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A hyperintensional epistemic logic would take the contents which can be known or believed as more fine-grained than sets of possible worlds. I consider one objection to the idea: Williamson’s Objection from Overfitting. I propose a hyperintensional account of propositions as sets of worlds enriched with topics: what those propositions, and so the attitudes having them as contents, are about. I show that the account captures the conditions under which sentences express the same content; that it can be pervasively applied (...) |
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This paper defends a theory of fictional truth. According to this theory, there is a fact of the matter concerning the number of hairs on Sherlock Holmes' head, and likewise for any other meaningful question one could ask about what's true in a work of fiction. We argue that a theory of this form is needed to account for the patterns in our judgments about attitude reports that embed fictional claims. We contrast our view with one of the dominant approaches (...) |
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Hyperlogic is a hyperintensional system designed to regiment metalogical claims (e.g., “Intuitionistic logic is correct” or “The law of excluded middle holds”) into the object language, including within embedded environments such as attitude reports and counterfactuals. This paper is the first of a two-part series exploring the logic of hyperlogic. This part presents a minimal logic of hyperlogic and proves its completeness. It consists of two interdefined axiomatic systems: one for classical consequence (truth preservation under a classical interpretation of the (...) |
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This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched (...) |
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Distinctively mathematical explanations (DMEs) explain natural phenomena primarily by appeal to mathematical facts. One important question is whether there can be an ontic account of DME. An ontic account of DME would treat the explananda and explanantia of DMEs as ontic structures and the explanatory relation between them as an ontic relation (e.g., Pincock 2015, Povich 2021). Here I present a conventionalist account of DME, defend it against objections, and argue that it should be considered ontic. Notably, if indeed it (...) |
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This is the second part of a two-part series on the logic of hyperlogic, a formal system for regimenting metalogical claims in the object language (even within embedded environments). Part A provided a minimal logic for hyperlogic that is sound and complete over the class of all models. In this part, we extend these completeness results to stronger logics that are sound and complete over restricted classes of models. We also investigate the logic of hyperlogic when the language is enriched (...) |
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Nominalists are confronted with a grave difficulty: if abstract objects do not exist, what explains the success of theories that invoke them? In this paper, I make headway on this problem. I develop a formal language in which certain platonistic claims about properties and certain nominalistic claims can be expressed, develop a formal language in which only certain nominalistic claims can be expressed, describe a function mapping sentences of the first language to sentences of the second language, and prove some (...) |
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What is the connection between valid inference and true conditionals? Many conditional logics require that when A is a logical consequence of B, "if B then A" is true. Taking counterlogical conditionals seriously leads to systems that permit counterexamples to that general rule. However, this leaves those of us who endorse non-trivial accounts of counterpossible conditionals to explain what the connection between conditionals and consequence is. The explanation of the connection also answers a common line of objection to non-trivial counterpossibles, (...) |
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This paper considers two problems—one in philosophy of religion and another in philosophy of physics—and shows that the two problems have one solution. Some Christian philosophers have endorsed the views that (i) there was a first finitely long period of time, (ii) God is in time, and yet (iii) God did not have a beginning. If there was a first finitely long period of time and God is in time then there was a first finitely long period of time in (...) |
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The common view has it that there are two families of approaches towards the logical structure of impossible worlds – Australasian and North American. According to the first, impossible worlds are closed under the relation of logical consequence of one of the non-classical logics. The North American approach is more liberal, allowing for impossible worlds where no logic holds. After pointing out the questionable consequences of each view, I propose a third one. While this new perspective allows for worlds where (...) |
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This paper clarifies and defends the global approach to defining logical validity for meta- and higher-level inferences. This is contrary to an emerging consensus in favour of local validity. Prevalent recent arguments claim that global validity is either superfluous in virtue of collapsing into local, or else untenable because it overgenerates validities, compromises the formality of logic, or breaks symmetry with regular validity. Accordingly, the literature on higher inferential logic has come to focus almost exclusively on local validity. Many key (...) |
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Counterfactuals abound in science, especially when one deals with models. Some models, namely highly idealized models, have assumptions that are metaphysically impossible. This means that in science one has often to deal with counterpossibles. According to the standard semantics for counterfactuals, all counterpossibles are vacuously true. But scientific practice shows that counterpossibles are not always regarded as vacuously true by scientists. To do justice of the use of counterpossibles in science, some authors think that we should adopt a semantics that (...) |
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Critics of Divine Command Theory (DCT) argue that DCT implies the following counterpossible is true: If God commanded us to perform a terrible act, then the terrible act would be morally obligatory. However, our intuitions tell us that such a counterpossible is false. Therefore, DCT fails. This is the counterpossible terrible commands objection. In this paper, I argue that the counterpossible terrible commands objection fails. I start by considering a standard response by DCT proponents that appeals to vacuism—the view that (...) |
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[Use code AUFLY30 for 30% off on the OUP website.] One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should (...) |
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In this paper, I consider the question of whether calibration is required for modalizing mechanisms to be reliable, that is, whether it is necessary for modalizing mechanisms to be adjusted to prevent overgeneration and undergeneration of modal beliefs. I first argue that the calibration requirement affects differently what I call bootstrapping and ordinary cases. Identifying different ways in which a modalizing mechanism could be calibrated, I argue that not all of them are effective or even viable in bootstrapping cases. Then, (...) |
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