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Jun 17, 2019



Jun 17, 2019

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Mark Delp2 1

Mark Damien Delp

Zaytuna College

Mark Damien Delp’s research interests include logic and the history of Christian philosophy.

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Blessed Opposition

A Meditation on the Principle of Non-Contradiction


View from the Dunes with Beach and Piers, Domburg, Piet Mondrian, 1909


Aristotle devotes the entirety of the fourth book of his Metaphysics to developing and defending what philosophers and theologians have traditionally considered to be the primary and self-evident principle of being and thought. He ends up stating the principle in two ways: (1) “The same attribute cannot at the same time belong and not belong to the same subject in the same respect” and (2) “No one can suppose the same thing to be and not to be.” In traditional logic and philosophy, this principle was called the “principle of non-contradiction,” while in modern times it has been called the “law of contradiction.” In what follows, I will refer to it for the sake of convenience simply as “the Principle.”


In applying the Principle primarily to the natures of things themselves, Aristotle was correcting a long tradition of philosophers in the world of the ancient Greeks. “There are some who... assert that it is possible for the same thing to be and not to be, and say that people can judge this to be the case. And... many writers about nature use this language.”1 As W. D. Ross summarizes the matter, “They maintain the possibility of contradiction 1) in fact—‘A may be both B and not B,’ and 2) in belief—‘a man may judge that A is B and also that A is not B.’”2 In the Metaphysics, Aristotle chooses to defend the Principle “in belief”—that is, by showing how those who argue against it end up contradicting themselves. Accordingly, his argument took the form of a reductio ad absurdum.


“Aristotle has in his defense of the law of contradiction… used an argument derived from the necessity of a fixed meaning for every term.”3 If the opponent is to argue at all, he must assume that his words keep the same meaning throughout—that is, he must “say something which is significant both for himself and for another.”4 But if he does this, he concedes the truth of the Principle even while attempting to disprove it. “Again, if contradictory statements are all 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 man, if of everything it is possible either to affirm or to deny anything.”5 “If the meanings are unlimited, no account can be given of the thing. Not to mean one thing is to mean nothing, and if words mean nothing rational intercourse with others is destroyed, and even with oneself, for if we do not think one thing we do not think at all.”6 Aristotle goes so far as to state several times that a person acting in such a way is “no better than a vegetable.”7


The law of identity, implicit in ancient and medieval philosophy, did not assert the mathematical principle “A is A” but rather the logical principle that “A is B,” such that B states the essence of A. In other words, B states explicitly what A is. Thus, “Every human being is an animal” does not say that “human being” is “animal” but that the definition of “animal” is contained in the definition of “human being.”


While contradiction by negating absolutely the nature of a thing is the strongest of the species of opposition, the other main species, that of contrary opposition, presupposes a reconciling third term that allows the contrary terms to participate in a common nature. Contrary opposites are both like and unlike: spiders are “like” flies insofar as both are animals (i.e., both share the same remote genus). And they are unlike not only in appearance but because each has a specific difference that sets it apart in its own species within that genus. Virtue does not contradict vice, for there are degrees in each that approximate the other; one need not be vicious if one is lacking in virtue, even severely so. “Wherever there is a metaxy,8 we can observe it changing into the extremes between which it lies (for change is just from extreme to extreme, from extreme to intermediate, or from intermediate to extreme).”9 But if we say that “a fly is a spider” or “an elephant is a palm tree,” we unqualifiedly deny the nature of the terms. “Therefore there is no such thing as a metaxy of contradictories in the sense of a mere neutral between them.”10 There is nothing in-between two contradictories, and thus we have the principle of the excluded middle, which for Aristotle is a way of expressing the absolute difference between contradictory and contrary opposition: “There cannot be an intermediate between contradictories, but of one subject we must either affirm or deny any one predicate.”11


The English term principle, itself deriving from the Latin principium, translates the Greek archē, which means both “first” and “rule.” We have seen how it serves as a rule, and it is first not because it comes prior in time but because by it everything capable of being known can be given a logos, an account of its essential nature, of what it is. But this means that the Principle, as constituting the ultimate criterion for certainty, is even prior to our knowledge of truth. The Principle is the strictest and most universal limit to thinking and being, applicable everywhere and at all times, present seminally or virtually in the hidden part of the mind—Aristotle went so far as to maintain there was a separate faculty in the mind, “nous,” that intuited the Principle—and unfolding into actuality with every mental or spoken judgment, no matter how seemingly trivial or important. Those who deny it “seek a reason for things for which no reason can be given; for the starting-point [the archē or Principle] of demonstration is not demonstration.”12 Ultimately, then, to every existing thing there must be an abiding essential nature, and to each word there must be an abiding essential definition. To deny the former is to violate the Principle in fact, to deny the latter is to deny the Principle in belief.


For us who live today, who have become accustomed by the authority of science to believe many fantastic things, Aristotle’s Principle may seem trite. Indeed, modern philosophers have denied its primacy and/or denied its legitimacy. What great scientific advance does it provide or even promise? What effort of the mind does it cost to understand it? That everyone can understand it immediately upon trying to violate it seems rather to be the best proof of its unimportance. However, since the infancy of science, one can witness how great a challenge it was for philosophers to arrive at a convincing account of how there could be certain knowledge of the world. When one seeks for absolute certainty, the stability one was accustomed to seeing in nature seems to evaporate into a constant state of flux. Aristotle expresses the desire of the early scientists by the analogy of a soldier who makes a stand amid a route on the battlefield, making it possible for others to take a stand and eventually regain the ground they lost: in the battle to achieve stable knowledge amid the flux of mutable phenomena, the philosopher achieves the first “universal”—that is, the first stage of conceptual knowledge that allows others to do the same and eventually achieve science.


During the scholastic era of medieval Europe, the Principle assumed a new importance, exceeding even the authority granted to it by Aristotle, for its absolute certitude now applied even to statements about God’s nature. For example, Thomas Aquinas appealed to it in his account of the divine will in creation, asserting that while God in His omnipotence could obviously have made the world better than it is, He could not have made the world other than it is (i.e., could not have made another world altogether). To have done so would be as though He were “to change a man into a horse,” thus violating the principle of non-contradiction. But if God is truly omnipotent, how can He be thought to obey a law of nature? Aquinas explains that contradiction of natures is not strictly speaking possible, for “possible” referred in his time primarily to “potency,” and every potency is part of a nature. Accordingly, while it is possible for a spider to weave a web (i.e., it is one of the potencies of its nature), it is not possible for it to become a fly. Thus, because contradiction is not a possibility, to affirm that God cannot violate the Principle does not affect His omnipotence.


The Principle became so powerful an influence in the later Middle Ages that William of Ockham became so bold as to assert that God could present before the senses the exact image of a non-existing thing, or that He could will that someone would feel hate for Him and not sin—for none of these statements constitute contradictions. Aquinas would have said that Ockham applied the Principle needlessly and inappropriately. But each believed that it applied even to God. The medieval philosophers believed that true contradiction not only cannot occur in speech without resulting in absurdity and the total breakdown of meaning in language but it literally cannot be imagined. Let one violate it in speech as often as one wishes, one will never be able to see it. It is the province of the imagination to conjure opposites, to portray things other than they are, but the condition for this activity is that things themselves do remain what they are, and correlatively, what they are not. As we said above, things must retain their differences to continue to be what they are, but it is also true that it is not the novel phenomenon in itself that is of interest but the contrast it makes with our accustomed sense of reality.


Physicists have asserted that certain consequences of the theory of relativity violate the Principle, while Marxist theorists have asserted the same thing in their doctrine of dialectical materialism. Whether they are right or wrong, it nevertheless remains that what they assert is literally unimaginable. For example, when Ross tells us “‘That the diagonal is commensurate with the side’ is Aristotle’s favorite instance of what is not only false but impossible,” he is not leading us to believe that Aristotle was claiming that upon seeing the diagonal and the side together, we “see” a contradiction. It is certainly true that we can see the diagonal with the side, that both are straight lines, etc. But the impossibility of their commensurability is not itself an image but an idea abstracted from the image. Once the idea is conceived, though, it communicates the mystery of a truth beyond that of rational measure.


Strictly speaking, a contradiction in thought should not even be said to result in the absurd, which typically results from a continuum of departure from rational measure—that is, the absurd must involve contrary opposition. “Don’t be absurd” does not mean “Don’t deny that you are a human being,” but rather “Don’t become extremely ridiculous”—that is, don’t distort yourself to the extremity of what it means to be human. (A person may be malevolent, but to say that he is the devil is to drive the contrary opposition to its impossible contradictory in a total negation of one’s humanity.)


We make delightful play by distorting the images we derive from things; the humor that such play often evokes is linked with that of instructive irony. But, again, for there to be delight and humor, there must be the understanding of a continuum of values that both begins and ends in an absolute meaning or nature. In metaphor, it is the imaginary departure from the thing that makes the thing more human and, at the same time, more interesting to us. But the thrill one can feel at the absolute distortion of what is given (literally, datum) can lead not to the play of intelligible qualities but to the annihilation of some quality or other—or rather, to the abstract possibility of that annihilation. Here we see the abstract opposition striving to become concrete and thus contradict joyful, meaningful play. In refusing to recognize that even the smallest creature possesses its own specific nature, medieval metaphysicians believed that for all intents and purposes, one contradicts the entire created world, and indirectly, its creator. In contrast with the mystic, who sees all things as non-being in relation to and in dependence upon the necessary Being, the devotee of meaningless contradiction finds in the act of imagining the absolute negation, not only of beings but of long-standing human traditions, a thrill of god-like power. Such a person takes delight not in changing something in his imagination for purposes of instruction or benevolent play but in reducing it to the utterly insignificant.

Tableau No 2 Composition No V By Piet Mondriaan

Tableau no. 2 / Composition no. V, Piet Mondrian, 1914


Contradictory statements meant in earnest to apply to reality can be compared to voluntary departures from religious teachings; while some heresies were in fact contrary to the faith but not contradictory (they were properly called “heterodox”), they could also be contradictions. Aquinas, I think, would have said that Ockham’s belief that there is no contradiction in saying that God could make someone hate Him was both a contradiction—if God is Love, He cannot possibly beget hate—and a heresy in the strong sense of the term.


The population of a society as a whole embarks on a very dangerous path when it gradually ceases being repulsed or getting angry when arbitrarily contradicted by a totalitarian force. Reckless, arbitrary, compelled contradiction wrenches from the human mind its first and last solid ground. The victim will eventually be forced to beg from the perpetrator of contradiction the cause for being compelled to accept it as well as the correct answer that will keep him out of trouble—neither of these is ever granted. Before such a state of affairs can ever occur on a universal scale, however, individuals will have ceased to be able to “take care of themselves.” An artificial intelligence does not care that a spider is not a fly or vice versa, for it associates a spider with a fly by means of a purely formal language that, by definition, has no stake in preventing something becoming totally other than it is. (True nonsense is non-sense—that is to say, absolutely other than sense.) To have a stake would presuppose sensual contact with real things, imaginative assimilation of their images, the power to alter them prudently, and the power of gaining theoretic consistency only by using these images as foundation. Imagination both perfects and hinders human competition with computers. The chess player cannot restrict himself to thinking only of the formal potentialities of the pieces with respect to each other; for every player, the game will be far more than the sum of its parts. Not so for the computer.


No essentially human attribute could survive a society in which an external power had so limited the channels of communication that no sign, symbol, or word retained an unchanging semantic content. No direction could be given except by contact, as happens to the wretched souls in Plato’s myth at the end of the Phaedo who were driven toward Hell by demons solely by the pain inflicted by discrete jabs of their spears. Nothing could be communicated save by the brutal self-evidence of commands to do this, do that, move, stop, which were effective by the sheer primitive immediacy of physical pain, along with, perhaps, the most rudimentary pantomime. But this is analogous to the way people are moved by the primitive binary commands of the computer, which drives the mind into making unreasoned micro- or even nano-decisions, the smallness and compulsory nature of them masking each minute quantum of pain inflicted. Here, it is not so much the principle of non-contradiction but the principle of the excluded middle that is being violated, and at the level of interior experience: since free choice is completely nullified in the grip of the primitive binary mechanism of the machine, the two options become one in the actuality of obedience.

Successful mutations contribute to the balance and perpetuity of an ecosystem, the strange becoming beautifully integrated with the familiar. This is blessed opposition.


If some power were capable of forcing us to violate the Principle in regard to our memories, then memory itself would cease to mean anything at all, for the sense of recognition—the very sense of the againness of the mental image—that is essential to memory must then be absent. What is now called memory would simply be a stream of images appearing in our mind, images that could signify anything or nothing at all, for each would appear, as it were, ex nihilo. Memories presuppose likeness, but likeness presupposes the principle of non-contradiction. In any case, at least in the medieval account, where there is no imagination there is no memory.


There can be contrariety in memories, for nothing is more self-evident to people of sound mind than that memory, especially memory of images, is for the most part approximate; it certainly possesses degrees. In most of us, the vagaries of “good” and “bad” memory remain near the center of the spectrum; however, as with other contraries, in memory, too, extremes are found at either end of the spectrum (e.g., so-called photographic memory and fragmented memory suffered by diseases of the brain). But each extreme is connected and made sense of by the metaxy of the continuum.


Even mythical creatures have natures. (I do not say “were assigned natures,” since their origin is shrouded in pre-history.) Their puzzling behavior was accounted for by specific differences: elves and fairies acted in this kind of strange way, centaurs and cyclopes in that kind of strange way. The dancing hippopotamuses in the cartoon movie Fantasia are not contradictions of real ones, for although they display a power that does not belong to a real hippopotamus, their power has a resemblance to and is indeed suggested by the quick succession of their feet (which are relatively small compared with their enormous bulk) when running, the motion as a whole seeming somehow incongruously delicate. At any rate, one can obviously imagine them dancing, even ballet style, because someone already has done so.


The Principle holds even in hallucinogenic states. When under the influence of, say, opium, one sees an impossible creature transform into an equally but entirely different impossible creature, because the transformation is sequential: while each is seen in itself, each will retain its own form—its own, as it were, transient nature. When we say that true contradiction is unimaginable, we appeal to the phantasm and discover that it can no more suffer simultaneous and total negation and affirmation than the real data of sense can. In reply to one who says that, under different distortions of perception, one can see phantom A as phantom B, we can only say this means he sees A in the process of taking on the characteristics of B; as long as A remains recognizable, we must say that it is what it is; and we cannot say that it is B until the slightest resemblance to A no longer exists. Moreover, we cannot even detect the moment when A ceases to exist and B begins to exist. If in an opium dream a flower begins to transform into a fish, the dreamer may rest assured that the flower will never become a fish. In computer-generated imagery, any image can be morphed into another. We watch the flower become a fish, but do so within a continuum of qualitative changes that, for its special effect, must always presuppose that we keep the concepts themselves discrete. And once we see nothing but a fish, we then settle in our minds to what we know.


In literary accounts that describe the effects of withdrawal from opium, we often read that it is not the nightmarish images themselves that prove most terrifying but rather their sudden changing into other nightmarish images, the sequence from the one to the other contributing to the totality of the delirium tremens. But what happens when a society as a whole withdraws from, so to speak, its entire worldview? Even when it happens gradually, as it did when the heliocentric replaced the geocentric cosmos, should we not expect a long and drawn-out delirium tremens as a result of the mass perception that the Principle has been violated?


The notion that there is consolation in limit was ingrained in ancient and medieval thought. The specific difference itself is both positive and negative, for it tells us what a thing is as well as what it is not. Moreover, it is the sign of a real division of species. And by being informed by that difference, each existing member of a species is placed into harmonious opposition with other species of things. In relation to themselves, these differences are not contradictions but contraries, for they are reconciled at the level of the genus, as the differences between individuals are reconciled at the level of the species. Even in modern biological taxonomies this is obvious; and it is obvious that there are limits at the superior and inferior levels.


Nature puts on display the exception to her rule; such exceptions are never symptoms of decay but signs of her finitude, her contingency before the necessity of the Creator. Her creative power is not distributed to everything equally or in the same way; in small, providential advents, her rule, far from being violated, is rational. Adaptive mutations are not contradictions; they do not signal something becoming what it is not, but how it may manage to continue to be itself. Successful mutations contribute to the balance and perpetuity of an ecosystem, the strange becoming beautifully integrated with the familiar. This is blessed opposition.

Piet Mondrian 1911 Gray Tree De Grijze Boom Oil On Canvas 79 7 X 109 1 Cm Gemeentemuseum Den Haag Netherlands

Gray Tree, Piet Mondrian, 1911


We call many systems of signs languages and imply thereby that we follow rules that must be learned in order to speak or read them. But there are also pseudo-languages that, rather than facilitate communication, thrive on disintegrating natural languages. Natural species remain the same, however much we are told disingenuously that they are in constant flux. And so, consequently, the meanings of our words manage to remain mostly the same. There has, however, always been a natural fluctuation in the meanings of our words that, because it took place metaxy, was not usually noticed. Meanings moved back and forth between the limits of words to signify. Like contrary opposition, their sweetness became a little sour, their warmth mixed with a feeling of coldness. This tension in the signification of words, when arising from natural founts of the spiritual imagination, is ideally the work of poets, who know very well how, throughout all the changes, there must run filaments of recognition, reassuring voices of familiarity that make the difference between their being received gladly and being rejected as unrecognizable.


To be compelled arbitrarily to do something is the same as being compelled to do it for no reason. One is not granted an account that can put the mind at rest regarding that which is to be done; one is granted no middle term to an argument, no overriding genus in which to reconcile the differences. To receive an account that is not relevant or radically misrepresents the circumstances makes matters even worse, for by giving the pretense of an account, one is made to realize the depth of the real privation of meaning. In times past, it was common to hear people utter the kindly expletive “For the love of God!”, which was in its own way a rebellion, one that opposed the senseless act.


The factory was perhaps the first societal institution that experimented in making people accommodate themselves to contradiction in their understanding of work. The worker needed the work to make sense, he needed to recognize the matter upon which he worked and its potency to become something valuable to the community. The factory, however, offered no such immediate meaning, for the work done was done by it, the motions of the worker being just that: motions. Moreover, by definition, work is to be completed, which implies that one returns from the end of a task to its beginning. But since the worker makes the same motions day in and day out, he never moves from beginning to end, and thus he never completes work; and work never meant to be completed is, by ancient customs of meaning, no work at all.


The devotee of contradiction is titillated by the thought of absolute opposition, and even more so by the manifest grief and pain it causes in the unwary mind. But every proffered image that inverses what is expected or what is revered can only suggest and not realize the nihil that the devotee himself desires with an intensity that borders on worship. Nature worshippers shun absolute opposition; they derive satisfaction and security in the belief that all is held within the womb of nature or of the cosmos, with everything, even the more terrifying gods and goddesses, ultimately reassuring them of the unity of the whole. All things for them are reconciled as it were by a dazzling variety of mediating thirds. The rationalist atheist, too, eschews contradictory extremes, for his atheism is anything but untasteful, and his claims must point to an integrity, if not of character, of reason.


There are people, however, who involuntarily nurture what Edgar Allen Poe called the “imp of the perverse,” his imagined demon who compels a person to harbor a strange, morbid obsession with nothing in particular. This is a curious phrase—for in logic, nothing signifies as a universal, not as a particular. But it is precisely the possibility of nothing becoming manifest, of non-being entering into the world as a being, that haunts the imagination of these people. They do not worship the spirit of annihilation; indeed, they are perhaps more repulsed by it than is any other type of person; rather, they are caught between the authentically religious awe before the absolute otherness of divine being, which lies at the extremity of the power of human knowledge, and the absolute otherness of evil, which lies at the extremity of the privation of human ignorance. Those who are caught in this dread interval cannot experience contraries in any other way than as leading to their respective and unimaginable extremity. It is as though a shadow had the power to overwhelm that which casts it. But as long as he remains in this state, he will always yearn for the reconciling third, some blessed difference that could reveal to his soul a spiritual genus of sorts in which he could become what he is instead of constantly being lured to be what he is not.


The ability to deny the Principle exerts a strange compulsion for the modern mind, a reckless passion to contradict anything that betrays a trace of the old authority of religion, that absolute and supremely bothersome check on the ways we exercise our imagination and thought. Immediately upon encountering someone who admits to believing in a supreme authority, be it God or book of grammar, this person is seized by an intense desire to oppose, and ultimately, to oppose he knows not what or whom. But even the most vehement attempt at negation cannot, by definition, contradict authority that has been universally recognized as self-evident; rather, the best it can do is set up a contrary opposition, an opposition of degree, according to which one would stretch the opposed virtue in the opposite direction and along a continuum of inverse value, as though one who disliked sweet food kept adding sourness until the sweet was hardly discernable.


One might simply assert, as others throughout history have done, that goodness and evil, justice and injustice, are in the minds of those who defend them or attack them. But as a revolutionary, which all who are devoted to opposition per se seem destined to be, one must take care that the meaning of the rebellion is understood clearly by those against whom one is rebelling. There is nothing more frustrating to the revolutionary than the possibility that the powers that be may not understand the nature of the rebellion, and God forbid, may mistake it for a non-rebellion. To accomplish this, he must convey the same message now that he conveyed yesterday, let alone a minute ago. In other words, he must obey the Principle in his speech.


It does seem, however, that today we are encountering a tendency of speech that is so protean that it sometimes seems to approach a pure state of flux. To what state of affairs would this rebellion be opposed? It requires some terrible vitiation of the soul for it no longer to feel an existential repulsion at the assertion that A is non-A. Nevertheless, the denial of the absoluteness of the Principle is easier today precisely because so many apparent violations of it are set forth by scientists, suggested as “options” by multifarious forms of media, or stated with insane matter-of-factness by machines. Indeed, it seems that the Principle is now routinely denied, but none of the denials ever explicitly confront its authority. They are made, as it were, in absentia.


Though the scholastics universally affirmed the absoluteness and primacy of the Principle, they, too, seemed compelled to challenge it in certain respects. For example, in visions of the divine, the mystic not only accepts the theological tenet that all beings are non-beings when compared with true Being or God, but he also experiences its truth, as though all things were indeed nothing in the presence of their Creator. A theorist could blithely conclude that the mystic was stating that A is not A. And yet when pressed, the mystic, refusing to interpret the negation as mere annihilation, will turn the tables and say, rather, that God is actually non-being in comparison with beings, not, though, as a contradiction to them, but as the “ocean of being,” the “infinite plenitude of being.” Although his mind maintains that the divine extreme is unattainable—unlike the revolutionary, he is not blind to this fact—his faith tells him he can attain it. There is another difference: the mystic believes that by coming as close as possible to the divine extreme, he will finally become what he was meant to be. This is, indeed, the most blessed opposition.