Logical consequence and paradoxical reasoning

• Applicant: Dr. Luca Tranchini
• Subject Area: Theoretical Philosophy ; Mathematics
• Term: from 2015 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 289086941

The traditional analysis of the relation of logical consequence due to Alfred Tarski explains consequence in terms of truth. A more recent rival view developed by Dag Prawitz aims at replacing the notion of truth with the one of proof. What is common to both approaches is the characterization of consequence as `transmission': B is a logical consequence of A if and only if truth (resp. provability) is transmitted from A to B.The project develops an alternative conception of consequence, which rejects the ``transmission view''. This is achieved by grounding consequence on local features of inference rules, rather than on global properties of deduction.The local character of consequence offers the possibility to distinguish, among the proofs whose steps are all locally correct, those that are also globally valid from those that are not. The gap between local correctness and global validity provides an original account of how each step in a paradoxical argument may be sound, without the conclusion of the whole argument being acceptable.

• DFG Programme: Research Grants