Philosophical Accounts of First-Order Logical Truths

Abstract

Starting from certain metalogical results (the completeness theorem, the soundness theorem, and Lindenbaum-Scott theorem), I argue that first-order logical truths of classical logic are a priori and necessary. Afterwards, I formulate two arguments for the idea that first-order logical truths are also analytic, namely, I first argue that there is a conceptual connection between aprioricity, necessity, and analyticity, such that aprioricity together with necessity entails analyticity; then, I argue that the structure of natural deduction systems for FOL displays the analyticity of its truths. Consequently, each philosophical approach to these truths should account for this evidence, i.e., that first-order logical truths are a priori, necessary, and analytic, and it is my contention that the semantic account is a better candidate.

Logical Maximalism in the Empirical Sciences

“…SeePutnam (2012) for a captivating story of the philosophical development of quantum logic.19 In addition, there are also some general considerations which suggest that logic cannot be treated in the same manner in which the physical hypotheses are, although both of them are criticizable. For a philosophical discussion on the status of classical logic, viewed from a metalogical point of view, seeBrîncuş (2019).…”