interesting_interpretation_of_heraclitus

The Luv Boat

or Unelected Affinities between Logical Positivists and Deconstructionists

I.  An Interesting Approach to Heraclitus

II. Logical Positivism Revisited

Πῶς πάντα εἶπες;

Theaetetus

Let me suggest a brief definition for the purposes of this essay of something that I will call the traditional theory of linguistic meaning. According to this view the meaning of a given singular declarative positive statement is largely determined by a fact or state of affairs that is correlated to that singular declarative positive statement. Some philosophers oppose the traditional theory by means of an interesting argument. Instead of attacking the theory head on as inconsistent, insufficiently explanatory, conceptually confused or in contradiction with other views we prefer to hold, and instead of throwing out unsourced sample statements (from, say, ordinary language) which constitute counterexamples to the traditional view, these philosophers examine actual historical statements in the philosophical corpus to show that those actual statements are not just counterexamples to the traditional theory, they positively contradict it. If such an actual statement comes from a philosopher who advocates the traditional theory, then the opponents of that theory who use this interesting argument try to show that the form, the syntax or the presuppositions of the statement from the advocate contradicts his explicit message, i.e. contradicts the traditional theory that superficially his statement or the rest of his philosophy appears to affirm. If the statement cited comes from a philosopher whom the opponents understand as agreeing with their opposition, they try to make manifest the rhetorical strategy whereby the philosopher they agree with establishes his opposition. A rhetorical strategy is needed because some opponents of the traditional theory run the risk of self-contradiction (More on this below). Accordingly the same strategy of distinguishing form, syntax and presuppositions from apparent meaning is employed in elucidating the philosophers considered doctrinally sympathetic as well.

Bollack and Wismann (B&W) range themselves among the opponents of the traditional theory I described above. Kindred spirits include Derrida and De Man  as well as assorted literary critics. Derrida’s hostile interpretations of Plato (Cf. “La Pharmacie de Platon” in La Dissémination ) and Husserl  (Cf. La Voix et le phénomène and the Introduction to Husserl’s The Origin of Geometry) attack advocates of the traditional theory along the lines I mentioned above. In Héraclite ou la séparation B&W address a philosopher they consider to be a kindred spirit. Their approach consists in showing how Heraclitus exhibits and makes plausible a view they appear to share.

It may be worthwhile to summarize a view of linguistic meaning that took hold among many philosophers, social scientists and humanists during the second half of the last century, a view that differs significantly from the traditional theory. This does not mean that B&W subscribe to this view or that they attribute it to Heraclitus, but it does form a background for their exegesis and their vocabulary is infused with terms made popular by this view. The view states that the meaning of a word is not determined by its referent but by the position the word occupies in a significatory system. The position is a locus vacated by competing terms. Semantic units are distinguished by being different from all the other linguistic units that are qualified by the thesaurus and the rules of the significatory system to occupy a particular position in a sentence. This semantic model is derived from structuralist phonology according to which phonemes can be identified as phonemes not by standing for something (The relation between signifier and signified is internal to the phoneme and, moreover, constitutive signifiers and signifieds are themselves identified differentially) but by their difference from the finite set of other phonetically significant sounds that are qualified to occupy their place in the utterance of a word or other phonetic string.  Since the concept of truth is not invoked in its definition of linguistic meaning, the structuralist view of meaning leaves open the question of how we are to regard truth. The structuralist model for meaning is internally self-sufficient, so it doesn’t have much to say about whether and when sentences (or uttered sentences) are true or false, and how truth and falsity may interact with the concept of meaning. However, issues about truth come into play for the philosophers mentioned above. Accordingly they use the structuralist view of linguistic meaning and specifically (and misleadingly in my opinion) the structuralist concept of difference to question the acceptability of the traditional theory, which is truth based, and to begin to model an alternative view of truth.

I do not believe that B&W succeed in their project. But my intention is not to completely reject their book. In the first place, I am not qualified to question their philological claims. But, above that there is a richness of observation and interpretative ingenuity regarding the mass of individual fragments that should not be jettisoned because the overall approach is marred by severe defects. If being largely mistaken were a reason not to a read a philosophical text, we wouldn’t have any motive to read anything at all – an eventuality I’m sure the milkmaids and frat boys out there would welcome. But sometimes it’s through error that we learn the most about philosophy.

It is also not my intention to defend any of the interpretations of Heraclitus that B&W criticize, although I am most sympathetic to what Plato and Aristotle said on the subject not only because they were the closest to the source but also because their views raise philosophical issues that are still worthy of consideration. I am not interested in B&W’s hermeneutics of Heraclitus so much as the validity (or anti-validity!) of the conclusions they draw for philosophical problems  independent of the doctrine of a given philosopher.

B&W envision three possible approaches to Heraclitus. The first is that Heraclitus espoused a distinctive doctrine completely different from any of those attributed to him by philosophers and historians of philosophy hitherto (with the possible exception of Hegel). B&W reject this option out of hand (Cf. e.g. pp. iii, 16, 43, 49 and 52). The second is that Heraclitus’ texts do not function like anything we recognize as philosophy. They do not state, much less argue for anything. They simply exhibit or call up or suggest (“évoquer” p. 53 or “faire voir” p. 138) – usually contrasting – concepts that we in our interpretation may choose to make explicit. This approach treats the texts like artifacts somewhat akin to pottery shards that illustrate a depicted scene and may even suggest a contrasting scene but say nothing about what is illustrated. I hesitate to say that this is to treat Heraclitus’ sayings as non-philosophical literature, for literature, and in particular the poetry of Hesiod and Homer, can convey a specifiable and perhaps even “univocal” narrative or cosmology (On Homer cf. pp. 20 and 193 ff.). And, what is worth paying attention to in Heraclitus, according to B&W, is that there is no univocal narrative or cosmology. (There may be a relation to the Orphic hymns. In their commentary on DK93 (pp.273-274) B&W highlight oracular speech, whose meaning apparently cannot be adequately captured by the traditional theory. I suppose what they are doing is their own kind of indiquer or σημαίνειν. However, what they say in this passage is far too sketchy to merit critical discussion. One runs the risk of putting words in their mouths, but unless that is done, they don’t appear to be saying anything worthwhile.) Moreover, the institution of literature inspires attitudes and value judgments in the context of philosophical debate. To call Heraclitus’ work “just literature” would be to disparage it in the eyes of some philosophers. Perhaps a sympathetic reading of Heraclitus requires a leap over a sort of translation gap whereby the reader must assume a distinct and non-philosophical persona. For these reasons I find the somewhat value-free term “artifact” a preferable basis for describing a supposedly philosophical corpus that does not assert anything. The third approach (Cf. e.g. pp. 20 and 21 ff.) might be to take an idea from Hegel and view Heraclitus’ thought as speculative in the Hegelian sense. That is, no single statement in his texts is statically true or false. Rather, there is a kind of movement of self contradiction that is neither a specific doctrine nor a simple string of terms whose truth status is irrelevant. B&W seem in different passages of their book to adopt both of the last two consequences. Stated this way the Hegel inspired approach is far from clear and raises a flurry of problems. In certain chapters, however, B&W argue for a sufficiently sharpened version of this idea such as to permit worthwhile critical evaluation. The evidence is strong that B&W’s purpose is to argue for a Hegelian interpretation of Heraclitus with some adjustments for the vocabulary of modern semiotics (Cf. e.g. the Preface to the second edition). At least part of their approach is to supplement with philological considerations the brief and general thesis that Hegel lays out in his lectures on the history of philosophy. A look at individual passages will show how this is the case.

At this stage a couple of definitions and distinctions are in order to help reduce confusion in what follows. I do not claim that these definitions are either complete or completely precise, but I do believe they are clear and comprehensive enough for the points I want to make. A sentence is a string of sounds or written characters. A statement is a sentence proffered, e.g. voiced or written down, with meaning. An utterance can be viewed as the occurrence of a statement, but it is unclear where the notion of a statement leaves off and that of an utterance takes over. A proposition is the meaning of a statement. These definitions are similar to but not identical with Strawson’s definitions of the same terms, and indeed Strawson’s own definitions varied over time (Cf. Logico-Linguistic Papers passim). B&W do not define their terms and so when they use terms like discours, dire, dit, énoncé or énonciation it is not exactly clear what they mean. For example, does “dire” mean a particular utterance of a statement, a possible statement endowed with meaning or meaningful speech in general? Admittedly much of the ambiguity comes from Heraclitus himself, but B&W don’t even seem aware that such ambiguity exists. In what follows I will make my best guesses when that is possible.

In their Introduction B&W do not attribute to Heraclitus a general doctrine (alternatively, they deny that Heraclitus advocates a positive doctrine) to the effect that (1) all statements (alternatively propositions) or at least all philosophically relevant statements are neither true nor false, and (2) instead statements (or propositions) call up, so to speak, their own negation or suggest concepts opposite to or counter to one or more of the concepts they contain such that neither the concepts they contain nor the counter concepts have referential meaning. (Unfortunately this move is immediately contradicted by their interpretation of DK1 (Following B&W all Diels-Kranz references are to B). Cf. below.)  If Heraclitus were to make such a general claim then the statement in which the claim was couched would call up its own negation and the concepts in that proposition would call up their counter concepts. The result is paradox, which is a nice term for self-contradiction. There would be no reason for someone hearing what Heraclitus has to say to draw any consequences he may consider worthwhile. (Quite often B&W assert that paradox is OK. Their reason might be Hegelian: paradoxes are OK because they will eventually be reconciled. Or else they may simply believe paradoxes are OK.) If Heraclitus were not making a general claim, but simply creating phrases that themselves exhibit the properties B&W attribute to them, then the paradox disappears. One of course is left to wonder what to make of it, but at least there is no evident self-contradiction.

By way of aside, Wittgenstein faced an analogous problem in the Tractatus where his assertions to the effect that (1) nothing could be said about the relations between logic and the world and (2) nothing could be said about the entirety of the world contradict themselves. Wittgenstein’s solution is unsatisfactory because it is a true yogi rope. Any crackpot preacher of transcendent realities could resort to a similar device and say “Ya just gotta believe.” After all that is the upshot of Wittgenstein’s 'pataphysical anti-’pataphysical axioms.

Paradox plays an important role B&W’s interpretation of Heraclitus. The nature of the paradoxes they deal with, similarly to Wittgenstein, are an amalgam of what set theoreticians have distinguished as semantic paradoxes, such as the liar paradox, and set theoretical paradoxes such as Russell’s paradox (Cf. e.g. Suppes pp. 5 ff.). The two are different branches of the same root. The statement, “This statement refers to all and only those statements that don’t refer to themselves,” is a version of both. Set theoretical paradoxes can always be expressed in the form of semantically paradoxical statements. Equally semantic paradoxes are paradoxical because they refer to the totality of a closed universe (A universe is a set) of which the utterance of the paradox itself is a member. In either case contradictory self-referentiality is the product of the inclusion of some specific entity (a set or a statement) in some closed domain. A domain is closed in this sense when its membership is sufficiently though not consistently specified by the set concept of the domain (domains being sets). Everything characterized by the concept belongs to the domain. When the set concept of the domain specifies that a statement or a set both belongs and does not belong to the domain, the result is paradox. It is interesting that Zermelo-Fraenkel set theory incorporates a position that could be viewed as at the extreme opposite (!) end of a spectrum from the one B&W seem to imply. You could argue that B&W are indulging in philo-babble. Or you could argue that Zermelo-Fraenkel throws the baby out with the bath water.

B&W may have avoided paradox in Heraclitus by recourse to rhetorical strategies, but a threshold of a paradox returns in the status of the statements or propositions constituting their own treatment of Heraclitus. If they contend that their analysis is true, which they obviously do particularly in the course of their vigorous defense of their philological evidence, then at least some meta-statements about the Heraclitus’ fragments have the sort of truth value those statements deny about the fragments. Which comes down to reaffirming that some fairly traditional view of meaning and truth, if not the traditional theory itself, applies to at least some philosophical or quasi-philosophical statements, namely their own. Does this mean that they don’t intend to draw generalizable conclusions from the views Heraclitus’ fragments evoke? Without generalizable consequences their book becomes a study in cultural history, the description of one Weltanschauung among others. There may be nothing wrong with that, but we should recognize that that is a likely outcome, and one that B&W do nothing to resist. This sort of uncomfortable situation is what Derrida brilliantly uncovers in traditional philosophers who claim to overcome or surpass or “refute” metaphysics. If, on the other hand, their own statements share the “dialectical” properties of the Heraclitean fragments (a possibility B&W do not raise, but which Derrida addresses with indifferent success), then we are left with the possibility that the fragments simply may or may not be such as B&W describe them or both at the same time. The upshot is we don’t know how to react short of crossing the veil of radical interpretation.

To be fair B&W never state that they intend anything more than straight historical scholarship, something akin to debates about Heraclitus’ floruit. There is the sense underlying their text, however, that their interpretation of Heraclitus corresponds to a philosophical vision that is currently valid and radically different from the positions held or assumed by classic hermeneutists such as Heidegger or Kirk (Cf. their commentaries on DK66 (pp. 218-219) where they reject a purely cosmological interpretation of Heraclitus’ fragments about reconciliation, and also DK80 (p.245) which contains statements specifically at odds with any reconciliation theory), not to mention the doxographical, Stoic and Neo-Platonist schools. I will therefore operate under the assumption that such a philosophical (or perhaps anti-philosophical, to stay in the spirit simultaneous contrariety) vision is the goal.

A Heraclitean fragment calling up its negation and a Heraclitean term calling up its contrapositive are not the same thing, nor are they analogous. The former is automatic; it can be performed algorithmically. For example, “Construct a two column table and label the columns A and B. If p appears in column A write ¬p in Column B.” B&W do not specify the scope of the negation operator; an algorithm is still possible that specifies scope, it’s just a bit more detailed. However, the concept a negation of a statement is related to (More accurately, a negation of a simple atomic proposition “a is an F” that takes the form “a is a non-F.” Difference in the scope of the negation sign does result in different propositions. “It is not the case that a is an F” does not specify a set complementary to the set of F’s.) is not the contrapositive of the subject concept of the original proposition; it is its complement. The negation of “Phryne is beautiful” does not yield “Phryne is ugly.” It yields “Phryne is not beautiful” (or alternatively “It is not the case that Phryne is beautiful”). As things stand right now, there are no algorithms for generating contrapositive concepts; finding them is more or less intuitive. Aristotle’s contrapositive propositions as identified in the Square of Oppositions are unrelated to contrapositive concepts of the sort Heraclitus names. By way of historical aside: If I understand him correctly, Mádhava Áchárya distinguishes between complements and contrapositives in his summary of  the Pantanjali-Darśana (pp. 250 ff.).

Let us now turn to the individual fragments.

1.  B&W interpret DK 1 as a kind of laying out of Heraclitus’ position, a positive assertion of the general view of language and utterances that will underlie his other fragments. The idea is that there is a separation between an utterance (le signifiant, le dire, τοῦ δὲ λόγου τοῦδ’ ἐόντος; they translate λόgoς as discours) and the content of the utterance (le signifié, le dit). Uttering introduces a dimension of meaning that directly contradicts the apparent content of the utterance. Unintelligent men are incapable of dealing with this phenomenon of language. Heraclitus explicitly opposes discourse to its own content. This will be the proper way to read those Heraclitean fragments that appear to simply repeat banal folk wisdom. (By way of aside, le signifiant and le dire are not obviously the same thing. The term “signifiant” in structuralist linguistics refers to a phonemic or graphic unit or string without reference to what the unit or string may mean. The term “dire” does not mean that in ordinary French and may not really mean that in B&W. It carries the weight of what I have translated as “utterance” (literally “the act of saying”). To pursue the point, B&W are not at all clear whether, when they refer to Heraclitus’ sayings, they mean by “le dire” a single historical event - the moment in time when Heraclitus spoke or wrote the words in question - or a kind of template for multiple events, namely possible utterances or statements. Nor, when they are talking about utterances in general, presumably ὁ λόγος, they mean actual or possible utterances.)

Attributing to Heraclitus a positive statement about his own use of language, however, reintroduces the contradictions that ostensibly B&W hoped to avoid by treating the fragments as artifacts. By definition DK 1 should call up (I use the intentionally vague phrase “call up” because no effective method is presented for specifying whatever gets called up; “suggest” might work as well although that may have unwarranted psychological or behavioral overtones) its own contradiction (more precisely negating utterance), namely an assertion or statement to the effect that (liberally distributing negations) utterances do not call up their own negation and that the men who don’t treat them this way are not unintelligent. B&W seem to try to escape this conundrum by saying that the negating utterance elicited is not really an affirmation contraire although it is a contradiction (p. 63), a suggestion that in context I find hard to understand.   It’s kind of like saying, “When a girl says ‘No’ she really means yes, but I didn’t really mean that.” Another way out is to say that not all utterances and not all of Heraclitus’ utterances elicit their negation. Some are simply positive assertions. That may be the only viable solution.

2. B&W’s interpretation of DK10 contains a tantalizing exposition of how Heraclitus can oppose a philosophical doctrine without actually proposing a counter doctrine or even stating anything that’s not a quotation or a repetition. Clearly DK10 does not express a proposition at all. However, according to B&W, a claim is made. One passage is worth quoting at length:

Tandis que la spéculation idéaliste s’en sert (i.e. it uses opposition – W.D.) pour soumettre le multiple à l’un en privilégiant l’un des contraires…, Héraclite oppose le concept à lui-même. L’intégration debouche sur la désintegration….Le tout ne laisse pas intacte les différences qu’il assemble. Il ampute les identités particulières du rapport exclusive qu’ils entretiennent avec leur négation; la raison des contraires résiste à la raison des ensembles. Mais sans contraires la totalité n’est pas totale. Pour les comprendre elle se nie elle-même. Entière elle n’est pas entière, et sitôt que elle ne l’est pas, elle l’est. Présence, absence la raison triomphe dans la négation. (p.83)

This is a lot to make out of just three words, but it raises an interesting point and does mark out a possibly defensible viewpoint whether or not that viewpoint can be rightly attributed to Heraclitus. It is based on problems with the logic, or more properly the semantics of the concept of everything. The classic paradox runs: We cannot conceive of everything without simultaneously conceiving of those things that are not included in everything. I use the language of conceivability here because I believe this is largely an epistemological and semantic issue; it has to do with how we understand the notion of everything how our word “everything” actually relates to its purported referent. It is equally acceptable to rephrase this in purely ontological language: Everything does not include those things that are not part of everything and so it is not everything. The paradox rests on the assumptions that every concept has a complement, that such a complement is conceived at the same time the original concept is conceived, that the word “everything” stands for a concept etc. I will take these assumptions as given without trying to defend them. One could conclude from this paradox that there are no such things as things that are not part of everything. That is the conclusion apparently drawn by Parmenides (la spéculation idéaliste). But Parmenides at least, in that he confuses being and predication, goes on to draw a much stronger conclusion, namely that the only things that exist are things that can be spoken about in our language. What B&W seem to be arguing is that Heraclitus’ fragment exemplifies, so to speak, a view opposed to what idealistic speculation concludes. That is, there are things, namely the opposites of what Heraclitus names in his fragment, that are not part everything. To use set theoretical language: There are things that do not belong to the set of all things. These things are the opposites of terms that are evoked and sometimes specifically named in the fragments from Heraclitus. Of course, if these opposites are contrapositives (See above), then either Heraclitus or B&W wrongly associate them with the paradox of everything.

Plato had a pretty firm grasp of the paradoxicality of the concept of everything as addressed by Parmenides. In fact we understand the rather Sybillic utterances of Parmenides' poem the way we do largely because of Plato's Parmenides. For anyone who needs reminding, cf. 159 C and 160 B. The phrase πᾶν τὸ ὄν (the totality of entities - If we clear away the confusion caused by thinking of Being with a capital "B," then the relation of the Parmenidean paradox to the set theoretical paradoxes of all things becomes quite clear) appears explicitly in 165 B. Cf. also Theaetetus 186 A  where Plato again explicitly associates ἡ οὐσία with "all things" (ἐπι πάντων). Assuming as B&W do that Heraclitus thought within a Parmenidean framework, then the idea of everything forms a background to his fragments as well.

B&W make the same association of opposition with the paradox of everything in several passages. In their commentary on DK 115 (p. 320) a passing reference is made to an identification on Heraclitus’ part of physical principles of the Ionian sort (ἀρχάι) with “la totalité de ce qui est.” B&W imply that Heraclitus’ point is that, while the totality of what is may be subject to the paradox of everything, reason itself as represented in his fragments by the terms “fire” and “breath/soul (ψuχή)” obeys a different logic of self-opposition and self-propelled infinite growth. In their commentary on DK123 (p.337) B&W attribute to φύsiς (translated as “la chose comme elle vit”) largely the same function they found for fire and ψuχή in DK115, namely that of an all embracing and transcendent (more literally, hidden) thing to which opposites are related. The specific opposites to which φύsiς is related are emergence (surgissement) and closing (fermeture). Two comments. First, as hidden, φύsiς is subject to a second order opposition between the visible and the invisible (Notably a case of genuine complementarity) and so presumably it doesn’t escape the supposed logic of opposition altogether. Secondly, the theme of a transcendent creative or ontologically revelatory agent is one that Heidegger stresses mightily in his interpretation of Heraclitus. The danger, which Heidegger seems to entertain and B&W never really address, is whether this transcendent agent - fire, lightning, reason, Zeus, φύsiς or ψuχή - is somehow endowed with anthropomorphic intentions as in the cosmologies of Anaxagoras and Plato.

The general problem I have with Heidegger’s interpretation of Heraclitus is not so much that it’s wrong as that it doesn’t result in a particularly interesting philosophical doctrine, certainly not nearly as interesting as the flux doctrine attributed to him by Plato, Aristotle and Hegel. Nevertheless one indication that it may be wrong is that Heidegger interprets Parmenides to say pretty much the same thing as Heraclitus, despite much evidence that their contemporaries (roughly speaking) considered them as espousing two opposed views. As far as Heideggerian ἀπόφανσις is concerned, it is stated nowhere better in classical philosophy than by Plato himself in the Cratylus, a period in his development when Plato was not yet burdened by the stifling dogma of the theory of forms.

In DK10 Heraclitus appears to extend this viewpoint, and by extension the rhetorical strategy by which it is expressed (assuming the B&W interpretation is correct), beyond everything or the set of all things to other groupings as well. This is the import of using the term συλλάψιες (translated into French as assemblages) in place of “everything” or “being” (but other passages do mention τὸ πᾶν or just πᾶν (Cf. e.g. DK11 )). The problem, if problem there be, however, is that, for any grouping (or most groupings) except that of everything or all things, the paradox disappears and with it the need for a paradoxical positive assertion that there are things that are not part of everything. Heraclitus’ manner of expression may, under those circumstances, retain a certain pleasing literary value, but what he says is not dictated by the logic (broadly understood) of the situation, i.e. the meanings of the words in question. B&W attribute the paradox or dialectic of everything to DK10 by assuming that all συλλάψιες are prone to a paradox of inclusion. This is obviously not the case. It is not paradoxical, for example, to state that hot things do not belong to the finite set of cold things. B&W elide from the word ὅλα straight to the paradox of everything even though ὅλα just means “complete” or “whole” and not “everything.” It is not simply the case, however, that finite groupings and their opposites are not subject to the paradox of everything. The opposites of finite concepts are not even logically or semantically or conceptually generated, so to speak, by the concepts themselves. There is nothing about the concept cold that need evoke the concept hot, for example, in the same way that the concept of everything by way of negation evokes what is not part of everything. This is because the group of things that are not part of everything constitutes the logical complement of the concept everything. The complement of the concept cold, on the other hand, is the concept not-cold, not the concept hot. The logic of a language that does not express the opposite of a finite concept (its contrapositive) loses nothing whereas there cannot be a logic of a language that does not express the complement of a finite concept since that logic would lack negation or at least one significant meaning of negation. We may be strongly inclined to conceive of hot if we think of cold, but that is a psychological and not a logical situation.

It is in this extension of the paradox of everything to finite groupings that the contrapositives attributed to Heraclitus find their place. Hot things, for example, constitute a finite grouping and so does the contrapositive grouping of cold things (Cf. the commentary on DK102 (p. 292) for a similar gloss on justice and injustice). Because the group of things that are not hot is not coextensive with the group of things that are cold, however, the argument that may have been valid for the group of all things and the group made up of what does not belong to the group of all things does not apply. Other instances of opposition mentioned by Heraclitus fail for additional reasons. In DK61 Heraclitus attributes opposite and apparently incompatible qualities to sea water. It is both potable and non-potable.  It both gives life and it kills. B&W see in this something that can only be a Hegel inspired dialectic of same and other (p. 208). Sea water is itself and not itself (at the same time? Sometimes Hegel talks as if the contradictions of identity are time dependent and sometimes he doesn’t. B&W seem to opt for the latter in this instance. Cf., however, their commentary on DK88 (pp.260-261) where the dynamic between certain opposites at least is described as occurring over non-cyclical time.). “…elle est constamment elle-même et autre chose.”  That, as a result of this and other examples, there is no such thing as a referentially truthful sentence or proposition in language is my take on their assertion to the effect that “Le dédoublement des prédicats…conduit à dénoncer la prétention…du langage <<absolu>>.” (Ibid.) But perhaps things are not so dire for le langage absolu. We don’t need the apparatus of modern logic to unravel the mystery.  Socrates already identified the problem in Parmenides 128A ff. in addressing a rather more rarefied and abstract set of concepts. As regards the potability of sea water, it is not the case that it is both itself and non itself. The problem, rather, is that “deadly” is an incomplete predicate. We don’t understand what it means outside the context of a more complete two-place predicate such as “deadly to….” Sea water (setting aside any cavils about Heraclitus’ biology) is not deadly; it is deadly to humans. It is not life-giving (and therefore not not-deadly); it is life giving to fish. The semantic unit “deadly” is only comprehensible in the context of a more complete phrase. Its meaning is its contribution to the meaning of more complete phrases. The same explanation in terms of incomplete predication may apply to the supposed paradoxically reconciled opposites of heat and cold in the probably spurious DK126. This is one occasion where B&W themselves opt for the more common sense solution (p. 345).

B&W run into another problem in their commentary on DK10. That is, they state as a positive assertion (i.e. that there are things that are not part of everything) what we assume Heraclitus could not state because of the risk of self-contradiction. What’s sauce for the goose, however, and I see no reason why B&W should be any less wary of self-contradiction than Heraclitus was supposed to have been. One could take the position, and they seem to do that in several passages, that self-contradiction is OK. Without diving down the rat hole of trying to unravel that position, I will simply ask, if self-contradiction is OK, why does Heraclitus, according to their interpretation, go to such lengths to try to avoid it?

To move beyond the specifics of Heraclitus interpretation for a moment, let me suggest an alternative approach to the paradox of everything. Parmenides, we will remember, drew the strong conclusion from the paradox that there was nothing in the world that could not be referred to by a term of language, by which I assume he meant a term of his language, Attic-Ionic Greek. Plato sort of follows along, but his position is more complex. The weak conclusion that there are no such things as are not included in everything is presupposed by the strong conclusion because the word “everything” is part of language and, according to Parmenides, it has to refer successfully. At the other end of philosophical history Russell focused his attention on self-inclusive and non-self-inclusive sets. The paradox he found is really a version of the paradox of everything since the set of all things presumably would have to include the set of all non-self-inclusive sets. Russell simply found a specific thing that could not be a member of the set of everything. In addition, the Russell paradox arises in the context of his attempt to provide an interpretation of the universal quantifier. His Theory of Types incorporates the view that apparent paradox can be avoided if we stipulate that assertions about everything in a given universe (in which “everything in a given universe” is a referring term) or domain of interpretation belong to a language whose own domain of interpretation is a different type. Assertions about objects belonging to a higher type are forbidden on pain of paradox. Zermelo-Fraenkel set theory, on the other hand, reverts to a kind of Parmenidean viewpoint by excluding objects, namely certain sorts of sets, from the universe of set theory whose inclusion would lead to self-contradictory theorems. Hegel is the other major player in the philosophical history of everything but I won’t address his approach here because – and I don’t say this as a criticism – it is incredibly complex and not altogether clear.

Quine's rather cavalier treatment of nothing (Word and Object p. 133) stems from his ignorance of the fact that the source of paradox and thereby ambiguity lies not in the concept pair being/nothing. The source, rather, is the concept pair everything/nothing. Confusion occurs because of the false assumption that everything exists, excluding thereby things that don't exist from the supposed absolutely universal class of everything. Parmenides also made the different assumption that everything can be represented in language, an assumption ostensibly shared by practitioners and heirs of the logicist program. Parmenides did not understand that these assumptions are distinct because of the famous ambiguity of the term "to be" in Greek as well as English - its ability both to signify existence and to function as the grammatical copula. So deciding that the indefinite singular term (to use Quine's terminology) "nothing" cannot function as a definite singular term goes only part way to unraveling the confusion. (And why can't it? There is nothing in grammar that tells us that while the indefinite singular term "red" can also function as a definite singular term, the grammatically similar term "nothing" cannot. There is nothing in grammar that says that while Red can be an abstract object Nothing cannot. Discriminations like that depend on a content laden theory, an ontology one of whose methodological principles is the avoidance of paradox.) Quine's solution tends to mask the problem as merely grammatical and not conceptual. Properly understood, the ambiguously phrased paradox of being and nothing belongs to a family of paradoxes that include semantic paradoxes like the paradox of the liar and Russell's set theoretical paradoxes. Those latter, as we saw, occasioned a great deal of emergency scaffolding on the part of Russell, Tarski and Zermelo and Fraenkel to keep the logical edifice from crumbling. Carnap - literal minded M. Homais that he was - didn't bother his head too much with paradoxes. This caution may apply to Quine as well.

Consider subordinate clauses in natural language. The proposition “There are things that are not included in the set of everything” is self contradictory for all the reasons given above. The proposition, however, “I believe that there are things that are not included in the set of everything” is not. This is not only because, as a report of my belief, it could be perfectly true even if my belief is self-contradictory. It is also because the concept of everything in the embedded clause may mean something different from what it means outside the embedded context. Obviously we don’t need modalities like belief and the problems they raise to achieve the same effect. “It is true that there are things that are not included in the set of everything” is also not self-contradictory (It is not truth functionally equivalent to the embedded clause because the meaning of the embedded clause is opaque). I find it interesting that this suggestion does not require different languages or metalanguages or type distinctions. It is simply a phenomenon of ambiguity of meaning and multiplicity of reference within a single language that has the capacity for indirect reference. Frege's syncategorematic definition of everything, on the other hand, does not solve the paradoxes attending the concept of everything. It simply avoids them. The same is true for his syncategorematic definition of existence. Russell saw this for the concept of everything and used the Theory of Types to try to solve it. Russell's analysis of existence statements, however, is just a more detailed version of the Fregean dodge. Neither Frege nor Russell noticed the conceptual connection between the universal quantifier and the set of everything (one of whose members is the set of all non self-containing sets). So Russell did not see the impact that the Theory of Types has on the uninterpreted universal quantifier and the semantics of a logic such as the predicate calculus that includes the universal quantifier as a primitive. Changes of meaning across the veil of indirect discourse bear a resemblance to the way that set membership is specified differently across types. You could regard the Theory of Types and the device of metalanguage in formal semantics as no more than fancy versions of what appears in ordinary grammar as indirect discourse. However, formal semantics of the Tarski kind doesn’t really address paradoxes like the paradox of everything because it preserves truth, and, in Davidson’s application to natural language, meaning across the metalinguistic biconditional. “Everything includes what is not part of everything” is true if and only if everything includes what is not part of everything. A theorem like that would be forbidden by the Theory of Types if the domains of the embedded occurrence of "everything" and the non-embedded occurrence belong to different types. However, it could be deduced and still be untrue in a formal semantics in case Zermelo-Fraenkel restrictions on the domain of interpretation are assumed for the metalanguage and not assumed for the object language. For this reason Tarski semantics is not by itself a satisfactory substitute for Russell’s Theory of Types.

An associated problem worth noting is that an issue which we identify with Plato's dialogue was already in play for Parmenides himself and even Heraclitus. Plato's intervention actually helps us understand Parmenides' actual poem, but any extrapolation to Heraclitus' fragments takes a great deal of good will to say the least. Nevertheless, since the issue of totalization appears with Anaximenes and opposites are important to the later Presocratics, it is hard to defend Heraclitus not being concerned with these issues if he is to fit into the Presocratic philosophical tradition.

3. Heraclitus’ opposites just seem to appear without logical or semantic motivation (DK2, DK6, DK10, DK67, DK99) Occasionally B&W assert that just by saying one of the opposites Heraclitus conjures up both of them (p. 66). In their analysis of DK10 (pp.96-97) they call this a negative procedure (Cf. my section (2) above). I gather this means that death is not mentioned by the Dionysiac rites (of life), but rather elicited by its absence. One could regard the procedure as confirmed (but equally well as contradicted) by the next sentence of the fragment where Dionysus and Hades are paired. B&W see this as “saying” that life and death are identical but opposite (l’opposé dans le même)in that they both have to do with deprivation. B&W return to this theme in their interpretation of DK67 (p. 221) where they use the phrases “une charge identique” and “Le renversement …s’effectue dans l’identité même.” Nothing in their commentary on DK67 addresses the problems with the fallacy of contrapositive paradoxicality that I raised in (2).

4. B&W’s comments about DK32 (p. 138) are both tantalizing and puzzling. In the first place they seem to have nothing to do with the fragment and appear suddenly after a possibly tendentious etymology of the name “Zeus” and the concept of τὸ οοφόν which they render as “art.” The first point they make is that contraries (They say contraires and antithèse and négation without explicitly distinguishing them) as part of the content of a saying elicit (figure) the separation (l’écart) between the content of the saying and its verbal form – le signifié and its signifiant. The name Zeus, in addition, is supposed to invoke à la fois la totalité contradictoire et la contradiction de la totalité. This latter has been a genuine though probably resolvable philosophical issue and I discussed some of its aspects above (2). However, loading the paradox or dialectic of universality into the simple utterance of the name “Zeus” seems to me to be pretty extreme. There may be an argument that Anaximander touched on the problem, but I see no evidence that Heraclitus picked up on this interpretation of Anaximander. Furthermore, the use of terms like invoking or eliciting (figurer) does nothing to solve the paradoxes B&W court. For, if the name “Zeus” invokes the separation between a saying and its content by way of contraries, then that name also should have a contrary (Saturn perhaps? Or Hera?) that invokes the non-separation of a saying and its content.

5. DK50. B&W’s interpretation of this tricky fragment is an example of their intention, announced in the introduction to treat Heraclitus’ sayings as artifacts, something on the order of written pottery shards, things that may exhibit a sort of conceptual tension without actually asserting that such a tension obtains. They attribute to a so-called traditional interpretation of this fragment an assertion to the effect that the listener should agree with the commonly held or rational belief that everything is one. B&W contrast the traditional view with their own which does not regard Heraclitus as specifically weighting the commonly held over the individual (ἐμοῦ). Rather the one elicits the other via negation. The discourse (I assume by discourse they mean the significant and the signifié interacting) calls up the distinction and contradiction between the individual and the universal without a reconciliation favoring one or the other. The reconciliation, rather, lies only in the fact that one term of the opposition cannot be thought without immediately eliciting the other. I see no reason why this latter sort of reconciliation is valid. Complements may be inseparable but not contrapositives, as I indicated above.

Although they mention Heidegger’s view (Cf. esp. Vorträge und Aufsätze pp. 199 ff.) elsewhere (p. 405), they do not bring it up in this context and never qualify a rather gnomic statement to the effect that Heidegger regarded this fragment and Heraclitus’ doctrines in general as part of the birth of Greek ontology. In fact Heidegger is trying to elaborate a theory of ἀπόφανσις or Unverborgenheit according to which language does not determine our view of the world, i.e. we do not view or conceive the things of the world though a veil of language. Rather we become aware of things or sorts of things simultaneously with developing concepts for them and words that will refer to them.

Here’s my take on the matter: It is not excluded that ἕν and πάντα are contrapositives (in my sense of “contrapositive” which covers some usages of “opposite” and “contrary”). They are not complements without further definition, as I explained above. I am inclined to think that contrapositives are somewhat spontaneously generated through no mechanical procedure in the way that rival sporting teams can in a motivated but non-logical way be viewed as directly opposed to each other to the exclusion of other teams in their league. There is nothing in the logic or semantics of the concepts Steeler and Cowboy that force us to deductively conclude that the Steelers and the Cowboys are contrapositives. Complementarity, on the other hand, understood as set complementarity, is a logical concept. However, the elective contrapositivity of ἕν and πάντα raises problems. For one thing it means that simply mentioning one concept does not automatically, i.e. logically, elicit the other despite B&W’s claim. The negation (i.e. complement) of ἕν does not algorithmically produce πάντα, it produces not-one (where “one” is a singular referring term). There is no natural contradiction here to be held in a reconciling tension. At the same time B&W imply (admittedly without actually asserting) that there is some sort of homology between the contrapositives ἕν and πάντα and another pair of concepts, namely ἐμοῦ and λόγος. Presumably ἕν corresponds to ἐμοῦ and πάντα corresponds to λόγος. But it is hard to see where this incipient chiasmus takes us. I kind of suspect it derives from Hegel’s assimilation of other types of Heraclitean opposition to the opposition of the epistemological subject and object (Vorlesungen Über die Geschichte der Philosophie, pp. 337-343) but B&W don’t say anything to that effect. Their comments on the dire and the dit, however, are novel, as I mentioned above, though they may constitute no more than a nod to modernity.

Let’s introduce yet another paradox. I am rather inclined to think that the concepts of ἕν and πάντα allude to a Parmenidean dialectic (treated at length in Plato’s Parmenides and The Sophist). This argument begins with the premise that all is one. I am going to interpret that Delphic statement to mean that the group of all things is itself a particular (For simplicity’s sake let me just specify that I use “particular” in roughly the sense Strawson uses it in Logico-Linguistic Papers and Individuals; however, let us stipulate that sets can be particulars and members of sets ). Indeed that interpretation is the best way to generate even a semblance of paradox. Indeed some Greek philosophers regarded the statement as paradoxical. Their (probably erroneous) reason was that all could not be one since it would then be part of itself and therefore not all. Looked at from a more rigorous set theoretical viewpoint, however, there is no obvious contradiction. It is not the inclusion of itself that leads to paradox when we talk about the set of all things; it is the inclusion of other sets as members that by their nature can only be referred to by way of paradoxical or self-contradictory propositions. B&W may be right in that DK50 does not seem to assert anything about the paradoxacality of this situation. It simply mentions the concepts together. The concepts that we should probably take away from all this are (1) all things (2) individual particulars that belong to all things (i.e. are members of the set of all things) and (3) the unity of all things as a whole (i.e. the set of all things is itself a particular, namely a set). I doubt whether there is a real paradox here and furthermore I doubt both the basis and the conclusion of B&W’s belief that, since ἕν and πάντα are contrapositives (and not complements), one is automatically elicited by way of negation whenever the other is mentioned.

I can’t resist inserting an interesting fact from the history of philosophy. A version of my argument that a philosopher who makes a universal statement presupposes that his own statement can be characterized by what it asserts, and furthermore that if his universal statement asserts a contradiction, then, by its own terms, it is either false or vacuous, can be found in Áchárya’s reconstruction of the Rámánuja school of Indian philosophy (The Sarva-Darśana-Samgraha, p. 67. Cf. also p. 98 on the Purna-Prajna system.)

B&W pick up on a familiar Hegelian theme throughout their book in a way that is particularly prominent in their interpretation of DK50. That is the idea that no proposition (or assertion or utterance or statement; these terms seem to capture distinctions like those between énoncé and énonciation, dire and dit etc. Presumably a proposition is the énoncé or the dit while an assertion is the énonciation or the dire. (Cf. Logico-Linguistic Papers passim for various similar distinctions.)) or alternatively some propositions (or assertions) is (alternatively are not) true or false or its (alternatively their) truth or falsehood does not matter. What is important is the movement of thought by which, through negation and contradiction, all (or some) propositions (or assertions) unavoidably elicit their opposite (that is, call forth positions making assertions about a contrapositive concept or else simply negating the original proposition (or assertion). The complexity of the immediately preceding sentences underlines not only the real complexity of what Hegel has to say but also the fact he may confuse distinct concepts and find paradox where none exists. A college boy version of the history of modern philosophy would have it that Hegel taught that if you pursue the path of ideational contradiction long enough you will eventually reach a state where the contradictions are reconciled. Later views in the Hegelian tradition, on the other hand, are supposed to contend that contradiction is permanent and the truth or falsity of a given assertion (or proposition or philosophical position) is not as important as the movement itself through contradiction and negation. In their commentary on DK103 B&W attribute something like this later position – You might call it the non-reconciliation view to Heraclitus:

Le terme de commun (xunon)…n’évoque pas la continguité qui…réconcilie l’identité et l’altérité. Il dédouble le même. Cette forme d’identité se distingue du Même (tauton) en ce qu’elle maintient la différence en deçà et au-delà de l’inévitable retour de l’Autre. (p. 294)

 I am inclined to think that as stated this philosophical problematic may simply disappear because of the conceptual confusions involved in its statement. However, real issues underlie the way it is currently framed such that something like it may be restated without the conceptual confusion. But – who knows?

6. DK51. B&W seem to envision at least two types of contrariety (or difference or separation – these terms appear to be interchangeable) in Heraclitus (In their commentary on DK72 (p. 230) B&W more or less define the λόgoς in Heraclitus as the logic of contrariety (la raison des contraires). Presumably what they mean is a semantics of contrariety.) The first is a kind of spontaneously generated contrapositivity, such as the contrariety between cold and hot. There is as far as I can see no logical way of framing this kind of contrariety. I argued this above (2 and 5). A contrapositive concept just seems to occur to us given some base concept. (Cowell, the translator of the relevant chapter in Áchárya’s, uses the apposite phrase “the imagining of a thing in what is not that thing” (p. 253) with respect to the eliciting of contrapositives.) For that reason contrapositives are not subject to the kind of general theses that B&W articulate either in the form of positive assertions on the part of Heraclitus or as exemplified artifact-wise in Heraclitus’ fragments. Simply stating a concept does not automatically call up its contrapositive, nor indeed can we be sure that we can’t devise more than one contrapositive to a given concept. DK99 deals with an interestingly ambiguous example. Day and night are opposites of sorts. Are they complements or contrapositives? Our conclusion would seem to be based on whether we define night as not-day and vice versa. But if we decline to define night as the complement of day and choose to regard it rather as some sort of contrapositive (At the earth’s poles during certain times of the year, the true complement of day is not night, which never occurs, but perhaps twilight), then there is no semantic algorithm that generates the notion of night from that of day (Imagine a planet or a side of a planet that experiences only day and twilight all year round). In this case B&W’s assertion (or alternatively Heraclitus’s assertion in their reading of this fragment (Cf. p.285)) that there is both an “irreducible difference” and a “genuine link” between day and night cannot be justified.

The second kind of contrariety is very specific and limited to just one admittedly much ramified pair of concepts. These concepts are (1) everything and (2) whatever is not part of or does not belong to everything. The contradiction in this case is logically or semantically generated since presumably all concepts have complements (i.e. there must be a set complementary to the set determined by the concept) just as any proposition can be negated. Therefore, if at least part of what we mean by the word “everything” is a concept, then it must have a complement. But if it has a complement, then it is not the concept of everything. This is a form of the paradox of being such as appears in Plato’s The Sophist shorn of the language of being or thinkability. Likewise it is closely related to the paradox that motivates much of Hegel’s dialectic, but also without the misleading being/nothing terminology. (This simplification of the terminology is justified because the concept pair everything/the complement of everything is paradoxical without invoking the accretion of being or existence. The concept pair being/nothing is not paradoxical unless being comprises everything, i.e. something is not part of everything unless it is a part of being. The idea of nothing does imply that being is meant to be equivalent to everything, so that may be the source of the confusion.  Hence if we want to get to the heart of the paradox, it is advisable to jettison accretive and misleading concepts such as being or thinkability or conceivability.)

This second contrariety is the one B&W attribute to several of Heraclitus’ fragments and most particularly to DK51, probably in the form of direct positive assertion or syntactically implied direct assertion and not exemplification. They focus their interpretation on the words διαφερόμενον ἑωυτῷ ὁμολογέει. B&W see a tension in this phrase, presumably between the words διαφερόμενον and ὁμολογέει, roughly differing and reconciling. They say “…la tension est toute entière exprimée par la divorce d’avec soi.” (p. 180) Apparently this is just one way of stating the dilemma. Heraclitus adopts the terminology of those “…qui, prenant les choses dans leur totalité, découvrent que leur négation ne peut pas être pensée.” (ibid.) For B&W the word ὁμολογέει (which they translate as “dit en accord” or “states in or as agreement or harmony”) acts as (fait figure de) a reply (réplique) to the abovementioned persons to the effect that the impossible (i.e. the paradox) is possible. The fragment or at least this portion of it surmounts the aporia. To continue to see a paradox assigns a limited or partial applicability to reason “que l’immanence protège et qu’elle soustrait au regard spéculatif.” (Ibid.) They go on to say that the images of the bow and the lyre, like that of the river in DK91 (Cf. also the commentary on DK59), are representations in more vivid language of the non-aporetic tension of speculative reason. (“Le lien (holding the strings in tension – WD) tient les opposés ‘ensemble’, comme la raison (le logos) dit ensemble le contradictoire.” (p. 181))

I can’t say with any authority as to whether this is a valid or invalid reading of Heraclitus. I have my doubts, and at the very least it is highly overdetermined. Let me simply point out that B&W’s reading attributes a positive doctrine to Heraclitus. One result is that they contradict their assertion in their Introduction that Heraclitus doesn’t state anything positively, that he merely exemplifies things by his syntax and choice of words (This should be old hat by now). Another result can be discussed on its own merits whether or not B&W’s interpretation of Heraclitus is acceptable. That result is that the same movement of contrariety should oppose the purportedly Heraclitean position to that of “those who take things in their totality,” producing a possibly higher order paradox and raising the specter of an endless chain of self-contradiction. B&W do not mention that eventuality but it is embedded in the logic of their interpretation. It was also a preoccupation of Hegel himself who did foresee a kind of reconciliation but only at the end of some very long conceptual developments. Indeed words like “reason” and “speculative” as B&W use them are thoroughly Hegelian terms of art and their view that opposites can be held in a sort of acceptably contradictory stasis (or alternatively perpetuum mobile) appears to fit into a way of thinking most associated with Hegel.

If we entertain the possibility that the second result is a valid doctrine, whether or not it is a doctrine espoused by Heraclitus, we are tempted to ask “Et alors?” -  “So what?” Where do we go from there? Are there any further conclusions that can be drawn or does it influence how we shape our lives? There are implications among some Hegel oriented philosophers such as Adorno that subscribing to the second result validates a kind of left wing politics. But no further consequences are drawn by B&W themselves. (Cf., however, (1) their commentary on DK 78 (p. 240) that attributes to Heraclitus a view of humans as undergoing a  kind of anti-theistic  self-transcendence (dépassement perpétuel) animated (qu’animent) by the opposites, and (2) their commentaries on DK 104 (p.296) and DK107 (“La phrase (i.e. spoken utterances – WD) saisit les contradictions de la particularité: incommunicable, elle n’apporte rien; communiqué, elle cesse d’être”) p. 304) that allude to the Hegelian/Sartrean paradox to the effect that the desire for individuality among humans results in a loss of individuality in that all or most humans want to be individuals.)

7. DK55. B&W walk a tightrope of comprehensibility and there are times, in my opinion, when they fall completely off (into the abîme?). Their commentary on this fragment is one of those occasions. After all the fragment simply says, “I most prefer the things grasped by sight, hearing and learning” (B&W’s own translation differs significantly. For example, they translate μάθησις as “perception”). If B&W think, as they seem to, that there is more to Heraclitus and by extension more to this fragment than a limitation of what we believe exists or what can be grasped in the perceptible world, then they are most likely correct. But they claim or appear to claim that there is a great deal more.

Let’s first try to recreate what paragraphs 3.2 and 3.3 (pp. 191-192) have to say by way of translation/paraphrase: (3.2) Our visible world does not reflect a hidden order of things. This assertion is in response to the analogical interpretation of Heraclitus’ view as it appears in Hippolytus. What links together contraries in the hidden order destroys the visible links between phenomena and breaks up the universe of things in a multiplicity of visible relations. Reason is negation. It is not the foundation or origin of things. It is their abîme, their destruction. Identity doesn’t guarantee the presence of being in its totality; it projects absence, an absolute elsewhere. The hidden order or intelligible world in relation to phenomena is really just one mirror reflecting another. Self-reflexive being exhausts the negativity by which it is constituted and prepares the way for becoming. (3.3) Perception shows the structure of sense impressions. It shows the identity of the perceived object by way of its contrary understood as its negation. This is an intention that destroys the network of speculative categories that tends to cover the totality of the real. It is a preference that joins the rebellion of things and the reassuring idea of a single system of thought, i.e. the vise of collective reason.

There appears to be some relation to issues raised in B&W’s interpretation of other fragments. For example, they allude to the Parmenidean dialectic of everything. They also bring up the notion of contraries. However, they continue to write as if these issues were always linked, and we have seen that they are not. The dialectic of everything inflects the idea of contraries (more properly, contrapositives) only when we are dealing with a contrapositive (or complementary) concept to the concept of everything. Otherwise they are quite separate. Furthermore, it is not a given that every concept has a contrary. We saw above that contrapositives are not logically or semantically generated from a given concept. They result from a somewhat unstructured activity on the part of our imaginations. Since nothing in the fragment states any contraries (contrapositives), we are not entirely justified in believing that Heraclitus has contraries (contrapositives) in mind. B&W also allude to a kind of ontological anarchism, a “rebellion of things” (Cf. also p. 204 about “blowing up the same (fait éclater le même)”) which is all very charming but there is no evidence for this rebellion in the fragment itself. I won’t go any further. I conclude that B&W’s interpretation of this fragment is mostly incoherence laced with situationist and deconstructionist code words.

There is one facet of Hegel’s view of Heraclitus that B&W do not address. That is the idea based on various fragments about rivers and lyres and bows etc. to the effect that one instance of how a thing can evoke its opposite occurs in change over time. Hegel assimilates this sort of occurrence to his other examples of a “logic” of opposites, namely the opposition of contrapositive concepts and the paradox of everything and nothing (being and non-being). In the Vorlesungen Hegel suggests that what a thing becomes is the non-being of what it is now. Because a thing becomes what it is not, it enters into a dialectic of being and non-being. (It is unclear whether by a thing’s “being” he means what it is or that it exists.) This oppositional process, however, is not the same as the opposition of being and non-being in the Parmenidean dialectic. By using the same terms Hegel seems to think they are the same or somehow fundamentally related and thereby he introduces a great deal of confusion. The confusion of the two different points is pretty clear on p. 329 (e.g "Ihr (time's - WD) Wesen ist, zu sein und nicht zu sein") and 331. But recognizing the confusion helps explain why Hegel regards a theory of becoming as a resolution of the Parmenidean paradox and at the same time a correct restatement of Heraclitus’ view that independent completely defined objects are fictions (Quine talks about logical fictions. A better approach is to treat interpreted logical formalisms as a part of language and use the term “linguistic fiction.” Both Fregean  logic and set theory subscribe to the notion of independent fully specified particulars. To call the fiction linguistic is to suggest that it is our language and not a convenience of some formalization that  imposes the notion of an object upon us and that this notion does not necessarily reflect reality.)

There is an intriguing idea hidden in Hegel’s point despite the obvious infelicities. At this juncture I’m not quite sure what that idea is so let me just underline the infelicities. Hegel improperly assimilates the differences in a particular over time, the assertions of which are instances of the negation of an identity proposition (“It is not the case that a at timet is identical to a at timet1 where timet is not identical to timet1”) to differences in the properties of a particular the assertions of which are instances of one-place predicates. To say that a particular is not identical to itself (over time) is very different from saying that a concept evokes its own complement. Furthermore, the particular at timet1 does not necessarily fall under a concept (i.e. such a concept is not truly predicated of) contrapositive to the (same?) particular at timet. And, of course, all this is completely unrelated to the Parmenidean paradox which is the only instance of all these examples that has some slight logical motivation.  I did say that Hegel’s ideas about object identity over time are intriguing and, despite the fact that Hegel falsely assimilates this to other issues, it deserves further consideration.

B&W seem to refer to the Hegelian paradox of self-identity in their commentary on DK119 (p. 329). There they assert that Heraclitus contests the notion of “abstract and frozen” self-identity at least as it applies to persons. Men are supposed to be the negation of (the opposite pole to) to the phenomena of the external world in that they cognize those phenomena. But this does not constitute a positive identity of the species man. Is there a confusion in the course of this argument between the self-identity of individual persons and the definition by which a certain class can be identified? I think so, but let’s continue. The word ᾖθος indicates a contrapositivity within the notion of being human. As a mortal man is part of the phenomena; as the opposite pole of the phenomena man is immortal or god (δαίμων). “L’identité est alterité.” Presumably this is the tolerable sort of contradiction that is the province of reason as opposed to conceptual or categorical thought. B&W’s gloss most likely derives from the end of Hegel’s discussion of Heraclitus where he refers to the passages about perception of Diogenes Laertius.

8. DK90. There are at least two ways to regard the role of fire in Heraclitus’ philosophy. The first is to regard fire as a kind of agent, perhaps exercising anthropomorphic volition, in the constitution of the things of the world. “Constitution” could here mean either material fabrication or the constitution of the human mental or conceptual apparatus such as to enable our perceiving the things in the world as we do. This is the interpretation Heidegger favors (presumably without the anthropomorphism); he understands “constitution” in the second sense. The interest he finds in this interpretation lies in its similarity to his own doctrine of Unverborgenheit. In his interpretation the roles of Zeus, lightning and fire partially overlap in the Heraclitean fragments. The other interpretation proposed by B&W is based on this fragment. Fire is (represents? The nature of the parallel isn’t clear) the exchange value of all things in the same way that gold represents the exchange value of goods for sale. But this is somewhat paradoxical since fire is also one thing among many. By way of the (erroneous, as I noted above) identification of the concepts of everything and all things with the semantics of contrapositives, fire also becomes a representation of (alternatively what underlies) the contrapositivity of things “…dans l’unité que forme leur négation… (p. 267. I render forment as forme on the assumption that the plural is a typo.) It is tantalizing to speculate that, if B&W are right, then the concept of fire is an expression of the same logical intuition (Cf. the phrase “…l’unité sous-jacente…” on p. 267) that impelled Aristotle to propose the notions of ὕλη and ὑποκείμενον not to mention Marxian dialectics. The physical sense of the concept of fire that results from this interpretation, however, seems closer to that of ether from traditional natural philosophy.

9. DK91 probably has the honor of being the single most quoted fragment from Heraclitus. B&W cite three original sources which in each instance occur at an important juncture in the development of the doctrine of a major philosopher. It is also the fragment most associated in the popular mind with what Heraclitus supposedly stands for. B&W assert (pp.268-269) that it is a mistake to assume that Heraclitus meant his dictum to apply only to the inanimate cosmos, citing DK12 and DK49 in support. They go on to conclude that Heraclitus is making a much broader philosophical point that applies to our conceptual schemes and the movement of our reasoning as well. Actually there is nothing in a literal reading of any of the three fragments that justifies the latter claim. Furthermore if the cosmos is understood as comprising not just inanimate objects but the realm of biology (la vie physiologique) as well (an amalgam much closer to the spirit of Presocratic philosophers in general), then both DK91 and DK 12 could easily tolerate a purely cosmographical interpretation. And, if human activity is also part of the cosmos, the same could be said for DK49. (Eventually B&W make the claim for a general ontology in the fragments: “L’image du fleuve contient la totalité des choses en cours.”) I am of the opinion that the doctrine of flux as an ontology of the physical world is not a trivial position. In fact it may not be an ontological theory at all but instead an important empirical observation. Our difficulties with the doctrine of physical flux may lie in the inability of our supposedly static conceptual schemes to adequately capture a constantly changing physical world – a Gordian situation that has led Platonists throughout the ages to simply deny the reality of what they observe.

By way of aside let me speculate that the invention of the calculus furnished us with a mathematical method for conceptually capturing the constant flux embodied in motion. But, far from solving the conundrums involved in Heraclitean observations, the calculus introduced a host of new ontological issues. Leibniz, Kant and perhaps Hegel – I speculate further – had an inkling of these issues and tried to address them each in his own way. Whatever its other benefits, the advent of modern logic unfortunately put a stop to the ontological tinkering inspired by the calculus. A few philosophers, most notably Quine and Marxist neo-Hegelians, have talked separately about ontological theory and a non-static world without relating their ideas back to the calculus.

The doctrine of flux poses a problem at one level if we assume that our conceptual schemes, logical and semantic reasoning and mental functions are indeed static. At the same level this is an important assumption, for we could not even conceptualize the notion of flux if we didn’t have its complement, non-flux, as a conceptual contrast. If we can’t recognize non-movement, we can’t recognize movement either. But what if, hypothetically speaking, our minds and their conceptual schemes were also in a state of constant flux? What if the stream of consciousness was a river just as relentless as the Scamander? Presumably in that case our recognition of the immobility of a given conceptual scheme would be an illusion, a deceptive slice or mental stopping point to be immediately replaced by another deceptively static mental stopping point. Note the different image that emerges. Instead of a constantly flowing river that we try to arrest by way of a static net, we now have two rivers superimposed and flowing perhaps in parallel and perhaps in different directions. It’s the sort of possibility best explored after a ’shroom or two

There is a less extreme version, however, namely the Hegelian idea I referred to above that our concepts and reasoning are in a state of flux that can be grasped by the notion of a supposed logic of contrapositivity and a stepwise ascension of what can only be labeled meta-levels where each new level captures without contradiction the conceptual framework of the level of reasoning it encompasses. I have already mentioned that B&W endorse this kind of logic and, following Hegel, credit Heraclitus as its founder. On this reading the three fragments in question do not just express physical observations; they are also metaphorical expressions for a doctrine that our reasoning is also in constant flux. It is not unlikely, in my opinion, that Heraclitus intended them as some kind of metaphor and perhaps a metaphor for the very theory Hegel proposes. The conclusions B&W draw, however, are paradoxical. They call the physical doctrine of flux a “doxa figée”, an effusion of bon sens that neglects speculative movement and threatens to assimilate different levels of reflection (what I called meta-levels). But in the very next breath they attribute to Heraclitus the quite reasonable doctrine that flux cannot be understood and observed unless we understand what non-flux is and might look like: “…Héraclite établit la relation nécessaire entre ce qui demeure et ce qui s’en va, entre le lit et le courant.” But what exactly is the sentence just quoted but a doxa figée? Either Heraclitus or B&W or both are contradicting themselves. Moreover, in none of the three fragments does Heraclitus so much as mention a river bank or river bed (purportedly the static background to the perpetual movement of the river), although DK51 suggests possibly analogous images.

Epode: Semantic paradoxes are the favorite targets of undergraduate parodies of what it means to be a philosopher. And they are right to the extent that the point of philosophy is to reflect about things in the world in a general way. Semantic paradoxes as a reduced version of the Parmenidean paradox are an easily digestible consequence of the perils of that kind of reflection. But their caricature is limited in the same way that popular culture jokes about Einstein are limited. They capture only the superficies of philosophy and of general relativity such as the limited capacities of milkmaids and frat boys are capable of understanding. As far as philosophy is concerned the choice is not between practicing philosophy and not, it is between unquestioningly accepting metaphysical prejudices and examining those prejudices fuckosophically. B&W have taken something of a beating throughout my essay, so it’s only fair to let them, in a gloss on Heraclitus, have the last word: “Si l’éloignement (from the logic of oppositions – WD) consiste à vivre moins intensément la tension des contraires,  ils (men – WD) ne la vivent jamais de telle sorte qu’ils puissant s’en éloigner.” (p. 230)