Heraclitean logic is the logos. This Greek word condenses many English translations, of which three give a sense of its wide range: ‘speech’ (language), ‘reason’ (thought), and ‘structure’ (world). Whenever he invokes the logos, Heraclitus exploits this range and alludes to all three domains. Indeed, holding in mind at once all three—world, thought, and language—is essential to the Heraclitean way of thinking. Thus, when he insists that “all things come to pass in accordance with this logos,” he means that everything coming to pass—in the temporal world, that is—shares the same structure. But he also means that accurate reasoning about this world shares this structure, just as accurate speech must too. This accurate speech is presumably his aphoristic style, so to understand it, its characteristic way of thinking, and the world it describes, we must understand this shared structure. It cannot be consistency, as “Truth in conflict” argued; instead, as this post argues, it is chiasmus.

Chiasmus is usually known as the literary figure in which elements are repeated but in crosswise order (A : B :: B : A). Here is an example from Shakespeare: “Who dotes, yet doubts, suspects, yet strongly loves.” A pleasant change of consonants adorns the reversal of meanings: strongly loving is doting; to suspect is to doubt. The elements reversed can also be syntactic, however, as in this example from Milton: “Love without end and without measure Grace.” Here, a noun and a prepositional phrase trade order.  Again, a substitution of words introduces some pleasant variety, though now it also adds layers of concealed meaning. By substituting ‘Grace’ for ‘Love,’ and thereby assimilating them, Milton suggests that divine love is freely given. By adding synonymous prepositional phrases, he suggests that the gift is eternal and boundless. For Christians like Milton, the sign of this love and grace is the cross. With this crosswise figure, then, he communicates a Christology—a logos, or account, of his God.

No figure could be more appropriate to the logos of Christ, for a cross has always symbolized this word, beginning as it does with a Greek letter that resembles one. Chi looks like our English X—so much like it, in fact, that we shorten “Christmas” to “Xmas,” usually without recognizing the Greek contribution to our abbreviation. The same letter appears more faithfully on the candles and vestments of Christian churches, where it joins the letter Rho to symbolize the Messiah. But before there were any Christian churches, the letter Chi symbolized the literary figure it names. Chiasmus comes from chiazō, which the Greek grammarians used to convey the crosswise pattern of its principal letter. The association between Christ and the pattern of chiasmus was thus natural enough, at least in the symbolic imagination of the Hellenistic world. The association is more substantial for Heraclitean philosophy, which reveals chiasmus as the concealed structure of the world, just as Christian revelation proclaims Christ as the truth of the world.

To appreciate the depth of this association, we must first understand how a literary figure could reveal the concealed structure of the world. Let us begin by recalling the polysemy of logos: in order to signify one chiasmus shared by world, reason, and speech, Heraclitus crafts aphorisms (logoi) that exhibit what they report. Here is an especially dramatic example of the technique: “All things are a requital for fire, and fire for all things, as goods for gold and gold for goods.” In this faithful English translation, the complex chiasmus of meanings shines through (A : B :: B : A ::: C : D :: D : C). Below this semantic pattern, additionally, is a dazzling arrangement of nouns whose syntax cannot be rendered into English. Their cases (Nominative and Genitive) and their numbers (Singular and Plural) make the following pattern, GS : NP :: NS : GP ::: GS : NP :: GP : NS. In the first half of the sentence is a chiasmus according to case (G : N :: N : G). In the second half, one according to number (S : P :: P : S). This is a fugue in Greek, weaving linguistic opposition into a complex unity, but what is its philosophical significance?

“Truth and conflict” adduced Heraclitean fire not only to humble the principle of non-contradiction but also to herald its more catholic rival. Analyzing fire’s burning into moments, we found it to be an opposition of “need and satiety” at each one. This came as a surprise, no doubt, because when we do not deliberately analyze fire in this way—whenever we use it to warm our hands or cook a meal; whenever we fear it as the destroyer of homes and cities; whenever, that is, its burning affects us in time, entering into the narratives woven by our emotional engagement with the world—we contemplate something whose unity appears undisturbed by the opposites it synthesizes. Analysis may reveal a fire that is in conflict with itself at every moment, but through the continuity of time it synthesizes these opposites into a unity. Whenever we relax our analysis, returning to affective engagement with fire, we overlook its momentary dissonance and appreciate instead this synthetic unity. Correlatively, whenever we disengage emotionally from fire by activating consistent reason, we lose sight of its continuity and consonance, foregrounding instead its opposition and conflict.

Were we to select one perspective exclusively—whether purely consistent cognition or purely emotional engagement—our comprehension of fire would be limited by omission of the other. Neither by pure cognitive analysis nor by pure emotional synthesis can we comprehend fully anything temporal. Neither by a narrow focus on its instantaneous opposition nor by attending to its temporal unity alone can we understand it. Its concealed structure reveals itself only through an impure chiasmus of both. Beginning with a unified flame, accordingly, we analyzed its burning into moments of contradictory opposition. Synthesis and unity were thus conjoined with analysis and opposition. Stepping back from this conjunction, we now recognize its fresh contradiction: consistency forbids the simultaneity of unity and opposition, synthesis and analysis. And yet their harmony is nonetheless accomplished—just as fire accomplishes its own burning—through the continuity of time. Conjoined with this additional analysis into opposites, then, is another synthesis into unity. And so on, world without end.

All told, our comprehension of fire reveals the following pattern. Unity : opposition :: opposition : unity (U : O :: O : U). This particular set of terms, and the artless aphorism it informs, puts the emphasis on the object of our comprehension, the structure of fire itself. Putting the emphasis instead on the structure of our comprehension, as subjects, we may switch to the following set of terms. Synthesis : analysis :: analysis : synthesis (S : A :: A : S). Whichever set we choose—one focusing on the world, the other on our thought of it—we find the same crosswise pattern. This is of course chiasmus, and it can be iterated infinitely (SU : AO :: AO : SU ::: SU : AO :: AO : SU …). More than a complex literary figure, however, this very iteration is the crosswise logic of the temporal world. “Kosmos,” writes Heraclitus, “the same for all, no god nor man has made, but it ever was and will be: fire everliving, kindled in measures and in measures quenched.” More than a mere figure of speech, in other words, chiasmus is the eternal structure of both our fiery temporal cosmos and the activity of comprehending it in thinking and speech.

Heraclitean philosophy is a meditation on this kosmos (Greek for ‘order’ or ‘structure’). Heraclitus consummates this meditation with a principle that has a more legitimate claim than non-contradiction to be the firmest of all: “wholes and not wholes, convergent divergent, consonant dissonant, from all things one and from one all things.” This principle describes a complex activity that is as synthetic as it is analytic. Wholes consonant and converging are synthesized into one from all things, while not-wholes dissonant and diverging are analyzed into all things from one. Exhibiting the structure of chiasmus it also reports, as Becoming God argues, this logos challenges the principle of non-contradiction. Indeed, this principle of chiasmus appears to have been the target of Parmenides and the Platonic tradition founded upon his rejection of it. Thus, if we defy this tradition, emboldened by its failure to think the temporal world, if we adopt Heraclitus’s more capacious mode of reasoning, bolstered by its chiasmus of consistent thought and passionate longing, if we assimilate ourselves to this cross—a task that is by no means easy, requiring a spiritual discipline of its own—we can reasonably confess a philosophy that is neither immanent nor transcendent, but both.

Lest this mode of impure reason seem too abstract, complex, or even impossible, here are two analogies that might make it seem less so. First, we can compare crosswise logic to looking at the duck-rabbit drawing popularized in philosophy by Ludwig Wittgenstein. Looked at in one way, the drawing appears to be of a duck; looked at in another, it appears as a rabbit. We alternate between seeing it one way and then another, back and forth, often quickly, and sometimes involuntarily. When we willfully contemplate not just the drawing but also these very alternations, we rise to a higher level of reflection, coming to see the drawing as duck-rabbit, a unity in opposition (or opposition in unity). Similar epiphanies occur, secondly, when we study contrapuntal music. Listening to a Bach fugue, for example, we can with disciplined effort discern not only one theme or its counter-point, nor only both in alternation, but both at once. Beyond this already difficult accomplishment, the highest comprehension of the fugue discerns the concealed structure of its harmonic conflict. To fully appreciate it, in other words, we must hear the unity in opposition as well as the opposition in unity that is Bach’s composition.

Music presents the best analogy to crosswise logic because it likewise touches our hearts as well as our minds. Whether listening to it attentively, performing it well, or composing it creatively, we must both think and feel deeply. To practice chiasmus, similarly, we must turn our emotion as well as our cognition toward the world of becoming. Engaging it emotionally, we affirm the continuity of time; cognizing it simultaneously, we affirm the conflict of its every moment. After recognizing the opposition between these activities, furthermore, crosswise logic unites them in chiasmus: a higher unity of the opposition between opposition and unity. And so on, ideally, although not all emotions will engage the world equally, nor is all cognition consistent.

Not everything should be permitted to reason. To think consistently, after all, we must practice the principle of non-contradiction, recognizing the conflict inherent in the temporal world. With this practice, notice, we show crosswise logic to be more generous than its rival. For although it dethrones non-contradiction, it installs it as the prince of all logical offices, second only to the king, namely, chiasmus itself.

Nor should every emotion be permitted to it. Resentment is forbidden because it disengages from the world that crosswise logic seeks to engage. For the goal of resentment is destruction. Anger and hatred seek to destroy, too, but for them destruction is always a means to preserve some other end, some thing considered good independent of the act of destruction. Resentment, by contrast, seeks the preservation of nothing but itself. In fact, according to Nietzsche, “nothing on earth consumes a man more quickly than the passion of resentment.” It destroys even the resentful self. Its ulterior motive, so rarely recognized by the soul being consumed by it, is destruction for its own sake, destruction of everything that opposes it, destruction ultimately of the whole world. Fortunately, as Connolly’s grid acknowledges, resentment is opposed by love, an emotion that engages more deeply with the world than any other because it is most open to its differences, least limited by defenses against its inevitable conflict, and most single-mindedly invested in the creation of independent good.

Requiring extraordinary strength of character, then, crosswise logic demands that we love the whole world of becoming while thinking consistently about it. Indeed, it is the supreme activity of loving and thinking together: Love without end and without measure Reason. This eternal cross thus manages to bind our deepest longings—which, Augustine rightly argued, cannot be satisfied by the temporal world—together with our intellectual powers—which cannot conceive a meaningful life in eternity without contradiction. Requiring a love so strong and pure that it remains undiminished in the midst of the world’s conflict, such an achievement would appear beyond any mere mortal. Confessing the immortal mortal, however, the Heraclitean tradition is uniquely “equipped to honor Jesus by offering a distinctive interpretation of his calling and mode of inspiration.” Making this confession will be the aim of the next and final post.

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.”