The world, the facts, and primary logic

Abstract

Frege gave priority to propositional logic over term or predicate logics analyzing categorical forms like ‘every A is B’ and ‘some A is B’ in terms of compound forms like ‘Ax→Bx’ and ‘Ax & Bx’ Leibniz hoped to do the reverse by treating ‘p→q’ and ‘p & q’ as categoricals of form ‘every {P} is a {q} and ‘some {P} is a {q} More generally he believed it possible to reduce all compound forms to categoricals using the old term connectives ‘A’, ‘E’, ‘I’, ‘O’. The paper shows how Leibniz’s program of treating propositions as terms and truth functions as term connectives can be realized. Where ordinary nonvacuous terms denote things in the world and signify their characteristics (e.g., ‘wise’ denotes wise things and signifies wisdom or being wise) propositional terms denote the world itself, signifying facts (e.g., ‘There are elks’ signifies the existence of elks and denotes the world characterized by their presence). False propositions are vacuous. Because all true propositions denote one and the same world (though signifying different world characteristics) ‘some {p} is {q} ’ (the categorical form of 'p & q’ will entail ‘every {p} is {q} ’ (p→ q). The paper shows that this approach regards existence and nonexistence as world properties (facts). © 1993, Duke University Press. All Rights Reserved.