Monday, December 17, 2012

Epistemology and Logic (Part Three): On the Derivation of Propadeutic Logic

    
Logic is at once self-reflexive art and it is propadeutic to science. It is self-reflexive art because the direction which this art gives is meta-direction --that is, logic is the art of the direction of that which directs all arts (including logic). If meta-direction accounts for the manner in which logic relates to all possible art, then its relation to all possible science is accounted for by its being a propadeutic. It is a propadeutic because it is reason's knowledge of itself, but only at the level of an art and not yet a science, since, for Aristotle, the causes of reason lie outside of reasoning, in the matter (τὸ ὄν)  being reasoned about.
        This double orientation of logic gives it, as an art, a twofold uniqueness. Because logic is meta-directively oriented toward art, the formulation of its rules happens in the same medium as does the appropriation of that unarticulated domain (from out of which  those rules are derived), namely rational speech, λόγος. No other art can be acquired from out of the same domain as its rules can be expressed. On other hand, because of its orientation to science, namely, as a propadeutic, logic is the only art that is supposed to expressly offer its rules as a part of its art; it passes on a set of criteria by which the sciences can secure the correctness of their inquiry. But this security that logic as a propadeutic is supposed to offer, raises questions about the security required by logic itself. The rules for the metadirection of logic must themselves be derived correctly. But how is this to be accomplished? It would seem prima facie that one would need an infinite set of rule books for the derivation of rules. And of course this, as a reductio ad infinitum, reduces to the logically absurd. And yet for all these meddlesome considerations, logic gets underway and establishes itself through the truth of its practice. We could ask, in good Kantian fashion: granted that logic actually establishes itself, how is this achievement possible? Not only can we ask this question; we must ask it, if, that is, logic is properly characterized as a propadeutic to scientific endeavor. What causes the apparent problem of logical derivation? In coming to a reductio ad infinitum we might consider that our own rule-oriented approach has been misguided from the outset, as it were. It may even be that this misguidance is not to be understood only as an error, but also as a clue --a pitfall that may yet harbor the possbility of truth on the matter its seems to deviate from. But however the case, everything depends on this (and here we echo Hegel's words from part one of these posts): that we recognize the impossibility and even undesirability of establishing yet another meta-direction to avoid initial misdirection.

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