Samuel Elgin

This paper develops and defends a novel theory of modality. There is a single mosaic of spacetime points; possible worlds are partitions of this mosaic into occupied and unoccupied points. The resulting view is, in some respects, similar to modal realism. Propositions, properties, and relations depend upon the mosaic in much the same way. There are also significant differences. Unlike modal realism, this view allows for trans-world identity. Because the same points occupy multiple worlds, the same object exists in multiple worlds. It closes by exploring two puzzles for the view involving our causal interaction with and reference to merely possible objects.

The Principle of Sufficient Reason is the principle that there is an explanation for everything. While historically significant, it has largely fallen from favor in contemporary metaphysics; in full generality, it is widely held to have untenable implications. Foremost among these is necessitarianism—the claim that everything actually true is necessarily true. This paper consists of two arguments: one negative, the other positive. The first establishes that the standard argument linking the PSR to necessitarianism fails; rationalists have independent reasons to reject the argument’s background assumptions. The second provides a positive reason to hold that the PSR allows for contingency; there are distinct models of facts that are each compatible with the PSR. The PSR thus allows for it to be contingent which model obtains. I conclude that, if we are to reject the PSR, it is not because it gives rise to necessitarianism

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.

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.

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.

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.

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.

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

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.

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.

I provide an analysis of sentences of the form ‘To beFis to beG’ 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 somethingFalso makes itG. 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 onlyFs areGs. I motivate my account over Correia and Skiles’ [11] prominent alternative and close by defining an irreflexive and asymmetric notion of analysis in terms of the symmetric and reflexive notion.

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, 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, 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.

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 claim that their argument fails to establish this result for two reasons. First, their assumptions force our hand on a controversial debate within counterfactual logic. In particular, they license 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 many reject. Second, the system they develop is provably equivalent to appending Deduction Theorem to a T modal logic. It is unsurprising that the combination of Deduction Theorem with T results in necessitation; indeed, it is precisely for this reason that many logicians reject Deduction Theorem in modal contexts. If Deduction Theorem is unacceptable for modal logic, it cannot be assumed to derive the necessity of mathematics

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.

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, then S knows that all analytic parts of p are true as well. 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. I close by arguing that contextualists who maintain that knowledge attributions are closed within—but not between—linguistic contexts are tacitly committed to this principle’s truth

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.

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 is that which makes it G. This approach is hyperintensional, and possesses desirable logical and modal features. 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. I close by defining an asymmetric and irreflexive notion of analysis in terms of the reflexive and symmetric one.

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.

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 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