Logic and mathematics

Jan Woleński

pp. 69-89

in: Joseph Agassi, Ludwig Wittgenstein's philosophical investigations, Berlin, Springer, 2018

Abstract

It is Frege, not Boole, who is the father of modern logic. What exactly is modern about modern logic? Why did Frege develop it? The answers given here are these. Modern logic is both comprehensive and fully formal. The comprehensiveness in question is the sufficiency for the purposes of mathematics. (Other kinds of comprehensiveness are possible.) Fully formal systems are such that computers can use them. The idea of a fully formal language is Frege's; he offered fully formal inferences. Russell was the first to offer a formal language proper. These days, when computers are parts of everyday life, developing a formal system is hardly a challenge. At the time, Russell noted, only two formal systems were available, his and that of Wittgenstein. Most significantly, it was Frege who rendered logic unmistakably the logic of statements; analysis of concepts thus turned into (post-Wittgenstein) analysis of statements. (Regrettably, on this too many analytic philosophers are not au courant.)