A Completeness heorem for Unrestricted First-Order Languages
Agustín Rayo, Timothy L. Williamson · 2004
Abstract Here is an account of logical consequence inspired by Botzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The Logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents, and the syntactic differences between their non-logical constituents, treated as variables. A constituent of a sentence is logical just if it is formal in meaning, in the sense roughly that its application is invariant under permutations of individuals.