My research is focused primarily on grounding, philosophical regresses, and the natures of properties, relations, propositions, facts, and states of affairs.  I also have interests in other areas of metaphysics, including mereology, modality, and the philosophy of time and time travel. In addition, I have interests in other areas of philosophy, primarily in logic and the philosophies of mathematics and religion.

Works in Progress

Research Articles

Maureen Donnelly has recently argued that directionalism, the view that relations have a direction, applying to their relata in an order, is unable to properly treat certain symmetric relations. She alleges that it must count the application of such a relation to an appropriate number of objects in a given order as distinct from its application to those objects in any other ordering of them. I reply by showing how the directionalist can link the application conditions of any fixed arity relation, no matter its arity or symmetry, and its converse(s) in such a way that directionalism will yield the correct ways in which it can apply. I thus establish that directionalism possesses the same advantage Donnelly's own account of relations, relative positionalism, has over traditional positionalist accounts of relations, which do not properly treat symmetric relations. I then note some advantages that directionalism has over its closest competitors. This includes Donnelly's relative positionalism, since directionalism is not, like relative positionalism, committed to the involvement of relative properties in every irreducibly relational claim. I close by conceding that, as Donnelly notes, directionalism is committed to the primitive relation of order-sensitive relational application. But I don't find this notion as mysterious as Donnelly does. I conclude that, even if one construes this feature of directionalism as a drawback, the two views are at worst at a draw, other things being equal, since this drawback is mitigated by the advantage directionalism has over relative positionalism.

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There are two ways to characterize symmetric relations. One is intensional: necessarily, Rxy iff Ryx. In some discussions of relations, however, what is important is whether or not a relation gives rise to the same completion of a given type (fact, state of affairs, or proposition) for each of its possible applications to some fixed relata. Kit Fine calls relations that do 'strictly symmetric'. Is there a difference between the notions of necessary and strict symmetry that would prevent them from being used interchangeably in such discussions? I show that there is. While the notions coincide assuming an intensional account of relations and their completions, according to which relations/completions are identical if they are necessarily coinstantiated/equivalent, they come apart assuming a hyperintensional account, which individuates relations and completions more finely on the basis of relations' real definitions. I establish this by identifying two definable relations, each of which is necessarily symmetric but nonetheless results in distinct facts when it applies to the same objects in opposite orders. In each case, I argue that these facts are distinct because they have different grounds.

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I propose a way to accommodate plausible examples of cyclic grounding chains that have been proposed in the literature while preserving a good measure of the metaphysical foundationalist’s grounding hierarchy with a foundational level. This precludes the need to adopt a strong form of coherentism, such as the view that everything grounds everything, or even the view that everything grounds everything other than itself. I do this by developing axiomatizations of grounding which allow for localized cycles of ground at the non-foundational and foundational levels, but which still place certain foundationalism-like constraints on the grounds that grounded facts must have. In addition, I point to considerations, previously put forth in favor of foundationalism and a strong form of coherentism, that also help support the views I develop.

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There are at least three vaguely atomistic principles that have come up in the literature, two explicitly and one implicitly. First, standard atomism is the claim that everything is composed of atoms, and is very often how atomism is characterized in the literature. Second, superatomism is the claim that parthood is well-founded, which implies that every proper parthood chain terminates, and has been discussed as a stronger alternative to standard atomism. Third, there is a principle that lies between these two theses in terms of its relative strength: strong atomism, the claim that every maximal proper parthood chain terminates. Although strong atomism is equivalent to superatomism in classical extensional mereology, it is strictly weaker than it in strictly weaker systems in which parthood is a partial order. And it is strictly stronger than standard atomism in classical extensional mereology, and, given the axiom of choice, in such strictly weaker systems as well. Though strong atomism has not, to my knowledge, been explicitly identified, Shiver appears to have it in mind, though it is unclear whether he recognizes that it is not equivalent to standard atomism in each of the mereologies he considers. I prove these logical relationships which hold amongst these three atomistic principles, and argue that, whether one adopts classical extensional mereology or a system strictly weaker than it in which parthood is a partial order, standard atomism is a more defensible addition to one's mereology than either of the other two principles, and it should be regarded as the best formulation of the atomistic thesis.

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Once one accepts that certain things metaphysically depend upon, or are metaphysically explained by, other things, it is natural to begin to wonder whether these chains of dependence or explanation must come to an end. This essay surveys the work that has been done on this issue--the issue of grounding and infinite descent. I frame the discussion around three questions: (1) What is infinite descent?, (2) Is infinite descent possible?, and (3) What considerations are there for or against infinite descent? When relevant, I connect the discussion to the three main views about the way reality can be structured by grounding: metaphysical foundationalism, metaphysical coherentism, and metaphysical infinitism.

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Maureen Donnelly's (2016) relative positionalism correctly handles any fixed arity relation with any symmetry such a relation can have, yielding the intuitively correct way(s) in which that relation can apply. And it supplies an explanation of what is going on in the world that makes this the case. But it has at least one potential shortcoming--one that its opponents are likely to seize upon: it can only handle relations with fixed arities. It is unable to handle relations with variable arities. I argue that, all else being equal, relative positionalism ought nonetheless to be preferred to its closest competitors--at least to the extent that the explanation it supplies of relational application is plausible--even though those competitors can handle variable arity relations in addition to fixed arity relations.

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Kit Fine (2000) breaks with tradition, arguing that, pace Russell (e.g., 1903: 228), relations have neither directions nor converses.  He considers two ways to conceive of these new "neutral" relations, positionalism and anti-positionalism, and argues that the latter should be preferred to the former.  Cody Gilmore (2013) argues for a generalization of positionalism, slot theory, the view that a property or relation is n-adic if and only if there are exactly n slots in it, and (very roughly) that each slot may be occupied by at most one entity.  Slot theory (and with it, positionalism) bears the full brunt of Fine's (2000) symmetric completions and conflicting adicities problems.  I develop an alternative, plural slot theory (or pocket theory), which avoids these problems, key elements of which have been considered by Yi (1999: 168 ff.), McKay (2006: 13), and Gilmore himself (2013: 229--30).  Like the slot theorist, the pocket theorist posits entities (pockets) in properties and relations that can be occupied. But unlike the slot theorist, the pocket theorist denies that at most one entity can occupy any one of them.  As a result, she must also deny that the adicity of a property or relation is equal to the number of occupiable entities in it. By abandoning these theses, however, the pocket theorist is able to avoid Fine's problems, resulting in a stronger theory about the internal structure of properties and relations.  Pocket theory also avoids a serious drawback of anti-positionalism.

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Realists about universals face a question about grounding. Are things how they are because they instantiate the universals they do? Or do they instantiate those universals because they are how they are? Take Ebenezer Scrooge. You can say that (i) Scrooge is greedy because he instantiates greediness, or you can say that (ii) Scrooge instantiates greediness because he is greedy. I argue that there is reason to prefer the latter to the former. I develop two arguments for the view. I also respond to some concerns one might have about the view defended. I close by showing that analogous views regarding the truth of propositions (that if the proposition that p is true, then it is true because p) and the existence of facts (that if the fact that p exists, then it exists because p) are supported by analogs of one of these arguments.

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Partial grounding is often thought to be formally analogous to proper parthood in certain ways. For example, both relations are typically understood to be asymmetric (and hence irreflexive) and transitive, and as such, are strict partial orders. But how far does this analogy extend? Proper parthood is often said to obey the Weak Supplementation Principle. In this paper I argue that partial grounding does not obey a ground-theoretic analog of this principle. The case that causes problems for the supplementation principle for grounding also serves as a counterexample to another principle, Minimality, defended by Paul Audi.

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Speaks (2014) defends the view that propositions are properties: e.g., the proposition that grass is green is the property being such that grass is green. We argue that there is no reason to prefer Speaks’s theory to analogous but competing theories that identify propositions with, say, 2-adic relations. This style of argument has recently been deployed by many, including Moore (1999) and King (2007), against the view that propositions are n-tuples, and by Caplan and Tillman (2013) against King’s view that propositions are facts of a special sort. We offer our argument as an objection to the view that propositions are unsaturated (non-zero-adic) relations.

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A number of philosophers think that grounding is, in some sense, well-founded. This thesis, however, is not always articulated precisely, nor is there a consensus in the literature as to how it should be characterized. I consider several principles that one might have in mind when asserting that grounding is well-founded, and I argue that one of these principles, which I call 'full foundations', best captures the relevant claim. My argument is by the process of elimination. For each of the inadequate principles, I illustrate its inadequacy by showing either that it excludes cases that should not be ruled out by a well-foundedness axiom for grounding, or that it admits cases that should be ruled out.

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  Supplemental Proofs

Geoffrey Hellman is a mathematical structuralist. He is also a nominalist. Hellman’s nominalism leads him to a unique account of structuralism, known as modal structuralism. The goal of this paper is not to evaluate nominalism, but to highlight what some may take to be an important problem facing Hellman’s modal structuralist account, and to demonstrate that this problem can be overcome without having to abandon nominalism. On Hellman’s account, an arbitrary statement of a mathematical theory is true just in case it is possible that there exists a system of which the axioms of that theory hold. In this way, mathematical truth is reduced to modal truth. Although Hellman provides a model-theoretic semantics of the modal operators, he does not provide an interpretation of those models. Rather, Hellman takes the modal operators as primitive. There has been, however, in the literature concerning the metaphysics of modality, a common tendency to prefer a reductive account of modality. Those who find unacceptable the approach of taking the modal operators as primitive will undoubtedly find modal structuralism, as formulated by Hellman, unacceptable as well. I argue that there is an alternative to taking the modal operators as primitive, which does not conflict with the nominalistic commitments of modal structuralism, and which has advantages over Hellman’s account. Specifically, one can adopt a concrete modal realist account of modality as the foundation of modal structuralism.

Proceedings Table of Contents

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I answer questions surrounding some of the more controversial formal properties of grounding, which is generally understood as metaphysical dependence or metaphysical explanation. I also consider questions about how grounding interacts with various other important issues in metaphysics. Questions about the well-foundedness of grounding are closely related to questions about philosophical regresses. In addition, there are questions to be asked about how grounding interacts with the notion of instantiation. In chapter 1, I determine exactly what one might mean when one says that grounding is well-founded. A number of philosophers think it is, but the thesis is rarely precisely articulated. Roughly, the idea is that every explanation must ``bottom out'', or that there is a ``bottom level'' of facts. I consider a number of plausible ways to precisely characterize the claim, and argue for a particular one--that every non-fundamental fact is fully grounded by some fundamental facts. In chapter 2, I connect the notion of the well-foundedness of grounding to the notion of a vicious grounding regress. I propose that the viciousness of a vicious grounding regress can be explained by its incompatibility with the well-foundedness axiom I defend in chapter 1. I also argue for a particular analysis of the notion of a grounding regress. In chapter 3, I show that what Karen Bennett (2011) calls `the fact regress' does not violate the well-foundedness of grounding, contrary to her claims. In chapter 4 I show that, pace Plato et al., things instantiate the universals they do in virtue of how they are, rather than vice versa. One of the reasons I provide for thinking this is that, otherwise, a vicious grounding regress results. The final chapter is devoted to the questions of whether grounding, like parthood, obeys a supplementation principle, and whether it is minimal, in the Paul Audi's (2012) sense. I argue that it does not obey a ground-theoretic analog of either weak supplementation or quasi-supplementation (see Gilmore 2009), and that it does not obey Audi's principle either. Appendix A comprises a number of proofs which, together with several models discussed in chapter 1, exhibit the logical relationships that exist among the candidate well-foundedness axioms considered there. In appendix B, I discuss a number of plausible examples of a new type of grounding structure, which add to the overall case made in chapter 1.

Published Version

M. A. Thesis

The most important attempts to reconcile presentism with scientific findings concerning the nature of time, specifically, with the special theory of relativity (STR), fail. Presentism is the view that only the present exists, while eternalism is the opposing view that the past, present, and future exist. Presentism is usually motivated by claiming that it provides a metaphysical account of time which fits better with our intuitions concerning time than does eternalism. I claim that presentism faces a dilemma. Either the presentist modifies presentism to accommodate STR as it is usually formulated, and faces the consequence that events are present (and thus extant) only relatively to reference frames, or the presentist adopts the Lorentzian formulation of STR, which possesses the resources by which to define an absolute present, but in doing so, loses the intuitive appeal which set presentism apart from eternalism in the first place.

Published Version

© 2016 T. Scott Dixon All Rights Reserved