# Logic and Modern Philosophy of Mathematics

## Concluding Remark

Whately would be astonished at the current range and variety of logics. However, there is often still a considerable professional distance between logicians and both mathematicians and philosophers; in the mid-1930s an Association of Symbolic Logic was created to provide a venue and a journal for those active in the field. Now perhaps too many logical and philosophical flowers are blooming, and many may wither for want of genuine need. One area of exploration is metametalogic and metametaphilosophy of mathematics, which have been largely ignored so far.

## BIBLIOGRAPHY

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.

*I.* *Grattan-Guinness*

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