I provide a theory of the metaphysical foundations of identity: an account what grounds facts of the form a=b. In particular, I defend the claim that indiscernibility grounds identity. This is typically rejected because it is viciously circular; plausible assumptions about the logic of ground entail that the fact that a=b partially grounds itself. The theory I defend is immune to this circularity.

This paper concerns the grounds of nonground: what it is in virtue of that facts of the form [F1 does not ground F2] hold. While the literature on iterated ground is expansive, there is comparatively little written on the grounds of nonground. I argue that nonground is grounded in distinctness from ground. If F1 does not ground F2, then [F1 does not ground F2] is grounded in the fact that F1 is distinct from that which does ground F2. While this (...) proposal strikes me as natural, it faces puzzles involving conjunction, contingency, and cardinality. The bulk of this paper explores how the view might be precisified, and how these puzzles might be resolved. (shrink)

Purity is the principle that fundamental facts only have fundamental constituents. In recent years, it has played a significant role in metaphysical theorizing—but its logical foundations are underdeveloped. I argue that recent advances in higher-order logic reveal a subtle ambiguity regarding Purity’s interpretation; there are stronger and weaker versions of that principle. The arguments for Purity only support the weaker interpretation, but arguments that employ it only succeed if the stronger interpretation is true. As a result, nearly every metaphysician who (...) has appealed to Purity has made a mistake—in that the inferences that they make are not justified by the arguments that they provide. (shrink)

This paper investigates the metaphysics in higher-order counterfactual logic. I establish the necessity of identity and distinctness and show that the logic is committed to vacuism, which entails that all counteridenticals are true. I prove the Barcan, Converse Barcan, Being Constraint and Necessitism. I then show how to derive the Identity of Indiscernibles in counterfactual logic. I study a form of maximalist ontology which has been claimed to be so expansive as to be inconsistent. I show that it is equivalent (...) to the collapse of the counterfactual into the material conditional---which is itself equivalent to the modal logic TRIV. TRIV is consistent, from which it follows that maximalism is, surprisingly, consistent. I close by arguing that stating the limit assumption requires a higher-order logic. (shrink)

This paper consists of an investigation of three debates concerning propositional identity: the tension between structured propositions and higher-order logic, the principle Only Logical Circles, and Kaplan’s Paradox. The literature at large has mistaken the consequences of each of these debates. Structuralists are not committed to the claim that identical properties have different extensions; rather, they are committed to existence monism. Only Logical Circles does not preclude the identification of green in terms of grue; some further (and, as of yet, (...) undisclosed) principle is required for that result. And Kaplan’s Paradox does not count against the possible-worlds conception of propositions; it applies to every account of propositions whatsoever. (shrink)

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 (i.e., 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 F is the same as G), Irreflexivity (...) (there are no reflexive definitions) and Leibniz’s Law. Additionally, it possesses the resources to resolve the paradox of analysis. (shrink)

I show that the theory of definition in Definition by Proxy can consistently embrace the principles I show to be inconsistent in Definition.

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 \textit{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. (shrink)

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. (shrink)