-
14Imagination and Belief: The Microtheories Model of Hypotheical ThinkingJournal of Consciousness Studies 23 (3-4): 31-49. 2016.Beliefs about hypothetical situations need to be 'quarantined' from factual representations, so that our inference processes do not make false conclusions about the real world. Nichols argued for the existence of a place where these special beliefs are kept: the pretence box. We show that this theory has a number of drawbacks, including its inability to account for simultaneously keeping track of multiple imagined worlds. We offer an explanation that remedies these problems: beliefs of content i…Read more
-
20Towards a theory of singular thought about abstract mathematical objectsSynthese 196 (10): 4113-4136. 2019.This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and sema…Read more
-
21This thesis addresses an issue in the philosophy of Mathematics which is little discussed, and indeed little recognised. This issue is the phenomenon of a ‘change of setting’. Changes of setting are events which involve a change in a scientific framework which is fruitful for answering questions which were, under an old framework, intractable. The formulation of the new setting usually involves a conceptual re-orientation to the subject matter. In the natural sciences, such re-orientations are a…Read more
-
469On the Varieties of Abstract ObjectsAustralasian Journal of Philosophy 97 (4): 809-823. 2019.I reconcile the spatiotemporal location of repeatable artworks and impure sets with the non-location of natural numbers despite all three being varieties of abstract objects. This is possible because, while the identity conditions for all three can be given by abstraction principles, in the former two cases spatiotemporal location is a congruence for the equivalence relation featuring in the relevant principle, whereas in the latter it is not. I then generalize this to other ‘physical’ propertie…Read more
-
758Towards a theory of singular thought about abstract mathematical objectsSynthese 196 (10): 4113-4136. 2019.This essay uses a mental files theory of singular thought—a theory saying that singular thought about and reference to a particular object requires possession of a mental store of information taken to be about that object—to explain how we could have such thoughts about abstract mathematical objects. After showing why we should want an explanation of this I argue that none of three main contemporary mental files theories of singular thought—acquaintance theory, semantic instrumentalism, and sema…Read more
-
125Grounding Concepts: an Empirical Basis for Arithmetical Knowledge – C.S. JenkinsPhilosophical Quarterly 61 (242): 208-211. 2011.
-
41Do we see numbers?: James Franklin: An Aristotelian realist philosophy of mathematics (review)Metascience 24 (3): 483-486. 2015.
Mississauga, Ontario, Canada