A Secular Age:

Truth in conflict

posted by Patrick Lee Miller

My previous post argued that anyone who wishes both to think well and to feel well about the world should seek a way of thinking as immanent as it is transcendent, a crosswise way of thinking that is more capacious than the logic of consistency defined by the principle of non-contradiction. Fortunately there has long been such a way, the way of Heraclitus: “A thing agrees in disagreement with itself; it is a crosswise harmony (palintropos harmoniē), like that of the bow and the lyre.” In Becoming God I have argued that Heraclitean logic is not only more ancient, but also more accurate than the logic of consistency that Parmenides and the Platonic tradition deployed against it. This tradition has been dominant from the moment of its founding, thanks in part to the rhetorical genius of its founder, making non-contradiction the supreme principle of reason in the eyes of nearly every philosopher since. This post aims first to humble it before the next seeks to revive its Heraclitean rival.

Humble it, that is, but not reject it. For without it, as philosophers say, everything is permitted. Some recent ones have questioned it nonetheless, reviving the Liar Paradox of late antiquity: “This sentence is false.” It appears to be a normal declarative sentence, so it should be true or false. But which? If it were true, what it says must be the case, so it should be false. Yet if it be false, this is exactly what it says, so it should be true. Despite elaborate attempts to defuse it, this paradox persistently threatens an explosion, the logical equivalent of a nuclear detonation, destroying the principle of non-contradiction and thus the imperative to think consistently. But even those who champion the paradox recognize the incoherence of abandoning this principle altogether. Their goal is to humble it, not reject it. Similarly respectful of it, this post seeks only to demote it from the status Aristotle assigned it, namely “the firmest of all.”

Whether or not it can be saved from the Liar—which could perhaps be dismissed as an anomaly, radioactive uranium to be safely contained somehow, somewhere where it will not corrupt the rest of our thinking—the principle of non-contradiction exhibits a more serious flaw: it cannot accommodate anything in time, let alone time itself, where we live and breathe and have our being. Here, in brief, is the problem: this logical principle requires that everything temporal be consistent at a moment, although no moment is itself consistent. Aristotle formulates the principle this way: “The same attribute cannot at the same time belong and not belong to the same subject in the same respect.” He adds that we may supply other qualifications as needed, but the most important of all he has already mentioned: time. Yesterday, for example, was not contradictory if it was both cloudy and not-cloudy; it may have been cloudy in the morning and sunny in the afternoon; the attributes cloudy and not-cloudy belonged to yesterday at different times. If anything were to undermine the principle, then, it would have to do so at the same time—in other words, in a moment, in the twinkling of an eye.

Now, ironically, Aristotle himself observed that if time were a succession of moments, each one would have to perish, for only so could these moments yield to one another and produce the flow of time. When, however, could a particular moment perish? In which moment could it do so? Not in itself, for then it would both exist and not exist; nor could it perish in any other moment, for then it would be simultaneous with a different moment. Both options, in short, would violate the principle of non-contradiction. So too would the same options available to any moment that is supposed to be born. It could only be born in itself or in another moment, and both are equally contradictory. Indeed, the paradoxical options available to anyone who freezes time into moments resemble nothing so much as the dilemmas produced by a student of Parmenides, Zeno of Elea.

Zeno’s most beguiling paradox, the Flying Arrow, invites us to imagine the flight of an arrow frozen in a moment. Were we to freeze a flying arrow in a ‘now’—catching it on film with a high-speed camera, so to speak—it would occupy a space equal to itself. For if it should occupy a space longer than itself, it would be moving, not frozen. In our photographic analogy, it would be as if our shutter speed were too slow; rather than catching the flying arrow at a moment, we caught it over several moments, creating a blur. Catching it in a ‘now,’ we would find it occupying a space equal to itself, which is to say motionless. In every ‘now,’ at every moment, it must be motionless. Yet at each moment it must also be moving. After all, it is a flying arrow: if it never moves, it cannot fly. In sum, then, at every moment it must be both moving and still. The flying arrow would seem to violate the principle of non-contradiction.

According to Aristotle, however, such an absurd “result follows from the assumption that time is composed of moments: if this assumption is not granted, the conclusion will not follow.” In other words, if “time is not composed of indivisible nows,” but is instead infinitely divisible, there is no freezing the flying arrow in a moment. For if a motion happens over time that is infinitely divisible, every division of its duration should reveal it to be moving. While moving, it must always occupy a space longer than itself, only less so with each finer division. Because there is no final division, neither is there any moment at which the arrow turns out to be still. One solution to this paradox, therefore, is to claim that time is not composed of ‘nows’; instead, it is infinitely divisible, a flowing continuum rather than a particulate succession.

Is the same Aristotelian solution available to explain a related puzzle, the paradoxical change of everything in time? Consider an especially vivid instance of this change: fire. As a process, it is ever-changing, a sort of motion. Dividing the duration of its burning—where this burning is parallel to the arrow’s moving—we shall never reach a moment when it ceases to burn, anymore than we shall reach a moment when the arrow is still. The parallel is important to keep in mind, because the same photographic temptations arise for fire that arose for the flying arrow. We imagine capturing a fire on film, and with the image of such a fire before our minds, we are tempted to think that we have frozen it in exclusive satisfaction, the way we were tempted by Zeno to think of the arrow as perfectly still in a ‘now.’ But if time is infinitely divisible, however finely we divide the duration of the fire’s burning, it is no more static in this division of its duration than was the arrow perfectly still in its own. In every division, no matter how fine, the flying arrow is moving. Correlatively, in every division, no matter how fine, the fire is burning.

This burning is a satisfaction with fuel, lest it be extinguished, but it is also a need for fuel, lest it be static. Fire, wrote Heraclitus, is “need and satiety.” It cannot consistently burn in a moment, anymore than an arrow can fly in a moment, and so it should come as no surprise that any analysis that freezes it so creates a conflict. Thanks to the analyses of Aristotle and Zeno, though, we can say more precisely that the logical offense occurs only when we conceive of time as divisible into ‘nows.’ Yet there is a deep irony here that Aristotle himself does not seem to recognize: the principle of non-contradiction that he himself codified requires us to conceive time and change this way. It analyzes time into moments in order to insist, as a necessary condition of being and knowledge, that the attributes of everything so analyzed be consistent with one another.

Yesterday was both cloudy and not-cloudy, but this was no true conflict because its contradictory attributes belonged to it at different times. No such analysis is available when we use the principle to think fire, however, because its satisfaction and neediness remain forever intertwined in each moment. So likewise, it turns out, whenever we scrutinize anything else in time, which is itself both dying and being born, inextricably together, in every moment and forever. If the principle of non-contradiction really is a necessary condition of knowledge, as Aristotle claimed, knowing any object must require freezing it in a moment and finding it consistent then. But if everything in time—everything that undergoes process, change, and motion, albeit less visibly and dramatically than fire—must be inconsistent in each moment, nothing temporal can be known as such. Indeed, because Aristotle thinks that nothing contradictory can be, nothing temporal can ever exist as such.

Philosophers who revere the principle of non-contradiction thus require true existence to be unchanging, timeless, and eternal. Plato’s Forms are but the paradigms of this requirement, showing most clearly how devotion to consistent thinking favors transcendence by rendering the immanent world impossible, unknowable, and even an evil illusion. If the argument of “Love and reason” was accurate—that a purely transcendent philosophy inhibits love of the world—the emotion associated most often with this way of thinking should be resentment. This was Nietzsche’s abiding critique of philosophers, principally those in the Platonic tradition; this critique drove him and those indebted to him, especially Heidegger, to seek a way of thinking otherwise. Finding his alternative in the philosopher whom Parmenides attacked for his “crosswise” way of thinking, Nietzsche wrote that “the world forever needs the truth, hence the world forever needs Heraclitus.” The next post turns to him, attempting to reveal his concealed logic before using it in a final post to answer Connolly’s invitation “to honor Jesus by offering a distinctive interpretation of his calling and mode of inspiration.”

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5 Responses to “Truth in conflict”

  1. avatar Jeff McCurry says:

    This post and the previous one were very thoughtful, and indeed I am very eager for the next two. I think that Miller is doing, in his own way, something similar to what Derrida, Lyotard, and Zizek are doing, which is to reclaim the truth of the contradiction. But whereas the above, as far as I understand them, want to say that the contradiction is “impossible,” at least in fundamental respects, even though it is real, Miller, I think, wants to say that the contradiction is both possible and real, which sets him against the above in certain ways. I am interested in how Miller might express his philosophy of contradiction, of crosswise-ness, in terms of a spirituality. What would it mean, for example, to pray cross-wise, believing in transcendent immanence? I certainly don’t know the answer, and maybe I don’t even know what I mean by the question, but I am very keen to see how Miller’s philosophy gets fleshed out in concrete existential life. I assume that’s what coming next?

  2. The distinction McCurry draws between what I am trying to do and what he understands Derrida, Lyotard, and Zizek to be doing is insightful. Allow me to say a little more along these same lines. For having worked in both continental and analytic schools of philosophy, I have found the paramount difference between them to be their divergent attitudes to contradiction. Whereas continental thinkers can be heedless of the principle that forbids it, writing in a way that seems to permit and even celebrate it, analytic thinkers treat the same principle as a shibboleth, tolerating only those objections against it that are highly technical, tightly contained, and thus threatening no fundamental revisions.

    But just as my first post in this series appropriated the Augustinian critique of Nietzschean immanence as well as the Nietzschean critique of Augustinian transcendence in order to expose the false dichotomy between immanence and transcendence, here I want to endorse both the analytic and continental critiques of each other in order to accomplish a similar goal. Specifically: analytic critics of continental thought are correct that its rejection of the principle of non-contradiction often generates hypocrisy or obscurity, while continental critics of analytic thought are correct that its defensive loyalty to this principle blinds it to some fundamental challenges. Or so I have found in both cases, discerning the following false dichotomy: disregard for the principle, on one hand; on the other, affirming it as the firmest of all.

    One thing I am trying to do in this series of posts, and more fully in my book, is to escape this false dichotomy. In other words, I am trying to *preserve* the principle of non-contradiction (contra some continental thought), while *demoting* it from the supreme status Aristotle accorded it (contra most analytic thought). I hope this distinction will become clearer in my next post, on the crosswise thinking of Heraclitus, because his logic encompasses the principle of non-contradiction, and its characteristic activity of analysis, while assigning it a supporting role to his own more capacious principle and activity.

    That is my hope, but it may be forlorn. No matter how emphatically I make this distinction—between demoting the principle of non-contradiction and outright rejecting it—some analytic philosophers hear me as yet another Derridean, vulnerable to the same objection (or, as is more often the case, the same ridicule). Continental philosophers, for their part, have proven a more receptive audience to my conclusion, but they usually appear indifferent to the argument I adduce in its favor (perhaps because it uses a principle they presume I am rejecting, perhaps from an inveterate contempt of argument). It would be sad if these ideas—whether right or wrong—were to remain trapped in the no man’s land between the trenches that mar today’s philosophical landscape. For if these ideas are wrong, their errors cannot be fully exposed without the critical scrutiny of a community of thinkers; and if they are right, they will likewise need a community to promote their growth.

    This brings me to the crucial question McCurry poses: what would crosswise spirituality look like in practice? That is how these ideas, if they do survive critical scrutiny, should grow. Here my hope—a tentative one, I should add—is that the next two posts will be the very beginning, but far from the end, of an answer to this question. Only after we have the crosswise logic before us can we begin to investigate how it will look in practice. So I invite McCurry and anyone else who shares our curiosity to keep reading, returning with the same question later, when we might be a little more precise about the terms of the question.

    In the meantime, though, I can suggest a general answer. After reading my post yesterday, a Polish friend wrote to tell me about “Bóg się rodzi, moc truchleje,” her country’s most famous Christmas carol, which resounds with Heraclitean overtones. Here is a translation of the first verse:

    God is born, great powers tremble,
    Lord of Heaven lies forsaken.
    Fire is frozen, splendor darkens,
    feeble nature God has taken.
    Lowly born, yet Lord to Praises,
    Mortal yet the King of Ages.
    Now indeed the Word made Flesh has
    come on earth to dwell among us.

    Crosswise Christianity would allow the believer to sing this carol not only with the lips and heart, but also with the mind.

  3. avatar Louis Butler says:

    The work put forth here by Miller is a tremendous effort, and for that I applaud him. But despite my willingness to accept the principle of chiasmus, I cannot worry how it can be easily implemented. This is in reference to the call for a community of chiastic thinkers above. This group would seek to reconcile the two extreme groups (in this case, analytics and continentals). But how does one accomplish this feat without being ostracized and ignored by both? It seems as daunting as resolving an argument between die-hard football fans of rival teams.

    By human nature, we seem to have a propensity for dividing ourselves into opposing groups: take, for instance, the Democratic and Republican parties. Here a funny phenomenon occurs: as much as people starkly differentiate themselves into these groups, no one truly is a paradigmatic Republican or Democrat, but rather holds positions and beliefs associated to both groups, in different ratios among different politicians. Yet there still lingers the stark contrast between the groups — and the animosity that goes along with it — albeit a superficial one (since, again, no one is a true Republican or Democrat).

    So it is, perhaps, with analytics and continentals. But the problem of how to bring this odd phenomenon to the fore without stirring hostility and from both sides remains a problem. Thus, before one can think about how to found a community to support chiastic ideas, one must decide how to prevent the other communities from closing their doors to these ideas.

  4. avatar David U. B. Liu says:

    As the author and his commentator Louis Butler confess, Miller’s attempt to conciliate analytic and Continental philosophers to each other and create a fertile discursive zone between them is indeed both worthy and arduous. When I said in my earlier response to his first post of this series (Love and reason) that his work would gain traction in both philosophic guilds, I certainly did not mean it would be easy or popular, but that his deft movement between styles and concerns of the two would continue to provoke friendly and unfriendly response in both directions. In other words, it would generate diverse thought.

    Thus the condition of possibility and becoming for the “community of chiastic thinkers” (or at least one friendly to Miller’s chiasm) as Butler dreams of is a kind of movement, an oscillation, across the proverbial philosophic septum—not only by Miller himself, but by his interlocutors. This does not mean the mastery of two fields, but a sagittal movement between them (to play with Miller’s Zeno)—hence also inclusive of agon. This movement does not need to be synchronic or simply spatial, but diachronic and transtemporal. In this sense, we might take as analogy for our supposed (in the Medieval sense) “community of chiastic thinkers” the ancient Christian notion of the “community of saints,” which is a fellowship of perforated realities, of and ‘tween time past and present, the tellurial and paradisal realms (note too my allusion to the T/I gap).

    In some ways, Miller’s effort is a tribute to the likes of Rorty, Serres, Habermas, J.-P. Dupuy (the French polymath who has been a tireless tirthankara between Continental and Anglo-American thought) and others, and as such follows a certain tradition. This tradition, however, goes much farther back to at least the Medieval Scholastics, for whom Aristotelian logic and Christian doctrine (loosely following Averroes/Ibn Rushd in Islamic thought) were not to be divorced or antagonized from each other, but servants in the same household. This synergy was nowhere stronger than in Ockham. Unlike Rorty, who had to abandon the theory of representation in his own analytic tradition to embrace a pragmatist contingency, Ockham was at once the Doctor invincibilis for his staunch practice and defense of the principle of non-contradiction AND the philosopher of contingency in his own age (no greater admirer was there of him than Boccaccio himself). The germs of Rorty’s conversion in Wittgenstein were already present also in Ockham. That is, Ockham’s terminist logic, by which terms enacted their own (mental) reality by virtue of enabling certain conceptions of the larger (extramental) reality, was a presociological and prehistoriorgraphic conception of Wittgenstein’s own packaging of ordinary language philosophy into a social and (proto)historical dynamic—made fully historical by the Yale theologian George Lindbeck, seconded of late by Latour (and I suggest it is here that Miller’s humbled “non-contradiction” will find its conditioned utility). I mention all this in order to alert Miller’s readers to the ample archive from which to draw for the cultivation of a new generation of “thinkers without borders”—in hopes of spawning hope.

    Now it must be remembered that Miller, unlike Ockham, does not wish to fortify, but to “humble” the principle of non-contradiction. Thus he stands in the middle between Ockham, who thought that the principle of non-contradiction was infinitely pliable, extensible, and therefore omni-regnant, and Kierkegaard, who insisted that truth, at least the one that mattered the most, was an irreconcilable paradox—the Christian mystery of the Incarnation, the eternal God in caducal human form. To make it clearer what Kierkegaard meant, we might call this paradox an incompossibility (two things that can’t both obtain or existentially coincide in the same world)—which was Leibniz’s reelaboration (and transformation) of the relation between the Medieval Two Powers of God (only that what was at stake in Leibniz were the new “laws of nature” and their hypothetical—though nonexistent—transgressions rather than ecclesial authority and the punishable aberrations from it). Simone Weil, in her notion of decreation, pushed Kierkegaard’s paradox back to the moment of creation. Weil did so because of her allegiance to the Stoic conception of necessity, which in turn was a bastard (though also sensitive) child of Parmenidean ontology, compelled by the reality of Empire.

    Hence back to what Miller previously indicated as the origin of the principle of non-contradiction, which is at root a problem of ontology (as its own (meta)representation) and its consequent logic of identity. Parmenides committed two philosophic raids on the ordinary Greek language: estin (is, or is possible) and to on (what is). Of the first word he deprived all contingent grammatical subjects, suppleting them with an abstract, pantological whole (to houlon, another booty of his linguistic marauding). From the second term he excised all variable adjectives (and subjects), melding all realities into their monolithic ungrunt (Eckhardt’s One), an abstraction of the Metareality at best, an erasure of all useful distinctions, at worst. In the thus traumatized ontological tradition since Empedocles and the Atomists, this last effect was averted, but by purchase of a costly logic of identity, where reality becomes irreducibly representable in its particular diversities, if only one knew the right level of mereology to peg one’s analytic perception. (A concomitant of such a logic is also the denaturing in Plato and Aristotle of the Presocratic kinēsis, motion/change, into kinēsis for motion and metabolē for change.) It is this logic of identity that undergirds the representation that Rorty (and increasingly van Baassen and Putnam in tandem with him) rejected after the collapse of Aristotelian aesthetics in art and (Continental) philosophy’s (initially indecisive) departure from ontological metaphysics over a century ago. It is also this logic which, having been precluded by Heraclitus (as Miller makes clear), became the Eleatic Frankenstein’s principle of non-contradiction.

    The paradox of the arrow was Zeno’s apology of the Parmenidean rejection of motion and change as errors of contradiction. But it is a paradox founded on the same principle it wished to defend (that of non-contradiction). At the same time it betrayed the (contemporary) Protagorean impulse to measure, i.e., spatialize, all things. This spatialization in Zeno is the spatialization not only of the arrow as constant length, but of time. Like Western musical notation since the Baroque (with bars to each “measure”), however, the spatialization of time is an abstraction that can never congeal into static moments (however divisible). The musical aesthetician Karol Berger has talked about the unfolding of (linear) time in Mozart (and Beethoven), which he calls Mozart’s arrow (in contrast to Bach’s cycle). A clear demonstration of this sagittal music can be heard in the finale of Mozart’s 39th symphony (at least when sensibly conducted), where the 2/4 measure of the rollicking contredance topic can never be arrested in discrete moments and bars, but flows one into the next without any fixed identity or length equal to itself. Indeed, like Bergson’s durée, the only discernable units of time here are sensible phrases that form syntactical (and existential) meaning in the sentient subject. In other words, there can be no separation between time and event. As in the Adagio of Beethoven’s 4th symphony, for example, the marking of the time (as first introduced by the upbeat figure of the solo timpani) IS (generative of) the main musical event. Somewhere between the linearity of Classical music and Zeno’s arrow is our American football, where the division of time is constituted by the succession of yardage (uniformly divided space) gained, lost or maintained. Sometimes the missile attains to its desired reach. Sometimes it never gets there, and the process begins again from the opposed end.

    The Heraclitean fragment Miller cites (“A thing agrees in disagreement with itself…”) is precisely the grand argument of Deleuze’s Difference and Repetition, in which what is repeated is always difference itself, rather than being or self-identity. But I will refrain from further comment until I read Miller’s third post: Crosswise logic (where he also will unfurl its praxis—of which McCurry asked).

  5. avatar Steve Gabor says:

    The earliest record of the Principle of Non-Contradiction (PNC) is from Parmenides, whose One either is or is not. Plato extended the PNC to action of or on the Many. But the PNC only applies to discrete objects frozen in space and time.

    Heraclitus denies discrete objects. Since all is in flux, meaning that nothing is fixed or unchanging, objects cannot possibly be permanently discrete. Instead, each event is extended both in space and time, with a beginning and an end. Since events are extended, they must have parts, and various aspects. Events may overlap or interact with each other. Events have various rates of occurrence over time.

    Therefore, Heraclitean logic for the determination of truth and falsity cannot be as simple as that of Plato and Parmenides. However, the act of looking at a Heraclitean event, also freezes it momentarily in a “state”. That state of affairs is now capable of binary logic.

    That Heraclitean logic necessarily denies all three Laws of Thought, the PNC, Identity, and the Law of Excluded Middle (LEM). A coin cannot be either heads or tails, it must be both or neither. It cannot be equal to itself because the parts do not add up to the whole! Relations inside and to its complementary environment are also necessary. Thus, the energy (Fire) of the combined system is conserved, and not the matter of an object.

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