Definition (Philosophical Studies)
This paper presents a puzzle about the logic of real definition. I demonstrate that five principles concerning definition definition – that is coextensional and irreflexive, that it applies to its cases, that it permits expansion and that it is itself defined – are logically incompatible. I then explore the advantages and disadvantages of each principle – one of which must be rejected to restore consistency.
Knowledge is Closed Under Analytic Content (Synthese)
I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true and that q is an analytic part of p, then S knows that q. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox.
The Semantic Foundations of Philosophical Analysis (The Review of Symbolic Logic)
I provide an analysis of sentences of the form ‘To be F is to be G‘ in terms of exact truth-maker semantics – an approach that identifies the meanings of sentences with the states of the world directly responsible for their truth-values. Roughly, I argue that these sentences hold just in case that which makes something F also makes it G. This approach is hyperintensional and possesses desirable logical and modal features. In particular, these sentences are reflexive, transitive and symmetric, and if they are true, then they are necessarily true and it is necessary that all and only Fs are Gs.
Counterfactual Logic and the Necessity of Mathematics (Journal of Philosophical Logic)
This paper is concerned with counterfactual logic and its implications for the modal status of mathematical claims. It is most directly a response to an ambitious program by Yli-Vakkuri and Hawthorne (2018), who seek to establish that mathematics is committed to its own necessity. I demonstrate that their assumptions collapse the counterfactual conditional into the material conditional. This collapse entails the success of counterfactual strengthening (the inference from ‘If A were true then C would be true’ to ‘If A and B were true then C would be true’), which is controversial within counterfactual logic, and which has counterexamples within pure and applied mathematics. I close by discussing the dispensability of counterfactual conditionals within the language of mathematics.
Physicalism and the Identity of Identity Theories (Erkenntnis)
It is often said that there are two varieties of identity theory. Type-identity theorists interpret physicalism as the claim that every property is identical to a physical property, while token-identity theorists interpret it as the claim that every particular is identical to a physical particular. The aim of this paper is to undermine the distinction between the two. Drawing on recent work connecting generalized identity to truth-maker semantics, I demonstrate that these interpretations are logically equivalent. I then argue that each has the resources to resolve problems facing the other.
Merely Partial Definition and the Analysis of Knowledge (Synthese)
Two families of positions dominate debates over a metaphysically reductive analysis of knowledge. Traditionalism holds that knowledge has a complete, uniquely identifying analysis, while knowledge-first epistemology contends that knowledge is primitive, admitting of no reductive analysis whatsoever. Drawing on recent work in metaphysics, I argue that these alternatives fail to exhaust the available possibilities. Knowledge may have a merely partial analysis: a real definition that distinguishes it from some, but not all other things. I demonstrate that this position is attractive; it evades concerns that its rivals face.
On Question-Begging and Analytic Content (Synthese)
Among contemporary philosophers, there is widespread (but not universal) consensus that begging the question is a grave argumentative flaw. However, there is presently no satisfactory analysis of what this flaw consists of. Here, I defend a notion of question-begging in terms of analyticity. In particular, I argue that an argument begs the question just in case its conclusion is an analytic part of the conjunction of its premises.
The Unreliability of Foreseeable Consequences (Ethical Theory and Moral Practice)
Consequentialists maintain that an act is morally right just in case it produces the best consequences of any available alternative. Because agents are ignorant about some of their acts’ consequences, they cannot be certain about which alternative is best. Kagan (1998) contends that it is reasonable to assume that unforeseen good and bad consequences roughly balance out and can be largely disregarded. A statistical argument demonstrates that Kagan’s assumption is almost always false. An act’s foreseeable consequences are an extremely poor indicator of the goodness of its overall consequences. Acting based on foreseeable consequences is barely more reliably good than acting completely at random.
Higher-Order Counterfactual Logic
A higher-order counterfactual is one that imbeds higher-order claims in either its antecedent or consequent. For example, ‘If Sarah and Jane had nothing in common, they would not both be Norwegian’ is naturally read asserting that if there were not to exist a property borne by both Sarah and Jane, then they would not both bear the property is Norwegian. While there are substantial literatures on both counterfactual logic and on higher-order logic, higher-order counterfactuals have been almost entirely overlooked. In this paper, I formalize a family of higher-order counterfactual logics. I then establish their equivalence to existing higher-order modal systems, and draw out some of their most controversial implications. Notably, most entail vacuism – the claim that all counterpossibles are vacuously true , the substitution of logically equivalent expression in antecedent position, the counterfactual excluded middle, the Barcan and Converse Barcan formulas – and necessitarianism – the claim that all objects necessarily exist.
I take some initial steps toward a theory of real definition, drawing upon recent developments in higher-order logic. The resulting account allows for extremely fine-grained distinctions (it can distinguish between any relata that differ in their syntactic structure, while avoiding the Russell-Myhill problem). It is the first account that can consistently embrace three desirable logical principles that initially appear to be incompatible: the Identification Hypothesis (if F is, by definition, G, then there is a sense in which F is the same as G), Irreflexivity (there are no reflexive definitions) and Leibniz’s Law. Additionally, it possesses the resources needed to resolve the paradox of analysis.
Haecceities and the Triviality of the Identity of Indiscernibles
The Identity of Indiscernibles is the principle that objects cannot differ only numerically. It is widely held that one interpretation of this principle is trivially true: the claim that objects that bear all of the same properties are identical. This triviality ostensibly arises from haecceities (properties like is identical to a). I argue that this is not the case; we do not trivialize the Identity of Indiscernibles with haecceities, because it is impossible to express the haecceities of indiscernible objects. I then argue that this inexpressibility generalizes to all of their trivializing properties. Whether the Identity of Indiscernibles is trivially true ultimately turns on whether we can quantify over properties that we cannot express.
The Levels of Scientific Disciplines
It is plausible that the scientific disciplines are leveled. Many maintain that physics is more fundamental than chemistry is, for example, aand that chemistry is more fundamental than biology is. I use truth-maker semantics to provide an account of level. In particular, I exploit the mereological structure of states of affairs (which is integral to the truth-maker approach) to provide conditions for one scientific discipline to occupy a higher level than another.
Works in Progress
Monism Via Logic
Monism is the claim that only one object exists. While few contemporary philosophers endorse monism, it has an illustrious history – stretching back to Bradley, Spinoza and Parmenides. In this paper, I show that plausible assumptions about the higher-order logic of property identity entail that monism is true. Given the higher-order framework I operate in, this argument generalizes: it is also possible to establish that there is a single property, proposition, relation, etc. I then show why this form of monism is inconsistent; because all propositions are identical, p is identical to ~p – and so they have the same truth-value. At least one of the assumptions that generate higher-order monism must be rejected.
Indiscernibility and the Grounds of Identity
This paper concerns the metaphysical foundations of identity: with what it is that grounds facts of the form a = b. One view (that has often been discussed, yet has never been endorsed) is that identity is grounded in indiscernibility. That is, the fact that a = b is grounded in the fact that a and b bear all of the same properties. This is typically rejected on the grounds that it is viciously circular; standard assumptions about the logic of ground entail that the fact that a =a partially grounds itself. Here, I develop a noncircular theory of identity via indiscernability.
(Please feel free to contact me if you would like to see drafts of these works in progress)