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Area: Philosophy of Mathematics

| Maddy |

Maddy, P.

Maddy,# P. (1992). Indispensability and Practice. Journal of Philosophy 89 (6):275-289

Kw: Logic; mathematics; physics; set theory

This paper examines the efficacy of the familiar indispensability arguments for the existence of mathematical entities. It suggests that these arguments rest on inaccurate portrayals of scientific and mathematical practice.

Maddy,# P. (1991). Philosophy of Mathematics: Prospects for the 1990s. Synthese 88 (2): 155- 164.

Kw: set theory; Benacerraf's epistemological challenge

For some time now, academic philosophers of mathematics have concentrated on intramural debates, the most conspicuous of which has centered on Benacerraf's epistemological challenge. By the late 1980s, something of a consensus had developed on how best to respond to this challenge. But answering Benacerraf leaves untouched the more advanced epistemological question of how the axioms are justified, a question that bears on actual practice in the foundations of set theory. I suggest that the time is ripe for philosophers of mathematics to turn outward, to take on a problem of real importance for mathematics itself.