Which Logic for the Radical Anti-Realist ?

Denis Bonnay
Université Paris Nanterre
Mikael Cozic
Université Paris-Est Créteil
Since the ground-breaking contributions of M. Dummett (Dummett 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, J. Dubucs and M. Marion (?) and (Dubucs 2002) have recently argued that a proper understanding of anti-realism should lead us to the so-called substructural logics (see (Restall 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 justi cation to the shift to substructural logics
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