Séance commune. PhilMath et Logiques Non Classiques
Guido Bacciagaluppi (University of Aberdeen)
Quantum Logic meets Logical Pluralism
In a classic paper, Putnam suggested that we have good empirical reasons for adopting a (non-distributive) quantum logic as the 'true logic', and that the classical logical connectives are the quantum loigical connectives 'in disguise'. While very few believe that this move would solve the paradoxes of quantum mechanics, Putnam's paper is still interesting for the debate on logical monism vs pluralism. Recently, this debate has been steered in a new direction by J.C. Beall and Greg Restall, whose logical pluralism is a pluralism about logical validity. Thus for instance they take the difference between classical and intuitionist logic to lie not in the meaning of the logical connectives, but in the different standards of proof (in their formal apparatus, different 'precisifications of cases' in the 'generalised Tarski thesis'). Both approaches share the feature that in different logics the meaning of the connectives is the same, but this is cashed out by Putnam in terms of monism (and revisionism), by Beall and Restall in terms of pluralism. This talk will provide a viable formal apparatus for Putnam's claim (comparable to Beall and Restall's) and suggest that both Putnam and Beall and Restall could be read in either monist or pluralist terms.