Logic and Modern Philosophy of Mathematics

Abramsky, S., Dov Gabbay, and T. S. E. Maibaum, eds. Handbook of Logic in Computer Science. 5 vols. Oxford and New York: Oxford University Press, 1992–2000.

Aspray, William, and Philip Kitcher, eds. History and Philosophy of Modern Mathematics. Minneapolis: University of Minnesota Press, 1988.

Barwise, Jon, ed. Handbook of Mathematical Logic. Amsterdam and New York: North-Holland, 1977.

Benacerraf, Paul, and Hilary Putnam, eds. Philosophy of Mathematics: Selected Readings. 2nd. ed., Cambridge, U.K., and New York: Cambridge University Press, 1983.

Fraenkel, Abraham. Abstract Set Theory. Amsterdam: North-Holland, 1953. Outstanding bibliography.

Gabbay, Dov, and F. Guenthner, eds . Handbook of Philosophical Logic. 1st ed. 4 vols. Dordrecht and Boston: Reidel, 1983–1987. 2nd ed., much expanded, in progress. Dordrecht: Kluwer, 2000–.

Grattan-Guinness, Ivor. The Search for Mathematical Roots, 1870–1940: Logics, Set Theories, and the Foundations of Mathematics from Cantor through Russell to Gödel. Princeton: Princeton University Press, 2000.

Grattan-Guinness, Ivor, ed. Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. 2 vols. London: Routledge, 1994. Reprint, Baltimore: Johns Hopkins University Press, 2003. See especially Part 6.

Haack, Susan. Philosophy of Logics. Cambridge, U.K.: Cambridge University Press, 1978.

Jacquette, Dale, ed. Philosophy of Mathematics: An Anthology. Oxford and Malden, Mass.: Blackwell, 2002.

Kitcher, Philip. The Nature of Mathematical Knowledge. New York: Oxford University Press, 1983.

Kneale, William, and Martha Kneale. The Development of Logic. Oxford: Clarendon, 1962.

Krüger, Lorenz et al., eds. The Probabilistic Revolution. 2 vols. Cambridge, Mass.: MIT Press, 1987.

Priest, Graham. Beyond the Limits of Thought. Cambridge, U.K.: Cambridge University Press, 1995.

Shapiro, Stewart, ed. The Limits of Logic. Aldershot, U.K.: Dartmouth, 1996. Source book, mainly oriented around model theory and higher-order logics.

van Heijenoort, Jean, ed. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Cambridge, Mass.: Harvard University Press, 1967.