
24A reconstruction of steel’s multiverse projectBulletin of Symbolic Logic 179. forthcoming.This paper reconstructs Steel’s multiverse project in his ‘Gödel’s program’ (Steel [2014]), first by comparing it to those of Hamkins [2012] and Woodin [2011], then by detailed analysis what’s presented in Steel’s brief text. In particular, we reconstruct his notion of a ‘natural’ theory, describe his multiverse axioms and his translation function, and assess the resulting status of the Continuum Hypothesis. In the end, we reconceptualize the defect that Steel thinks CH might suffer from and is…Read more

8Rigor and Structure, by John P. Burgess: Oxford: Oxford University Press, 2015, pp. xii + 215, £35 (review)Australasian Journal of Philosophy 95 (2): 397400. 2017.

79Revising Carnap’s Semantic Conception of ModalityStudia Logica 100 (3): 497515. 2012.I provide a tableau system and completeness proof for a revised version of Carnap's semantics for quantified modal logic. For Carnap, a sentence is possible if it is true in some first order model. However, in a similar fashion to second order logic, no sound and complete proof theory can be provided for this semantics. This factor contributed to the ultimate disappearance of Carnapian modal logic from contemporary philosophical discussion. The proof theory I discuss comes close to Carnap's sema…Read more

41Computation in NonClassical Foundations?Philosophers' Imprint 16. 2016.The ChurchTuring Thesis is widely regarded as true, because of evidence that there is only one genuine notion of computation. By contrast, there are nowadays many different formal logics, and different corresponding foundational frameworks. Which ones can deliver a theory of computability? This question sets up a difficult challenge: the meanings of basic mathematical terms are not stable across frameworks. While it is easy to compare what different frameworks say, it is not so easy to compare …Read more

67WHAT CAN A CATEGORICITY THEOREM TELL US?Review of Symbolic Logic (3): 524544. 2013.f The purpose of this paper is to investigate categoricity arguments conducted in second order logic and the philosophical conclusions that can be drawn from them. We provide a way of seeing this result, so to speak, through a first order lens divested of its second order garb. Our purpose is to draw into sharper relief exactly what is involved in this kind of categoricity proof and to highlight the fact that we should be reserved before drawing powerful philosophical conclusions from it

99Sets and supersetsSynthese 193 (6): 18751907. 2016.It is a commonplace of set theory to say that there is no set of all wellorderings nor a set of all sets. We are implored to accept this due to the threat of paradox and the ensuing descent into unintelligibility. In the absence of promising alternatives, we tend to take up a conservative stance and tow the line: there is no universe. In this paper, I am going to challenge this claim by taking seriously the idea that we can talk about the collection of all the sets and many more collections bey…Read more

63Naive Infinitism: The Case for an Inconsistency Approach to Infinite CollectionsNotre Dame Journal of Formal Logic 56 (1): 191212. 2015.This paper expands upon a way in which we might rationally doubt that there are multiple sizes of infinity. The argument draws its inspiration from recent work in the philosophy of truth and philosophy of set theory. More specifically, elements of contextualist theories of truth and multiverse accounts of set theory are brought together in an effort to make sense of Cantor’s troubling theorem. The resultant theory provides an alternative philosophical perspective on the transfinite, but has limi…Read more

93Truth, Dependence and Supervaluation: Living with the GhostJournal of Philosophical Logic 42 (2): 221240. 2013.In J Philos Logic 34:155–192, 2005, Leitgeb provides a theory of truth which is based on a theory of semantic dependence. We argue here that the conceptual thrust of this approach provides us with the best way of dealing with semantic paradoxes in a manner that is acceptable to a classical logician. However, in investigating a problem that was raised at the end of J Philos Logic 34:155–192, 2005, we discover that something is missing from Leitgeb’s original definition. Moreover, we show that onc…Read more

44Rigor and Structure, by John P. Burgess: Oxford: Oxford University Press, 2015, pp. xii + 215, £35 (review)Australasian Journal of Philosophy 95 (2): 397400. 2017.

77Unpicking Priest's BootstrapsThought: A Journal of Philosophy 4 (3): 181188. 2015.Graham Priest has argued that the fruits of classical set theory can be obtained by naive means through a puzzling piece of reasoning often known as the bootstrapping argument. I will demonstrate that the bootstrapping involved is best understood as viciously circular and thus, that these fruits remain forbidden. The argument has only one rehearsal in print and it is quite subtle. This paper provides reconstruction of the argument based on Priest and attempts some fixes and alternative construal…Read more

98An account of modality is produced which takes as its foundation the idea that modal concepts are parasitic upon our background theoretical commitments. This position is distinguished from the majority of philosophies of modality, which are either primitivist or reductionist. It is in this sense that our account is less burdened by metaphysics. The primary purpose of the document is to demonstrate that our approach is a coherent one. It supports this claim in three stages. First, we identify the…Read more

University of California, IrvineThe Department of Logic and Philosophy of ScienceAssistant Professor
Irvine, California, United States of America
Areas of Specialization
Logic and Philosophy of Logic 
Philosophy of Mathematics 
Areas of Interest
Philosophy of Language 
Aesthetics 
20th Century Philosophy 
PhilPapers Editorships
Set Theory 