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IS THERE A COUNTABLE OMEGA-UNIVERSAL LOGIC?

Published online by Cambridge University Press:  10 March 2025

ALEXANDER C. PASEAU*
Affiliation:
FACULTY OF PHILOSOPHY UNIVERSITY OF OXFORD OXFORD, UK
FELIX WEITKÄMPER
Affiliation:
INSTITUT FÜR INFORMATIK LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN MUNICH, GERMANY E-mail: [email protected]

Abstract

Some informal arguments are valid, others are invalid. A core application of logic is to tell us which is which by capturing these validity facts. Philosophers and logicians have explored how well a host of logics carry out this role, familiar examples being propositional, first-order and second-order logic. Since natural language and standard logics are countable, a natural question arises: is there a countable logic guaranteed to capture the validity patterns of any language fragment? That is, is there a countable omega-universal logic? Our article philosophically motivates this question, makes it precise, and then answers it. It is a self-contained, concise sequel to ‘Capturing Consequence’ by A.C. Paseau (RSL vol. 12, 2019).

MSC classification

Type
Research Article
Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

BIBLIOGRAPHY

Harzheim, E. (2005). Ordered Sets. New York: Springer.Google Scholar
Paseau, A. C. (2019). Capturing consequence. The Review of Symbolic Logic, 12, 271295.Google Scholar
Paseau, A. C. (2021), Propositionalism. The Journal of Philosophy, 118, 430449.Google Scholar