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Andrew Bacon
University of Southern California
Andrew Bacon
Carleton College
  1. The Broadest Necessity.Andrew Bacon - forthcoming - Journal of Philosophical Logic:1-51.
    In this paper we explore the logic of broad necessity. Definitions of what it means for one modality to be broader than another are formulated, and we prove, in the context of higher-order logic, that there is a broadest necessity, settling one of the central questions of this investigation. We show, moreover, that it is possible to give a reductive analysis of this necessity in extensional language (using truth functional connectives and quantifiers). This relates more generally to a conjecture that (...)
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  2. Non-Wellfounded Mereology.Aaron Cotnoir & Andrew Bacon - 2012 - Review of Symbolic Logic 5 (2):187-204.
    This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to (...)
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  3. Can the Classical Logician Avoid the Revenge Paradoxes?Andrew Bacon - 2015 - Philosophical Review 124 (3):299-352.
    Most work on the semantic paradoxes within classical logic has centered around what this essay calls “linguistic” accounts of the paradoxes: they attribute to sentences or utterances of sentences some property that is supposed to explain their paradoxical or nonparadoxical status. “No proposition” views are paradigm examples of linguistic theories, although practically all accounts of the paradoxes subscribe to some kind of linguistic theory. This essay shows that linguistic accounts of the paradoxes endorsing classical logic are subject to a particularly (...)
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  4. Non-Classical Metatheory for Non-Classical Logics.Andrew Bacon - 2013 - Journal of Philosophical Logic 42 (2):335-355.
    A number of authors have objected to the application of non-classical logic to problems in philosophy on the basis that these non-classical logics are usually characterised by a classical metatheory. In many cases the problem amounts to more than just a discrepancy; the very phenomena responsible for non-classicality occur in the field of semantics as much as they do elsewhere. The phenomena of higher order vagueness and the revenge liar are just two such examples. The aim of this paper is (...)
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  5. Tense and Relativity.Andrew Bacon - 2016 - Noûs 50 (4).
    Those inclined to positions in the philosophy of time that take tense seriously have typically assumed that not all regions of space-time are equal: one special region of space-time corresponds to what is presently happening. When combined with assumptions from modern physics this has the unsettling consequence that the shape of this favored region distinguishes people in certain places or people traveling at certain velocities. In this paper I shall attempt to avoid this result by developing a tensed picture of (...)
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  6. Higher-Order Free Logic and the Prior-Kaplan Paradox.Andrew Bacon, John Hawthorne & Gabriel Uzquiano - 2016 - Canadian Journal of Philosophy 46 (4-5):493-541.
    The principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior’s paradox and Kaplan’s paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment (...)
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  7.  41
    Some Results on the Limits of Thought.Andrew Bacon & Gabriel Uzquiano - forthcoming - Journal of Philosophical Logic:1-9.
    Generalizing on some arguments due to Arthur Prior and Dmitry Mirimanoff, we provide some further limitative results on what can be thought.
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  8. Quantificational Logic and Empty Names.Andrew Bacon - 2013 - Philosophers' Imprint 13.
    The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as ∃x t=x; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has often been noted that in order (...)
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  9. The Logic of Opacity.Andrew Bacon & Jeffrey Sanford Russell - forthcoming - Philosophical and Phenomenological Research.
    We explore the view that Frege's puzzle is a source of straightforward counterexamples to Leibniz's law. Taking this seriously requires us to revise the classical logic of quantifiers and identity; we work out the options, in the context of higher-order logic. The logics we arrive at provide the resources for a straightforward semantics of attitude reports that is consistent with the Millian thesis that the meaning of a name is just the thing it stands for. We provide models to show (...)
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  10. Giving Your Knowledge Half a Chance.Andrew Bacon - 2014 - Philosophical Studies (2):1-25.
    One thousand fair causally isolated coins will be independently flipped tomorrow morning and you know this fact. I argue that the probability, conditional on your knowledge, that any coin will land tails is almost 1 if that coin in fact lands tails, and almost 0 if it in fact lands heads. I also show that the coin flips are not probabilistically independent given your knowledge. These results are uncomfortable for those, like Timothy Williamson, who take these probabilities to play a (...)
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  11. A New Conditional for Naive Truth Theory.Andrew Bacon - 2013 - Notre Dame Journal of Formal Logic 54 (1):87-104.
    In this paper a logic for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field's recent results establishing consistency and omega-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have heretofore failed to provide.
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  12. Stalnaker’s Thesis in Context.Andrew Bacon - 2015 - Review of Symbolic Logic 8 (1):131-163.
    In this paper I present a precise version of Stalnaker's thesis and show that it is both consistent and predicts our intuitive judgments about the probabilities of conditionals. The thesis states that someone whose total evidence is E should have the same credence in the proposition expressed by 'if A then B' in a context where E is salient as they have conditional credence in the proposition B expresses given the proposition A expresses in that context. The thesis is formalised (...)
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  13. Curry's Paradox and Omega Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...)
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    Is Reality Fundamentally Qualitative?Andrew Bacon - forthcoming - Philosophical Studies:1-37.
    Individuals play a prominent role in many metaphysical theories. According to an individualistic metaphysics, reality is determined by the pattern of properties and relations that hold between individuals. A number of philosophers have recently brought to attention alternative views in which individuals do not play such a prominent role; in this paper I will investigate one of these alternatives.
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  15. Paradoxes of Logical Equivalence and Identity.Andrew Bacon - 2013 - Topoi (1):1-10.
    In this paper a principle of substitutivity of logical equivalents salve veritate and a version of Leibniz’s law are formulated and each is shown to cause problems when combined with naive truth theories.
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  16. Representing Counterparts.Andrew Bacon - 2014 - Australasian Journal of Logic 11 (2):90-113.
    This paper presents and motivates a counterpart theoretic semantics for quantifi ed modal logic based on a fleshed out account of Lewis's notion of a `possibility.' According to the account a possibility consists of a world and some haecceitistic information about how each possible individual gets represented de re. A semantics for quanti ed modal logic based on evaluating formulae at possibilities is developed. It is shown that this framework naturally accommodates an actuality operator, addressing recent objections to counterpart theory, (...)
     
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  17. A Paradox for Supertask Decision Makers.Andrew Bacon - 2011 - Philosophical Studies 153 (2):307.
    I consider two puzzles in which an agent undergoes a sequence of decision problems. In both cases it is possible to respond rationally to any given problem yet it is impossible to respond rationally to every problem in the sequence, even though the choices are independent. In particular, although it might be a requirement of rationality that one must respond in a certain way at each point in the sequence, it seems it cannot be a requirement to respond as such (...)
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  18. Vagueness at Every Order: The Prospects of Denying B.Andrew Bacon - manuscript
    A number of arguments purport to show that vague properties determine sharp boundaries at higher orders. That is, although we may countenance vagueness concerning the location of boundaries for vague predicates, every predicate can instead be associated with precise knowable cut-off points deriving from precision in their higher order boundaries. I argue that this conclusion is indeed paradoxical, and identify the assumption responsible for the paradox as the Brouwerian principle B for vagueness: that if p then it's determinate that it's (...)
     
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  19. In Defence of a Naïve Conditional Epistemology.Andrew Bacon - manuscript
    Numerous triviality results have been directed at a collection of views that tie the probability of a conditional sentence to the conditional probability of the consequent on its antecedent. -/- In this paper I argue that this identification makes little sense if conditional sentences are context sensitive. The best alternative, I argue, is a version of the thesis which states that if your total evidence is E then the evidential probability of a conditional evaluated in a context where E is (...)
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  20. Restricting the Knowability Principle.Andrew Bacon - unknown
    Could there unknowable truths? Truths which, regardless of any extension to ones capacities or resources, remain impossible to know. The answer to this question is central in the evaluation of semantic anti-realism. But even for a metaphysical realist, the matter is far from closed.
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    Scharp on Replacing Truth.Andrew Bacon - forthcoming - Inquiry : An Interdisciplinary Journal of Philosophy:1-17.
    Kevin Scharp’s ‘Replacing Truth’ is an ambitious and far reaching account of the semantic paradoxes. In this critical discussion we examine one the books central claims: to have provided a theory of truth that avoids the revenge paradoxes. In the first part we assess this claim, and in the second part we investigate some features of Scharp’s preferred theory of truth, ADT, and compare it with existing theories such as the Kripke–Feferman theory. In the appendix a simple model of Scharp’s (...)
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    Scharp on Replacing Truth.Andrew Bacon - forthcoming - Inquiry : An Interdisciplinary Journal of Philosophy:1-17.
    Kevin Scharp’s ‘Replacing Truth’ is an ambitious and far reaching account of the semantic paradoxes. In this critical discussion we examine one the books central claims: to have provided a theory of truth that avoids the revenge paradoxes. In the first part we assess this claim, and in the second part we investigate some features of Scharp’s preferred theory of truth, ADT, and compare it with existing theories such as the Kripke–Feferman theory. In the appendix a simple model of Scharp’s (...)
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  23. Vagueness and Thought.Andrew Bacon - 2018 - Oxford University Press.
    Vagueness is the study of concepts that admit borderline cases. The epistemology of vagueness concerns attitudes we should have towards propositions we know to be borderline. On this basis Andrew Bacon develops a new theory of vagueness in which vagueness is fundamentally a property of propositions, explicated in terms of its role in thought.
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  24. Vagueness and Uncertainty.Andrew Bacon - 2009 - Dissertation, BPhil Thesis, Oxford University
    In this thesis I investigate the behaviour of uncertainty about vague matters. It is a fairly common view that vagueness involves uncertainty of some sort. However there are many fundamental questions about this kind of uncertainty that are left open. Could you be genuinely uncertain about p when there is no matter of fact whether p? Could you remain uncertain in a vague proposition even if you knew exactly which possible world obtained? Should your degrees of belief be probabilistically coherent? (...)
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