Penelope Maddy (born 4 July 1950 in Tulsa, Oklahoma) is a UCI Distinguished Professor of Logic and Philosophy of Science and of Mathematics at the University of California, Irvine. She is well known for her influential work in the philosophy of mathematics, where she has worked on realism and naturalism.
Maddy received her Ph.D. from Princeton University in 1979. Her early work, culminating in Realism in Mathematics, defended Kurt Gödel's position that mathematics is a true description of a mind-independent realm that we can access through our intuition. However, she suggested that some mathematical entities are in fact concrete, unlike, notably, Gödel, who assumed all mathematical objects are abstract. She suggested that sets can be causally efficacious, and in fact share all the causal and spatiotemporal properties of their elements. Thus, when I see the three cups on the table in front of me, I also see the set as well. She used contemporary work in cognitive science and psychology to support this position, pointing out that just as at a certain age we begin to see objects rather than mere sense perceptions, there is also a certain age at which we begin to see sets rather than just objects.
In the 1990s, she moved away from this position, towards a position described in Naturalism in Mathematics. Her "naturalist" position, like Quine's, suggests that since science is our most successful project so far for knowing about the world, philosophers should adopt the methods of science in their own discipline, and especially when discussing science. As Maddy stated in an interview, "If you’re a ‘naturalist’, you think that science shouldn’t be held to extra-scientific standards, that it doesn’t require extra-scientific ratification." However, rather than a unified picture of the sciences like Quine's, she has a picture on which mathematics is separate. This way, mathematics is neither supported nor undermined by the needs and goals of science, but is allowed to obey its own criteria. This means that traditional metaphysical and epistemological concerns of the philosophy of mathematics are misplaced. Like Wittgenstein, she suggests that many of these puzzles arise merely because of the application of language outside its proper domain of significance.
- Defending the Axioms, Oxford University Press, 2011. ISBN 0-19-959618-2
- Second Philosophy, Oxford University Press, 2007. ISBN 0-19-927366-9
- Naturalism in Mathematics, Oxford University Press, 1997. ISBN 0-19-825075-4
- Realism in Mathematics, Oxford University Press, 1990. ISBN 0-19-824035-X
- Maddy, Penelope (Jun 1988). "Believing the Axioms, I". Journal of Symbolic Logic. 53 (2): 481–511. doi:10.2307/2274520. (a copy with corrections is available at the author's web page)
- Maddy, Penelope (Sep 1988). "Believing the Axioms, II". Journal of Symbolic Logic. 53 (3): 736–764. doi:10.2307/2274569.
- Frápolli, María J. (2001). "Review: Penelope Maddy, Naturalism in Mathematics". Modern Logic. 8 (3–4): 113–116.
- Hirsch, Morris (1995). "Review: Realism in mathematics, by Penelope Maddy". Bull. Amer. Math. Soc. (N.S.). 32 (1): 137–148. doi:10.1090/s0273-0979-1995-00552-5.