Is there a countable omega-universal logic?

Journal article

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).

Authors: Paseau, AC; Weitkämper, F

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Cambridge University Press
• Journal: Review of Symbolic Logic
• Volume: 18
• Issue: 3
• Pages: 963-970
• Publication date: 2025-03-10
• Acceptance date: 2025-02-08
• DOI: 10.1017/S1755020325000048
• EISSN: 1755-0211
• ISSN: 1755-0203
• Language: English
• Keywords: applications of logic; formalization; universal logic; abstract logic; conservative translation; consequence isomorphism