
190Coincidence Avoidance and Formulating the Access ProblemCanadian Journal of Philosophy. 2020.In this article, I discuss a trivialization worry for Hartry Field’s official formulation of the access problem for mathematical realists, which was pointed out by Øystein Linnebo (and has recently been made much of by Justin ClarkeDoane). I argue that various attempted reformulations of the Benacerraf problem fail to block trivialization, but that access worriers can better defend themselves by sticking closer to Hartry Field’s initial informal characterization of the access problem in terms o…Read more

158(Probably) Not companions in guiltPhilosophical Studies 175 (9): 22852308. 2018.In this paper, I will attempt to develop and defend a common form of intuitive resistance to the companions in guilt argument. I will argue that one can reasonably believe there are promising solutions to the access problem for mathematical realism that don’t translate to moral realism. In particular, I will suggest that the structuralist project of accounting for mathematical knowledge in terms of some form of logical knowledge offers significant hope of success while no analogous approach offe…Read more

130Gunk Mountains: A puzzleAnalysis 79 (1): 310. 2019.This note points out a conflict between some common intuitions about metaphysical possibility. On the one hand, it is appealing to deny that there are robust counterfactuals about how various physically impossible substances would interact with the matter that exists at our world. On the other hand, our intuitions about how concepts like MOUNTAIN apply at other metaphysically possible worlds seem to presuppose facts about ‘solidity’ which cash out in terms of these counterfactuals. I consider se…Read more

116Modal Structuralism SimplifiedCanadian Journal of Philosophy 48 (2): 200222. 2018.Since Benacerraf’s ‘What Numbers Could Not Be, ’ there has been a growing interest in mathematical structuralism. An influential form of mathematical structuralism, modal structuralism, uses logical possibility and second order logic to provide paraphrases of mathematical statements which don’t quantify over mathematical objects. These modal structuralist paraphrases are a useful tool for nominalists and realists alike. But their use of second order logic and quantification into the logical poss…Read more

99External World Skepticism, Confidence and Psychologism about the Problem of PriorsSouthern Journal of Philosophy 57 (3): 324346. 2019.In this paper I will draw attention to an important route to external world skepticism, which I will call confidence skepticism. I will argue that we can defang confidence skepticism (though not a meeker ‘argument from might’ which has got some attention in the 20th century literature on external world skepticism) by adopting a partially psychologistic answer to the problem of priors. And I will argue that certain recent work in the epistemology of mathematics and logic provides independent supp…Read more

83Default Reasonableness and the MathoidsSynthese 190 (17): 36953713. 2013.In this paper I will argue that (principled) attempts to ground a priori knowledge in default reasonable beliefs cannot capture certain common intuitions about what is required for a priori knowledge. I will describe hypothetical creatures who derive complex mathematical truths like Fermat’s last theorem via short and intuitively unconvincing arguments. Many philosophers with foundationalist inclinations will feel that these creatures must lack knowledge because they are unable to justify their …Read more

66It's currently fashionable to take Putnamian model theoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. But I will argue that (under certain mild assumptions) merely securing determinate reference to physical possibility suffices to rule out nonstandard models of our talk of numbers. So anyone who accepts realist reference to physical possibility should not reject reference to the standard model of the natural numbers on Putnamian m…Read more

65The Construction of Logical Space, by Augustin Rayo (review)Mind 124 (496): 13751379. 2015.Review of "The Construction of Logical Space", by Augustin Rayo. Oxford: OxfordUniversity Press, 2013. Pp. xix+220. H/b$35.00

60Malament–Hogarth Machines and Tait’s Axiomatic Conception of MathematicsErkenntnis 79 (4): 893907. 2014.In this paper I will argue that Tait’s axiomatic conception of mathematics implies that it is in principle impossible to be justified in believing a mathematical statement without being justified in believing that statement to be provable. I will then show that there are possible courses of experience which would justify acceptance of a mathematical statement without justifying belief that this statement is provable

58A range of current truthvalue realist philosophies of mathematics allow one to reduce the Benacerraf Problem to a problem concerning mathematicians' ability to recognize which conceptions of pure mathematical structures are coherent – in a sense which can be cashed out in terms of logical possibility. In this paper I will clarify what it takes to solve this `residual' access problem and then present a framework for solving it.

37Σ01 soundness isn’t enough: Number theoretic indeterminacy’s unsavory physical commitmentsBritish Journal for the Philosophy of Science. forthcoming.It’s sometimes suggested that we can (in a sense) settle the truthvalue of some statements in the language of number theory by stipulation, adopting either φ or ¬φ as an additional axiom. For example, in ClarkeDoane (2020b) and a series of recent APA presentations, ClarkeDoane suggests that any Σ01 sound expansion of our current arithmetical practice would express a truth. In this paper, I’ll argue that (given a certain popular assumption about the modeltheoretic representability of language…Read more

19Coincidence Avoidance and Formulating the Access ProblemCanadian Journal of Philosophy 50 (6). 2020.In this article, I discuss a trivialization worry for Hartry Field’s official formulation of the access problem for mathematical realists, which was pointed out by Øystein Linnebo (and has recently been made much of by Justin ClarkeDoane). I argue that various attempted reformulations of the Benacerraf problem fail to block trivialization, but that access worriers can better defend themselves by sticking closer to Hartry Field’s initial informal characterization of the access problem in terms o…Read more

12Physical Possibility and Determinate Number TheoryPhilosophia Mathematica. forthcoming.ABSTRACT It is currently fashionable to take Putnamian modeltheoretic worries seriously for mathematics, but not for discussions of ordinary physical objects and the sciences. However, I will argue that merely securing determinate reference to physical possibility suffices to rule out the kind of nonstandard interpretations of our number talk Putnam invokes. So, anyone who accepts determinate reference to physical possibility should not reject determinate reference to the natural numbers on Put…Read more

12The three papers which make up this dissertation form part of a larger project, which aims to solve the `access problem' for realism about mathematics by providing a clear and plausible example of what a satisfying explanation of human accuracy about objective mathematical facts could look like. They ﬁt into this project as follows

4A Logical Foundation for Potentialist Set TheoryCambridge University Press. 2022.In many ways set theory lies at the heart of modern mathematics, and it does powerful work both philosophical and mathematical – as a foundation for the subject. However, certain philosophical problems raise serious doubts about our acceptance of the axioms of set theory. In a detailed and original reassessment of these axioms, Sharon Berry uses a potentialist approach to develop a unified determinate conception of settheoretic truth that vindicates many of our intuitive expectations regarding …Read more
Ashoka University

Ashoka UniversityAssociate Professor
Rochester, Michigan, United States of America
Areas of Specialization
Philosophy of Mathematics 
Epistemology 
Metaphilosophy 
MetaEthics 