Questions

This is a list of all the questions and their associated study carrel identifiers. One can learn a lot of the "aboutness" of a text simply by reading the questions.

identifier	question
4908	But what if these molecules, indestructible as they are, turn out to be not substances themselves, but mere affections of some other substance?
4908	But why should we labour to prove the advantage of practical science to the University?
4908	and how much is there of it?
254	( he stretches) Socrates: So, boy, we can change the parts of the ratios, without changing the real meaning of the ratio itself?
254	A ratio makes a rational number?
254	And getting farther is largely a matter of guesswork, is it not?
254	And that must mean it ca n''t be a member of the last group, does n''t it?
254	And what of two?
254	And what shall I offer you as a return wager?
254	Any other kind?
254	Are all great thoughts as simple as these, once you see them clearly?
254	Boy: Are you sure we have proved this properly?
254	Boy: I thought I had demonstrated that, Socrates?
254	Boy: We want to see if this square root of two we discovered the other day is a member of the rational numbers?
254	Boy: Yes, Socrates, though I remember thinking that there should have been a number which would give eight, Socrates?
254	Boy: Yes, shall I tell you?
254	Boy: You mean anything?
254	Boy: You want me to call the numbers made from ratios of whole numbers something called rational?
254	Can you divide by other numbers than two?
254	Can you do as well, today?
254	Can you do it?
254	Could we make any other kind?
254	Do all school children know that, Meno?
254	Do thoughts get simpler as they get greater?
254	Do you know how long that line is, boy?
254	Does it violate our agreement?
254	Does that suit you?
254	Have I failed?
254	He comes to Meno) Boy: Do you see?
254	His teacher must be proud, for I have taught him nothing of this, have I?
254	How is that with you?
254	If we multiply these numbers times themselves, what do we get, boy?
254	Is it odd or even?
254	Is this much correct?
254	Is this not the way to virtue?
254	Meno: And in giving you freedom, I would be remiss if I did not give you a job and a coming out party of equal position with your wealth, would I not?
254	Meno: Therefore, I would have to give to you the freedom to own the money, before I could give you the money, would I not?
254	Meno:( turns to the boy) You are aware that a servant may not own the amount of gold I would have to give you, should you win the day?
254	Now, this number, do you remember if it had to be larger or smaller than one?
254	Shall I tell the boy what he shall receive?
254	Shall we go on?
254	So the square root of two is smaller than the side two which is the root of four, and larger than the side one which yields one?
254	Socrates: And an even number is two times one whole number?
254	Socrates: And can our square root of two be in that group?
254	Socrates: And could an even number be double an odd number?
254	Socrates: And how many of them were there?
254	Socrates: And if a number is two times any whole number, it must then be an even number, must it not?
254	Socrates: And if the top number is four times some whole number, then a number half as large would have to be two times that same whole number?
254	Socrates: And shall have we a wager on the events of today?
254	Socrates: And the one particular square on the diagonal we made, whose area was two, do you remember that one?
254	Socrates: And the second, or bottom number, is the result of an odd number times itself?
254	Socrates: And would you like to hire the Pythagoreans to run your household, Meno?
254	Socrates: And you know the way to undo multiplication?
254	Socrates: Can you give me an estimate?
254	Socrates: Do I?
254	Socrates: Do you agree with the way I told him this, Meno?
254	Socrates: Let''s try odd over even next, shall we?
254	Socrates: Meno, have you anything to contribute here?
254	Socrates: Now if a number is to be twice as great as another, it must be two times that number?
254	Socrates: Now think carefully, boy, what kind of ratios can we make from even numbers and odd numbers?
254	Socrates: Now, boy, do you remember me, and the squares with which we worked and played the other day?
254	Socrates: So can it be a member of the ratios created by an even number divided by an odd number and then used as a root to create a square?
254	Socrates: So if we use this even number twice in multiplication, as we have on top, we have two twos times two whole numbers?
254	Socrates: So the number on the bottom is two times that whole number, whatever it is?
254	Socrates: So we can eliminate one of our four groups, the one where even was divided by even, and now we have odd/ odd, odd/ even and even/ odd?
254	Socrates: So you agree that this is correct?
254	Socrates: So you have, my boy, has he not Meno?
254	Socrates: So, in our ratio we want to square to get two, the top number can not be odd, can it?
254	Socrates: So, indeed, this could be where we find a number such that when multiplied times itself yields an area of two?
254	Socrates: So, the first, or top number, is the result of an even number times itself?
254	Socrates: Then is can not be a member of the group which has an odd number on the bottom, can it?
254	Socrates: Then you know what odd and even are, boy?
254	Socrates: They are not lacking so much that they can not be improved, are they boy?
254	Socrates: To Meno, surely he is a fine boy, eh Meno?
254	Socrates: Very good, and have your teachers ever called these numbers ratios?
254	Socrates: Well, how long did it take the Pythagoreans?
254	Socrates: What do you say, Meno?
254	Socrates: What happens when you multiply an even number by an even number, what kind of number do you get, even or odd?
254	Socrates: Would you have me continue, Meno?
254	Socrates: Yes boy, can you do that?
254	Socrates: Yes, but is it not true that we stumble and fall over the obstacles which we make for ourselves to trip over?
254	Socrates:( Turning to Meno) So now he is as far as most of us get in determining the magnitude of the square root of two?
254	Socrates:( back to the boy) And what have you learned about ratios of even numbers, boy?
254	Socrates:( nudges Meno) and therefore the top number is four times some whole number times that whole number again?
254	Socrates:( standing) And if it is two times a whole number, then it must be an even number, must it not?
254	Socrates:( taking the boy aside) What would you like the most in the whole world, boy?
254	They give us 1,4,9 and 16 as square areas, did they not?
254	We have divided the rational numbers into four groups, odd/ even, even/ odd, even/ even, odd/ odd?
254	What are they?
254	What can we say about such a number?
254	Would that be fun to try?
254	Would you like that?
254	You know multiplication, boy?
39713	Burali- Forti''s reasoning,I said,"does it not seem to you irreproachable?"
39713	What more do you want?
39713	Yes, I know; but then what good are you?
39713	( 2) Can we reduce to one and the same measure facts which transpire in different worlds?
39713	201 The Mind Dispelling Optical Illusions 202 Euclid not Necessary 202 Without Hypotheses, no Science 203 What Outcome?
39713	2º Once in possession of the concept of the mathematical continuum, is one safe from contradictions analogous to those which gave birth to it?
39713	A naturalist who never had studied the elephant except in the microscope, would he think he knew the animal adequately?
39713	After all, have we any other reason to believe in the existence of material objects?
39713	After what we have just said, is there still need to answer this objection?
39713	Among all these possible explanations, how make a choice for which the aid of experiment fails us?
39713	Among the terms proportional to the squares of the velocities, how distinguish those which come from_ T_ or from_ U_?
39713	Among these thousand routes opening before us, it is necessary to make a choice, at least provisional; in this choice, what shall guide us?
39713	And Newton''s law itself?
39713	And after that?
39713	And are such signals inconceivable, if we admit with Laplace that universal gravitation is transmitted a million times more rapidly than light?
39713	And besides, why do we speak of measuring?
39713	And does our ether really exist?
39713	And first of all, are they such uncompromising realists as has been said?
39713	And first what does this question mean?
39713	And first what should we understand by objectivity?
39713	And first, can we conserve the principles of relativity?
39713	And first, what is chance?
39713	And for these, then, what is the measure of their objectivity?
39713	And further: how is error possible in mathematics?
39713	And here a question arises: How can a demonstration not sufficiently rigorous for the analyst suffice for the physicist?
39713	And how is this deduction made?
39713	And if it can not, how dare we reason about it?
39713	And if the law should one day be found false?
39713	And if there are, how recognize them?
39713	And if there were not this accord, should we not have also the right to say experience had proven the falsity of the non- Euclidean geometry?
39713	And if we wish to combat them, which should be favored?
39713	And in mathematics?
39713	And inversely, if the experiment succeeds, shall we believe that we have demonstrated all the hypotheses at once?
39713	And now, why have I entitled this chapter_ French Geodesy_?
39713	And on the other hand what means the phrase''very complex''?
39713	And then a question presents itself: among all these quantities measured experimentally, which shall we choose to represent the parameters_ q_?
39713	And then comes a question: Is not this amorphous continuum, that our analysis has allowed to survive, a form imposed upon our sensibility?
39713	And then when we ask: Can one imagine non- Euclidean space?
39713	And then, has one the right to say that the scientist creates the scientific fact?
39713	And this convention of language once adopted, when I shall be asked: Is it such an hour?
39713	And to return to America, is not the_ Monist_ published at Chicago, that review which even to us seems bold and yet which finds readers?
39713	And to- day, a century and a half after the victory of the Newtonians, think you geodesy has nothing more to teach us?
39713	And what gives us the right to make this hypothesis?
39713	And what group?
39713	And what is the null class?
39713	And why are they more noteworthy?
39713	And why do we say this transportation is effected without deformation?
39713	And why may this probability be regarded as constant within a small interval?
39713	And why?
39713	And yet if we accept Gouy''s ideas on the Brownian movement, does not the microscope seem on the point of showing us something analogous?
39713	And yet is this legitimate, if the unknown be the simple and the known the complex?
39713	And yet, in this case, would it have any meaning, to say the earth turns round?
39713	And yet, think you the partisans of the kinetic theory are adversaries of determinism?
39713	And, in this latter case, do we not risk marring everything?
39713	And, this group chosen, which of its sub- groups shall we take to characterize a point of space?
39713	And, yet, would it not be more logical in remaining silent?
39713	Another thing: whence does space get its quantitative character?
39713	Are not appearances against him?
39713	Are the chances that these circles will cover a great number of times the celestial sphere?
39713	Are the differential equations of the problem too simple for us to apply the laws of chance?
39713	Are the law of acceleration, the rule of the composition of forces then only arbitrary conventions?
39713	Are there more points in space than points in a plane?
39713	Are these mechanical actions too small to be measured, or are they accessible to experiment?
39713	Are they absolutely refractory, I do not say to metaphysic, but at least to everything metaphysical?
39713	Are they disguised conventions?
39713	Are they experimental verities?
39713	Are they imposed on us by logic?
39713	Are they obtainable by deductive reasoning?
39713	Are they synthetic_ a priori_ judgments, as Kant said?
39713	Are they the characteristics of a form imposed either upon our sensibility or upon our understanding?
39713	Are they then arbitrary?
39713	Are we absolutely sure they are unimportant?
39713	Are we on the eve of a second crisis?
39713	Because it is''lived,''that is, because we love it and believe in it?
39713	Besides how do we know whether this law, true for so many centuries, will still be true next year?
39713	Besides, do you think they have always marched step by step with no vision of the goal they wished to attain?
39713	But I can understand also: Will such a chemical effect happen?
39713	But am I sure the body_ P_ has retained the same weight when I have transported it from the first body to the second?
39713	But are there any simple facts?
39713	But at what moment should we stop?
39713	But by what right do we consider as equal these two figures which the Euclidean geometers call two circles with the same radius?
39713	But can we not then pass over immediately to the goal?
39713	But can we regret that earthly paradise where man brute- like was really immortal in knowing not that he must die?
39713	But could I not just as well say: The points which turn up on the two dice can form 6 × 7/2= 21 different combinations?
39713	But could not experience have given a contrary result?
39713	But did not M. LeRoy make it still too great?
39713	But do you think mathematics has attained absolute rigor without making any sacrifice?
39713	But even stopping short of such models, does he not already expose himself to the same danger?
39713	But even this, what does it mean?
39713	But for that how does he proceed?
39713	But has any one ever experimented on bodies withdrawn from the action of every force?
39713	But has even this any meaning?
39713	But have we the right to admit the hypothesis of central forces?
39713	But he means something more; and we think we understand it because we think we know what impact is in itself; why?
39713	But how can it be possible that there are several parameters whose variations are independent?
39713	But how do we decide that this object is more noteworthy?
39713	But how does one perceive these analogies and these differences?
39713	But how generalize?
39713	But how has he not understood that what remained to do was not less considerable and would be not less profitable?
39713	But how have the stars composing it reached all at the same time adult age, an age so briefly to endure?
39713	But how is this prediction made?
39713	But how many different ideas are hidden under this same word?
39713	But how measure force, or mass?
39713	But how much after?
39713	But how much heat would thus be produced?
39713	But how reconcile that with what we have said above on the absence of a noteworthy proportion of dark matter?
39713	But how shall we ascertain experimentally whether it belongs to this or that concrete object?
39713	But how shall we justify it in the presence of discoveries that show us every day new details that are richer and more complex?
39713	But how shall we recognize that the antecedents_ A_ and_ A''_ are''slightly different''?
39713	But how should electricity in its turn enter into the general unity, how should it be reduced to the universal mechanism?
39713	But if truth be the sole aim worth pursuing, may we hope to attain it?
39713	But in the end the Copernicus would come-- how?
39713	But is it always needful to say it so many times?
39713	But is it at least logic, or, better, is it correct?
39713	But is that true?
39713	But is the art of sound reasoning not also a precious thing, which the professor of mathematics ought before all to cultivate?
39713	But is this definition altogether satisfactory?
39713	But may not this assemblage be compared to that of the molecules of a gas, whose properties the kinetic theory of gases has made known to us?
39713	But of what importance is that?
39713	But once equal, if asked about the anterior state, what can we answer?
39713	But still more; how define energy itself?
39713	But then doubtless men can no longer live and must give place to other beings-- should I say far smaller or far larger?
39713	But then why have we this right?
39713	But then, if experiment is everything, what place will remain for mathematical physics?
39713	But then, what have we gained by this stroke?
39713	But then, why is the principle true only if the motion of the movable axes is rectilinear and uniform?
39713	But then, why not say the mass is the quotient of the force by the acceleration?
39713	But this hypothesis is improbable; why, in fact, would all the corpuscles of the same mass take always the same velocity?
39713	But this is not enough; who does not feel that this is still to leave to chance too great a rôle?
39713	But this simplicity being only apparent, will the ground be firm enough?
39713	But to answer the question: Is this theorem true?
39713	But to know this is to know something and then why tell us we can know nothing?
39713	But we always meet again the same difficulty; at what precise moment does it begin to be too much so?
39713	But what could they deduce from it?
39713	But what does that mean?
39713	But what does this signify?
39713	But what good is it?
39713	But what is chance?
39713	But what is the nature of these rules?
39713	But whence came the error of this philosopher?
39713	But whence can come to us this revelation, if not from the accord of a theory with experiment?
39713	But where is the simple fact?
39713	But why assemble these elements in this way when a thousand other combinations were possible?
39713	But why?
39713	But why?
39713	But why?
39713	But, after all, what have we done?
39713	But, first, what do you understand by geometric properties of the bodies?
39713	But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction?
39713	By operating upon the canal rays as Kaufmann did upon the[ beta] rays?
39713	By what mechanism?
39713	By what right do we strive to put them into the same mold, to measure them by the same standard?
39713	CHAPTER III MATHEMATICS AND LOGIC INTRODUCTION Can mathematics be reduced to logic without having to appeal to principles peculiar to mathematics?
39713	CHAPTER IV CHANCE I"How dare we speak of the laws of chance?
39713	CHAPTER IX THE FUTURE OF MATHEMATICAL PHYSICS_ The Principles and Experiment._--In the midst of so much ruin, what remains standing?
39713	CHAPTER VII THE HISTORY OF MATHEMATICAL PHYSICS_ The Past and the Future of Physics._--What is the present state of mathematical physics?
39713	CHAPTER VIII THE PRESENT CRISIS OF MATHEMATICAL PHYSICS_ The New Crisis._--Are we now about to enter upon a third period?
39713	Can it even be defined?
39713	Can it return of itself?
39713	Can logic give it to us?
39713	Can one apply to all matter what has been proved only for such light corpuscles, which are a mere emanation of matter and perhaps not true matter?
39713	Can science teach us the true relations of things?
39713	Can that be regarded as a true solution?
39713	Can the straight line be defined?
39713	Can this demonstration be deduced from experiments or from_ a priori_ considerations?
39713	Can this law be verified by experiment?
39713	Can we not be content with just the bare experiment?
39713	Can we show this deformation?
39713	Can we subscribe to this conclusive condemnation?
39713	Can we without danger act as if it were?
39713	Complex causes we have said produce a blend more and more intimate, but after how long a time will this blend satisfy us?
39713	Consequently, how distinguish the two parts of energy?
39713	Considering the slight density of the milky way, is it the image of gaseous matter or of radiant matter?
39713	Could Galileo and the Grand Inquisitor, to settle the matter, appeal to the witness of their senses?
39713	Could it be otherwise?
39713	Could we recognize with a little attention that this pure intuition itself could not do without the aid of the senses?
39713	Do we find it in nature, or do we ourselves introduce it there?
39713	Do we say that it is impossible for us to understand anything about this machine so long as we are not permitted to take it to pieces?
39713	Do you think American geometers are concerned only about applications?
39713	Do you think that in such a world we should be what we are?
39713	Do you think the moralists themselves are irreproachable when they come down from their pedestal?
39713	Do you think the second phase could have come into existence without the first?
39713	Does it make us understand its unity and harmony?
39713	Does it mean that we_ represent_ to ourselves external objects in geometric space?
39713	Does the earth rotate?
39713	Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence?
39713	Does the mathematical method proceed from the particular to the general, and, if so, how then can it be called deductive?
39713	Does this form exist, or, if you choose, can we represent to ourselves space of more than three dimensions?
39713	Does this mean that nothing is left of this objection of the philosophers?
39713	Does this mean that our most legitimate, most imperative aspiration is at the same time the most vain?
39713	Does this mean that the definition guarantees, as it should, the existence of the object defined?
39713	Does this mean that these atoms or these cells constitute reality, or rather the sole reality?
39713	Does this mean the work of Fresnel was in vain?
39713	Doubtless we should first bend our efforts to assuage human suffering, but why?
39713	Even if they had entirely succeeded, would the Kantians be finally condemned to silence?
39713	Experiments have been made which should have disclosed the terms of the first order; the results have been negative; could that be by chance?
39713	For subtraction it is quite otherwise; it may be logically defined as the operation inverse to addition; but should we begin in that way?
39713	From this rapid exposition, what shall we conclude?
39713	Has chance thus defined, in so far as this is possible, objectivity?
39713	Has not M. de Cyon said that the Japanese mice, having only two pair of semicircular canals, believe that space is two- dimensional?
39713	Has one the right to give this extension to the meaning of the word_ logic_?
39713	Has one the right, therefore, to say he knows the distance between two points?
39713	Has probability been defined?
39713	Has science any place for such theories?
39713	Has the discarded hypothesis, then, been barren?
39713	Has this a meaning, and if so what?
39713	Has this word the same meaning for all the world?
39713	Have I the right to believe this?
39713	Have the peoples whose ideal most conformed to their highest interest exterminated the others and taken their place?
39713	Have these relations an objective value?
39713	Have we finally attained absolute rigor?
39713	Have we not just seen that it is by astronomy that, to speak his language, humanity has passed from the theological to the positive state?
39713	Have we the right to reason in this way?
39713	Have we the right, for instance, to enunciate Newton''s law?
39713	He has set himself questions like these: Are there more points in space than whole numbers?
39713	How am I led to regard these two series_ S_ and_ S''''_ as corresponding to the same displacement_ AB_?
39713	How are we led thereto?
39713	How are we led to conclude thence that they are identical?
39713	How can a law become a principle?
39713	How can intuition deceive us on this point?
39713	How can that be?
39713	How can we estimate the value of the new weapon thus won?
39713	How can we explain the very singular appearances presented by the spiral nebulæ, which are too regular and too constant to be due to chance?
39713	How can we explain this apparent contradiction?
39713	How can we know that two possible cases are equally probable?
39713	How could he be so short- sighted?
39713	How could he do it if we should leave between instruments and objects the deep chasm hollowed out by the logicians?
39713	How could that be, if time were not a form pre- existent in our minds?
39713	How could they have believed that motion stops when the cause which gave birth to it ceases?
39713	How could we know there were empty compartments, if these compartments were revealed to us only by their content?
39713	How define this group then without moving some solids?
39713	How do they accomplish it?
39713	How do we know whether two points of space are identical or different?
39713	How does Hilbert demonstrate this essential point?
39713	How does it happen that so many refuse to understand mathematics?
39713	How does it happen there are people who do not understand mathematics?
39713	How enunciate rules applicable to circumstances so complex?
39713	How is it possible?
39713	How is it then for the milky way?
39713	How long would it be necessary to wait?
39713	How many dimensions has this continuum?
39713	How many unexpected guests must be stowed away?
39713	How save ourselves from this_ petitio principii_?
39713	How shall we decide between these two hypotheses?
39713	How shall we define force?
39713	How shall we even reconcile it with the belief in the unity of nature?
39713	How should the equations of mathematical physics be treated?
39713	How should we picture a receptacle filled with gas?
39713	How so?
39713	How then am I led to distinguish them?
39713	How then choose the interesting fact, which is that which begins again?
39713	How then could we have been led to distinguish between the two?
39713	How then do they choose between the facts of nature?
39713	How then shall we recognize the equivalence of these two series?
39713	How was the order of the universe understood by the ancients; for instance, by Pythagoras, Plato or Aristotle?
39713	How was this triumph obtained?
39713	How, under these conditions, can we make out in this total mass the part of the real mass and that of the fictitious electromagnetic mass?
39713	How?
39713	However, because no painter has made a perfect portrait, should we conclude that the best painting is not to paint?
39713	I am asked: Did the eclipse happen at the hour predicted?
39713	I can understand that that means: Will such a mechanical effect happen?
39713	I have shown above by examples that the first two can not give us certainty; but who will seriously doubt the third, who will doubt arithmetic?
39713	I repeat my question: Do you think that in such a world we should be what we are?
39713	I should like to know who was to prevent him, and can it be said a thing does not exist, when we have called it[ Omega]?"
39713	I will explain myself; how did the ancients understand law?
39713	III I once said no to this question:[12] should our reply be modified by the recent works?
39713	II_ Comparison with Astronomic Observations_ Can the preceding theories be reconciled with astronomic observations?
39713	IV Why now have all these spaces three dimensions?
39713	If Larmor has failed, as it seems to me he has, does that mean that a mechanical explanation is impossible?
39713	If a modern physicist studies a new phenomenon, and if he discovers its law Tuesday, would he have said Monday that this phenomenon was fortuitous?
39713	If it was perceived that the concordance of the two effects, mechanical and chemical, is not constant?
39713	If it were ruled by caprice, what could prove to us it was not ruled by chance?
39713	If it were so, how should the Greeks have failed to recognize it?
39713	If not, why had this combination more right to exist than all the others?
39713	If science did not succeed, it could not serve as rule of action; whence would it get its value?
39713	If the coefficient of inertia is not constant, can the attracting mass be?
39713	If there is no absolute space, can one turn without turning in reference to something else?
39713	If there is no longer any mass, what becomes of Newton''s law?
39713	If therefore, during an eclipse, it is asked: Is it growing dark?
39713	If they deceived themselves, do we not likewise cheat ourselves?
39713	If this is only an illusion, why is this illusion so tenacious?
39713	If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting?
39713	If we construct a theory based on a number of hypotheses, and if experiment condemns it, which of our premises is it necessary to change?
39713	If you put the question to me: Is such a fact true?
39713	If, then, experiment confirms his conclusions, will he think that he has demonstrated, for instance, the real existence of atoms?
39713	In a word, is not the subliminal self superior to the conscious self?
39713	In fact, how will a gaseous mass let loose in the void act, if its elements attract one another according to Newton''s law?
39713	In fact, what is mathematical creation?
39713	In how far is it exact?
39713	In other words, do we mean that we must be sure not to meet contradictions, on condition of agreeing to stop just when we are about to encounter one?
39713	In other words, should we constrain the young people to change the nature of their minds?
39713	In presence of this general collapse of the principles, what attitude will mathematical physics take?
39713	In the applications we have to make of these three concepts, do they present themselves to us as defined by these three postulates?
39713	In the edifices built up by our masters, of what use to admire the work of the mason if we can not comprehend the plan of the architect?
39713	In the first place, what instrument have we at our disposal for this conquest?
39713	In the measurements of which we speak in the preceding section, what is it we determine in measuring the two deviations?
39713	In this multitude how shall we choose those which are worthy to fix our attention?
39713	In what measure does the mind get this satisfaction and why is it not content with it?
39713	Is Mr. Russell preparing to show that one at least of the two contradictory reasonings has transgressed the code?
39713	Is experience the source of geometry?
39713	Is is really deductive, as is commonly supposed?
39713	Is it a simple chance which confers this privilege?
39713	Is it by caprice?
39713	Is it certain it will never be contradicted by experiment?
39713	Is it certain our imaginary astronomers would do the same?
39713	Is it desired that this common part of the enunciations be expressible in words?
39713	Is it impossible that experiment may some day contradict our postulate?
39713	Is it impossible to conceive physical phenomena, the mechanical phenomena, for example, otherwise than in space of three dimensions?
39713	Is it likely that it is able to form all the possible combinations, whose number would frighten the imagination?
39713	Is it meant that we could not experimentally demonstrate Euclid''s postulate, but that our ancestors have been able to do it?
39713	Is it not as if one strove to measure length with a gram or weight with a meter?
39713	Is it not evident that from the principle so understood we could no longer infer anything?
39713	Is it possible to fulfill so many opposing conditions?
39713	Is it possible to reconcile it with the principle of the conservation of energy?
39713	Is it the radius of the disc?
39713	Is it the same with two physical facts?
39713	Is it the thickness?
39713	Is it this which Russell calls the''zigzaginess''?
39713	Is it thought that ordinary language by aid of which are expressed the facts of daily life is exempt from ambiguity?
39713	Is it true they afford means of proving the principle of complete induction without any appeal to intuition?
39713	Is it well to let them know this is only approximative?
39713	Is its orientation about to be modified?
39713	Is mathematical analysis, then, whose principal object is the study of these empty frames, only a vain play of the mind?
39713	Is nature governed by caprice, or does harmony rule there?
39713	Is not chance the antithesis of all law?"
39713	Is not human intelligence, more specifically the intelligence of the scientist, susceptible of infinite variation?
39713	Is not my present nearer my past of yesterday than the present of Sirius?
39713	Is not the very spectrum of the spark, in which we recognize the lines of the metal of the electrode, a proof of it?
39713	Is not this the means of escaping the ridicule that we foresee?
39713	Is space revealed to us by our senses?
39713	Is that not something of a paradox?
39713	Is the abyss which separates them less profound than it at first appeared?
39713	Is the milky way thus constituted truly the image of a gas properly so called?
39713	Is the principle of inertia, which is not an_ a priori_ truth, therefore an experimental fact?
39713	Is there a law of errors?
39713	Is there in nature some familiar object which is so to speak the rough and vague image of it?
39713	Is there something to change in all that when we pass to the following stages?
39713	Is this a simple illusion of ours, or are there cases where this way of thinking is legitimate?
39713	Is this a third way of conceiving chance?
39713	Is this a truth imposed_ a priori_ upon the mind?
39713	Is this a useless luxury?
39713	Is this a verifiable fact?
39713	Is this affirmative answer forced upon us by the facts I have just given?
39713	Is this apparent contiguity a mere effect of chance?
39713	Is this because it is too remote from all other bodies to experience any appreciable action from them?
39713	Is this enough?
39713	Is this evolution ended?
39713	Is this hypothesis rigorously exact?
39713	Is this not enough to show they are capable of making ascensions otherwise than in a captive balloon?
39713	Is this not for us mathematicians in a way a professional procedure?
39713	Is this possible in particular when it is a question of giving a definition?
39713	Is this the case here?
39713	Is this then a question of method?
39713	Is this to say that the principle has no meaning and vanishes in a tautology?
39713	Is this way of looking at it legitimate?
39713	It is doubtless something intermediate; but what can we say then of the thickness itself, or of the radius of the disc?
39713	It is evident from the first that systematic errors can not satisfy Gauss''s law; but do the accidental errors satisfy it?
39713	It is useless to seek to change anything of that, and besides would it be desirable?
39713	It may be asked, for instance, what is the present distribution of the minor planets?
39713	May we not fear lest some day a new experiment should come to falsify the law in some domain of physics?
39713	Might it not happen that it can accord with experience only by violating the principle of sufficient reason or that of the relativity of space?
39713	Might not new experiments some day lead us to modify or even to abandon them?
39713	Might there not be an abrupt fall of potential in the neighborhood of one of the armatures, of the negative armature, for example?
39713	Moreover, do we not often invoke what Bertrand calls the laws of chance, to predict a phenomenon?
39713	Must geometry be regarded both as a branch of kinematics and as a branch of optics?
39713	Must not this existence be established, in order that the existence of the class of which it is a part may be deduced?
39713	Must we believe that the evolution of the milky way began when the matter was still dark?
39713	Must we combat them?
39713	Must we continue to use the method of least squares?
39713	Must we lament this?
39713	Must we show those content with the pure logic that they have seen only one side of the matter?
39713	Must we therefore translate as follows?
39713	Must we use them?
39713	Must we, therefore, abandon science and study only morals?
39713	Need I also recall that M. Hermite obtained a surprising advantage from the introduction of continuous variables into the theory of numbers?
39713	Need I point out that the fall of Lavoisier''s principle involves that of Newton''s?
39713	Need I recall that thus have been made all the important discoveries?
39713	Need we add that mathematicians themselves are not infallible?
39713	No one doubts it; but whence comes this confidence?
39713	Nor may you ask: Does the infallibility of arithmetic prevent errors in addition?
39713	Now can we affirm that the hypotheses I have just made are absurd?
39713	Now how do we know that this continuum of displacements has six dimensions?
39713	Now on what condition is the use of hypothesis without danger?
39713	Now what do we see?
39713	Now what is science?
39713	Now what is this creed?
39713	Now when we say that the Euclidean motions are the_ true_ motions without deformation, what do we mean?
39713	Now why is the first method of enumerating the possible cases more legitimate than the second?
39713	Now, what do we see?
39713	Of these two inverse tendencies, which seem to triumph turn about, which will win?
39713	On the other hand, if the principles of mechanics are only of experimental origin, are they not therefore only approximate and provisional?
39713	On the other hand, what happens with regard to the straight line?
39713	On what then could be based experiments which should serve as foundation for geometry?
39713	One could at most have said to us:''Your fillips are doubtless legitimate, but you abuse them; why move the exterior objects so often?''
39713	Only a privileged few are called to enjoy it fully, it is true, but is not this the case for all the noblest arts?
39713	Only, is the compensation perfect?
39713	Or again that every body if nothing prevents, will move in a circle, the noblest of motions?
39713	Or can we, despite all, approach truth on some side?
39713	Or further, what criterion will enable me to apprehend this?
39713	Or is there here a play of evolution and natural selection?
39713	Or is this action by so much the less as the medium is less refractive and more rarefied, becoming null in the void?
39713	Or need we say to those not so cheaply satisfied that what they demand is not necessary?
39713	Or rather what is the probable value of the sine of the longitude at the instant_ t_, that is to say of sin(_ at_+_ b_)?
39713	Or, perhaps, does the apparent correspond to a real contiguity?
39713	Our body is formed of cells, and the cells of atoms; are these cells and these atoms then all the reality of the human body?
39713	PART III THE OBJECTIVE VALUE OF SCIENCE CHAPTER X IS SCIENCE ARTIFICIAL?
39713	Pardon, can you not imagine that the door opens, or that two of these walls separate?
39713	Probability opposed to certainty is what we do not know, and how can we calculate what we do not know?
39713	Scarcely fifteen years ago was there anything more ridiculous, more naïvely antiquated, than Coulomb''s fluids?
39713	Shall I recall to you how it was in its turn thrown into discredit?
39713	Shall we believe that with one single equation we have determined several unknowns?
39713	Shall we ever arrive at that?
39713	Shall we know then what is a point thus defined by its relative position with regard to ourselves?
39713	Shall we let ourselves be guided solely by our caprice?
39713	Shall we say that if we introduce others, of which we are fully conscious, we shall only aggravate the evil?
39713	Shall we say that the first has been useless?
39713	Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying_ A_ is_ A_?
39713	Shall we think God, contemplating his work, feels the same sensations as we in watching a billiard match?
39713	Should each therefore decide according to his temperament, the conservatives going to one side and the lovers of the new to the other?
39713	Should we abandon one of the two hypotheses, and which?
39713	Should we here understand by finite number every number to which by definition the principle of induction applies?
39713	Should we not always have been able to justify these fillips by the same reasons?
39713	Should we retain the classic definition of parallels and say parallels are two coplanar straights which do not meet, however far they be prolonged?
39713	Should we simply deduce all the consequences and regard them as intangible realities?
39713	Should we therefore conclude that the axioms of geometry are experimental verities?
39713	Should your rules be followed blindly?
39713	Since several geometries are possible, is it certain ours is the true one?
39713	So much for the rotation of the earth upon itself; what shall we say of its revolution around the sun?
39713	So that to ask what geometry it is proper to adopt is to ask, to what line is it proper to give the name straight?
39713	So we shall put the question otherwise; can geodesy aid us the better to know nature?
39713	So what must we conclude?
39713	Suppose we find the ray of light does not satisfy Euclid''s postulate( for example by showing that a star has a negative parallax), what shall we do?
39713	THE IMPLICIT AXIOMS.--Are the axioms explicitly enunciated in our treatises the sole foundations of geometry?
39713	That granted, what do we do?
39713	That is an experimental truth, but it can not be invalidated by experience; in fact, what would a more precise experiment teach us?
39713	That means: Are these relations the same for all?
39713	That supposes the field uniform; is this certain?
39713	That would be easy, I have said, but that would be rather long; and would it not be a little superficial?
39713	The English are right, that goes without saying; but how could the other method have been persisted in so long?
39713	The engineer should receive a complete mathematical education, but for what should it serve him?
39713	The example ordinarily cited is that of a ball rolling a very long time on a marble table; but why do we say it is subjected to no force?
39713	The experimenter puts to nature a question: Is it this or that?
39713	The nominalist attitude is justified only when it is convenient; when is it so?
39713	The principle is intact, but thenceforth of what use is it?
39713	The rule of tric- trac is indeed a rule of action like science, but does any one think the comparison just and not see the difference?
39713	The rules of perfect logic, are they the whole of mathematics?
39713	The way these cells are arranged, whence results the unity of the individual, is it not also a reality and much more interesting?
39713	Then does the scientist create science?
39713	Then what are we to think of that question: Is the Euclidean geometry true?
39713	Then what happens?
39713	There is connection between the warning_ A1_ and the parry_ B1_, this is an internal property of our intelligence; but why this connection?
39713	There is no difficulty as to_ U_, but can_ T_ be regarded as the_ vis viva_ of a material system?
39713	There is the event, what is the cause?
39713	There steeples were not lacking: but to install oneself in them with mysterious and perhaps diabolic instruments, was it not sacrilege?
39713	Therefore two difficulties:( 1) Can we transform psychologic time, which is qualitative, into a quantitative time?
39713	Therefore, when we ask what is the objective value of science, that does not mean: Does science teach us the true nature of things?
39713	These principles on which we have built all, are they about to crumble away in their turn?
39713	This it is that we are about to consider, and we shall put the question in these terms: When we say that space has three dimensions, what do we mean?
39713	Thus all seems arranged, but are all the doubts dissipated?
39713	Thus would not the horse harnessed to his treadmill refuse to go, were his eyes not bandaged?
39713	To minds so unlike can the mathematical theorems themselves appear in the same light?
39713	To what need does it respond?
39713	To- day, what do we see?
39713	Truth which is not the same for all, is it truth?
39713	Two psychological phenomena happen in two different consciousnesses; when I say they are simultaneous, what do I mean?
39713	Under these conditions, how imagine a sieve capable of applying them mechanically?
39713	Upon what condition will this latter definition, which plays an essential rôle in Whitehead''s proof, be''predicative''and consequently acceptable?
39713	V We seek reality, but what is reality?
39713	VII_ The True Solution_ What choice ought we to make among these different theories?
39713	VI_ Zigzag Theory and No- class Theory_ What is Mr. Russell''s attitude in presence of these contradictions?
39713	Was it merely because I do not speak the Peanian with enough eloquence?
39713	Was that to reject it?
39713	Was the Academy wrong?
39713	We say now_ post hoc, ergo propter hoc_; now_ propter hoc, ergo post hoc_; shall we escape from this vicious circle?
39713	Well, is it not a great advance to have distinguished what long was wrongly confused?
39713	Well, now, has this generalized law of inertia been verified by experiment, or can it be?
39713	What are the axes to which we naturally refer the_ extended space_?
39713	What are the problems it is led to set itself?
39713	What are these''things''?
39713	What are we to understand by that?
39713	What assurance is there that a thing we think simple does not hide a dreadful complexity?
39713	What authorizes me so to do?
39713	What can they do in this sense?
39713	What can this advantage be?
39713	What difference is there then between the statement of a fact in the rough and the statement of a scientific fact?
39713	What do I say?
39713	What do we do when we wish to apply the calculus of probabilities to such a question?
39713	What do we mean by_ sufficiently near_?
39713	What does it matter then whether the simplicity be real, or whether it covers a complex reality?
39713	What does that mean?
39713	What does that mean?
39713	What does that mean?
39713	What does that mean?
39713	What does that prove?
39713	What does that prove?
39713	What does the celebrated German geometer do?
39713	What does the word_ exist_ mean in mathematics?
39713	What does this mean?
39713	What does this mean?
39713	What geometry will they construct?
39713	What good are the efforts so expended by the geodesist?
39713	What happens now if the electrons are in motion?
39713	What happens now if we have recourse to some instrument to supplement the feebleness of our senses, if, for example, we make use of a microscope?
39713	What happens then according to the theory?
39713	What happens then?
39713	What happens then?
39713	What has experimental physics to do with such an aid, one which seems useless and perhaps even dangerous?
39713	What has it to do with the method of the physical sciences?
39713	What has made necessary this evolution?
39713	What has taught us to know the true, profound analogies, those the eyes do not see but reason divines?
39713	What is a good definition?
39713	What is a point of space?
39713	What is after all the fundamental theorem of geometry?
39713	What is at the instant_ t_ the probable distribution of the minor planets?
39713	What is for them the real definition of force?
39713	What is geometry for the philosopher?
39713	What is it indeed that gives us the feeling of elegance in a solution, in a demonstration?
39713	What is it necessary to do to give a mechanical interpretation of such a phenomenon?
39713	What is it, to understand?
39713	What is its future?
39713	What is meant when we say that a mathematical continuum or that a physical continuum has two or three dimensions?
39713	What is more complicated than the confused movements of the planets?
39713	What is necessary in order to deduce from this a mechanical explanation?
39713	What is the cause of this evolution?
39713	What is the cause that, among the thousand products of our unconscious activity, some are called to pass the threshold, while others remain below?
39713	What is the curve of probability of each of them?
39713	What is the force that should produce this recoil?
39713	What is the meaning of this?
39713	What is the nature of mathematical reasoning?
39713	What is the origin of this word and of other words also?
39713	What is the probability of his turning up the king?
39713	What is the probability of this push having this or that value?
39713	What is the probability that he is a sharper?
39713	What is the probability that he is a sharper?
39713	What is the probability that its third decimal is an even number?
39713	What is the probability that one of the two at least turns up a six?
39713	What is the probability that one or more representative points may be found in a certain portion of the plane?
39713	What is the probability that the fifth decimal of a logarithm taken at random from a table is a''9''?
39713	What is the probable present distribution of the minor planets on the zodiac?
39713	What is the probable value of sin_ nu_?
39713	What is the result?
39713	What is the rôle of the preliminary conscious work?
39713	What is this_ something else_?
39713	What is zero?
39713	What is_ force_?
39713	What is_ mass_?
39713	What it joins together should that be put asunder, what it puts asunder should that be joined together?
39713	What may be drawn from this comparison?
39713	What meaning according to them has this affirmation?
39713	What means have I then of knowing that these fibers are contiguous?
39713	What means the phrase''very slight''?
39713	What more?
39713	What new islets raise their fronded palms in air within thought''s musical domain?
39713	What now does the principle of least action tell us?
39713	What now will happen when great causes produce small effects?
39713	What prevents our being content with a calculation which has told us, it seems, all we wished to know?
39713	What remains then of the principle of the equality of action and reaction?
39713	What says M. Couturat to the first of these objections?
39713	What science could have been more useful?
39713	What should we conclude?
39713	What should we have done then if experience had given this contrary result?
39713	What simpler than Newton''s law?
39713	What then is a good experiment?
39713	What then is the rôle of experience?
39713	What then is to be done?
39713	What then remains of M. LeRoy''s thesis?
39713	What then should be thought of that direct intuition we should have of the straight or of distance?
39713	What things do they hide?
39713	What victory heralded the great rocket for which young Lobachevski, the widow''s son, was cast into prison?
39713	What was done then?
39713	What was this rash person who, upon our heights so recently set free, dared to raise the hateful standard of the counter- revolution?
39713	What we are free to do as we please-- is it any longer a serious business?
39713	What we are free to think as we please-- is it of any further interest to one who is in search of truth?
39713	What will happen?
39713	What would be its natural generalization?
39713	What would happen if one could communicate by non- luminous signals whose velocity of propagation differed from that of light?
39713	What, first of all, are the properties of space, properly so called?
39713	What, in fact, is a magnetic pole?
39713	When I am asked: Is it growing dark?
39713	When I am asked: Is the current passing?
39713	When I awake to- morrow morning, what sensation shall I feel in presence of such an astounding transformation?
39713	When I observe a galvanometer, as I have just said, if I ask an ignorant visitor: Is the current passing?
39713	When I say that a physical phenomenon, which happens outside of every consciousness, is before or after a psychological phenomenon, what do I mean?
39713	When I say, from noon to one the same time passes as from two to three, what meaning has this affirmation?
39713	When it is said then that we''localize''such and such an object at such and such a point of space, what does it mean?
39713	When it shall have vanished, will hope remain and shall we have the courage to achieve?
39713	When shall we have sufficiently shuffled the cards?
39713	When shall we say two forces are equal?
39713	When shall we say, then, that we have a complete mechanical explanation of the phenomenon?
39713	When slight differences in the causes produce vast differences in the effects, why are these effects distributed according to the laws of chance?
39713	When we have discovered in what direction it is advisable to look for the elementary phenomenon, by what means can we reach it?
39713	When we say space has three dimensions, what do we mean?
39713	When we use the pendulum to measure time, what postulate do we implicitly admit?
39713	When we wish to check a hypothesis, what do we do?
39713	When will it have accumulated sufficient complexity?
39713	Whence come in general the difficulties encountered in seeking rigor?
39713	Whence come the first principles of geometry?
39713	Whence comes the feeling that between any two instants there are others?
39713	Whence comes this certainty and is it justified?
39713	Whence comes this concordance?
39713	Where then is the boundary between the fact in the rough and the scientific fact?
39713	Wherein do these permanently electrified molecules differ from Coulomb''s electric molecules?
39713	Wherein does this syllable form an integrant part of this intuitive idea?
39713	Which group shall we choose, to make of it a sort of standard with which to compare natural phenomena?
39713	Which shall we prefer to regard as the derivatives of these parameters?
39713	Which then are the facts likely to reappear?
39713	Who could doubt that an angle may always be divided into any number of equal parts?
39713	Who delivered us from this illusion?
39713	Who shall choose the facts which, corresponding to these conditions, are worthy the freedom of the city in science?
39713	Who shall tell us which to choose?
39713	Who will regret it; who will think that this time and this strength have been wasted?
39713	Who would dare affirm that?
39713	Who would venture to say whether he preferred that Weierstrass had never written or that there had never been a Riemann?
39713	Who, now, is to decide whether a definition may be regarded as simple enough to be acceptable?
39713	Why are the English scientist''s ideas with such difficulty acclimatized among us?
39713	Why are the decimals of a table of logarithms, why are those of the number[ pi] distributed in accordance with the laws of chance?
39713	Why are the lines of the spectrum distributed in accordance with a regular law?
39713	Why be a''neo- vitalist,''or an''evolutionist,''or an''atomist,''or an''Energetiker''?
39713	Why be astonished then at the resistance we oppose to every attempt made to dissociate what so long has been associated?
39713	Why change them if they were infallible?
39713	Why did this stranger climb the mountains to make signals?
39713	Why do children usually understand nothing of the definitions which satisfy scientists?
39713	Why do the drops of rain in a shower seem to be distributed at random?
39713	Why do the rays distribute themselves regularly?
39713	Why do these rays distribute themselves regularly?
39713	Why do we assert this?
39713	Why do we avoid points making angles and too abrupt turns?
39713	Why do we not make our curve describe the most capricious zig- zags?
39713	Why do we put such a value on the invention of a new transformation?
39713	Why do we reject this interpretation?
39713	Why does this principle occupy thus a sort of privileged place among all the physical laws?
39713	Why has it been said that every attempt to give a fourth dimension to space always carries this one back to one of the other three?
39713	Why has space properly so called as many dimensions as tactile space and more than simple visual space?
39713	Why have the continental savants who have sought to get out of the ruts of their predecessors been usually unable to free themselves completely?
39713	Why have the meteorologists such difficulty in predicting the weather with any certainty?
39713	Why is it necessary to give them others?
39713	Why is this detour advantageous?
39713	Why not limit our philosophy of science strictly to such a counsel of resignation?
39713	Why not''take the cash and let the credit go''?
39713	Why reason on a polygon, for instance, which is always decomposable into triangles, and not on the elementary triangles?
39713	Why should I have the right to apply the name of straight to the first of these ideas and not to the second?
39713	Why then am I led to decide that these two sensations, qualitatively different, represent the same image, which has been displaced?
39713	Why then do we think this initial distribution improbable?
39713	Why then does it not fail me in a difficult piece of mathematical reasoning where most chess- players would lose themselves?
39713	Why then does this judgment force itself upon us with an irresistible evidence?
39713	Why then is it that I seek to trace a curve without sinuosities?
39713	Why then take this détour?
39713	Why, then, does science actually need general theories, despite the fact that these theories inevitably alter and pass away?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Why?
39713	Will it be by a convention?
39713	Will it be necessary to seek to mend the broken principles by giving what we French call a_ coup de pouce_?
39713	Will it be said that good sense suffices to show us what convention should be adopted?
39713	Will it thus shrink in convergence toward zero, or will there remain an irreducible residue which will then be the universal invariant sought?
39713	Will nature be sufficiently flexible for that?
39713	Will our experiments, interpreted in this new manner, still be in accord with our''law of relativity''?
39713	Will the difficulty be solved if we agree to refer everything to these axes bound to our body?
39713	Will the number of shoes be equal to the number of pairs?
39713	Will the two principles of Mayer and of Clausius assure to it foundations solid enough for it to last some time?
39713	Will they still be the same for those who shall come after us?
39713	Will things go better if we admit the new dynamics?
39713	Will you say that if the experiments bear on the bodies, they bear at least upon the geometric properties of the bodies?
39713	With what eyes, if not with his intellect?
39713	Without doubt, numerous observations are in accord with it; but is not this a simple effect of chance?
39713	Would all geometry thus have become impossible?
39713	Would not the same reasoning be applicable in his case?
39713	Would not this animal be the true philosopher?
39713	Would the metamorphosis have been possible, or at least would it not have been much slower?
39713	Would the probability of the cause being comprised between two limits_ n_ kilometers apart still be proportional to_ n_?
39713	Would this contrary result have been absurd in itself?
39713	Would this planet act the same if it went a thousand times faster?
39713	XI Another difficulty; have we really the right to speak of the cause of a phenomenon?
39713	Yet is it an instrument not to be done without, if not for action, at least for philosophizing?
39713	Yet is that certitude absolute?
39713	Yet would the mind of these astronomers be completely satisfied?
39713	You ask then of what use is the hypothesis of Lorentz and of Fitzgerald if no experiment can permit of its verification?
39713	_ Conventions Preceding Experiment._--Suppose, now, that all these efforts fail, and, after all, I do not believe they will, what must be done?
39713	_ Identity of Two Points_ What is a point?
39713	_ Objectivity of Science_ I arrive at the question set by the title of this article: What is the objective value of science?
39713	_ Shall we thence conclude that the facts of daily life are the work of the grammarians?_ You ask me: Is there a current?
39713	_ Shall we thence conclude that the facts of daily life are the work of the grammarians?_ You ask me: Is there a current?
39713	_ The Objective Value of Science_ CHAPTER X.--Is Science Artificial?
39713	_ The Philosophy of M. LeRoy_ There are many reasons for being sceptics; should we push this scepticism to the very end or stop on the way?
39713	_ The Rôle of the Analyst._--And as to these doubts, is it indeed true that we can do nothing to disembarrass science of them?
39713	_ They have not changed nature; they have only changed place._ III Could these principles be considered as disguised definitions?
39713	_ This convention being given_, if I am asked: Is such a fact true?
39713	_ What Outcome?_--What now is the definite, the permanent outcome?
39713	and, if so, how was it known that these bodies were subjected to no force?
39713	and, on the other hand, how could we admit Newton''s conclusion and believe in absolute space?
39713	but it means: Does it teach us the true relations of things?