From 2012 to 2014, I spent at LOGOS a Marie Curie Intra-European Research Fellowship on A Non-Contractive Theory of Naive Semantic Properties: Logical Developments and Metaphysical Foundations (NTNSP).
Here is a brief description of the research objectives of the project:
NTNSP has concerned the development of a theory of truth that solves the semantic paradoxes by preserving naive truth and by restricting classical logic. In particular, the theory developed has as distinguishing feature that of restricting the logical property of contraction, according to which, very roughly, the validity of an argument is not affected by the number of times that its premises are used in deriving the conclusion. NTNSP has shown that the restriction on contraction effectively blocks the semantic paradoxes. However, there are other well-known alternative ways of blocking the paradoxes by preserving naive truth and by restricting classical logic in such a way as to retain contraction, and so NTNSP’s general aim has been that of raising the non-contractive theory to the status of serious competitor in the debate among theories restricting classical logic.
This general aim has been achieved by meeting four research objectives in progressive order. The theory has first been provided with the necessary philosophical support grounded in a robust conception of truth as correspondence with the relevant facts. The theory has then been extended to a theory of naive reference, showing that it affords an innovative solution to the paradoxes of reference. The theory has subsequently been argued to enjoy substantial philosophical advantages over its rivals, in particular in its treatment of various conditionals (from one that allows for a definition of logical consequence in terms of truth preservation to one that allows for a smooth treatment of restricted generalisations). The theory has finally been given solid metaphysical foundations: failure of contraction has been explained in terms of a certain “instability” of the states-of-affairs expressed by paradoxical sentences, and the failure of the principle of distributivity has been justified in terms of an original, global conception of indeterminacy, which has been connected with previous work I have done on the paradoxes of vagueness.
Here is a partial list of the research papers stemming from the project (some are missing as they are still under review):
‘∀ and ω’, forthcoming in A. Torza (ed.), Quantifiers, Quantifiers and Quantifiers, Dordrecht, Reidel.
‘The Opacity of Truth’, forthcoming in Topoi.
‘Restriction by Non-Contraction’, forthcoming in Notre Dame Journal of Formal Logic.
‘The General Missing from the Hierarchy’, forthcoming in F. Bacchini, S. Caputo, M. Dell'Utri (eds), New Frontiers in Truth, Cambridge Scholars Publishing, Cambridge.
‘Evans Tolerated’, forthcoming in A. Abasnezhad, K. Akiba (eds), Vague Objects and Vague Identity, Springer, Dordrecht.
‘Breaking the Chains. Following-from and Transitivity’, forthcoming in C. Caret, O. Hjortland (eds), Foundations of Logical Consequence, Oxford University Press, Oxford.
‘Getting One for Two, or the Contractors’ Bad Deal. Towards a Unified Solution to the Semantic Paradoxes’, forthcoming in T. Achourioti, K. Fujimoto, H. Galinon, J. Martínez (eds), Unifying the Philosophy of Truth, Springer, Dordrecht.
‘First-Order Tolerant Logics', forthcoming in The Review of Symbolic Logic.
‘The Role of Utterances in Bradwardine's Theory of Truth', forthcoming in Recherches de théologie et philosophie médiévales.
2014, ‘Context and Consequence. An Intercontextual Substructural Logic’, Synthese 191, pp. 3473–3500.
2014, ‘Naive Truth and Naive Logical Properties', The Review of Symbolic Logic 7, pp. 351–384.
2013, ‘Naive Logical Properties and Structural Properties', The Journal of Philosophy 110, pp. 633–644.
2013, ‘It Is Not the Case that [P and ‘It Is Not the Case that P’ is true] nor Is It the Case that [P and ‘P’ Is Not True]’, Thought 1, pp. 309–319.
2012, ‘Truth Preservation in Context and in Its Place’, in C. Dutilh Novaes, O. Hjortland (eds), Insolubles and Consequences. Essays in Honour of Stephen Read, College Publications, London, pp. 249–271.