Frege's role in the history of logic

Abstract

While Kant's claim has been discredited — namely that logic had, by his time, neither progressed nor regressed ever since Aristotle — both the exact reason while he was wrong and the partial core of truth his assertion contained ought to be elucidated. Aristotle's was a logic of terms that ignored the calculus of statements, cultivated instead by the Stoic logicians and later Scholastics. However a unified — yet unsuccessful — logical account of terms and propositions was attempted by Leibniz. It was an anticipation of modern combinatory logic. Leibniz's successors took over his reduction of logic to a certain mathematical calculus. Boole asserted that all logical truths were algebraic equations. Nevertheless, existential statements showed themselves unamenable to his approach. It was Frege who really made a giant step forward by resorting to variables and inventing the quantifier, thanks to his theory of objects and functions. Thus, Aristotle's logic was at last somehaw overcome. Not quite, though, since both Aristotle's and Frege's accounts share common assumptions, which have been put to rest by nonclassical logics such as combinatory and many-valued logics.