The most important logician of the first half of the nineteenth century was Bernard Bolzano (1781–1848). His views are closest to those of Leibniz, who preceded him by more than a century (Bolzano was sometimes called the Bohemian Leibniz). Although he quoted often and extensively from philosophers and logicians of his own generation and the preceding one, among them Kant, Salomon Maimon, Hegel, J. F. Fries, J. G. E. Maass, and K. L. Reinhold, he did this almost always in order to criticize them, and rightly so from our modern point of view, because orders of magnitude separate Bolzano as a logician from his contemporaries.

One may doubt whether he deserves to be called a forerunner of mathematical logic and modern semantics. His approach is in many respects rather crude and old-fashioned in comparison with those of George Boole and Gottlob Frege, one and two generations later, respectively. But...