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.

[1]  W. Quine,et al.  Philosophy of mathematics: Truth by convention , 1984 .

[2]  R. Carnap.  Logical Syntax of Language , 1937 .

[3]  Penelope Maddy,et al.  Defending the Axioms , 2011 .

[4]  F. Gregory.  Scientific Materialism in Nineteenth Century Germany , 1977 .

[5]  Anthony Kenny,et al.  The Philosophical Writings of Descartes: Volume 3, The Correspondence , 1991 .

[6]  T. Burge.  Frege on Knowing the Foundation , 1998 .

[7]  Tyler Burge,et al.  Frege on Knowing the Third Realm , 1992 .

[8]  Kevin C. Klement.  THE FUNCTIONS OF RUSSELL’S NO CLASS THEORY , 2010, The Review of Symbolic Logic.

[9]  J. Mill.  A System of Logic , 1843 .

[10]  D. Stern.  The Methods of the Tractatus:: Beyond Positivism and Metaphysics? , 2003 .

[11]  Gottlob Frege,et al.  The Frege Reader , 1997 .

[12]  R. Carnap.  Empiricism, semantics and ontology , 1984 .

[13]  P. Gibbins.  Particles and paradoxes , 1987 .

[14]  H. Hahn.  Logic, Mathematics, and Knowledge of Nature , 1987 .

[15]  W. Quine,et al.  Carnap and logical truth , 2004, Synthese.

[16]  R. Jeffrey,et al.  The Philosophy of Rudolf Carnap , 1966 .

[17]  Hilary Putnam,et al.  Mathematics, Matter and Method: Philosophical Papers , 1979 .

[18]  R. L. Anderson,et al.  Neo-Kantianism and the Roots of Anti-Psychologism , 2005 .

[19]  A. J. Ayer,et al.  Language, Truth, and Logic , 1936 .

[20]  Reginald Jackson.  An examination of the deductive logic of John Stuart Mill , 1941 .

[21]  B. Russell,et al.  Introduction to Mathematical Philosophy , 1920, The Mathematical Gazette.

[22]  Rolf George,et al.  Theory of Science , 1973 .

[23]  Willard Van Orman Quine,et al.  From a Logical Point of View , 1955 .

[24]  L. Wittgenstein.  Tractatus Logico-Philosophicus , 2021, Nordic Wittgenstein Review.

[25]  R. Descartes,et al.  The Philosophical Writings of Descartes: Index , 1985 .

[26]  George Boole,et al.  The Laws of Thought , 2003 .

[27]  C. Wuthrich.  Philosophical Foundations of Quantum Mechanics , 2009 .

[28]  Arthur Bowes Frizell,et al.  Foundations of Arithmetic , 2012 .

[29]  T. Burge.  Truth, thought, reason , 2005 .