Andrew Bacon
· Professor of PhilosophyUniversity of Southern California · Philosophy
Active 2010–2023
About
Andrew Bacon is a professor involved in teaching courses such as PHIL 510: Logic, Mathematics and Metaphysics at the University of Southern California. His course explores the interaction between logical hypotheses associated with mathematics and metaphysics, examining how logical systems can constrain the behavior of mathematical and metaphysical entities if they were to exist. The course covers topics including extensionalism, abstractionism, structuralism, modal logicism, set theory, modal approaches to set theory, modality, nominalism, and potentialism, indicating his focus on foundational issues in logic, philosophy of mathematics, and metaphysics. The course materials and discussions suggest his research interests lie in the logical and philosophical foundations of mathematics and metaphysics, particularly in how logical systems relate to the ontology and structure of abstract objects and the nature of mathematical and metaphysical truths.
Research topics
- Computer Science
- Philosophy
- Physics
- Linguistics
- Mathematics
- Epistemology
- Programming language
- Optics
Selected publications
2023-09-12
book-chapter1st authorCorrespondingA Theory of Structured Propositions
The Philosophical Review · 2023-04-01 · 14 citations
articleOpen access1st authorCorrespondingThis paper argues that the theory of structured propositions is not undermined by the Russell-Myhill paradox. I develop a theory of structured propositions in which the Russell-Myhill paradox doesn’t arise: the theory does not involve ramification or compromises to the underlying logic, but rather rejects common assumptions, encoded in the notation of the λ-calculus, about what properties and relations can be built. I argue that the structuralist had independent reasons to reject these underlying assumptions. The theory is given both a diagrammatic representation and a logical representation in a novel language. In the latter half of the paper I turn to some technical questions concerning the treatment of quantification and demonstrate various equivalences between the diagrammatic and logical representations and a fragment of the λ-calculus.
2023-09-12
book-chapter1st authorCorrespondingHigher-order theories of granularity
2023-09-12
book-chapter1st authorCorrespondingMathematical Modality: An Investigation in Higher-order Logic
Journal of Philosophical Logic · 2023-11-28 · 1 citations
articleOpen access1st authorCorrespondingAbstract An increasing amount of contemporary philosophy of mathematics posits, and theorizes in terms of special kinds of mathematical modality. The goal of this paper is to bring recent work on higher-order metaphysics to bear on the investigation of these modalities. The main focus of the paper will be views that posit mathematical contingency or indeterminacy about statements that concern the ‘width’ of the set theoretic universe, such as Cantor’s continuum hypothesis. Within a higher-order framework I show that contingency about the width of the set-theoretic universe refutes two orthodoxies concerning the structure of modal reality: the view that the broadest necessity has a logic of , and the ‘Leibniz biconditionals’ stating that what is possible, in the broadest sense of possible , is what is true in some possible world. Nonetheless, I suggest that the underlying picture of modal set-theory is coherent and has attractions.
Counterfactuals, Infinity and Paradox
Outstanding contributions to logic · 2023-01-01
book-chapter1st authorCorresponding2023-09-12
book-chapter1st authorCorrespondingActual value in decision theory
Analysis · 2022-03-14 · 9 citations
article1st authorCorrespondingAbstract Decision theory is founded on the principle that we ought to take the action that has the maximum expected value from among actions we are in a position to take. But prior to the notion of expected value is the notion of the actual value of that action: roughly, a measure of the good outcomes you would in fact procure if you were to take it. Surprisingly many decision theories operate without an analysis of actual value. I offer a definition of actual value, and show that a form of decision theory due to Stalnaker can be reformulated so as to be in line with the edict to maximize expected value. By contrast, I show that there is no quantity — given by my definition or otherwise — that plays the role of actual value in Jeffrey's decision theory.
Routledge eBooks · 2021 · 38 citations
1st authorCorresponding- Physics
- Optics
In 1963 Prior proved a theorem that places surprising constraints on the logic of intentional attitudes, like ‘thinks that’, ‘hopes that’, ‘says that’ and ‘fears that’. Paraphrasing it in English, and applying it to ‘thinks’, it states: If, at t, I thought that I didn’t think a truth at t, then there is both a truth and a falsehood I thought at t. This chapter explores a response to this paradox that exploits the opacity of attitude verbs, exemplified in this case by the operator ‘I thought at t that’, to block Prior’s derivation. According to this picture, both Leibniz’s law and existential generalization fail in opaque contexts. In particular, one cannot infer from the fact that I’m thinking at t that I’m not thinking a truth at t, that there is a particular proposition such that I am thinking it at t. Moreover, unlike some approaches to this paradox (see Bacon et al., 2016) the failure of existential generalization is not motivated by the idea that certain paradoxical propositions do not exist, for this view maintains that there is a proposition that I’m not thinking a truth at t. Several advantages of this approach over the non-existence approach are discussed, and models demonstrating the consistency of this theory are provided. Finally, the resulting considerations are applied to the liar paradox, and are used to provide a non-standard justification of a classical gap theory of truth. One of the main challenges for this sort of theory—to explain the point of assertion, if not to assert truths—can be met within this framework.
Journal of Philosophical Logic · 2021-08-27 · 8 citations
article1st authorCorresponding
Frequent coauthors
- 4 shared
A. J. Cotnoir
- 4 shared
Jeremy Goodman
- 2 shared
Gabriel Uzquiano
Southern California University for Professional Studies
- 1 shared
John Hawthorne
University of Southern California
- 1 shared
Zeng Jin
University of Southern California
- 1 shared
Jeffrey Sanford Russell
Southern California University for Professional Studies
- 1 shared
C. A. Madsen
Center for Astrophysics Harvard & Smithsonian
- 1 shared
E. E. DeLuca
Center for Astrophysics Harvard & Smithsonian
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