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.

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).

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.

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.