Maddy's interest in the continuum hypothesis—which she had initially learned of during high school—and the fact that it could not be proved without introducing a new axiom,led her to question what could count as evidence for one axiom over another.[3] According to Maddy,at this point she was "already well down the slippery slope from mathematics to philosophy"[4] and she went to pursue a PhD in philosophy at Princeton University.[3] She received her PhD in 1979. Her dissertation,Set Theoretical Realism,was supervised by John P. Burgess.[5]
She taught at the University of Notre Dame and University of Illinois,Chicago before joining University of California,Irvine in 1987.[2] There she held positions as the chair of the philosophy department and later as the founding chair of the department of logic and philosophy of science. She was named Chancellor's Professor in 2002 and Distinguished Professor in 2007. She retired in 2020.[6] She is Distinguished Professor Emeritus.[7]
Maddy's 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 one sees three cups on a table, one also sees the set. 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."[12] However, rather than a unified picture of the sciences like Quine's, her picture has mathematics as separate. That is, 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.
She has been dedicated to understanding and explaining the methods that set theorists use in agreeing on axioms, especially those that go beyond ZFC.
Selected publications
Maddy, Penelope (June 1988). "Believing the Axioms, I". Journal of Symbolic Logic. 53 (2): 481–511. doi:10.2307/2274520. JSTOR2274520. (a copy with corrections is available at the author's web page)
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