Heidegger and the philosophy of logic

Heidegger's discussion of logic from the Being and Time-era contains an account of the nature of intelligibility that is relevant to contemporary mathematical logic as a plausible account of its scope and foundations. Intelligibility is commonly viewed as fundamentally a feature of discursive thought. Heidegger argues rather that the normativity of discursive thought derives from and articulates the intelligibility of the world itself conceived as a range of structured possibilities, such that a system of logic describes a part of the world. The normative constraints on discursive thought are founded on an original and implicit familiarity with the possibilities of the world, what Heidegger calls an understanding of Being. Heidegger's account of logic is thus part of his principal philosophical project: articulating the concept of Being. The tasks of this essay are thus to draw together the main themes of Heidegger's thoughts on logic, to show that they have a central place in his philosophical project, and to show that they are relevant to contemporary philosophy of logic.;Heidegger explicitly offers a critique of traditional logic---an account of the Aristotelian syllogism combined with Kantian arguments for the ideality of logic. Since mathematical logic supplanted Aristotelian logic a century ago, Heidegger's discussion might seem anachronistic. But although mathematical logic exhibits greater expressive power due to a more sophisticated conception of logical form, it presupposes the same normative constraints that Aristotelian logic presupposes, such that both articulate the inferential structure of the world. Since Heidegger claims to have clarified the foundations of normativity, he would claim to have clarified the foundations for any system of logic, including mathematical logic.;Comparing Heidegger's account of truth to Tarski's semantic definition of truth as satisfaction illustrates these claims. Heidegger argues that truth is not fundamentally correspondence between assertion and object, but the uncovering of objects that makes correspondence possible. Tarski offers a correspondence theory of truth, and Heidegger would argue that satisfaction constitutes a formal schema for uncovering, and so presupposes an understanding of Being. Heidegger would thus claim to offer an account of the foundations of formal semantics as Tarski sees it.