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A Non-Contractive Theory of Naive Semantic Properties: Logical Developments and Metaphysical Foundations (NTNSP)
Start date: Sep 1, 2012, End date: Aug 31, 2014 PROJECT  FINISHED 

"NTNSP concerns the logical developments and metaphysical foundations of a theory of naive truth (i.e. a theory validating the unrestricted equivalence between ‘P’ and ‘ ‘P’ is true’) which blocks the semantic paradoxes by restricting the structural rule of contraction. NTNSP’s main aim is to raise such theory to the status of a serious competitor in the debate among naive theories. This will be achieved by meeting four research objectives in progressive order. The theory will first be provided with the necessary technical framework (in particular an algebraic semantics and consistency proof). The theory will then be extended to a theory of naive reference, showing that it affords an innovative solution to the paradoxes of reference. The theory will subsequently be argued to enjoy substantial philosophical advantages over its naive rivals, in particular in its treatment of various conditionals (from one that allows for a definition of logical consequence in terms of naive-truth preservation to one that allows for a smooth treatment of restricted quantification). Finally, the theory will be given solid metaphysical foundations: failure of contraction will be explained in terms of the instability of the states-of-affairs expressed by paradoxical sentences, and failure of distributivity will be justified in terms of an original, global conception of indeterminacy. NTNSP will be carried out in the highly congenial collaborative research environment offered by LOGOS, involving the organisation of a regular research seminar and a final international workshop. NTNSP aims at the publication of papers on all the issues mentioned, plus the preparation of a monograph and of the workshop’s proceedings. NTNSP will consolidate the applicant’s expertise in philosophy of logic, language and metaphysics (and mathematical logic), as well as improving several of his research and communication skills, thus allowing him to reach a higher level of research autonomy and leadership."
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