 be predicated of its subject always, as belonging to its 
 essence, and in virtue of its being what it is. Plainly, then, 
 all universals are necessarily predicable of their subjects. 
 The phrases, " as belonging to its essence," and " in virtue 
 of its being what it is," have the same meaning ; thus, the 
 attribute of having points may be predicated of a line, both 
 essentially and as line. Similarly a triangle, as triangle, 
 contains angles equal to two right-angles, for it is of the 
 essence of a triangle to have its angles equal to two right- 
 angles. An attribute is predicable universally when it is 
 proved predicable in instances taken at random, and as they 
 present themselves. 
 
 48. The subject of an essential attribute is itself the 
 cause of the attribute. The universal being primary, is 
 therefore also the cause of its own attributes. 
 
 49. It is altogether impossible that there should ever be a 
 demonstration of all things, for we should at last come to the 
 infinite ; so that not even so would there be demonstration. 
 
 21 It is impossible to travel through an infinite progress in 
 thought. 
 
 50. Primary truths are such as are credible, not on other 
 grounds, but on their own authority. We have not, in the 
 case of scientific first principles, to investigate reasons ; but 
 each first principle must be credible on its own authority. 
 
 Preliminary (i.e. a priori) knowledge is of two kinds. 
 Either we must know the fact of an object's existence, or 
 we must have a conception of the meaning of a term; 
 and in some cases both the one and the other. 
 
16 OUTLINES OF LOGIC. 19 
 
 For instance, the statement that either the affirmation or 
 the negation of anything is true we must know as a fact. 
 Of the term " triangle " we must have a conception that 
 it has such and such a meaning; while in the case of an 
 unit we must both comprehend the meaning of the term, 
 and know the fact of its existence. 
 
 51. Not all knowledge is demonstrative, that of imme- 
 diate truths has not this character. This is plainly neces- 
 sary ; for if, in order to demonstrate, we must know the 
 prior laws from which demonstration proceeds, we come at 
 last to some point where immediate principles begin; and 
 these are necessarily indemonstrable. We assert, then, that 
 this is so ; and that not only has man scientific knowledge, 
 but also a foundation of science by which we know the 
 meaning of terms. 
 
 Not merely must all or some of the elementary laws be 
 first known, they must also be more fully known ; for a 
 predicate is always especially predicable of that which is 
 the cause of its predicability, e.g., we love our friend more 
 than the person whom we love only for his sake. Thus, if 
 primary laws are the sources of any given knowledge or 
 belief, it is plain that these themselves are more fully known 
 or believed, for it is only owing to them that the derived 
 propositions are believed. 
 
 52. All demonstration has, as its first principle, an 
 immediate proposition, and by " immediate n I mean that 
 than which no other is more elementary. 
 
 53. 22 An immediate syllogistic first principle is called a 
 Thesis when it is indemonstrable, but not a necessary ante- 
 cedent to all knowledge ; when indispensable for any know- 
 ledge whatever to be acquired it is called an Axiom. 
 
 54. The most primary truths are indemonstrable defini- 
 tions. 
 
 For definition is of the essence and fundamental character, 
 and the essence is always postulated and taken for granted 
 in all sciences ; mathematics, for example, postulating the 
 nature of unity and inequality, and all other sciences pro- 
 ceeding on the same plan. 
 
 Definition is the explanation of the essence. 
 
20 OUTLINES OF LOGIC. 17 
 
 55. Definition declares either the essence of the thing 
 (real), or the meaning of the name (nominal). 
 
 It is plain that all those who, in whatever way, try to 
 declare the meaning of a term simply by means of a name, 
 do not declare the real definition of the thing, inasmuch as 
 every definition is a kind of sentence. 
 
 The geometer assumes the meaning of a triangle and 
 proves its existence. 
 
 56. In searching for a definition we must first, by 
 examination of a number of individuals like one another, 
 and without any essential difference, find what quality they 
 all possess in common. Then we must take another set 
 of the same genus as the former, but a different species, 
 though of the same species among themselves. Having 
 found some common characteristic of all of these, and simi- 
 larly in all the other sets, we must again examine if the 
 characteristics we have obtained share any point in common 
 until we come to one single character, and this will be our 
 definition. If we cannot arrive at any common charac- 
 teristic, but there are two or more (common to different 
 sets), it is plain that the subject of our investigation is no 
 one single thing, but two or more. For instance, if we 
 wish to find a definition of High-Spirit we must examine 
 the cases of such high-spirited characters as we know to 
 find what point they all have in common in respect to this 
 quality. Thus, if Alcibiades, Achilles, and Ajax are all 
 high-spirited, in what point do they all agree? we may 
 answer, In impatience of insult, which drove one to treason, 
 another to anger, and the third to suicide. Again, take 
 other instances, such as Lysander or Socrates : these showed 
 their High-Spirit in their unaltered bearing of prosperity 
 and adversity. Taking, then, these two answers, we must 
 examine what point is shared in common by calmness in 
 vicissitude and impatience of insult. If we cannot find 
 any we must say that there are two kinds of High-Spirit. 
 
 57. Of the component parts in a definition each will 
 be predicable of other things besides those defined; but 
 this will not be the case with the sum of the parts, 
 
18 OUTLINES OF LOGIC. 21 
 
 for the sum of the parts is necessarily the essence of the 
 thing defined. Thus of every triad we may predicate 
 number, inequality, and both kinds of primality that of 
 not being measurable by any number, and that of not being 
 compounded out of any numbers. This, then, is the 
 definition of a triad an unequal number prime in both 
 senses of the word; of these predicates two apply to all 
 odd numbers, and the third to the duad; but the sum of 
 the three predicates is applicable to nothing save the triad. 
 
 58. In treating of any whole we should divide the 
 genus until we reach the individuals most elementary in 
 species ; as, in the case of number, the triad and duad. 
 
 Every genus is divided by means of mutually opposing 
 differentiae, as living creatures into those that live on land, 
 in the air, or in the water. 
 
 If the opposing differentiae be such as to admit of no 
 intermediate, we do not beg the question in asserting that 
 the whole genus must be included in the divided parts ; for 
 it must necessarily be all included in one or other of them, 
 if it has really a principle of division. 
 
 Furthermore, we must divide by negation, the method of 
 the dichotomists. But of negation, as negation, there is no 
 differentia, for we cannot have species of that which is not, 
 e.g., we cannot have species of not-winged, not-footed 
 creatures in the same way as of winged and footed. 
 
 59. Definition is by genus and differentia. 
 
 We must keep the genus distinct from all other genera; 
 and the species, as marked by the differentia, from all other 
 species in the same genus. 
 
 A definition to be good must be made by means of the 
 genus and differentiae; and these belong to a class more 
 absolutely knowable and primary than the species itself. 
 
 There are three ways of defining, otherwise than by what 
 is more primary. 
 
22 OUTLINES OF LOGIC. 19 
 
 The first of these is of two opposites, defining one by 
 means of the other, e.g., good by means of bad; this is a 
 vicious method, for opposites are naturally coeval, and 
 some, moreover, think that the same science deals with 
 both, so that we cannot even say that one is better known 
 than the other. We must not forget, however, that in some 
 cases very probably no other method of definition is possible ; 
 thus we cannot define "double" without mentioning a 
 "half," and similarly in the case of all terms essentially 
 correlative. All these only exist in so far as they are in 
 some kind of relation, so that it is impossible to explain 
 one without the other ; and thus the one must necessarily 
 be included in the description of the other. 
 
 A second vicious method of definition is to make use 
 of the very thing to be defined. This escapes notice when 
 we do not make use of its actual name, as, for instance, in 
 the definition of the sun as " a star that shines by day," the 
 use of the term "day" being equivalent to that of "sun." 
 For this fault to be detected, we must substitute the idea 
 for the name, e.g., for the name "day," the idea of the 
 motion of the sun over the earth ; for plainly, in mention- 
 ing the motion of the sun over the earth, we mention the 
 sun, and thus, in using the term " day," we practically use 
 the term "sun." 
 
 Again, the definition is faulty where one opposing species 
 is defined by means of another ; for instance, the species 
 Odd, as that which is greater by unity than Even. The 
 opposing species of the same genus are naturally coeval, 
 and the Odd and the Even are opposed, they being the 
 differentiated species of number. 
 
 60. To know the nature of a thing, is the same as to 
 know the reason of it. What is an eclipse 1 The cutting 
 off of light from the moon by the intervention of the earth. 
 What is the reason of an eclipse 1 or why is the moon 
 eclipsed ? Owing to the failure of light, caused by the 
 intervention of the earth. What is harmony 1 A ratio 
 of numbers in acute or grave. Why is the acute in har- 
 mony with the grave 1 Because grave and acute have 
 a numerical ratio. 
 
s 
 
 s 
 
 20 OUTLINES OF LOGIC. 23 
 
 61. We investigate the reason when we know the fact. 
 In some cases the two come to light together ; bnt it is 
 quite impossible to know the reason before knowing the 
 fact. We cannot know what a thing is while we do not 
 know if it is. 
 
 The explanation seems to testify to the phenomena, and 
 the phenomena to the explanation. 
 
 62. The cause is the middle term. It is this which 
 is the object in every investigation. 
 
 63. A description, to rank as a definition, must not 
 merely exhibit the fact, as most definitions are content 
 with doing ; it must also contain a clear account of the 
 cause. As it is, the accounts of definitions are like the 
 conclusions of syllogisms. For instance, What is a square % 
 A square, we are told, is an equiangular and rectangular 
 figure, equal to another figure, of which the sides are un- 
 equal. But the man who tells us that the square is the 
 finding a mean proportional, tells us the cause of the 
 matter. 
 
 64. Not only does it appear that the knowledge of the 
 nature of substances is useful when we come to contem- 
 plate the causes of their essential properties, (as, for ex- 
 ample, in mathematics, to know the nature of a straight 
 line and a curve, or of a line and a plane superficies, is- 
 useful towards perceiving the number of right-angles to 
 which the angles of a triangle are equal), but the converse 
 of this is also true, the knowledge of the properties greatly 
 contributing to the knowledge of the nature of an object. 
 When we are able to give an account according to our 
 impressions of either all or most of the properties of an 
 object, we shall then best be able to describe its essential 
 nature. All demonstration begins with the nature of the 
 object ; so that any definition which does not give us a 
 knowledge of properties, and in which even to make a 
 guess at them is difficult, is evidently only idly laid down 
 for the purposes of argument. 
 
 65. In some cases, the cause is something distinct 
 from the object : in others, it is not. Of definitions, 
 therefore, which duly declare the nature of an object, it 
 is plain that some are immediate and elementary. 
 
24 OUTLINES OF LOGIC. 21 
 
 In these we must assume, or in some other way make 
 evident, both the fact of existence and the nature. We 
 see this in arithmetic, where both the nature and the 
 existence of the monad is assumed. Definitions which are 
 not immediate, and where the cause of an object's nature is 
 something distinct from it, may, as was before laid down, be 
 proved by demonstration. 
 
 66. A thesis, or assumption, may either take one or 
 other part of enunciation, so, I mean, as to assert or deny 
 the existence of an object, in which case it is an hypothesis ; 
 or it may make no assertion, and then is called a definition, 
 definition being a kind of thesis. The arithmetician em- 
 ploys a thesis when he assumes that the unit is indivisible 
 in quantity ; but this is not an hypothesis ; for it is not the 
 same thing to assume what is the nature of an unit, and 
 to assume the fact of its existence. 
 
 67. Every demonstrative science concerns itself with 
 three things, of which two are assumed as existing j these 
 being the genus whose essential attributes it investigates, 
 and the general axioms from which, as first principles, it 
 makes its demonstrations; and thirdly, the attributes of 
 which it assumes the respective meanings. 
 
 68. It is plain that we cannot demonstrate the peculiar 
 principles of each individual genus ; for these principles 
 will hold good universally, and the science of these will be 
 the sovereign science of the universe. For as the know- 
 ledge we derive from more primary causes is more perfect 
 for we speak of knowledge as derived from more primary 
 causes, when it is derived from causes themselves un- 
 caused as, I say, 23 such knowledge has an especial and 
 unusual perfection, so would the corresponding science be 
 especially and unusually perfect. 
 
 (a) 69. We have already laid down that without a know- 
 ledge of the elementary and immediate principles, demon- 
 strative science is an impossibility. The question may be 
 raised as to how this knowledge of immediate principles 
 
 (b) is obtained. Now every living creature is in possession 
 of an innate perceptive power, which we call sense. 
 
22 OUTLINES OP LOGIC. 25 
 
 While all have this sense, in the case of some creatures the (c) 
 impression made is permanent, in others it is not. Where (d) 
 it is not, or in so far as it is not, there is no knowledge 
 beyond that of the momentary sensation. Where there 
 is this permanence, the creatures, when not using their 
 organs of sense, still have the impression in their soul. 
 There are many with whom this is the case ; and they may (e) 
 be further subdivided into those who have and those who 
 have not a definite conception, derived from the perma- 
 nence of such impressions. From sensation, as we say, (/) 
 
 i springs memory, and from the oft-repeated memory of the 
 same thing, experience : for many memories are united 
 in a single experience. From experience, or the whole (g) 
 universal which abides unaltered in the mind an unity 
 besides a plurality, remaining ever the same in all its mani- 
 festations from this comes the beginning both of art and 
 of science : of art, if we have to do with production ; of 
 science, if with truth. Thus the faculties have not any (ft) 
 original and separate existence by themselves, nor are they 
 derived from other faculties with greater powers of know- 
 ledge, but they spring from sensation ; just as in a rout 
 one soldier, making a stand, is joined by another, and then 
 another, until their original formation is regained ; the soul 
 being naturally adapted for undergoing such a process. As (i) 
 soon as one of the individual sensations makes a stand, we 
 have the first beginning of a universal notion formed in the 
 mind ; for though our momentary sensations are of particu- 
 lars, 24 sense is of the universal, taking cognisance, not of this 
 or that particular man, but of man in general. Eound the 
 primary universals thus obtained a stand is made, until 
 at last there centre round them the indecomposable and 
 ultimate universals. First we have a kind of animal ; then 
 animal ; then again some higher genius, fixing itself on these. 
 
 / It is plain, then, that by us knowledge of primary objects (&) 
 can only be gained by induction; for it is in this way 
 also that the sense builds up the universal in our minds. 
 Of the intellectual faculties by which we attain truth, (I) 
 
26 OUTLINES OF LOGIC. 23 
 
 some are unerringly true, such as science and intuition; 
 others, such as opinion and calculation, admit of error. 
 Again, except intuition, there is nothing more accurate than 
 science. First principles, moreover, being more accessible 
 to knowledge than the demonstrations from them, and all 
 science being gained by reasoning, of first principles there 
 can be no science. Lastly, there being nothing more truth- 
 ful than science, with the one exception of intuition, we 
 draw the conclusion that first principles are the subjects of 
 (m) intuition. From this we see that the beginning of demon- 
 stration is not demonstration any more than that of science 
 is science; if, therefore, besides science we have nothing 
 else true, the beginning of science must be intuition. 
 
NOTES. 
 
 1 In this paragraph the ten Categories are enumerated, and 
 examples of each are given. They are Aristotle's mode of analysing 
 the parts of propositions, and are best understood by comparing them 
 with the parts of speech in Grammar. Thus, under the head of 
 Substance, come Nouns, which may be either the subject or predicate 
 of a proposition. Quantity, Quality, and Relation include Adjectives 
 denoting quantity, quality, or comparison. Place and Time include 
 the Adverbs of place and time. Position, State, Action, Passion are 
 all forms of the Verb, which is either the predicate, or forms part of 
 the predicate of a proposition. Position represents Verbs of Rest : 
 State, the Perfect Passive; Action, the Active Voice; Passion, the 
 Passive Voice. 
 
 2 Indefinite Propositions should be excluded from Logic as 
 ambiguous. If it is said that the same science deals with opposites, 
 it should be stated whether some opposites or all opposites are meant. 
 The proposition is true in the former case, false in the latter. Thus 
 medicine is the science of both sickness and health, which are 
 opposites, but not all science has to do with opposites. Take, for 
 instance, astronomy. Similarly, if it is asserted that pleasure is not 
 good, it should be explained whether some pleasure or all pleasure 
 is meant. 
 
 3 i] fikv Ka66\ov, etc.] This means that when we speak of a class as 
 man, for instance, we have cognition of it in the mind only; but 
 when we speak of a particular man, as Kallias, he is cognizable 
 by the senses. 
 
 4 This division of propositions in Aristotle corresponds to that 
 of later logicians, who divide them into Pure and Modal. Pure 
 propositions (rod virdpxeip) are those in which the predicate is pred- 
 icated of the subject without any qualification, as "All men are 
 mortal." Modal propositions are those in which the predicate i& 
 predicated of the subject in a qualified manner, and they are of two 
 
28 NOTES. 
 
 kinds: (1) necessary (tov 4% av&yKTjs v-rrdpxeiv), as "Every triangle 
 must have its angles equal to two right angles " ; (2) contingent (tov 
 ivdix <r6 aL virapxeip), as "The sun may rise and set for a thousand 
 years." Some logicians enumerated four kinds of modality, viz., 
 necessary, contingent, possible, impossible; but the two latter may 
 be dismissed, for what is impossible falls under necessity, and what 
 is possible is contingent. 
 
 5 ret 5' avrcL fiev /car' &Wwv, etc.] This is explained by the last 
 sentence in the section. " Genera can be predicated of their species, 
 but species cannot conversely be predicated of their genera." Thus, 
 in the proposition "All men are animals," the genus "animal" is 
 predicated of the species "man," but the species "man" cannot be 
 predicated of "animal." 
 
 6 bet trdv rb dXrjdes, etc.] This sentence contains the principle of 
 identity and contradiction, which may be put into the form "All A 
 is A " and " No A is not-A." 
 
 7 /cat irepl tovs itcrbs, etc.] i.e. when the copula of the pro- 
 position is "was," or "will be," as well as "is." 
 
 8 fiT] bjxwvTufxuis M.~\ i.e. in one case the proposition is positive, in the 
 opposite it is negative, as explained in the next paragraph. 
 
 9 avTideais jjs ovk %<jti /mera^v Kad ' avT'qv.'] The difference between 
 contradictory and contrary opposition is that between two contra- 
 dictory propositions there is nothing intermediate. If one is true, the 
 other is false. This is sometimes called the principle of the excluded 
 third between two contradictories. But contraries admit of an in- 
 termediate, as is stated below in the next section. Black and white 
 are contraries, but grey is intermediate. There is no intermediate 
 between man and not-man. 
 
 10 rb yap tivX t$, etc.] Two particular propositions, such as 
 "Some men are just," and "Some men are not just," are only 
 verbally opposed. Both may be true. Later logicians call this 
 opposition sub-contrary (virevavTias TrpoTao-eis). They cannot both 
 be false. 
 
 11 In this section Conversion is explained, as Opposition is ex- 
 plained in 10-13. The different kinds of Conversion applicable 
 to different kinds of propositions are summed up in the memorial 
 line : /eci simpliciter convertitur, BvAper acci cannot be converted. 
 
NOTES. 29 
 
 12 Of these four points of inquiry, the Fact and the Existence 
 correspond to each other, and the Reason and the Essence likewise. 
 
 13 KvpLdbrarov rod eldevai to 8iotl Oecapelv.] Astronomy, for instance, 
 was engaged for many ages in investigating the apparent motions 
 of the heavens ; from this it proceeded to the real motions as the 
 causes of the apparent, and finally to the discovery of the one 
 moving force, viz. gravitation, as the first cause. Readers of 
 Aristotle will remember the passage (Eth. Nic. I. 7. 20), to 5' on 
 irpQrrov kclI o.pxh-> and (I. 4. 7), &PXV l^P T T i. 
 
 14 To take an instance of this, if "gold is a metal," and we 
 predicate "ductility" of "metal," we are able to predicate it of 
 " gold " also. The " dictum de omni et nullo " is the general 
 assertion of this principle. Whatever is predicated, i.e. asserted 
 or denied, of the whole of a class may be predicated of each 
 particular member of that class. 
 
 15 TideTdi de to pLecrov . . . irpCoTov de ttj Oe'crei.'] i.e. the middle 
 term is predicated of both extremes in the premisses, and so stands 
 first in the Greek ; but in English it is the predicate of both premisses, 
 and stands last. 
 
 16 TideTdi de to pL^crov . . . ?ax aT0V ^ r V #&>"] In English, in 
 the third figure, the middle term stands first in both premisses. It 
 will be observed that in Aristotle there is no fourth figure. The 
 latter was added by later logicians, but is not much used. The moods 
 of the fourth figure may be regarded as indirect moods of the first. 
 Those of the first may be reduced to the fourth by transposing the 
 premises. 
 
 17 ttXtjv ov 5l6ti dXX' 8tl.] i.e. the conclusion is truly stated, but 
 its necessity is not proved, because one or both of the premisses 
 are false. As an instance of the former Aristotle gives, "No white 
 is an animal, All snow is white . \ No snow is an animal " ; as an 
 instance of the latter, " No man is an animal, Every stone is a man 
 . '. No stone is an animal." 
 
 18 dec de voelv t6 T, etc.] To compare the inductive syllogism 
 with the demonstrative let us take an example of the former, as 
 follows: Gold, silver, and iron, etc., are ductile; Gold, silver, and 
 iron, etc., are all metals . '. All metals are ductile. Here, from the 
 ductility (a) of gold, silver, and iron, etc. (c), and the fact that these 
 are all metals (b), we conclude that all metals are ductile. This 
 
30 NOTES. 
 
 is in form a syllogism in the third figure with a universal conclusion, 
 which arises from the fact that in the minor premiss the predicate (b) 
 is distributed. The corresponding syllogism in Barbara will be: 
 All metals are ductile, Gold is a metal .*. it is ductile, where the 
 conclusion is part of the major premiss of the inductive syllogism. 
 
 19 (TTjixeiov de j3oi5Xerai efocu, etc.] As an instance of a necessary 
 demonstrative proposition {reKfi^piov) Aristotle gives, " He is sick, for 
 he is feverish," where fever is a necessary sign of sickness, i.e. 
 feverishness is always a sign of sickness. As an instance of the 
 weaker kind (ZvdoZos), founded on opinion, he gives, "Wise men are 
 just, for Socrates was wise and just." This latter, which may be 
 stated as a syllogism in the third figure with a universal conclusion, 
 is invalid. 
 
 20 Just as the Enthymeme, including etibs and arjjuLetov, is a 
 rhetorical syllogism Example is like Induction. But the former 
 differs from the latter in that it assumes a universal proposition, and 
 proceeds to infer from one example of it, that has been known, 
 another effect of a similar nature. In the instance given it is 
 assumed that all wars with neighbours are dangerous; and because 
 the war with the Phocians was unprofitable to the Thebans, it is 
 inferred that the war with the Thebans will be unprofitable to the 
 Athenians. Aristotle gives another instance of Example in the 
 Rhetoric. ' Dionysius, when he asked for a body-guard, was proved 
 to be forming a design of becoming tyrant of Syracuse, for Pisistratus 
 at Athens and Theagenes at Megara proceeded in a similar manner. 
 
 21 els aireipov yhp hv padifri.] Cf. Aris. Eth. Nic. I. 2. 1 and 
 I. 7. 7, where this principle is applied (1) in determining the 
 summum bonum, (2) in limiting the circle within which avrapKeia is 
 to radiate. 
 
 22 Otaiv fiev \iyoj, etc.] On the passage (Eth. Nic. I. 5. 6) where 
 Aristotle says that no one would deem a man happy merely because 
 he is virtuous, el fir) 64<tlv dicMpvX&TTcov, Grant points out the difference 
 between deaeis in demonstration, which are those unproved principles 
 necessary to the existence of each separate science, just as d^c^uara 
 are to the existence of reasoning in general, and Oiaeis in dialectic, 
 which are paradoxical positions resting on the authority of some 
 great name. The latter kind of diais is defined {Topics, I. xi. 4) 
 to be V7r6\7)\f/is Trapddo^os. 
 
 23 itno-Trifn) t) iicelvwv, etc.] This science is Metaphysics, from 
 which as from their source all other sciences take their origin. Its 
 
NOTES. 31 
 
 principles are also those which lie at the foundation of all other 
 sciences (dp%at tdtat). They are not mere generalities, but, like 
 definitions, proceed from a genus in combination with a specific 
 difference. For instance, take the Science of Ethics (Eth. Nic. 
 I. 7. 10), where the definition of human happiness is derived from 
 the proper work and function of man, which is the 15 la dpxh of 
 the science. 
 
 24 7} 8' ata07](ns rod Ka66\ov io-riv.] Sense-perception is generally 
 applied to the particular, but in a wider point of view it also em- 
 braces a universal, or the whole of a class, which is perceived by the 
 mind. Such are the primary universals as opposed to the ultimate, 
 which are not cuV077T&, but votjtol. 
 
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