by Aristotle
Now since it is the work of one science to investigate opposites, and plurality is [10] opposite to unity, and it belongs to one science to investigate the negation and the privation because in both cases we are really investigating unity, to which the negation or the privation refers (for we either say simply that unity is not present, or that it is not present in some particular class; in the latter case the characteristic difference of the class modifies the meaning of ‘unity’, as compared with the meaning conveyed in the bare negation; for the negation means just the absence of [15] unity, while in privation there is also implied an underlying nature of which the privation is predicated),—in view of all these facts, the contraries of the concepts we named above, the other and the dissimilar and the unequal, and everything else which is derived either from these or from plurality and unity, must fall within the province of the science above-named.—And contrariety is one of these concepts, for [20] contrariety is a kind of difference, and difference is a kind of otherness. Therefore, since there are many senses in which a thing is said to be one, these terms also will have many senses, but yet it belongs to one science to consider them all; for a term belongs to different sciences not if it has different senses, but if its definitions [25] neither are identical nor can be referred to one central meaning. And since all things are referred to that which is primary, as for instance all things which are one are referred to the primary one, we must say that this holds good also of the same and the other and of contraries in general; so that after distinguishing the various senses of each, we must then explain by reference to what is primary in each term, [30] saying how they are related to it; some in the sense that they possess it, others in the sense that they produce it, and others in other such ways.
It is evident then that it belongs to one science to be able to give an account of these concepts as well as of substance. This was one of the questions in our book of problems.
And it is the function of the philosopher to be able to investigate all things. For [1004b1] if it is not the function of the philosopher, who is it who will inquire whether Socrates and Socrates seated are the same thing, or whether one thing has one contrary, or what contrariety is, or how many meanings it has? And similarly with [5] all other such questions. Since, then, these are essential modifications of unity qua unity and of being qua being, not qua numbers or lines or fire, it is clear that it belongs to this science to investigate both the essence of these concepts and their properties. And those who study these properties err not by leaving the sphere of philosophy, but by forgetting that substance, of which they have no correct idea, is [10] prior to these other things. For number qua number has peculiar attributes, such as oddness and evenness, commensurability and equality, excess and defect, and these belong to numbers either in themselves or in relation to one another. And similarly the solid and the motionless and that which is in motion and the weightless and that [15] which has weight have other peculiar properties. So too certain properties are peculiar to being as such, and it is about these that the philosopher has to investigate the truth.—An indication of this may be mentioned:—dialecticians and sophists assume the same guise as the philosopher, for sophistic is philosophy which exists [20] only in semblance, and dialecticians embrace all things in their dialectic, and being is common to all things; but evidently their dialectic embraces these subjects because these are proper to philosophy.—For sophistic and dialectic turn on the same class of things as philosophy, but this differs from dialectic in the nature of the faculty required and from sophistic in respect of the purpose of the philosophic life. [25] Dialectic is merely critical where philosophy claims to know, and sophistic is what appears to be philosophy but is not.
Again, in the list of contraries one of the two columns is privative, and all contraries are referred to being and nonbeing, and to unity and plurality, as for instance rest belongs to unity and movement to plurality. And nearly all thinkers [30] agree that being and substance are composed of contraries; at least all name contraries as their first principles—some name odd and even, some hot and cold, some limit and the unlimited, some love and strife. And everything else is evidently referred to unity and plurality (this reference we must take for granted), and the principles stated by other thinkers fall entirely under these as their genera. It is [1005a1] obvious then from these considerations too that it belongs to one science to examine being qua being. For all things are either contraries or composed of contraries, and unity and plurality are the starting-points of all contraries. And these belong to one [5] science, whether they have or have not one common notion. Probably they have not; yet even if ‘one’ has several meanings, the other meanings will be related to the primary meaning—and similarly in the case of the contraries.—And if being or unity is not a universal and the same in every instance, or is not separable from the particular instances (as in fact it probably is not; the unity is in some cases that of [10] common reference, in some cases that of serial succession),—just for this reason it does not belong to the geometer to inquire what is contrariety or completeness or being or unity or the same or the other, but only to presuppose these concepts.—Obviously then it is the work of one science to examine being qua being, and the attributes which belong to it qua being, and the same science will examine not only [15] substances but also their attributes, both those above named and what is prior and posterior, genus and species, whole and part, and the others of this sort.
3 · We must state whether it belongs to one or to different sciences to inquire into the truths which are in mathematics called axioms, and into substance. [20] Evidently the inquiry into these also belongs to one science, and that the science of the philosopher; for these truths hold good for everything that is, and not for some special genus apart from others. And all men use them, for they are true of being qua being, and each genus has being. But men use them just so far as to satisfy their [25] purposes; that is, as far as the genus, whose attributes they are proving, extends. Therefore since these truths clearly hold good for all things qua being (for this is what is common to them), he who studies being qua being will inquire into them too.—And for this reason no one who is conducting a special inquiry tries to say [30] anything about their truth or falsehood,—neither the geometer nor the arithmetician. Some natural philosophers indeed have done so, and their procedure was intelligible enough; for they thought that they alone were inquiring about the whole of nature and of being. But since there is one kind of thinker who is even above the natural philosopher (for nature is only one particular genus of being), the discussion of these truths also will belong to him whose inquiry is universal and deals with primary substance. Natural science also is a kind of wisdom, but it is not the first [1005b1] kind.—And the attempts of some who discuss the terms on which truth should be accepted, are due to a want of training in logic; for they should know these things already when they come to a special study, and not be inquiring into them while [5] they are pursuing it.—Evidently then the philosopher, who is studying the nature of all substance, must inquire also into the principles of deduction.
But he who knows best about each genus must be able to state the most certain principles of his subject, so that he whose subject is being qua being must be able to [10] state the most certain principles of all things. This is the philosopher, and the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both the best known (for all men may be mistaken about things which they do not know), and non-hypothetical. For a principle which every [15] one must have who knows anything about being, is not a hypothesis; and that which every one must know who knows anything, he must already have when he comes to a special study. Evidently then such a principle is the most certain of all; which principle this is, we proceed to say. It is, that the same attribute cannot at the same [20] time belong and not belong to the same subject in the same respect; we must presuppose, in face of dialectical objections, any further qualifications which mi
ght be added. This, then, is the most certain of all principles, since it answers to the definition given above. For it is impossible for any one to believe the same thing to [25] be and not to be, as some think Heraclitus says; for what a man says he does not necessarily believe. If it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this proposition too), and if an opinion which contradicts another is contrary to it, obviously it is impossible for the same man at the same time to believe the same [30] thing to be and not to be; for if a man were mistaken in this point he would have contrary opinions at the same time. It is for this reason that all who are carrying out a demonstration refer it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms.
4 · There are some who, as we have said, both themselves assert that it is [1006a1] possible for the same thing to be and not to be, and say that people can judge this to be the case. And among others many writers about nature use this language. But we have now posited that it is impossible for anything at the same time to be and not to be, and by this means have shown that this is the most indisputable of all [5] principles.—Some indeed demand that even this shall be demonstrated, but this they do through want of education, for not to know of what things one may demand demonstration, and of what one may not, argues simply want of education. For it is impossible that there should be demonstration of absolutely everything; there would be an infinite regress, so that there would still be no demonstration. But if there are [10] things of which one should not demand demonstration, these persons cannot say what principle they regard as more indemonstrable than the present one.
We can, however, demonstrate negatively even that this view is impossible, if our opponent will only say something; and if he says nothing, it is absurd to attempt to reason with one who will not reason about anything, in so far as he refuses to [15] reason. For such a man, as such, is seen already to be no better than a mere plant. Now negative demonstration I distinguish from demonstration proper, because in a demonstration one might be thought to be assuming what is at issue, but if another person is responsible for the assumption we shall have negative proof, not demonstration. The starting-point for all such arguments is not the demand that our [20] opponent shall say that something either is or is not (for this one might perhaps take to be assuming what is at issue), but that he shall say something which is significant both for himself and for another; for this is necessary, if he really is to say anything. For, if he means nothing, such a man will not be capable of reasoning, either with himself or with another. But if any one grants this, demonstration will be possible; for we shall already have something definite. The person responsible for the proof, [25] however, is not he who demonstrates but he who listens; for while disowning reason he listens to reason. And again he who admits this has admitted that something is true apart from demonstration [so that not everything will be ‘so and not so’.]1
First then this at least is obviously true, that the word ‘be’ or ‘not be’ has a definite meaning, so that not everything will be so and not so.—Again, if ‘man’ has [30] one meaning, let this be ‘two-footed animal’; by having one meaning I understand this: if such and such is a man, then if anything is a man, that will be what being a man is. And it makes no difference even if one were to say a word has several meanings, if only they are limited in number; for to each formula there might be [1006b1] assigned a different word. For instance, we might say that ‘man’ has not one meaning but several, one of which would be defined as ‘two-footed animal’, while there might be also several other formulae if only they were limited in number; for a special name might be assigned to each of the formulae. If, however, they were not [5] limited but one were to say that the word has an infinite number of meanings, obviously reasoning would be impossible; for not to have one meaning is to have no meaning, and if words have no meaning reasoning with other people, and indeed with oneself has been annihilated; for it is impossible to think of anything if we do not think of one thing; but if this is possible, one name might be assigned to this [10] thing. Let it be assumed then, as was said at the beginning, that the name has a meaning and has one meaning; it is impossible, then, that being a man should mean precisely not being a man, if ‘man’ is not only predicable of one subject but also has one meaning (for we do not identify ‘having one meaning’ with ‘being predicable of [15] one subject’, since on that assumption even ‘musical’ and ‘white’ and ‘man’ would have had one meaning, so that all things would have been one; for they would all have been synonymous).
And it will not be possible for the same thing to be and not to be, except in virtue of an ambiguity, just as one whom we call ‘man,’ others might call ‘not-man’; [20] but the point in question is not this, whether the same thing can at the same time be and not be a man in name, but whether it can in fact. Now if ‘man’ and ‘not-man’ mean nothing different, obviously ‘not being a man’ will mean nothing different from ‘being a man’; so that being a man will be not being a man; for they will be one. [25] For being one means this—what we find in the case of ‘raiment’ and ‘dress’—viz. that the definitory formula is one. And if ‘being a man’ and ‘not being a man’ are to be one, they must mean one thing. But it was shown earlier that they mean different things. Therefore, if it is true to say of anything that it is a man, it must be a two-footed animal; for this was what ‘man’ meant; and if this is necessary, it is [30] impossible that the same thing should not be a two-footed animal; for this is what ‘being necessary’ means—that it is impossible for the thing not to be. It is, then, impossible that it should be at the same time true to say the same thing is a man and is not a man.
The same account holds good with regard to not being man, for ‘being man’ [1007a1] and ‘being not-man’ mean different things, since even ‘being white’ and ‘being man’ are different; for the former terms are much more opposed, so that they must mean [5] different things. And if any one says that ‘white’ means one and the same thing as ‘man’, again we shall say the same as what was said before, that it would follow that all things are one, and not only opposites. But if this is impossible, then what has been said will follow, if our opponent answers our question.
And if, when one asks the question simply, he adds the contradictories, he is [10] not answering the question. For there is nothing to prevent the same thing from being both man and white and countless other things: but still if one asks whether it is true to call this a man or not our opponent must give an answer which means one thing, and not add that it is also white and large. For, besides other reasons, it is [15] impossible to enumerate the accidents, which are infinite in number; let him, then, enumerate either all or none. Similarly, therefore, even if the same thing is a thousand times man and not-man, we must not add, in answering the question whether this is a man, that it is also at the same time not a man, unless we are bound to add also all the other accidents, all that the subject is or is not; and if we do this, [20] we are not observing the rules of argument.
And in general those who use this argument do away with substance and essence. For they must say that all attributes are accidents, and that there is no such thing as being essentially man or animal. For if there is to be any such thing as being essentially man this will not be being not-man or not being man (yet these are [25] negations of it); for there was some one thing which it meant, and this was the substance of something. And denoting the substance of a thing means that the essence of the thing is nothing else. But if its being essentially man is to be the same as either being essentially not-man or essentially not being man, then its essence will be something else. Therefore our opponents must say that there cannot be such [30] a definition of anything, but that all attributes are accidental; for this is the distinction between substance and accident—white is accidental to man, because though he is white, whiteness is not his essence. But if all statements are acciden
tal, there will be nothing primary about which they are made, if the accidental always [1007b1] implies predication about a subject. The predication, then, must go on ad infinitum. But this is impossible; for not even more than two terms can be combined. For an accident is not an accident of an accident, unless it be because both are accidents of the same subject. I mean, for instance, the white is musical and the latter is white, [5] only because both are accidental to man. But Socrates is musical, not in this sense, that both terms are accidental to something else. Since then some predicates are accidental in this and some in that sense, those which are accidental in the latter sense, in which white is accidental to Socrates, cannot form an infinite series in the upward direction,—e.g. Socrates the white has not yet another accident; for no [10] unity can be got out of such a sum. Nor again will white have another term accidental to it, e.g. musical. For this is no more accidental to that than that is to this; and at the same time we have drawn the distinction, that while some predicates are accidental in this sense, others are so in the sense in which musical is accidental [15] to Socrates; and the accident is an accident of an accident not in cases of the latter kind, but only in cases of the other kind, so that not all terms will be accidental. There must, then, even in this case be something which denotes substance. And it has been shown that, if this is so, contradictories cannot be predicated at the same time.
Again, if all contradictories are true of the same subject at the same time, evidently all things will be one. For the same thing will be a trireme, a wall, and a [20] man, if it is equally possible to affirm and to deny anything of anything,—and this premise must be accepted by those who share the views of Protagoras. For if any one thinks that the man is not a trireme, evidently he is not a trireme; so that he also is a trireme, if, as they say, the contradictory is true. And we thus get the doctrine of [25] Anaxagoras, that all things are mixed together; so that nothing really exists. They seem, then, to be speaking of the indeterminate, and, while fancying themselves to be speaking of being, they are speaking about non-being; for that which exists potentially and not actually is the indeterminate. But they must predicate of every subject every attribute and the negation of it indifferently. For it is absurd if of [30] every subject its own negation is to be predicable, while the negation of something else which cannot be predicated of it is not predicable of it; for instance, if it is true to say of a man that he is not a man, evidently it is also true to say that he is either a trireme or not a trireme. If, then, the affirmative can be predicated, the negative must be predicable too; and if the affirmative is not predicable, the negative, at [35] least, will be more predicable than the negative of the subject itself. If, then, even the latter negative is predicable, the negative of ‘trireme’ will be also predicable; [1008a1] and, if this is predicable, the affirmative will be so too.—Those, then, who maintain this view are driven to this conclusion, and to the further conclusion that it is not necessary either to assert or to deny. For if it is true that a thing is man and not-man, evidently also it will be neither man nor not-man. For to the two assertions [5] there answer two negations. And if the former is treated as a single proposition compounded out of two, the latter also is a single proposition opposite to the former.