Part 3

The Study of Fundamental Laws of Thought

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 true reality. 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 merely for some special class of things. Also, all men use them, because they are true of existing things qua existing thing and each class of things exists. But men use them just so far as to satisfy their purposes; that is, as far as the class of things to which their demonstrations refer extends. Therefore since these truths clearly hold good for all things qua existing things (for this is what is common to them), the inquiry into these as well belongs to the inquirer who studies existing things qua existing things.

And for this reason no one who is conducting an inquiry in a specific area tries to say anything about their truth or falsity--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 about existence. But there is a kind of thinker who is above even the natural philosopher (for nature is only one particular kind of existing thing):...natural philosophy also is a kind of philosophy, but it is not the first kind.

Evidently then it belongs to the philosopher, i.e. to him who is studying the nature of all reality, to inquire also into the principles of reasoning. But he who knows best about each class of things 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. This is the philosopher.

Characteristics of the Most Fundamental Principle of Knowledge

And the most certain principle of all is that regarding which it is impossible to be mistaken; for such a principle must be both (a) the best known (for all men may be mistaken about things which they do not know), and (b) non-hypothetical. 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.

The Most Fundamental Principle of Knowledge: The Law of Non-Contradiction [LNC]

Which principle this is, let us proceed to say. It is this: the same attribute cannot at the same time belong and not belong to the same subject and in the same respect--we must presuppose, 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 (1) it is impossible that contrary attributes should belong at the same time to the same subject (the usual qualifications must be presupposed in this premise too), and if (2) an opinion which contradicts another is contrary to it, then obviously (3) 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....

Part 4

Aristotle on ("Heraclitean") Critics of the Law of Non-Contradiction

There are some who, as we said, both themselves assert that it is possible for the same thing to be and not to be true, and say that people can believe this to be the case. But we have just now assumed that it is impossible for anything at the same time to be and not to be the case, and by this means have shown that this is the most indisputable of all principles.

Some indeed demand that even this principle shall be demonstrated, but they do this 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, these persons could not say what principle they maintain to be more evident than the present one.

We can, however, demonstrate dialectically 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 argument [logos] for our views to one who cannot give an statement [logos] about anything, in so far as he cannot do so. For such a man, as such, is from the start no better than a vegetable.

Now dialectical demonstration I distinguish from demonstration proper, because in offering a demonstration [of LNC] one might be thought to be begging the question; but if another person is responsible for the assumption we shall have dialectical refutation, not demonstration.

The starting-point for all such arguments is not the demand that our opponent shall say that something either is or is not true (for this one might perhaps take to be a begging of the question), 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 discourse, either with himself or with another. But if any one does do this, then [dialectical] demonstration will be possible; for we shall already have something definite. The person responsible for the proof, however, is not he who demonstrates but he who listens; for while disowning reason he listens to reason. Moreover, he who admits this has admitted that something is true apart from demonstration (so that not everything will be 'so and not so').

Aristotle's Refutation of Critics of LNC

Some people have acquired this opinion as other paradoxical opinions have been acquired; when men cannot refute sophistical arguments, they give in to the argument and agree that the conclusion is true. This, then, is why some express this view; others do so because they demand a reason for everything. And the starting-point in dealing with all such people is definition. Now the definition rests on the necessity of their meaning something; for the form of words of which the word is a sign will be its definition....

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 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. 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 special name might be assigned to each of the definitions. If, however, they were not limited but one were to say that the word has an infinite number of meanings, obviously discourse would be impossible; for not to have one meaning is to have no meaning, and if words have no meaning intelligible discourse with one another, and indeed with ourselves, 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, 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' 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 'intelligent' and 'tall' 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', 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 'clothes' and 'dress' are, 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 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 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. 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.

A Further (Pragmatic) Argument against the "Heracliteans"

It is in the highest degree evident that neither any one of those who maintain this view nor any one else is really in this position. For why does a man walk to Megara and not stay at home, when he thinks he ought to be walking there? Why does he not walk early some morning into a well or over a precipice, if one happens to be in his way? Why do we observe him guarding against this, evidently because he does not think that falling in is alike good and not good? Evidently, then, he judges one thing to be better and another worse. And if this is so, he must also judge one thing to be a man and another to be not-a-man, one thing to be sweet and another to be not-sweet. For he does not aim at and judge all things alike, when, thinking it desirable to drink water or to see a man, he proceeds to aim at these things; yet he ought, if the same thing were alike a man and not-a-man. But, as was said, there is no one who does not obviously avoid some things and not others. Therefore, as it seems, all men make unqualified judgements, if not about all things, still about what is better and worse. And if this is not knowledge but opinion, they should be all the more anxious about the truth, as a sick man should be more anxious about his health than one who is healthy; for he who has opinions is, in comparison with the man who knows, not in a healthy state as far as the truth is concerned....

Part 5

Aristotle on Protagorean Relativism

From the same opinion proceeds the doctrine of Protagoras, and both doctrines must be alike true or alike untrue. For on the one hand, if all opinions and appearances are true, all statements must be at the same time true and false. For many men hold beliefs in which they conflict with one another, and think those mistaken who have not the same opinions as themselves; so that the same thing must both be and not be the case.

And on the other hand, if this is so, all opinions must be true; for those who are mistaken and those who are right are opposed to one another in their opinions; if, then, reality is such as the view in question supposes, all will be right in their beliefs.

Evidently, then, both doctrines proceed from the same way of thinking. But the same method of discussion must not be used with all opponents; for some need to have their beliefs changed, and others require the compulsion of proof. Those who have been driven to this position by difficulties in their thinking can easily be cured of their ignorance; for it is not their expressed argument but their thought that one has to meet. But those who argue for the sake of argument can be cured only by refuting the argument as expressed in speech and in words.

Those who really feel the difficulties have been led to this opinion by observation of the sensible world.

(1) They think that contradictories or contraries are true at the same time, because they see contraries coming into existence out of the same thing. If, then, that which is not cannot come to be, the thing must have existed before as both contraries alike, as Anaxagoras says all is mixed in all.

[In response to (1)] To those, then, whose belief rests on these grounds, we shall say that in a sense they speak rightly and in a sense they err. For 'that which is' has two meanings, so that in some sense a thing can come to be out of that which is not, while in some sense it cannot, and the same thing can at the same time be in being and not in being--but not in the same respect. For the same thing can be potentially at the same time two contraries, but it cannot actually be so. Moreover, we shall ask them to believe that among existing things there is also another kind of substance to which neither movement nor destruction nor generation at all belongs.

(2) Similarly some have inferred from observation of the sensible world the truth of appearances. For they think that the truth should not be determined by the large or small number of those who hold a belief, and that the same thing is thought sweet by some when they taste it, and bitter by others, so that if all were ill or all were mad, and only two or three were well or sane, these would be thought ill and mad, and not the others.

They also say that many of the other animals receive impressions contrary to ours; and that even to the senses of each individual, things do not always seem the same. Which, then, of these impressions are true and which are false is not obvious; for the one set is no more true than the other, but both are alike. And this is why Democritus, at any rate, says that either there is no truth or to us at least it is not evident....

And it is in this direction that the consequences are most troublesome. For if those who have seen most of such truth as is possible for us (and these are those who seek and love it most [i.e. philosophers])--if these have such opinions and express these views about the truth, is it not natural that beginners in philosophy should lose heart? For to seek the truth would be a wild goose chase.

And again, (3) because they saw that all this world of nature is in movement and that about that which changes no true statement can be made, they said that of course, regarding that which everywhere in every respect is changing, nothing could truly be affirmed. It was this belief that blossomed into the most extreme of the views above mentioned, that of the professed Heracliteans, such as was held by Cratylus, who finally did not think it right to say anything but only moved his finger, and criticized Heraclitus for saying that it is impossible to step twice into the same river; for he thought one could not do it even once....

[In response to (3)] But let us insist on this, that it is not the same thing to change in quantity and in quality. Grant that in quantity a thing is not constant; still it is in respect of its form that we know each thing.

And again, it would be fair to criticize those who hold this view for asserting about the whole material universe what they saw only in a minority even of sensible things. For only that region of the sensible world which immediately surrounds us is always in process of destruction and generation; but this is--in a word--not even a fraction of the whole, so that it would have been juster to acquit this part of the world because of the other part, than to condemn the other because of this....

[In response to (2)] Again, it is fair to express surprise at our opponents' raising the question whether magnitudes are as great, and colors are of such a nature, as they appear to people at a distance, or as they appear to those close at hand, and whether they are such as they appear to the healthy or to the sick, and whether those things are heavy which appear so to the weak or those which appear so to the strong, and those things true which appear to the sleeping or to the waking. For obviously they do not think these to be open questions; no one, at least, if when he is in Libya he has fancied one night that he is in Athens, starts for the concert hall.

Further Responses to Protagorean Relativism

Moreover, with regard to the future, as Plato says [in the Theaetetus], surely the opinion of the physician and that of the ignorant man are not equally weighty, for instance, on the question whether a man will get well or not.

And again...the same wine might seem, if either it or one's body changed, at one time sweet and at another time not sweet; but at least sweetness, such as it is when it exists, has never yet changed, but one is always right about it, and what it is to be sweet is of necessity of such and such a nature. Yet all these views destroy this necessity, leaving nothing to be of necessity, as they leave no essence of anything; for the necessary cannot be in this way and also in that, so that if anything is of necessity, it will not be 'both so and not so'.

And, in general, if only the sensible exists, there would be nothing if animate things were not; for there would be no faculty of sense. Now the view that neither the sensible qualities nor the sensations would exist is doubtless true (for they are affections of the perceiver), but that the substrata which cause the sensation should not exist even apart from sensation is impossible. For sensation is surely not the sensation of itself, but there is something beyond the sensation, which must be prior to the sensation; for that which moves is prior in nature to that which is moved, and if they are correlative terms, this is no less the case.

[In response to (2)] There are, both among those who have these convictions and among those who merely profess these views for the sake of argument, some who raise a difficulty by asking, who is to be the judge of the healthy man, and in general who is likely to judge rightly on each class of questions?

But such inquiries are like puzzling over the question whether we are now asleep or awake. And all such questions have the same force. These people demand that a reason shall be given for everything; for they seek a starting-point, and they seek to get this by demonstration, while it is obvious from their actions that they have no conviction. But their mistake is what we have stated it to be; they seek a reason for things for which no reason can be given; for the starting-point of demonstration is not demonstration.

These, then, might be easily persuaded of this truth, for it is not difficult to grasp; but those who seek merely compulsion in argument seek what is impossible; for they demand to be shown that they contradict themselves--a claim which [given their view that contradictory statements can both be true at the same time] contradicts their own position from the start.

But if not all things are relative, but some are self-existent, not everything that appears will be true; for that which appears is apparent to some one; so that he who says all things that appear are true, makes all things relative. And, therefore, those who ask for an irresistible argument, and at the same time demand to be shown that their views are false, must guard themselves by saying that the truth is not that what appears exists, but that what appears is true for him to whom it appears, and when, and to the sense to which, and under the conditions under which it appears.

And if they give an account of their view, but do not give it in this way, they will soon find themselves contradicting themselves. For to those who for the reasons named some time ago say that what appears is true, and therefore that all things are alike false and true, for things do not appear either the same to all men or always the same to the same man, but often have contrary appearances at the same time (for touch says there are two objects when we cross our fingers, while sight says there is one)--to these we shall say 'yes, but not to the same sense and in the same part of it and under the same conditions and at the same time', so that what appears will be with these qualifications true. But perhaps for this reason those who argue thus not because they feel a difficulty but for the sake of argument, should say that this is not true, but true for this man. And as has been said before, they must make everything relative -- relative to opinion and perception, so that nothing either has come to be or will be without some one's first thinking so. But if things have come to be or will be in that way, evidently not all things will be relative to opinion.

Aristotle's Conclusion

Let this, then, suffice to show (1) that the most indisputable of all beliefs is that contradictory statements are not at the same time true, and (2) what consequences follow from the assertion that they are, and (3) why people do assert this....