Copyright © 1992 Lorenzo Peña
That logic and ontology have something or other in common is widely, if not unanimously, admitted. But what? Many people have maintained that logic is formal and does not concern itself with content, so a logical theory can entail no ontological commitment then no subject matter would be common to both logic and ontology, but logic would be the unavoidable framework outside or without which no ontology could be set up, articulated or put forward. Such is the formalistic view of logic. Other conflicting views have also been held, of course. Frege, Russell, Ferdinand Gonseth came close to identifying logic with ontology. (Husserl's conception of logic as both formal ontology and formal apophantics lies somewhere in between.)
The author of the book under review, D.A. White, seems to take the formalistic view for granted. That is going to constitute one of his major grounds for challenging Heidegger's attempts to base logic upon an elucidation of Being. Another, still firmer assumption of D. A. White's approach is that there is only one logic, which is logic. Thus no forays are made by the author into an assessment of Heidegger's explorations from the standpoint of the existence of several, mutually discrepant, systems of logic. And yet that approach might well turn out to be most fruitful.
The former assumption, though -- i.e. the formalistic view of logic -- is not held on to through the book in an unyieldingly steadfast way. But, although White is willing to heed whatever considerations Heidegger might have to offer against such a view, he never appears to seriously entertain doubts about the assumption. This is why his strenuous endeavour to both understand and canvass Heidegger's position comes off not altogether successful -- even though, I hasten to add, Heidegger is far from being clear or one-minded on such issues. White's criticisms of Heidegger are not unfair, but he is bent on demanding compliance with a requirement no position in the neighbourhood of Heidegger's can help running afoul of, namely that the philosophical views to be proposed be shown to lie within the pale of (classical) logic, i.e. to be compatible with the standards of acceptability that logic enforces. White is aware such a requirement clashes with the goal of understanding a philosophical view like Heidegger's, according to which «Thinking» (Denken) is beyond and underneath logic, thus providing the ground for logic rather than the other way round, owing to which it isn't bound to be amenable to logical standards. White is wise enough to give a hearing to Heidegger's bold claims, but in the end (in his «Conclusion», pp. 206ff) repeats that, since `it is a fact about the philosophical activity of our time that it considers the canons of formal logic to be inviolate in themselves and independent of all substantive considerations' (p. 206), and since we feel a resident rightness to be inherent in the notions and principles of logic `as essential to thinking -- at least any kind or ordered thinking -- in a way that places them outside of history and outside of temporality' (p. 207), the Heideggerian challenge to such presuppositions is as such quite suspect on its own. What White sounds to be contending in his Conclusion is that, thought-provoking as Heidegger's project is, it, as any other intellectual proposal, has to be assessed from the viewpoint of the inviolate logical canons, even if those canons happen to be that precisely against whose supremacy or apodicticity Heidegger argues -- or, more accurately, from the viewpoint of those standards taken as unquestionable, absolute patterns infringement of which automatically renders a discourse unintelligible and so unworthy of being seriously entertained. White is not utterly dogmatic on that score, though, and in fact evinces wavering or hesitations to some extent. Nonetheless, he winds up stressing once more (pp. 208-9) that, since we find ourselves in a quandary once the logical difficulties implied by Heideggerian Denken have been forced into the open, the Heideggerian approach will not become acceptable until a way of consistently thinking through the logical difficulties encountered by Denken has been found. Yet, doesn't that mean that any approach which challenges some classical assumptions like (negational) consistency is bound to extricate itself from any suspicion of inconsistency in order to be looked upon as an proposal worth considering? White acknowledges he is in his assessment availing himself of those very same guidelines Heidegger criticizes, that his `study depends on at least a tacit endorsement of the supremacy of logic and metaphysics' (p. 210). And he proceeds to reply: `If so, then so be it. My own belief is that whether in the end a coherent account of human nature can be render ed from within the Heideggerian assumption of the primordiality of time and history will depend on... the capacity of Denken to elicit a structure faithful to the demands of the human need to speak with meaning...' Which seems to mean: the human need to speak in accordance with the requirements of (classical) logic -- in order to get a coherent, i.e. negationally consistent account. That may sound reasonable, but within the present context it is question-begging.
The two most outstanding chapters in the book are to my mind chapters 1 and 2, devoted respectively to the principle of (non)contradiction and to the ontological structure of negation. In the first chapter, White mentions Heidegger's claim to the effect that since the appearance of Hegel's Logik it is not immediately certain that that which is contradictory could not also be actual (p. 29). He remarks, though, that a `contemporary logician could maintain, with apparent propriety, that the principle of contradiction remains fundamentally the same throughout the checkered history of Western metaphysics... in its intrinsic formality'. Yes, many a contemporary logician will subscribe to something like that. But not all, far from it. For one thing, a number of logicians do not want to concern themselves with the history of ideas (and they will be well-advised to be wary, since a few metaphysicians among the greatest can be construed as maintaining that there are some contradictory truths: Plato when writing Parmenides and Sophist, some neo-Platonists, Nicholas de Cusa, let alone Hegel, and some contemporary energetists, like Stephane Lupasco). For another, many current-day logicians, including the reviewer, hold different views on the principle of noncontradiction itself. In fact, what both Heidegger and D. White call `the principle of contradiction,is to be split and analyzed into a number of different principles of several levels: (1) the assertion, for any formula «p», of the formula «not: p and not-p»; (2) the rule of avoiding theories containing for some formula «p» both «p» and «not-p»; and so on. (1) and (2) are particularly interesting. Some logical theories have (1) and comply with (2). Some have (1) but do not comply with (2) -- or, more generally, do not enforce compliance with (2). Some logics neither have (1) nor comply with (2). Some of them (e.g. Lukasiewicz's and Kleene's logics) comply with (2) but do not have (1). Such logics as do not enforce compliance with (2) are called paraconsistent logics. Now, the reviewer regards as most worth while to challenge Heidegger's challenge to the supremacy of logic and of its principle of noncontradiction from the vantage point of the acknowledgment of the existence of those different logical approaches, thus sifting Heidegger's claims with several screening tools in turn, and conversely scrutinizing each of those approaches on the background of Heidegger's challenge. Granted, Heidegger himself seems to be blissfully unaware of such complications and distinctions. He was never interested in the existence of alternative logics. However anyone wanting to examine Heidegger's views on philosophy of logic from a perspective appealing to philosophical logicians is bound to go into those matters and to take the existence of nonclassical logics most seriously -- esp. when it comes to the existence of paraconsistent logics, which are revolutionizing our thinking about contradiction, Thus, for instance, when White discusses Heidegger's contention that `the principle of contradiction can be restructured only in such a way that that structure hinders the unconcealment of Being as determined through the original meaning of Logos' (p.35), he proceeds to compare such a view with Strawson's on the related matter of what a contradiction could mean. I will in a moment have a look at Strawson's claims. For the time being let us envisage Heidegger's strictures against the principle from the viewpoint of a paraconsistent logician. Heidegger complains about the Aristotelian reduction of language to statements, whose abstractness is the hindrance he brands (at least such is White's construal). Now, some contemporary logical systems are combinatory logics, which do not concede any primacy to a particular kind of phrases singled out as statements or formulas, but on the contrary make any symbol whatever into a formula, so to speak. Some of those logics are paraconsistent, too. Those combinatory paraconsistent logics can hardly by open to Heidegger's objection, however grounded or ungrounded the latter may be when levelled against Aristotle. For one thing, they do not reduce language to a restricted class of symbols, statements. For another, they do not enforce the ruling out of any contradictory theory, and so their principle of noncontradiction -- if and when they in fact assert it -- can't be easily regarded as a hindrance. Of course that is not the end of the story (some of those logics recognize a strong negation, along with a natural one, enforcing (2) for such a strong negation; so, in a way they keep raising hindrances). Still, such new factors cannot easily be shrugged off as immaterial.
White sets off Heidegger's claims against Strawson's account of contradiction, as put forward in Introduction to Logical Theory. The reader is likely to be familiar with Strawson's remarks, so I'll be most brief, even cursory, in quoting them. Strawson thinks that contradicting oneself is like writing something down and then erasing it; a contradiction thus cancels itself and leaves nothing. All that White quotes and comments on. What he fails to mention or to discuss is what immediately follows upon the preceding remarks, namely that, even though quite often people say things which literally taken may be of the form «p and not p», they cannot mean what they say, or rather by uttering those sentences they are not «saying» (stating -- in the Strawsonian sense) the conjunction of two mutually contradictory sentences. There are lots of difficulties surrounding Strawson's position, difficulties White seems to be unaware of. For instance, if denying or negating is like erasing, one cannot understand why, in accordance to classical logic, to which Strawson cleaves, from a contradiction everything follows, whereas from an absence of premises only logical truths follow; moreover, it is not the case that negative sentences are uttered only when their affirmative counterparts had previously been advanced. Furthermore, if, as is apparently the case, Strawson wants to define a contradiction as a self-annulling message, a proof is then needed in order to show that contradictions, in that sense, have something to do with utterances of the form «p and not p». If, however, contradictions are defined to be utterances of that form, then new and further manoeuvres will be called for in order to deflect or diffuse the threat of contradictory statements. Strawson will end by distinguishing two senses of `contradiction', one syntactic, the other semantic. The price he has to pay is loss of general rules for getting at the semantic content from the syntactic form. Thus, Strawson's discussion of contradictory assertions turns out to reveal one of the weakest points of his approach to logic. And not only his. As a matter of fact, any logical system is either paraconsistent or else bound to doom as illogic lots of most usual, everyday utterances thereby finding most people guilty of commitment to every and any conclusion whatever (in virtue of the Scotus rule, which, as White reminds us is operative in classical logic -- or, for the matter, in any non-paraconsistent logic -- viz: p, not-p / q).
Now, what emerges from such debates does not coincide with what Heidegger is about, or after. Heidegger does not want to deny the principle of noncontradiction, i.e. to assert negations of instances of the principle, but more probably to uncover a field of non-propositional logos wherein the threat of contradiction does not arise and so noncontradiction cannot even be articulated. (And yet I cannot quite see how or why, then, the principle becomes a hindrance.) He looks for a domain beyond or beneath the reaches of logic, a domain obeying no (such) rule. So, the emancipation he seeks and sometimes announces is not the same as that which paraconsistent logics are able to facilitate. Those differences notwithstanding, there is something both enterprises -- the critical assessment, from a paraconsistent philosophy of logic, of accounts such as Strawson's and Heidegger's own proposal -- seem to share, viz. that some principles or rules of classical logic concerning contradiction lack absolutely universal validity.
Such a convergence,frail as it is, comes to the fore -- and may even become much stronger and deeper -- when the ontological status of negation -- or, if you want, the semantic content of `not' -- is gone into. White discusses Heidegger's views on that matter in chapter 2. Unfortunately I cannot allow myself the space I'd need in order to fairly comment on White's discussions, which I deem to be the best ones in the book. (I'd have appreciated a critical assessment of Carnap's and Stegmüller's objections against Heidegger's use of `nothing'.) In fact, Heidegger's quest for the ontological source or ground of the sentential negation is among his most brilliant -- if roaming -- inquiries. Granted, some of his arguments are lame, but they deserve to be strengthened and rescued, since he has pinpointed a most important fact, viz. that some real, existent determination is to be denoted, or meant, or whatever, by `not', such a determination being what nihilates, and accordingly something which both exists and suspectedly does also not exist. Heidegger is hopefully wrong about the frightful unsoundable depth of such a nihilating abyss -- in fact such a determination is, thank Goodness, no abyss, or anyway Heidegger has failed to convince the present reviewer that it is one. Nevertheless, without the nothing we'd be compelled to live in an Eleatic impossible world, as Plato's Sophist did show.
White's book is all in all a most commendable one. He's come to grips with appallingly difficult questions and has managed to make a lot of clever and relevant remarks about them. His comments are often critical, but never harsh or bigotic. His knowledge of Heidegger's works thorough. His scholarship level is high, while at the same time he writes clearly and often cogently. In fact I feel only a major objection is to be addressed to his book, its failing to take into account the philosophical significance of logics relevantly different from the classical one (i.e. Frege's, or Russell's), which could provide an entirely new setting for the discussion of Heidegger's contributions to the philosophy of logic.
Nevertheless, I also have another grumble to utter. White somehow blurs the discrepancies between the former and the latter Heideggerian philosophy. To myself he stresses too much Heidegger's idea that logic depends on time and history, lending it the implied suggestion that time and history would be the ultimate realities or something of that ilk. Yet, as I construe it, Heidegger's thought after the Kehre has -- even if in a rambling and stammering way -- more and more -- esp. in «Zeit und Sein» -- pointed to a more basic, genuinely ultimate ground of things, perhaps the «It» that gives Being to beings. Thus the ultimate grounding of logic would be provided by that sending of Being -- whether it be a self-sending or, as some of the last essays can plausibly be taken to imply, a gift, a donation. Although White does not fail to comment on some such aspects of the latter Heideggerian thought, his main emphasis is on the more allegedly anthropocentric views of Sein und Zeit.