Which Logic for the Radical Anti-realist?
Since the ground-breaking contributions of M. Dummett (Truth and Other Enigmas. Duchworth, London, 1978), it is widely recognized that anti-realist principles have a critical impact on the choice of logic. Dummett argued that classical logic does not satisfy the requirements of such principles but that intuitionistic logic does. Some philosophers have adopted a more radical stance and argued for a more important departure from classical logic on the basis of similar intuitions. In particular, Dubucs (Synthese. 132:213–237, 2002) and Dubucs and Marion (Philosophical Dimensions of Logic and Science. Kluwer, Dordrecht, 2003) have recently argued that a proper understanding of anti-realism should lead us to the so-called substructural logics (see Restall (An Introduction to Substructural Logics. Routledge, London, 2000)) and especially linear logic. The aim of this paper is to scrutinize this proposal. We will raise two kinds of issues for the radical anti-realist. First, we will stress the fact that it is hard to live without structural rules. Second, we will argue that, from an anti-realist perspective, there is currently no satisfactory justification to the shift to substructural logics.
We thank the audience of the colloquium (Anti-)Realisms: Logic & Metaphysics held in Nancy (July 2006), and especially J. Dubucs, M. Marion and G. Restall. We also wish to thank an anonymous referee for further thoughtful comments. The first author acknowledges support from ESF (the Eurocores LogICCC program).
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