It is a commonplace in recent metaphysics that one’s logical commitments go hand in hand with one’s metaphysics. Brouwer, Heyting and Dummett have each championed the move to constructive (intuitionistic) reasoning on the grounds of anti-realism. I hope to break this close connection, to explain why a realist ought to reason constructively.

The task of the philosopher is neither to belittle truth nor to exalt it, neither to deny it nor to defend it, but to explain why we need the concept and what it is to possess it. (Dummett, 2004, p. 116)

We present a new method for deciding Gödel-Dummett logic. Starting from a formula, it proceeds in three steps. First build a conditional graph based on the decomposition tree of the formula. Then try to remove some cycles in this graph by instantiating these boolean conditions. In case this is possible, extract a countermodel from such an instance graph. Otherwise the initial formula is provabl...

Gödel-Dummett logic LC and its finite approximations LCn are the intermediate logics complete w.r.t. linearly ordered Kripke models. In this paper, we use LCn logics as a tool to bound resource consumption in some process calculi. We introduce a non-deterministic process calculus where the consumption of a particular resource denoted • is explicit and provide an operational semantics which meas...

We propose a typed lambda calculus based on Avron’s hypersequent calculus for Gödel–Dummett logic. This calculus turns out to model waitfree computation. Besides strong normalization and nonabortfullness, we give soundness and completeness of the calculus against the typed version of waitfree protocols. The calculus is not only proof theoretically interesting, but also valuable as a basis for d...

Dummett, M. 1991. Logical Basis of Metaphysics. London: Duckworth. Gentzen, G. 1969. Untersuchungen über das logische Schliessen. In The Collected Papers of Gerhard Gentzen, tr. M. Szabo, 68–131. Amsterdam: North-Holland. Prawitz, D. 1977. Meaning and proofs: on the conflict between intuitionistic and classical logic. Theoria. 43: 2–40. Prior, A. 1960–61. The Runabout inference ticket. Analysis...

Axiomatization of Gödel-Dummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of non-prenexable formulas are given for those logics where some prenex operation is not available. Inter-expressibility of quantifiers is explored for each of ...