Now for each one class of things, as there is one perception, (20) so there is one science, as for instance grammar, being one science, investigates all articulate sounds. Hence to investigate all the species of being qua being is the work of a science which is generically one, and to investigate the several species is the work of the specific parts of the science.
If, now, being and unity are the same and are one thing in the sense that they are implied in one another as principle and cause are, not in the sense that they are explained by the same definition (though it makes no difference even if we suppose them to be like that—in fact this would even strengthen our case); for ‘one man’ and ‘man’ are the same thing, (25) and so are ‘existent man’ and ‘man’, and the doubling of the words in ‘one man and one existent man’ does not express anything different (it is clear that the two things are not separated either in coming to be or in ceasing to be); and similarly ‘one existent man’ adds nothing to ‘existent man’, (30) so that it is obvious that the addition in these cases means the same thing, and unity is nothing apart from being; and if, further, the substance of each thing is one in no merely accidental way, and similarly is from its very nature something that is:—all this being so, there must be exactly as many species of being as of unity. And to investigate the essence of these is the work of a science which is generically one—I mean, (35) for instance, the discussion of the same and the similar and the other concepts of this sort; and nearly all contraries may be referred to this origin; let us take them as having been investigated in the ‘Selection of Contraries’. [1004a]
And there are as many parts of philosophy as there are kinds of substance, so that there must necessarily be among them a first philosophy and one which follows this. For being falls immediately into genera; for which reason the sciences too will correspond to these genera. (5) For the philosopher is like the mathematician, as that word is used; for mathematics also has parts, and there is a first and a second science and other successive ones within the sphere of mathematics.1
Now since it is the work of one science to investigate opposites, and plurality is opposed to unity—and it belongs to one science to investigate the negation and the privation because in both cases we are really investigating the one thing of which the negation or the privation is a negation or privation (for we either say simply that that thing is not present, (10) or that it is not present in some particular class; in the latter case difference is present over and above what is implied in negation; for negation means just the absence of the thing in question, (15) while in privation there is also employed an underlying nature of which the privation is asserted):—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 contrariety is a kind of difference, (20) 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 know them all; for a term belongs to different sciences not if it has different senses, but if it has not one meaning and its definitions cannot be referred to one central meaning. (25) And since all things are referred to that which is primary, as for instance all things which are called 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 the case of each of the predicates in question, (30) saying how they are related to it; for some will be called what they are called because they possess it, others because 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),2 and that it is the function of the philosopher to be able to investigate all things. [1004b] For 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 all other such questions. Since, (5) 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,3 but by forgetting that substance, of which they have no correct idea, is prior to these other things. (10) 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 which has weight have other peculiar properties. (15) So too there are certain properties 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 Wisdom which exists only in semblance, (20) 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 reducible to being and non-being, and to unity and plurality, as for instance rest belongs to unity and movement to plurality. And nearly all thinkers agree that being and substance are composed of contraries; at least all name contraries as their first principles—some name odd and even,4 (30) some hot and cold,5 some limit and the unlimited,6 some love and strife.7 And all the others as well are evidently reducible to unity and plurality (this reduction we must take for granted), and the principles stated by other thinkers fall entirely under these as their genera. [1005a] It is 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 science, (5) whether they have or have not one single meaning. Probably the truth is that 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), even 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 common reference, (10) in some cases that of serial succession). And for this reason it does not belong to the geometer to inquire what is contrariety or completeness or unity or being or the same or the other, but only to presuppose these concepts and reason from this starting-point.—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 substances but also their attributes, (15) both those above named and the concepts ‘prior’ and ‘posterior’, ‘genus’ and ‘species’, ‘whole’ and ‘part’, and the others of this sort.8
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. Evidently, the inquiry into these also belongs to one science, (20) 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, because they are true of being qua being and each genu
s has being. (25) But men use them just so far as to satisfy their purposes; that is, as far as the genus to which their demonstrations refer extends. Therefore since these truths clearly hold good for all things qua being (for this is what is common to them), to him who studies being qua being belongs the inquiry into these as well. And for this reason no one who is conducting a special inquiry tries to say anything about their truth or falsity—neither the geometer nor the arithmetician. (30) 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 about being. But since there is one kind of thinker who is above even the natural philosopher (for nature is only one particular genus of being), (35) the discussion of these truths also will belong to him whose inquiry is universal and deals with primary substance. [1005b] Physics also is a kind of Wisdom, but it is not the first kind.9—And the attempts of some of those who discuss the terms on which truth should be accepted,10 are due to a want of training in logic; for they should know these things already when they come to a special study, (5) and not be inquiring into them while they are listening to lectures on it.
Evidently then it belongs to the philosopher, i. e. to him who is studying the nature of all substance, to inquire also into the principles of syllogism. 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 existing things qua existing must be able to state the most certain principles of all things. (10) 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. (15) For a principle which every one must have who understands anything that is, 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, let us proceed to say. It is, that the same attribute cannot at the same time belong and not belong to the same subject and in the same respect; we must presuppose, (20) to guard against dialectical objections, any further qualifications which might 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 be and not to be, as some think Heraclitus says. For what a man says, he does not necessarily believe; and 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 premiss too), (25) 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 thing to be and not to be; for if a man were mistaken on this point he would have contrary opinions at the same time. (30) It is for this reason that all who are carrying out a demonstration reduce it to this as an ultimate belief; for this is naturally the starting-point even for all the other axioms.11
4 There are some who, as we said,12 both themselves assert that it is possible for the same thing to be and not to be, (35) and say that people can judge this to be the case.13 And among others many writers about nature use this language. [1006a] 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 principles.—Some indeed demand that even this shall be demonstrated, (5) but this they do through want of education, for not to know of what things one should demand demonstration, and of what one should not, argues 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 things of which one should not demand demonstration, (10) these persons could not say what principle they maintain to be more self-evident 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 seek to give an account of our views to one who cannot give an account of anything, in so far as he cannot do so. For such a man, as such, is from the start no better than a vegetable. (15) Now negative demonstration I distinguish from demonstration proper, because in a demonstration one might be thought to be begging the question, but if another person is responsible for the assumption we shall have negative proof, not demonstration.14 The starting-point for all such arguments is not the demand that our opponent shall say that something either is or is not (for this one might perhaps take to be a begging of the question), (20) 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. (25) The person responsible for the proof, 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’].
First then this at least is obviously true, that the word ‘be’ or ‘not be’ has a definite meaning, (30) so that not everything will be ‘so and not so’.15—Again, if ‘man’ has one meaning, let this be ‘two-footed animal’; by having one meaning I understand this:—if ‘man’ means ‘X’, then if A is a man ‘X’ will be what ‘being a man’ means for him. (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 definition there might be assigned a different word. [1006b] For instance, we might say that ‘man’ has not one meaning but several, one of which would have one definition, viz. ‘two-footed animal’, while there might be also several other definitions if only they were limited in number; for a peculiar name might be assigned to each of the definitions. (5) If, however, they were not 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 our reasoning with one another, and indeed with ourselves, (10) 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 thing.)
Let it be assumed then, as was said at the beginning,16 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’, (15) if ‘man’ not only signifies something about one subject but also has one significance (for we do not identify ‘having one significance’ with ‘signifying something about one subject’, since on that assumption even ‘musical’ and ‘white’ and ‘man’ would have had one significance, so that all things would have been one; for they would all have had the same significance).
And it will not be possible to be and not to be the same thing, except in virtue of an ambiguity, just as if one whom we call ‘man’, (20) others were to call ‘not-man’; 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. For being one means this—being related as ‘raiment’ and ‘dress’ are, (25) if their definition is one. And if ‘being a man’ and ‘being a not-man’ are to be one, they must mean one thing. But it was shown earlier17 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’ meant18); and if this is necessary, it is impossible that the same thing should not at that time be a two-footed animal; for this is what ‘being necessary’ means—that it is impossible for the thing
not to be. (30) 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 a man’, for ‘being a man’ and ‘being a not-man’ mean different things, since even ‘being white’ and ‘being a man’ are different; for the former terms are much more opposed, so that they must a fortiori mean different things. [1007a] 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,19 (5) that it would follow that all things are one, and not only opposites. But if this is impossible, then what we have maintained will follow, if our opponent will only answer our question.
And if, when one asks the question simply, he adds the contradictories, he is not answering the question. For there is nothing to prevent the same thing from being both a man and white and countless other things: but still, (10) if one asks whether it is or is not true to say that this is a man, 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 impossible to enumerate its accidental attributes, (15) which are infinite in number; let him, then, enumerate either all or none. Similarly, therefore, even if the same thing is a thousand times a man and a not-man, he must not, in answering the question whether this is a man, add that it is also at the same time a not-man, unless he is bound to add also all the other accidents, all that the subject is or is not; and if he does this, he is not observing the rules of argument.20
And in general those who say this do away with substance and essence. (20) For they must say that all attributes are accidents, and that there is no such thing as ‘being essentially a man’ or ‘an animal’. For if there is to be any such thing as ‘being essentially a man’ this will not be ‘being a not-man’ or ‘not being a man’ (yet these are negations of it21); for there was one thing which it meant, (25) 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 a man is to be the same as either being essentially a not-man or essentially not being a man, then its essence will be something else. Therefore our opponents must say that there cannot be such a definition of anything, (30) 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 accidental, there will be nothing primary about which they are made, (35) if the accidental always implies predication about a subject. [1007b] The predication, then, must go on ad infinitum. But this is impossible; for not even more than two terms can be combined in accidental predication. For (1) an accident is not an accident of an accident, unless it be because both are accidents of the same subject. I mean, for instance, that the white is musical and the latter is white, (5) only because both are accidental to man. But (2) 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, (a) those which are accidental in the latter sense, in which white is accidental to Socrates, cannot form an infinite series in the upward direction;22 e. g. Socrates the white has not yet another accident; for no unity can be got out of such a sum. (10) Nor again (b) 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 to Socrates; and the accident is an accident of an accident not in cases of the latter kind, (15) but only in cases of the other kind, so that not all terms will be accidental.23 There must, then, even so be something which denotes substance. And if this is so, it has been shown that contradictories cannot be predicated at the same time.
The Basic Works of Aristotle (Modern Library Classics) Page 102