SHARON BERRY

Hi, I'm a philosophy PHD student working on a disseration on the "access problem" in philosophy of mathematics under: Warren Goldfarb, Peter Koellner , Ned Hall, and Bernard Nickel.

Dissertation Papers The Marriage of Rationalism and Empiricism: A Naturalistic Solution to the Access Problem for Realist Mathematics The access problem for Platonism about mathematical objects is this: if mathematics were really about abstract causally-inert objects like numbers and sets, how could creatures like us ever manage to get true mathematical beliefs? I propose that general methods of reasoning about what patterns of relationships between objects are combinatorially possible bridge the gap between human beliefs and facts about abstract mathematical objects, as follows. Good general principles of reasoning about combinatorial possibility would suffice to give us access to facts about what sets there are. For, I claim, what it takes for there to be a set is (just) for certain things to be combinatorially possible. For example, there's a set at level alpha corresponding to every combinatorially possible choice of some things that are either physical objects or sets at levels lower than alpha. And, given good general principles of reasoning about combinatorial possibility, we can work out from this characterization of what it takes for there to be a set that various other things (like the standard ZF axioms of set theory) would have to be true of these objects. And there is no access problem with regard to general principles of reasoning about combinatorial possibility because experience can `kick back' at us and correct us in two ways. First, everything that's actual must be combinatorially possible. This pushes us not to accept principles which say that too few things are combinatorially possible. Second, we need to explain patterns in what actually occurs in terms of some combination of facts about what's combinatorially impossible, contingent scientific laws, and more particular metaphysical or analytic facts about the particular properties and relations in question. Here considerations of general theoretical elegance can push us in the direction of not saying too many things are combinatorially possible. Philosophy of Math: Mathematical Knowledge and Combinatorial Possibility: A Two-Pronged Strategy for Solving the Access Problem plus the full length version [sorry the second link didn't work for a few weeks, the correct document should now be in place] Contra Detlefson on Lob's Theorem and Mechanism about the Mind On Malament-Hogarth Machines, Proof, Truth and Empirical Justification in Mathematics Metaphysics and Epistemology: The Doctoroids and the Problem of Acceptable Starting Points Quantifier Variance and Eklund's Criticisms (Contra) Kim on Belief and Epistemic Normativity (old) Just for fun: Investigator's Paradise: An Epistemic Formalist Theory of Beauty(old, very speculative!)

CV etc My CV Teaching/Educational Games Here's a link to the logic website I co-wrote this summer, as well as some games:Nested Quantifier Arcade (mac), Truthtabler (browser) and Latin Game Demo (mac) . Philosophy In Progress My blog with research in progress, notes and objections to articles I'm reading etc.