The philosophy of logic

what exactly are these logical This essay is the text of a retiring presidential address to the Association for Symbolic Logic. For a number of historical and sociological reasons, the largely mathematical membership of the Association is aware of the three great schools in the philosophy of mathematics at the turn of the 20th century—Platonism, Formalism, and Intuitionism—but unfamiliar with any school of thought in the philosophy of logic. This address was an effort to introduce the range of philosophical views about logic by rough analogy with the big three about mathematics. Along the way, it sketches the positions of Kant, the 19th-century German scientific materialists, Frege, Mill, early Wittgenstein, Carnap, Ayer, Quine, and Putnam, with gestures toward Descartes, Bolzano, and Russell, and ends with a second-philosophical alternative.