The Logics of Truth
Final Report Abstract
The aim of the project was to analyze how non-classical - and, especially, substructural - logics can provide a useful framework for the solution of the semantic paradoxes. Substructural approaches to semantic paradoxes were considered promising but fairly unexplored at the beginning of the project. The main sub-goal of this project was to develop some of these theories and their motivations, and to provide an answer for some of the open questions in the field. We have made great progress in answering the following questions: ● What is the precise sense in which operational and substructural approaches weaken classical logic? ● In what sense the cut-free approaches are classical and in what sense they are not? ● Is it possible to provide plausible philosophical interpretations of non-contractive consequence relations and, in particular, is this alternative is a plausible reading of the quantifiers? ● To what extent substructural proposals are revenge-free and what are the prospects of achieving such a goal? ● Can the problem of restricted quantification be satisfactorily dealt with paracomplete and paraconsistent theories? ● How should theory-choice in logic work, in particular when considering formal theories of truth? The main results we have obtained can be put into the following four large categories: (1) Substructural logics and the validity paradox (2) Non-contractive approaches (3) Recovering classical logic in non-classical frameworks (4) The role of metainferences in defining logics.
Publications
- (2019) Disagreement about logic. Inquiry 2019 1-23
Hjortland, Ole Thomassen
(See online at https://doi.org/10.1080/0020174X.2019.1651084) - (2020) Alethic Reference. J Philos Logic (Journal of Philosophical Logic) 49 (3) 417–438
Picollo, Lavinia
(See online at https://doi.org/10.1007/s10992-019-09524-w) - (2017) “Anti-Exceptionalism About Logic”, Philosophical Studies 174(3): 631-658
Ole Thomassen Hjortland
(See online at https://doi.org/10.1007/s11098-016-0701-8) - (2017) “Disquotation and Infinite Conjunctions”, Erkenntnis 83: 899–928
Lavinia Picollo & Thomas Schindler
(See online at https://doi.org/10.1007/s10670-017-9919-x) - (2017) “Naive Validity, Internalization, and Substructural Approaches to Paradox”, Ergo 4(4): 93-120
Lucas Rosenblatt
(See online at https://doi.org/10.3998/ergo.12405314.0004.004) - (2018) “A recovery operator for non-transitive approaches”, Review of Symbolic Logic
Eduardo Barrio, Federico Pailos & Damián Szmuc
(See online at https://doi.org/10.1017/S1755020318000369) - (2018) “Contraction, Infinitary Quantifiers, and Omega Paradoxes”, Journal of Philosophical Logic, 47(4): 611-629
Lucas Rosenblatt & Bruno Da Ré
(See online at https://doi.org/10.1007/s10992-017-9441-2) - (2018) “Inferentialism, structure, and conservativeness”, in From Rules to Meaning: New Essays on Inferentialism, eds. Ondrej Beran, Vojtech Kolman,Ladislav Koren. Routledge, London
Ole Thomassen Hjortland
(See online at https://doi.org/10.4324/9781315103587-6) - (2019) “Substructural logics, pluralism and collapse”, Synthese
Eduardo Barrio, Federico Pailos & Damián Szmuc
(See online at https://doi.org/10.1007/s11229-018-01963-3)
