Friday, August 29, 2014

Why is Hegel not a Dialetheist? A Reply to Graham Priest

Paraconsistent logic rejects the necessity of the principle of explosion, that renders all inferences from contradictory antecedents trivially true (i.e. ex falso quodlibet), and conversely affirms that there may be some non-trivially true inconsistent inferences. Dialetheism further affirms that there are some true contradictions, or true paradoxes (e.g. Zeno's paradoxes of motion).  Hegelian dialectics, to the contrary, does not reject the principle of explosion (i.e. ex falso quodlibet), but rather affirms that some contradictions are merely apparent contradictions, which may be resolved into a concept that preserves the difference of the contrary elements within the identity of the concept, as the self-identity of its differences.  The principle of explosion is not rejected by Hegel because his primary concern is, not the Philolian conditional of fixed propositions, but rather the concrete universal of speculative reason that subsumes within its self-identity the differentia of particular concepts.  The bearer of truth for Dialetheism is the true paradox of contradictory propositions, while the bearer of truth for Hegelian dialectics is the identity of difference of the concept.  The contrariness of the true paradox is the contradiction of the propositions, while the contrariness of the concept is the difference of the subordinate concepts nested within the self-identity of the superior concept.  Concepts are, for Hegel, not strictly contradictory because contradictions only obtain between propositions that affirm and deny one and the same thing in the same way.  Concepts are not reducible to propositions and thus do not affirm or deny one and the same thing in the same way because they are neither bivalent (i.e. either true or false) nor extrinsically referential (i.e. referring to some fact beyond themselves). Rather, concepts refer only to themselves and may be considered true only according to their own self-determined essence and purpose.  Since concepts are not contradictory, the contrariness of concepts cannot result in a contradiction that is true, or a true paradox. Thus, since the Hegelian dialectic of concepts cannot be contradictory, but merely the identity of differentia in the unity of opposites, Hegelian dialectic is essentially irreducible to the Dialetheist logic of true paradoxes.

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