A Secular Age:

Crosswise logic

posted by Patrick Lee Miller

My previous post sought to humble the principle of non-contradiction, and thus the logic of consistency it defines, finding it inadequate for thinking the temporal world in which we live and breathe and have our being. Parmenides first articulated this principle, calling “equally deaf and blind” those who would not think consistently according to it, those “hordes without judgment, for whom both to be and not to be are judged the same and not the same, and the path of all is crosswise (palintropos).” Without compromise, he recognized the conflict between his principle and our world of change and diversity. Consistently, he rejected time and the logic needed to understand it. His target here was Heraclitus, who claimed that “a thing agrees in disagreement with itself; it is a crosswise harmony (palintropos harmoniē), like that of the bow and the lyre.” This post aims to explain his earlier, contradictory, but nonetheless more accurate logic.

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.

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5 Responses to “Crosswise logic”

  1. avatar Jeff McCurry says:

    I can’t wait for the next post–especially because I am eager to see how and if Miller’s crosswise Christ will be different from the Chalcedonian Christ defined in 451 CE, which says that Christ is fully human and fully divine in one person, i.e. fully temporal and fully eternal in one reality. I bet the Church Fathers didn’t know they were so close to Heraclitus! But where I think Miller will differ is that for Chalcedonian Christology the point is still for time to be lifted up into eternity, humanity into God. And such a solution still seems to risk resentment of this world. I would put the question this way: can love of the world in time be one with some sort of enchantment of a love stronger than death? Though I am not a priest, I do look forward eagerly to hearing Miller’s confession.

  2. avatar David K. Miller says:

    I am blown away by this work. I am working on many of the same themes but from the context of 20th- and 21st-century philosophy and theology. I am critiquing Jean-Luc Marion’s saturated phenomenon and his phenomenology of givenness through the lens of Hayden White’s structure of master tropes and the dynamic of parts, wholes, convergence, and divergence. Marion’s givenness comes from beyond the horizons of object and being, folding back on itself as it gives phenomenality. He posits the event, painting, the face of the Other, and one’s own flesh as instances of the saturated phenomenon, where intuition overwhelms the subject’s capacity to intend. His givenness is purely transcendent, deflating the subject and ego. Now I have a vehicle to say that his transcendent phenomenology necessarily leads to resentment of the self.

    I’m using Maurice Merleau-Ponty’s phenomenology of chiastic touch and Jean Gebser’s integral phenomenology to construct a phenomenology that has the structure of all the tropes, positing a phenomenon where its parts and wholes simultaneously converge and diverge. When I explained my ideas to one of my dissertation committee members, he laughed and said, “Sure! Why be constrained by the principle of non-contradiction?” He was not shutting me down but was encouraging me to do the hard work needed to provide a foundation for the possibility of my ideas.

    I imagine I will now be citing Becoming God in my dissertation. Thanks!

  3. avatar David U. B. Liu says:

    Miller’s intervention is striking both for its passional plea on behalf of his Heraclitean logic – and the contrast it poses with that of René Girard. Where Girard’s Heraclitean fire is opposed to the logos of the Gospel (of John), the fire of Heraclitus secundum Miller is firmly allied to it.

    Who’s right? Or is this another duck-rabbit design? As Descartes once said, when two people disagree, it’s not so much that one is right over the other, but that they are looking at different things. One of Descartes’ better insights, and Jains and Buddhists would agree.

    In his Things Hidden since the Foundation of the World, Girard makes one of his characteristic late structuralist moves. He sets the logos of the pre-Christian Heraclitus starkly against the logos of John the Evangelist. Where the fire of Heraclitus symbolizes mimetic violence (the polemos of doubles), the light of the incarnate logos of God reveals the victim. The one articulates the perennial human condition, the other, its redress and redemption. By contrast Miller finds a congenial fit between the same pair of logoi, assigning to the cross of Christ the iconological surface to the deeper structure of Heraclitus’ contrarian logic, displayed (beautifully by Miller) in his famed chiastic locutions. In short, Miller detects a “crosswise harmony” between the two cruciform logics. Perhaps if one considered the structure of an early Christian baptismal liturgy through the eyes of Wayne Meeks, one would also grant that chiastic substructure (and not merely visible form) to the Christian logos. But baptism as such is not the concern of either Girard or Miller.

    To navigate these two serious but divergent courses of interpretation, we need to stick close to the crucial term, logos. In addition to three acceptations of logos Miller indicates for Heraclitus, there is a fourth, little known or noted outside classics circles. It is close to the meaning of speech, but with a generic specificity. Logos for late Archaic and Classical Greece also meant prose as distinguished from verse. As a form of writing or composition, it was (in Heraclitus’ time – around 500 BCE) still a rare thing. Most authors had composed in metric verse, from Homer down through the lyric and choral poets. Of course contracts were not drawn up in verse, neither were technical works as architects had begun to write in the 6th century BCE. Robert Hahn surmises the latter (an extension of business writing, certainly) to be in the literary backdrop of Anaximander’s prose writing, the earliest to have survived (though in fragments). It is significant that Heraclitus followed that philosophical precedent in his aphorisms – unlike his elder Xenophanes the rhapsode and the self-appointed foe Parmenides, who wrote in an archaicized Homeric hexameter. The difference between verse and prose here is not that prose is bland and verse elegant (scholars regard Heraclitus highly as a stylist, and dismiss Parmenides’ dry verse). Rather, it is that metrical compositions create their hieratic, idealized space, while prose logos adheres more closely (however elegantly, especially in Heraclitus’ Ionian form) to the world of lived life, how it flows and sounds on mortal lips.

    This difference is illustrated by the work of Heraclitus’ (elder) Milesian contemporary Hecataeus, credited by Herodotus to be the first investigative writer (hence historian) on human events. Like his senior compatriot Anaximander before him, he wrote in prose, probably titled (like Anaximander’s work) Gēs periodos, Tour of (or Way around) Earth, and accordingly (like Heraclitus also) made no appeal or recourse to gods in their thought (unlike Parmenides, who receives his doctrine as a revelation from his goddess). By treating of human life and events as basically immanent phenomena, Hecataeus was inventing a new kind of narrative-time.

    If we take the generic similarity of Heraclitus and Hecataeus as a clue to the nature of Heraclitus’ thought, we might see something evental behind his fiery chiasms. Born around the mid-6th century in Ephesus, Heraclitus would have grown up under the new yoke of the Persians (though mediated by semiautonomous local tyrants). About the time of his floruit (turn of the 5th century), something dramatic occurred. In 499, Aristagoras, the tyrant of Miletus, went with Persian support to conquer the Isle of Naxos. When his forces fumbled, Aristagoras was sacked by Darius. Resentful, he then organized Ionians (against Hecataeus’ own advice) for a revolt, only to be crushed after a promising start by the juggernaut of the Persian hosts. The ensuing attacks on the Greek mainland, punctuated by battles at Marathon, Thermopylae and Salamis, were meant to prevent the European Greeks from aiding their fellows in Asia Minor. It set up an enduring enmity (Girard’s mimetic rivalry) between Persian and Greek which became the subject of Herodotus’ Investigations (Historiai) – ruptured eventually by Alexander’s conquest one and a half centuries on. Herodotus, like Hecataeus, would have lived through the initial chapters of this long fiery exchange, in which the victory of one side would be succeeded by its defeat, and defeat by resurgent victory: the exchange of fire for all, and all for fire. Girard’s mimetic reading of Heraclitus (which highlights polemos, war), then, would seem to have some historical anchor and sense. Still, it does not invalidate Miller’s linguistic-logical reading. They trade, as it were, through the same fire.

    As volatile as this fire was for Heraclitus, it also exhibited, strangely, the symmetry of sacred architecture. As developed in Heraclitus’ native century, the monumental Greek temples from Asia Minor to Sicily shared a basic outline: a rectangle enclosed by a peripteral colonnade topped in its front by an isosceles pediment. Bringing the prose logos of architects, then, to their subject, we have another sense of “logos”: account(ing) and proportion – hence its Latin translation ratio (reckoning). If you look at the temple from its face, your eyes are drawn up to the central apex, draping back down to the sides. At every distance from atop the central vertical axis, the corresponding remove from the other side is at the same height, from the first to the last inch; the two sides are proportionately chiastic, and “the way up is the way down.” That this chiasm could also harbor an agonal moment is suggested by the pedimental program at the Zeus Temple at Olympia, built shortly after Heraclitus’ death. There the east pediment shows symmetrical figures of two chariot race teams on each side, while the (later) west pediment unleashes the violence of symmetry by enfolding smaller groups of combatants between Niobes and centaurs within each side, though their disposition in the larger bipartite scheme is again symmetrical. Here, then, the fire of struggle is evinced in its own kosmos (ordering,configuration).

    Miller’s right. This “unity in opposition [and] opposition in unity” (Miller, paraphrasing Heraclitus’ “wholes and not wholes, convergent divergent, consonant dissonant, from all things one and from one all”) is deeply polyphonic. His evocation of Bach in this regard is especially welcome, not because Bach is the greatest polyphonist in the West, purely speaking (greater exponents may be nominated leading up to the sixteenth century), but as Wilfrid Mellers pointed out, Bach appeared at the crossing of polyphony and homophony, counterpoint vs. chordal melody. Polyphony thrives on divergent, horizontal (diachronic) counterpoint (of which the strongest is that of contrary motion), while homophony proceeds by harmonious note distributions in synchronic (though shifting), vertical unity. For Mellers and others who view Bach as a theologian, this historical conjuncture is also a Lutheran dialectic, a complexio oppositorum. The counterpoint bespeaks ceaseless struggle, while the harmony affords a kairotic peace and unity in its midst. That Bach’s work is therefore chiastic in the Heraclitean sense is amply shown by his own B-minor Mass (as representative of many other smaller works), whose majestic chiastic unfolding has been well investigated as a witness to the theologia crucis of his patron theologian.

    This brings us back to the incarnation of the divine logos in John, the intersecting of time and eternity, God living in prose-time. As Kierkegaard understood it (i.e., paradoxically), this is not sensible proposition – it would not pass the scrutiny of the principle of non-contradiction. The same could be said of the doctrine of the Trinity, whose merit consists not in its doctrinal perfection (or even plausibility), but in its insistence that reality in its core is incommensurable, even incompossible, with itself. In Deleuzian language, the singular real is always differing from itself, and cannot be resolved into a Hegelian Aufhebung. As this applies theologically, so generally it obtains. The duck-rabbit drawing loses its grab if we construe it as a problem of parts vs. the whole. We would only end up with a monster, and a banal one at that (my local brewery uses it as its logo). So ontological identity does not carry us far. Likewise the duck-rabbit will lose its charm if we simply regard it from the enlightened, transcendent view (i.e., one that is aufgehoben) that it is a psychovisual trick constructed to consternate normal perception.

    The lie to this superior conceptual synthesis is that it alone is real or holds permanent sway over the feeble vacillations of the ambivalent drawing (viz. Serres’ “translation”): We would be taking away our eyes from the drawing only to valorize a concept. But ontology cannot be overcome with idealism. According to the Buddhist philosopher Nagarjuna (2nd c. CE), all being is conventional, and there are three sorts. The first is a thing as (conventional) unity, the second its constituent parts, and the third the relation of the whole to its parts (or vice versa). All of these are conditioned realities, none of them autonomous or absolute. In other words, the dharma consists in the realization that all reality (dharma) is non-dharmic (insubstantial). In Buddhism this applies first and foremost (that is, soterically) to the “self” (as in anattā, anātman), whose five aggregates are as provisional as the whole they compose, the principle of whose coherence in turn is also a matter of passing cause.

    In the Christian tradition, the conditionality of being and its apprehension may first apply to God (then to creatures, in a sort of univocity of non-being). This may form one axis of Miller’s crosswise logic, the one he abbreviates as the principle of non-contradiction. The other axis is articulated by Miller (and Connolly) both by its negative, resentment (the motive of suicide bombing and xenophobia alike), and its positive, love. In terms of an integral practice (or spirituality, as McCurry put it) of crosswise logic, then, I might suggest the experiment of Simone Weil: to love God while thinking he does not exist. Perhaps this is still Heraclitean, but it will have shed itself of forceful symmetry, balance, retribution.

    The symbol of the Christian cross is not a direct appropriation of the cross of the Christ. It is an invention of Coptic Christianity which superposed it visually with the ankh of Osiris, the instrument of his filial revenge. How to understand the significance of that ancient icon becomes the question of our present concern. Is the triumph of the Christ vindictive (thus closer to Girard’s Heraclitean fire), or is it the overcoming of resentment and revenge (Girard’s Johannine logos)? Given the history of persecution in 3rd-century Egypt, the first may have been tempting to the Copts. That danger remains ever alive. On the other hand, if the response to persecution was the desert war against temptation itself, then the Osirian appropriation also intimates the emergence (a certain transcendence) out of a choking bind, a saving renunciation. Both, it seems, mix up the transcendent with the immanent. Which to choose between two may not seem hard now, but it is with the retro-fit (palintropos harmoniē) of the two logoi (Heraclitean and Johannine) jointly that the choice has become clear.

  4. avatar David U. B. Liu says:

    Sorry, I meant the ankh of Horus, not of Osiris, whom he avenged.

  5. avatar Michael M. Morbey says:

    I just came across these interesting posts on “crosswise logic” yesterday but, if you would like an independent confirmation of the phenomenon, it reminds me of an impression I had that something similar and multi-aspectual was a tacit assumption of the transcendental critical philosophy of the Christian philosopher, Herman Dooyeweerd. What also makes this crosswise logic so interesting to me is that many years ago I studied a bit of Biophysics in the tradition of Ludwig von Bertalanffy. I do not know whether the antimetabolic and chiasmic pattern has ever been made explicit in the Kuyperian and Dooyeweerdian tradition but I did mention the Idea briefly on the Thinknet discussion group last year.
    Together with the relativization of the law of non-contradiction it may helpful to introduce the “flaw of the excluded middle”.

    Kuyper’s Cultural Mandate Antimetabole and chiasmus

    The Dooyeweerd Pages

    Flaw of the Excluded Middle

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