On the Adequacy of a Substructural Logic for Mathematics and Science

Bibliographic Data

ID4792595
AuthorsNeil Tennant (0000-0002-3523-2296, The Ohio State University, corresponding author)
Year2022
Volume72
Issue4
Pages1002-1018
Publication date2022-09-08
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueThe Philosophical Quarterly (JOURNAL)
Journal identifiersISSN: 0031-8094 • E-ISSN: 1467-9213
PublisherOxford University Press (PUBLISHER • GB)
DOI10.1093/pq/pqac001
OpenAlexW4205226904
LanguageEN
Citations received2
References cited13

Williamson argues for the contention that substructural logics are 'ill-suited to acting as background logics for science'. That contention, if true, would be very important, but it is refutable, given what is already known about certain substructural logics. Classical Core Logic is a substructural logic, for it eschews the structural rules of Thinning and Cut and has Reflexivity as its only structural rule. Yet it suffices for classical mathematics, and it furnishes all the proofs and disproofs one needs for the hypothetico-deductive method in science. We explain exactly what Classical Core Logic is, why it is a substructural logic par excellence, and what the basic requirements would be for a logic to be 'suited to acting as [a] background logic for science'. We also explain how Classical Core Logic meets all these requirements. We end by examining Williamson's argument in order to expose where its error lies

Argument (complex analysis) · Classical logic · Computational logic · Description logic · Discrete mathematics · Dynamic logic (digital electronics) · Epistemology · Higher-order logic · Intermediate logic · Many-valued logic · Philosophy of logic · Programming language · Substructural logic · Artificial Intelligence · Computer Science · Mathematics · Philosophy · Philosophy and History of Science · Quantum Mechanics and Applications

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