“Curry’s Revenge: the costs of non-classical solutions to the paradoxes of self-reference,” in The Revenge of the Liar, ed. JC Beall, Oxford University Press, pages 262–271, 2008.
I point out that non-classical “solutions” the paradoxes of self-reference are non-particularly easy to give. Curry’s paradox is very very hard to avoid, if you wish to give a semantically cohrerent picture.
Comments
Hi Greg
Very nice paper, but I disagree with its main conclusion.
Adopting linear logic you can obtain a cost-free solution to these paradox - at least, free of all the costs listed in your paper. You wouldn’t be forced to reject large disjunctions, or transitivity of entailment, or the “strong laws”, or - contrary to appearances - distribution, for multiplicative conjunction distributes over additive disjunction.
Claiming that non-classical solutions to the paradoxes of self-reference compel you to give up distribution - or other equally desirable principles - is like claiming that a rebuttal of Lewis’s independent proof compels you to give up either addition or the disjunctive syllogism. Actually, you may keep them both, provided you acknowledge that they hold of different connectives.
Posted by: francesco paoli at November 21, 2006 07:55 PM
Hi Greg
Very nice paper, but I disagree with its main conclusion. Adopting linear logic you can obtain a cost-free solution to these paradox - at least, free of all the costs listed in your paper. You wouldn’t be forced to reject large disjunctions, or transitivity of entailment, or the “strong laws”, or - contrary to appearances - distribution, for multiplicative conjunction distributes over additive disjunction. Claiming that non-classical solutions to the paradoxes of self-reference compel you to give up distribution - or other equally desirable principles - is like claiming that a rebuttal of Lewis’s independent proof compels you to give up either addition or the disjunctive syllogism. Actually, you may keep them both, provided you acknowledge that they hold of different connectives.
Posted by: francesco paoli at November 21, 2006 07:55 PM