Updated: May 26
Watson, John. “The Metaphysic of Aristotle. II.” The Philosophical Review 7, no. 2 (1898): 113. https://doi.org/10.2307/2175761
IN a former article an account was given of the line of reasoning by which Aristotle is led to the conclusion that the universal desire of knowledge can only receive ultimate satisfaction in a science which determines what are the first principles of reality ; that these principles are those of 'matter,' 'form,' 'change,' and 'end,' all of which are implied in the substantial unity of actual things; and that it is also the task of this science to discuss the fundamental antithesis of unity and plurality, in connection with the subordinate conceptions which fall under it. We have still to ask, however, whether metaphysics deals with the first principles of knowledge as well as of reality.
Now, the first principles of knowledge must be those which (1) cannot possibly be denied, (2) are the necessary condition of all other knowledge, (3) do not presuppose any principles higher than themselves. Of these none is more fundamental than the principle, that ' the same thing cannot at once belong, and not belong, to the same object in the same relation.' This principle does not require or admit of proof, just because it is a first principle, and, therefore, possesses the marks mentioned above. It cannot be proved because there can be no proof unless it is presupposed. But, though in the attempt to prove this principle we have to assume it, we can indirectly show that it is ultimate and indubitable by pointing out that those who set up a theory of reality which sets it at naught fall into contradiction with themselves. Some hold that Heraclitus, e. g., affirms that 'the something at once is and is not.' If he does, it may easily be shown that he cannot possibly believe what he says. No one can believe what is self-contradictory, for to do so is to hold two opposite opinions at the same time; hence neither Heraclitus nor anyone else can possibly believe that a thing is the same and not the same. He may give to his words the form of a judgment, but it will have no definite meaning. Anyone who attempts to prove anything whatever must presuppose this principle, or he cannot advance a single step.
The same remarks apply to the other principle mentioned above, that a thing must either be affirmed or denied, there being no third possibility. We, therefore, conclude that the first principles of knowledge as well as the first principles of reality belong to the province of metaphysics, since apart from them there can be no knowledge of any reality whatever.
The Aristotelian conception of the first principles of knowledge and reality receives additional light from the pregnant passage contained in the last chapter of the Posterior Analytics, in which it is maintained that the mind, in coming to the consciousness of those principles, reaches a universal point of view. There can be no science, properly so called, without a knowledge of principles! which are ultimate and unmediated, for upon these all proof depends. It must not be supposed, however, that we have an actual knowledge of these principles from the very beginning of our conscious life. To say so is, in fact, to maintain the absurd view that we have knowledge without being aware that we have it. Ianthe order of time, therefore, we do not begin with an insight into first principles. But, if at first, we have no such insight, how can it be said that they are the basis of all science? No knowledge can be acquired unless we already have knowledge in some sense. Obviously, therefore, we cannot come to the knowledge of first principles without presupposing the faculty of knowing them as a fundamental determination of our nature. The faculty, however, can only be developed by the process in which we gradually advance from the sensuous apprehension of things, through the intermediation of memory, to experience, and then to art and science. We start from particulars and rise to a comprehension of the principles or laws implied in them. Hence, we cannot say, either that we originally know them, or that we are at first conscious of the higher principles upon which they depend. The actual development of knowledge follows the reverse course, though from the very beginning of conscious life we are beyond the pure flux of sense falsely assumed by Crotyls and others. Even in sensible perception we grasp the universal though it is of the vaguest and most indefinite character, as is shown by the fact that a child calls every man 'father;' then, in ‘experience' a number of such sensuous universals are combined in a universal which contains what is common to them all; next, in 'art' and 'science’ we grasp the universal principle of a whole class of things ; and finally we reach the absolutely universal, i. e., the first principles which form the termination of the whole process. But the last in the order of time is the first in the order of thought. For these highest universals are directly contemplated by the intelligence and contemplated as they are in themselves. In coming to the consciousness of them, the intelligence at the same time knows them to be universally and necessarily true, and to be the foundation upon which all proof depends. If, indeed, we limit the term 'science' to those characteristics of reality which become known toes only through inferences, there is no 'science' of first principles, for that which is the necessary presupposition of all proof cannot itself be proved ; but in the wider sense they belong to the highest ‘science,' the science of metaphysics. The source of these principles is intelligence itself, which may therefore be called the principle of principles.
For Aristotle, then, the whole process of knowledge, as has already been pointed out, consists in the gradual ascent to first principles, in which the ultimate presuppositions of all knowledge and reality at last come to direct consciousness ; and metaphysics as the science of first principles, is therefore a systematic exposition of the forms of intelligence itself. Thus, knowledge in its highest phase grasps the essential nature of reality. To deny this is to make all knowledge impossible; for, if the mind does not come in contact with the very nature of the real, there is no knowledge whatever. We cannot deny the first principles of knowledge without destroying the whole edifice of science ; and, therefore, the principles of contradiction and excluded middle, which are simply formulations of the essential unity of intelligence itself, lie at the basis of all our knowledge of reality.
A. THE PRINCIPLE OF CONTRADICTION.
Since the principle that ' the same thing cannot at once be and not be ' rests upon the unity of intelligence with itself, it cannot fairly be demanded that proof of its validity should be given. All proof presupposes that the mind, in affirming that certain characteristics belong to the essential nature of a given class of things, cannot at the same time be denying that they so belong ;and if an attempt is made to prove this presupposition, we fall into an infinite series ; for in order to prove it we must base it upon prior principle, which must itself be proved, and so on ad infinitum. But though the principle cannot be proved, we can show that those who deny it must presuppose it, if they say anything intelligible at all, and we do not pretend to reason with those who are not prepared to abide by this test. Thus, we can indirectly establish the truth of the principle out of the mouths of its opponents. Now, those who tell us that ' the same thing may at once be and not be ' must give a definite meaning to the words 'be' and 'not be;' when they say that a thing 'is' they cannot mean that it 'is not.' If this is not allowed, the proposition has no meaning whatever. Further, the thing which is said to ' be 'or 'not to be ' must have someone definite meaning. Thus, if by the term 'man' is meant 'two-footed animal,' it is implied that whatever is 'man' is a ' two-footed animal;' in other words, that it is essential to the nature of ' man 'to be a 'two-footed animal.' The question is not whether 'man' is adequately defined when he is affirmed to be a 'two-footed animal,' but whether, define 'man' as we please, we must have some definite meaning. If it is said that the term has no definite meaning, were simply employing inarticulate sounds, and saying nothing at all. It is thus evident that all intelligible speech presupposes the conception of the real as having a definite or unchangeable nature Hence, 'to be man' and 'not to be man' cannot be the same unless we employ the two terms in the same sense. Our question, however, is not as to the mere signs, but as to what they signify, and what we contend is that, whatever signs we use, these must have a definite meaning.' Not to be man,' therefore, not only designates something different from 'to be man,' but its opposite; the one excludes the other. No doubt we may say, if we please, that 'man ' is 'not-man’ in the sense that there are accidental characteristics, such as ‘white' or 'cultured' or large which are not inseparable from the conception of 'man;' but this only shows that we cannot determine the nature of man by attempting to state all the accidents which may or may not belong to him, but must express by the term what we conceive to belong to his essential nature as 'man.'
The logical consequence, then, of the doctrine that ' the something may at once be and not be,' is the denial of any fixed nature in things which can be grasped by thought and expressed in a name. A science of things is, therefore, impossible. If all the predicates by which reality is characterized are accidental or unessential, there is evidently no fixed subject to which they belong, and we are set upon a transition from one accident to another which can have no end. We have, therefore, to insist upon the necessity of the real being conceived as the permanent subject of all accidents. The term 'man' implies the conception of that which constitutes the essential nature of ' man,' whatever that essential nature may be, and hence it is impossible that it should be identical with the conception of 'not-man,' or, what is the same thing, that it should not be identical with itself. On any other supposition the conception of 'man' is internally incoherent or has no intelligible meaning whatever. It is upon the basis of this definite conception of what is essential that we can predicate what is unessential. We cannot connect accidents with each other without referring them to a permanent 'subject.' White' may be connected with 'cultured,' or ' cultured' with ‘white,' but only because both presuppose 'man' as their common substrate. Since, therefore, the conception of man as having certain permanent nature is the basis of all predication, it is impossible that ' man' should be conceived as at once 'man' and' not-man;' in other words, it is impossible that the same essential characteristics should be conceived to belong and not to belong to the same thing.
It may easily be shown that those who hold that the ' something may at once be and not be,' destroy all distinction of one thing from another, and make all predication impossible. Fortney must either say that the principle of contradiction does not apply universally, or that it does not apply at all. Now (a) on the former view, it is not denied that there are certain things which have a fixed or permanent nature, and so far as these are concerned the principle of contradiction is admitted, (b) If the principle is denied absolutely, then we must either say (a) that whatever is affirmed may also be denied, and whatever is denied may also be affirmed, or (b) that whatever is affirmed may be denied, but what is denied need not be affirmed. In the latter case, we must hold that we know what is unreal, but not what is real, which is absurd, since the unreal can only be known as the opposite of the real. In the former case, we must either say (I) that what is at one time affirmed may at another time be denied, or (2) that what is affirmed may at the same time be denied. This second view evidently amounts to an absolute denial of all predication. Thus, if 'man' is at once 'man' and ' not-man’ evidently ‘man' is neither ‘man' nor 'not-man.' For, if it is affirmed that ' man 'is 'man,' we must also say, negatively, that ' man 'is ' not-man;' and if it is affirmed that ' man ' is 'not-man’ the negation is 'man is man;' so that there is neither true affirmation nor true negation, i.e., all predication is denied. And obviously, if whatever is affirmed may also be denied, there can be no distinction between one thing and another. For we are forced to say that every predicate, affirmative or negative, is applicable to every object ; so that there can be no distinction between 'man,' 'ship,' 'God,' or anything else, but each thing, as well as its opposite, will be the same as every other. The first view, again, brings us to the same conclusion; for if we deny at one time whatever we have affirmed at another, we must end by affirming and denying every possible predicate of each thing. The only difficulty in dealing with such a self-contradictory doctrines that it is impossible to attach any definite meaning to it; it neither says that a thing is of a certain nature, nor that it is not of a certain nature, but that it both is and is not of a certain nature, and again that it neither is nor is not of a certain nature. Those who thus affirm and deny in the same breath, and yet deny that they either affirm or deny, make all intelligible discourse impossible, and virtually abnegate their intelligence. The truth is that nobody really believes this preposterous doctrine. Even those who pretend to do so show by their actions what they believe. They do not leap into a river or throw themselves over a precipice, but assume that things have a definite nature, which distinguish them from one another. Thus, everyone tacitly admits the principle of contradiction, as we have indirectly proved by showing the absurd consequences to which its denial leads.
It is obvious that what Aristotle is concerned to show is, not that the principle of contradiction is a formal law of thought, but that the unity of intelligence with itself in conception, and the substantial reality and distinction of things, stand and fall together’. This is amply confirmed, if confirmation were needed, by the account which he elsewhere gives of the nature of proof. The aim of all scientific proof is to reach the 'universal' the principle or law which constitutes the essential nature of the actual and the 'universal' can be grasped only by thought. In the comprehension by thought of the 'universal' consists knowledge proper or ' science 'which is distinguished from 'opinion ‘in bringing to light what is necessary or cannot be otherwise. Unless we can know the universal and necessary, there is no possibility of 'science,' and where there is 'science ' there is no room for 'opinion.' Now, 'science,' as we have seen, arises out of and presupposes 'experience' in which the universal is apprehended as involved in a number of instances ; but it is only in 'science' that the universal is known as the universal. At the same time the faculty of intelligence is exercised from the very beginning of man's conscious life, and therefore even in sensible perception the mind operates with universals, though it is only in science that the universal as such is made a direct object of conceptual thought. Thus, in its earlier stage, intelligence is dependent upon sensible experience, from which it receives the material in which it discerns the universal. Induction, or the presentation of individual instances, is a necessary step in the process by which intelligence is enabled to grasp the universal as such, but it is only in science that the essential nature of the actual is known. Now, the universal is that which can be predicated of a whole class of things, just because it can be predicated. A judgment is universal in so far as it expresses what belongs essentially to every member of a class, and what so belongs to a thing cannot be separated from it without destroying its reality. The process of proof consists in the attainment of such judgments. Obviously, therefore, there can be no proof unless intelligence is capable of grasping the essential characteristics by which each class of things is determined, and if we express the presupposition of all proof in a formula, it will run: "It is impossible that, the same thing should belong, and not belong to the same object in\the same relation," or, as we might now put it: “It is impossible that the same essential characteristics should belong, along, to the same class of things. This principle is the basis of all proof because there can be no proof unless intelligence is capable of grasping the necessary connection of real elements. It is therefore, not a purely formal principle, but presupposes that reality has a fixed nature which is capable of being grasped by thought. If there is no fixed nature of things, there can be no universal judgments and therefore no science; and if thought cannot grasp this fixed nature, there can be no knowledge of reality. But thought cannot have any knowledge whatever, if it cannot have definite conceptions of the real, or, what is the same thing, if in affirming it is denying, and in denying it is affirming. Hence the denial of the principle of contradiction involves the denial of the unity of intelligence with itself, and therefore the destruction of all knowledge of reality. Aristotle, therefore, regards the principle of contradiction as established, when it is shown that its denial makes all knowledge impossible, and destroys the permanent character of the real.
That Aristotle, in his elaborate discussion of the principle of contradiction, is seeking to show that the basis of all science is the unity of intelligence with itself in the comprehension of the real, is placed beyond doubt by his polemic against the Protagorean doctrine of knowledge. That doctrine maintains that what seems true to each man is true. Now, since that which is affirmed by one is denied by another, it evidently follows that the same thing at once is and is not, and thus the principle of contradiction is denied. Conversely, those who hold that the same thing at once is and is not, virtually adopt the doctrine of Protagoras. There can be no truth if opposite characteristics may be affirmed of the same thing. But those who hold that the same thing at once is and is not, must admit that opposites may both belong to the same thing. Thus, they destroy the criterion by which truth is distinguished from falsehood, and make contradictory opinions equally true, which is precisely the doctrine of Protagoras. It will, therefore, be advisable to inquire what gives plausibility to the Protagorean doctrine, for in so doing we shall at the same time account for the denial of the principle of contradiction by thinkers who are not mere eristics, but are honest in their endeavor to arrive at the truth.
The Protagorean doctrine appeals to sensible perception, which seems to show that the same thing displays opposite qualities. And it is easy to understand how earlier thinkers, for whom the sensible was the real, were led to adopt a theory which virtually denies the principle of contradiction. To them it seemed self-evident nothing can arise from what 'is not,' but only from what 'is,' and they were, therefore, led to conclude that the opposite characteristics which the same thing successively displays must have been present in it from the first. Accordingly, Anaxagoras contends that all opposites were originally mixed together, and Democritus that all things are composed of the 'full' and the 'void,' i.e., of 'being' and 'not-being.' These doctrines are a perfectly natural result of the common assumption ethereality must be given as it is in sensible perception; for, as nothing is so given except that which is actually presented, it comes to be supposed that whatever is real is present all at once. Aristotle, therefore, challenges the assumption that what is real can be given in sense or in its completeness. The true nature of a thing can be known only by though because that nature is not something which is completely realized, but something which is revealed in the totality of the phases through which it passes. We have, therefore, to distinguish between what a thing is 'potentially ‘and what it is 'actually.' By the aid of this distinction Aristotle seeks to show that the doctrines of Anaxagoras and Democritus rest upon a misconception of the true nature of the real, and logically lead to the destruction of all reality. When it is argued that whatever is real must contain within it all the characteristics which it displays, and, therefore, opposite characteristics, it is overlooked that the real may be either 'potential' or 'actual,' and that, while opposites may be 'potentially’ real, they cannot be 'actually' real; i.e., they cannot exist together in the same thing at the same time. We can therefore say, in opposition to those thinkers, that what is arises from what 'is not;' i.e., that the 'actual' proceeds from the 'potential' or non-actual. We can also say that what 'is ‘does not come from what 'is not,' in the sense that nothing real can arise from absolute non-entity. It is a vague apprehension of the latter aspect of truth which gives seeming force to those doctrines ; but, as their advocates entirely overlook the former aspect, they are led to hold that the actual contains opposite characteristics, and, therefore, to deny the principle of contradiction.
The doctrines just considered are based upon the changes which sensible things undergo. The kindred doctrine of Protagoras, that ' whatever seems is true, is also based upon the nature of the sensible, and likewise leads to the denial of the principle of contradiction. There are conflicting opinions, it is said, in regard to the same sensible object. Whose opinion is tube accepted. There is no reason why those of the majority should be preferred; for, judged by that standard, in a community in which there were only a few healthy or sane persons, these would be pronounced by the others diseased or insane. We have, therefore, no right to call honey ' sweet 'merely because most people find it ‘sweet.' Besides, many of the lower animals are differently affected by the sensible properties of things from what we are, and even the same man is not always affected in the same way. We have, therefore, no criterion by which to determine what is true and what is false. Hence Democritus tells us that! Either nothing is absolutely true or at least we cannot discover it. It is here assumed that all knowledge comes from sensible perception; and that, as sensible perception is not consistent with 'itself, truth is merely that which seems true. On this assumption are built the doctrines of all the early thinkers. Even Homer has been cited as endorsing this view, because he speaks of Hector, when he was in a delirium, as ' of another mind.' That all these thinkers who loved, and earnestly sought for, truth, should agreeing to deny that there is any absolute standard of truth, is apt to suggest a despair of truth. To attain truth seems as hard as to catch a bird on the wing. We need not, however, take this hopeless view when we see the natural mistake into which these thinkers fell. Their mistake was in supposing that all reality insensible. But in sensible things, as has been pointed out above, much is unrealized and therefore indeterminate, and anyone who goes merely by sense cannot get at the truth of things, but only at what seems to be true. Finding the sensible in all its forms to be in continual change, it was thought that nothing true could be said about it. The followers of Heraclitus and Crotyls have pushed this view to such an extreme as to hold that the sensible cannot even be named, but can only be pointed at, and they accuse Heraclitus of inaccuracy in saying that we cannot enter the same river twice, the fact being that we cannot enter it even once. Now, there is no doubt a certain degree of truth in the contention that what is in process of change is not real. It is not real in the sense of actually containing all that it implies. But this does not entitle us to say that it contains no reality whatever. For nothing undergoes an absolute change; that which becomes is not completely different from that out of which it becomes, and it must already be in some sense that which becomes out of it. Similarly, that which perishes must have a certain reality before it perishes, and that which originates must arise out of something which really exists. In short, we cannot reduce reality to nothing but change, but must refer all changes to something permanent or unchanging. Without dwelling further on this point, it is enough to say here that, however things may change in their accidental properties e. g. in quality, the 'form' is permanent, and it is upon the comprehension of this permanent 'form' that all our knowledge of things depends. Not only, however, do these thinkers fail to see that the changes which sensible things undergo presuppose that there is in them something unchanging, but they unwarrantably identify the whole of the sensible world with that small part of it which immediately surrounds us, and therefore assume that all sensible reality is in perpetual change, origination, and decease. This is so far from being the truth, that eternal and unchangeable things far exceed in number the transient and changeable, and therefore it would be nearer the truth to say that the sensible world is permanent and unchanging. Nor can we admit that reality as a whole is coterminous with even the whole sensible world, including the heavenly bodies; for ultimately that world must be referred to a single unchangeable and supersensible reality. This, indeed, is tacitly admitted by those who contend that the world contains from the beginning all the characteristics which it ever displays; for, if all is realized from the first, how can there be any real change? Obviously, the truth underlying such doctrines is that changeable reality ultimately presupposes an eternal and unchangeable reality.
Postponing the consideration of these ultimate problems, let us return to the doctrine of the Protagoreans that truth is mere what seems true. Now, it may easily be shown that we cannot regard every appearance as true. The Protagoreans apply the same term 'appearance' to the special object of each sense color, sound, taste, etc. and the object of imagination and hence they assume that, because the former is free from error, the latter is also free from error. But imagination is by no means free from error, as is evident from the incoherent fancies which occur in dreams; and, therefore, we cannot admit that every appearance is true. Yet it is this indiscriminate use of the term 'appearance' that gives plausibility to their doctrine. They argue that bodies are larger or smaller, colors fainter or brighter, according to the position from which they are viewed ;that our sensations are different in health and sickness ; that things seem heavier or lighter to different persons ; that objects are not the same in dreams and in the waking state ; and from these facts they conclude that we must take every appearance as real. That they do not really believe their own doctrine is evident from their practice; they do not act upon their dreams, or prefer the opinion of the ignorant to the physician when they wish to know whether they are likely to recover their health. Thus, they virtually admit that by the exercise of thought and reason we can go beyond appearance and discover the fixed nature of things. As to the supposed contradiction in the reports of the different senses in regard to the same thing, or of the same sense under different conditions, no one really doubts that each sense is trustworthy so far as its proper object is concerned, and that a thing is more truly perceived when it is close at hand than when it is at a distance. No sense ever affirms and denies the same thing at the same time; nor even at different times is there any variation in the affection itself as felt, but only in the objector which the affection belongs. No doubt a certain wine, which, is sweet to the taste in health, may be bitter in sickness, but this does not imply any failure in the sense of taste to discriminate sweet from bitter as essentially distinct in their nature. It is thus evident that the fundamental weakness of the Protagorean doctrines in denying the permanent or essential nature of this and thus making any knowledge of reality impossible. In truth, that doctrine does not admit of any distinction between sensation and the object which excites it. Now, it is no doubt true that there is no sensible perception without a percipient subject, but this does not mean that the object is produced by the percipient] subject. Perception does not apprehend itself, but something which is presupposed as its condition, and the object as perceived is the effect of the combined activity of both. Were there nonpermanent object independent of sense, there would be no perception; and it is just because they do not recognize the fixed character of the object that the Protagoreans regard all appearances as true, and thus implicitly deny the principle of contradiction.
So far Aristotle has been dealing mainly with those who are led to doubt the principle of contradiction by genuine difficulties arising from the nature of the sensible ; now he goes on to consider objections to it which are raised partly by those who are in search of truth, and partly by those who merely seek to display their dialectical cleverness. The difficulty is raised as to whose opinion is to be taken as the standard of truth. This is like asking how we know that we are awake. To raise difficulties of this kind in regard to what is entirely free from doubt, can only be legitimate if it is assumed that nothing whatever can be admitted which has not first been proved. But, as has already] been pointed out, in all proof certain principles are presupposed! Which cannot be proved, as any honest thinker -is readily brought to admit. There are others, however, who demand that we should convince them by force of reason, while they make it impossible that we should meet their demand by assuming, at the very start, that contrary opinions may be true. They tell us that whatever seems true is true. Such a doctrine simply means that truth is relative to the individual; in other words, that there is no permanent reality whatever. Those who appeal to reason, and demand that everything should be proved by reason, must define precisely what they mean when they say that ' whatever seems true is true.' What they must mean is, that what appears true is true for him to whom, so far as, and in the manner in which it appears. This, then, is the sense in which we are to understand that all truth is relative. When it is thus limited the doctrine may be easily defended against those who maintain that what seems true to any one is true, and that all things are at once true and false. For things do not seem the same to all, nor always the same to the same individual. Thus, by crossing the fingers an object seems double to the touch, which to sights single. But though the same thing seems different to different persons, it is not different to the same sense at the same time and in the same manner. The doctrine of the relativity of truth, as we now see, does not affirm that what seems true to any one is true, but that what seems true to each man is true only for him, and for him only under precisely the same conditions. It is thus directly opposed to the doctrine that there is a permanent or universal nature of things. Upon such a nature, however, all fixity in the relations of things depends. Thus, the same thing is half or equal because there is a standard of unity, by reference to which it is judged. Those, on the other hand, who make everything relative to the opinion of each individual must deny that there is any objective standard. Thus, 'man,' in their view, is merely what he is supposed to be, and, therefore, there is no ' man' who is the subject, as distinguished from 'man' as the object, of the supposition. This absurdity is avoided when we see that all relation simply something permanent. The doctrine of relativity, on the other hand, in attempting to define the individual, not only compels us to suppose an infinite number of things, but makes each thing a class by itself; which simply means that things have no relations whatever to one another.
We have seen that the most certain of all the principles of knowledge is that contradictory assertions cannot be true at the same time,' and that those who deny this principle involve themselves in a ' nest of contradictions.' Now, as this principle rests upon the unity of thought with itself in the comprehension of the real, it is obvious that it is also impossible that contrary determinations should belong, at the same time, to the same thing. For contraries are related to each other as 'form' or 'substance' to 'privation' of 'form' or 'substance;' and manifestly ‘form' and 'privation' of 'form' are mutually exclusive. Thus if it belongs to the ' form ' of Socrates to 'see,' we cannot at once affirm that Socrates sees and that 'Socrates is blind,' any more than we can say that ' a stone is without feeling and that a stone feels. The principle of contradiction, therefore, applies both to contradictory and contrary assertions ; in other words, it tells us that we cannot at once affirm and deny that the same essential characteristics belong, and do not belong, to the same class of things. It is thus once more evident that which Aristotle in the whole of his defense of that principle in seeking to enforce, is that the knowledge of reality is possible! Because reality has a certain universal and necessary in the comprehension of which intelligence cannot contradict itself. To suppose either that reality has no permanent nature, or that thought cannot grasp it, is to reduce the former to a chaos of particulars and the latter to a disconnected series of sensations or opinions, and, therefore, to make all science impossible.
B. THE PRINCIPLE OF EXCLUDED MIDDLE.
The fundamental presupposition of all knowledge is for Aristotle the principle that ' the same essential characteristics cannot belong, and not belong, to the same object.' And, as those characteristics can only be grasped by thought, the principle may also be expressed in the form that thought cannot at once affirm and deny the same essential characteristics of the same object Or, since every true affirmative judgment states what elements are objectively combined, and every true negative judgment what elements are objectively separated, the principle implies that knowledge is possible, only if it is admitted that the same elements cannot be at once objectively combined and separated. Now, itis obvious that, as thus understood, the principle of contradiction implies that no true judgment can occupy a middle position between affirmation and negation, i. e. t there cannot be a true judgment which neither affirms nor denies, or, what is the same thing, which neither states what elements are combined nor what elements are separated in a thing. Hence, when certain elements are affirmed to be combined in an object, their separation is denied, and when certain elements are separated from the object, their combination in that object is denied. Now, this is what is expressed in the principle of excluded middle, which tells us that there is nothing intermediate between the two members of a contradiction, but we must necessarily affirm or deny the one or the other. In other words, the principle states that elements must either be combined in an object, or separated from it, there being no possibility that they are neither combined nor separated. It is true that Aristotle does not expressly derive the principle of excluded middle from the principle of contradiction, but the whole course of his reasoning shows that he regards the former as merely stating explicitly what is implied in the latter. Neither is for him a formal law of thought, but a principle which expresses the presupposition upon which all real knowledge is based. What Aristotle in the principle of excluded middle seeks to show, is that thought can grasp the real only if it comprehends the combination or separation of its elements, and that there cannot be anything real in which there no such combination and separation. That this is the idea which1he seeks to enforce, is evident from the reasoning by which he indirectly proves the principle of excluded middle.(I) That we must either affirm or deny one of the members of a contradiction is evident, he tells us, from the character of truth and falsehood. To say that the real 'is not,' or that the unreal ‘is,' is false; to say that the real 'is' and the unreal 'is not’ is true. Now, if it is maintained that there is something intermediate between contradictions, i. e., something which neither 'is' nor 'is not,' it is presupposed that there are judgments which are neither true nor false. As this presupposition is inconsistent with the very idea of truth and falsehood, we cannot admit that there is something which neither 'is' nor 'is not.' It is obvious that Aristotle is here dealing with the conditions of real knowledge. We might expand the argument just state in this way : A false judgment consists in denying the characteristics which belong to the essential nature of a thing, or in attributing to it, as essential, characteristics which do not belong to its essential nature ; a true judgment consists in stating the essential characteristics of a thing and denying that unessential characteristics belong to its essence. But, to maintain that there are characteristics which neither belong nor do not belong to a thing, simply means that there are no essential characteristics whatever. The denial of the principle of excluded middle, therefore, destroys the possibility of distinguishing between truth and falsehood, and thus makes all knowledge impossible. Things must have a permanent nature, which can be grasped by thought, or there is neither truth nor falsehood, and this obviously excludes the supposition that the real has no such nature.
(2) Let us suppose, however, that there is something intermediate between the two members of a contradiction. Then, this intermediate something must either (a) belong to the same class of things as the real and unreal, or (b) it must belong to a different class of things. In the former case it will be intermediate between two contraries, as 'gray ‘is intermediate between 'black' and 'white; ‘in the latter case, it will be an intermediate class of things, as 'dog' may be said to be intermediate between 'man ‘and 'horse.' Take the latter case first. Then we must suppose that there is a class of things intermediate between the real and unreal. But this makes the real and the unreal two distinct and separate classes ; so that, j us as ' man ' does not change into ‘horse,' or 'horse' into 'man,' so the real cannot change into the 'unreal,' or the ' unreal ' into the ' real.' But all change is from the ' real ' to the 'unreal’ or vice versa. Hence, we must, on this supposition, deny change. But change is a fact, and, therefore, there cannot be something intermediate between the 'real ‘and the 'unreal.' Now take the former case. There is, we must suppose, something intermediate between the ' real ' and the 'unreal, ‘which is the source of both. This intermediate something must pass over into the real and the unreal, while yet the real cannot pass over into the unreal, or vice versa. There is, therefore, no change from the real to the unreal, i. e., the real and unreal are mutually exclusive, which means that there is no change whatever, since change consists in the transition from the one to the other. Since, therefore, both suppositions lead to the denial of change, there cannot be something intermediate between the real and the unreal, but a thing must either be or not be as in the first argument.
Aristotle insists upon the permanent or essential characteristics of things, so in this second argument he brings forward the correlative idea of change. The obscurity arises from the incompleteness with which his thought is expressed. The basis of his argument is that, as he elsewhere says, reality is not a special class of things, with which other I classes of things can be contrasted ;it is that 'by reference to' which all things are predicated. Further, the conception of the real is inseparable from the conception of the unreal; or the determination of the positive characteristics implies the correlative conception of what they exclude. When, therefore, anything is said to change, we have to think of the contrast between the permanent
characteristics and the accidental. Nothing changes absolutely, but in all its changes it preserves its essential nature. It is thus the same thing which is present in all the changes. But if there is something which has no definite nature, this something can have neither permanent nor accidental characteristics; not the former, because it would then be real; not the latter, because it would then be unreal. But what has neither of these characteristics is nothing at all. Hence, while the real can change, the supposed intermediate something cannot change, because it is nothing. Change or process, in short, involves something permanent. Thus, it is only the real which can change, and the supposition of an absolutely 'unreal' is absurd. Nothing real originates from non-entity, but only from that which does not itself originate.
(3) Just as Aristotle's first argument for the principle of excluded middle was based upon the nature of the real, so he now argues, conversely, that the nature of thought shows that there cannot be anything intermediate between reality and unreality. All thought consists in affirmation or denial. We can either affirmer deny the combination of elements, but there is no possibility of a third operation in which we neither affirm nor deny. Truth and falsehood, therefore, consist in affirmation or denial, and hence there cannot be an intermediate act of thought different from both. The argument brings out the necessary correlation between thought and reality. The real, as Aristotle invariably assumes, can be grasped only by thought, and therefore the fundamental forms of thought are fitted for the comprehension of reality. Since, therefore, there is no possibility of thinking without either affirming or denying, the real cannot be known at all, if we suppose that there is something intermediate between reality and unreality ;for this intermediate something could not be grasped by thought, and there is no other organ by which existence can be grasped.
(4) The strict correlativity of thought and reality is more expressly stated in the next argument If there is something intermediate between contradictories, Aristotle tells us, there must be something intermediate between truth and falsehood as well as between reality and unreality. Hence there must be judgments which are neither true nor false. And as generation consists in the transition from the unreal to the real, and destruction in the transition from the real to the unreal, there must be a change of substance itself. As both of these suppositions are absurd, there cannot be anything intermediate between contradictories.
(5) There are classes of things in which contradiction involves contrariety; in numbers, e.g., whatever is not 'even' is necessarily ‘odd.' But, if there is something intermediate between contradictories, there must be numbers which are neither ' even ‘nor 'odd;' which is absurd and incompatible with the very idea of numbers.
(6) If there is a class of things intermediate between the real and unreal, we fall into an infinite series. For, if this intermediate something is affirmed to exist, it must also be denied existing, since the ground for assuming it is that neither affirmation nor negation is absolute. There must, therefore, be a fourth class of things, and so on to infinity. Thus, we never reach reality at all.
(7) There is no real judgment intermediate between affirmation and negation. A sensible thing, e.g., must either be 'white' or ‘not white,' and cannot be neither the one nor the other.
If the principle of excluded middle is thus beyond doubt, how are we to account for the fact that many deny it? Some have been led to do so from their inability to answer the sophistical reasoning by which it has been attacked, while others have been misled by the assumption that nothing can be admitted which is not established by a process of proof, though it is sufficiently obvious that the basis of all proof cannot itself be proved. But, though the principle of excluded middle, like that of contradiction, cannot be directly proved, it is placed beyond doubt when we see that by its denial all intelligible speech is made impossible. There can be no intelligible speech if we suppose that we can say that something neither is nor is not; for, on such a supposition, we neither affirm nor deny, i. e., we give no definite meaning to the terms we use. The necessity of intelligible speeches thus the common ground for both principles; and those doctrines which suppose that we can both affirm and deny the something, or that we judge without either affirming or denying, are open to the same general criticism, that they suppose we can think without giving a definite meaning to the object of our thought. Hence Heraclitus, in maintaining that all things at once ‘are' and 'are not,' violates the principle of contradiction; while Anaxagoras, by his assumption that there is something immediate between contradictories, violates the principle of excluded Middle.
These two principles being firmly established, it directly follows that we can neither maintain that all judgments are true north at all judgments are false. These two views are at bottom identical with the doctrine of Heraclitus, who says that every proposition is both true and false; for to say that every propositions true or false is the same as saying that nothing is true or false. That these doctrines violate the principles of contradiction and excluded middle is obvious. If all propositions are true, we must suppose that contradictory propositions are true, and us we violate the principle of contradiction. On the other, if all propositions are false, we have only to give a definite waning to our words in order to see that we violate the principle excluded middle. He who says that all propositions are true must admit the truth of the doctrine opposed to his own, and, therefore, he must admit that his own doctrine is false ; and he who affirms that all propositions are false must admit that the proposition in which his own doctrine is expressed is false. If the former replies that he does not mean that the doctrine of his opponents true, and the latter that he regards his own doctrine as an exception to the rule that all propositions are false, the whole basis of each doctrine is surrendered, and every man is entitled to regard his own doctrine as true and his opponent's as false.
The views of those who maintain that there is nothing but change, and of those who maintain that there is no change, are open to similar objections. For those who deny all change must hold that the same things are always true, which is manifestly false; while those who hold that there is nothing, but change make everything false. The truth is that change necessarily implies something permanent, for all change is from something and into something. Nor can we say that the world sometimes is changeless and sometimes in absolute change; but at all times there is change, while yet there is something permanent from which the change proceeds and which does not itself change.