Joan Weiner, Taking Frege at His Word, Oxford University Press 2020, xxvii + 317 pp.
In 1936 Edmund Husserl wrote in a private letter to Heinrich Scholz, the collector of Frege’s writings, that he had never met Frege in person and that Frege was considered at the time “a sharply intelligent outsider who bore fruit neither as a mathematician nor as a philosopher.” That was, of course, a misjudgment. We can see now more clearly that Frege contributed, in fact, at least three things to mathematics and philosophy after him. The first was his new logic (the propositional and predicate calculus) that replaced the old Aristotelian logic. Given the important role that the Aristotelian syllogistic had played in philosophy for more than two thousand years that was, indeed, a significant achievement. The second was Frege’s attempt to show that arithmetic can be reduced to logic. Frege’s logicist thesis has not remained uncontested and his way of trying to prove it has turned out to be defective, but the considerations that led him to it are still being taken seriously by philosophers of mathematics. The third are his thoughts about signs – the symbols and formulas of his logical calculus and the words and sentences of ordinary language – and the way they serve to convey meaning. These “semantic” considerations have contributed much to the subsequent development of the philosophy of language.