Papers in Metaphysics
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Review of Symbolic Logic, 18 (1): 28-51, 2025.
In the topic-sensitive theory of the logic of imagination due to Berto (2018a), the topic of the imaginative output must be contained within the imaginative input. That is, imaginative episodes can never expand what they are about. We argue, with Badura (2021), that this constraint is implausible from a psychological point of view, and it wrongly predicts the falsehood of true reports of imagination. Thus the constraint should be relaxed; but how? A number of direct approaches to relaxing the controversial content-inclusion constraint are explored in this paper. The core idea is to consider adding an expansion operator to the mereology of topics. The logic that results depends on the formal constraints placed on topic expansion, the choice of which are subject to philosophical dispute. The first semantics we explore is a topological approach using a closure operator, and we show that the resulting logic is the same as Berto's own system. The second approach uses an inclusive and monotone increasing operator, and we give a sound and complete axiomatisation for its logic. The third approach uses an inclusive and additive operator, and we show that the associated logic is strictly weaker than the previous two systems, and additivity is not definable in the language. The latter result suggests that involved techniques or a more expressive language is required for a complete axiomatization of the system, which is left as an open question. All three systems are simple tweaks on Berto's system in that the language remains propositional, and the underlying theory of topics is unchanged. -
Powers, Parts, and Wholes, (eds.) C.J. Austin, A. Marmodoro, A. Roselli, Routledge, 11--41, 2024.
Do powers have parts? Mereological thinking is typically guided by two different metaphors: building versus carving. The building picture treats wholes as constructed from fundamental bits; the carving treats wholes as the result of carving some interconnected space. After considering some suggestions for how to view powers as built from other components, this chapter opts for the carving picture and suggests that a mereology of powers can be generated by carving the underlying space of an interconnected web of fundamental powers. The space of powers is a network of manifestation/triggering connections that can be modelled graph-theoretically where the identity of a fundamental power is importantly tied up with its position in the overall structure. This chapter considers the idea that powers are completely identified by their position in the structure (as pandispositionalists have thought), which then places limits on the sorts of structures that powers theorists can help themselves to. This chapter also considers another novel suggestion on the identity of powers borrowed from non-well-founded set theory. It shows how to identify principles governing ‘carving’ the web into groups of closely connected powers, such that one group can naturally be called ‘part’ of another group, and explore the resulting mereology.
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Synthese, Special Issue: Mereology & Identity, (eds.) M. Carrara and G. Lando, 198: 4229--4245, 2021
Mereological principles are often controversial; perhaps the most stark contrast is between those who claim that Weak Supplementation is analytic—constitutive of our notion of proper parthood—and those who argue that the principle is simply false, and subject to many counterexamples. The aim of this paper is to diagnose the source of this dispute. I’ll suggest that the dispute has arisen by participants failing to be sensitive to two different conceptions of proper parthood: the outstripping conception and the non-identity conception. I’ll argue that the outstripping conception (together with a specific set of definitions for other mereological notions), can deliver the analyticity of Weak Supplementation on at least one sense of ‘analyticity’. I’ll also suggest that the non-identity conception cannot do so independently of considerations to do with mereological extensionality.
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Journal of Philosophical Logic, 48:5, 909--955, 2019
In a series of papers, Fine (1994, 1999) develops his hylomorphic theory of embodiments. In this article, we supply a formal semantics for this theory that is adequate to the principles laid down for it in. In Section 1, we lay out the theory of embodiments as Fine presents it. In Section 2, we argue on Cantorian grounds that the theory needs to be stabilized, and sketch some ways forward, discussing various choice points in modeling the view. In Section 3, we develop a formal semantics for the theory of embodiments by constructing embodiments in stages and restricting the domain of the second-order quantifiers. In Section 4 we give a few illustrative examples to show how the models deliver Finean hylomorphic consequences. In Section 5, we prove that Fine’s principles are sound with respect to this semantics. In Section 6 we present some inexpressibility results concerning Fine’s various notions of parthood and show that in our formal semantics these notions are all expressible using a single mereological primitive. In Section 7, we prove several mereological results stemming from the model theory, showing that the mereology is surprisingly robust. In Section 8, we draw some philosophical lessons from the formal semantics, and in particular respond to Koslicki’s main objection to Fine’s theory. In the appendix we present proofs of the inexpressibility results of Section 6.
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Graham Priest on Dialetheism and Paraconsistency: Outstanding Contributions to Logic 18, (eds.) C. Baskent, and T. Ferguson, Springer, 217--229, 2019.
Priest’s 2014 theory of unity and identity, based on a paraconsistent logic, has a wide range of applications. In this paper, I apply his theory to some puzzles concerning mereology and topology. These puzzles suggest that the classical mereotopology needs to be revised. I compare and contrast the Priest-inspired solution with another, based on classical logic, that requires the co-location of boundaries. I suggest that the co-location view should be preferred on abductive grounds.
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Review of Symbolic Logic, 12:1, 201--208, 2019.
We present a new axiomatization of classical mereology in which the three components of the theory—ordering, composition, and decomposition principles—are neatly separated. The equivalence of our axiom system with other, more familiar systems is established by purely deductive methods, along with additional results on the relative strengths of the composition and decomposition axioms of each theory.
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Australasian Journal of Logic, 15:4, 642--645, 2018.
In the last several years, paraconsistent mereology has begun to be developed and applied to a range of philosophical issues, from puzzles about boundaries, to the Meinongian ‘problem of nothingness’, to the metaphysics of unity. Because these formal systems are fresh out of the package, as it were, there will inevitably be some wrinkles that need ironing out. In this note, I’ll point out a problem with the system in Priest (2014a, 2014b), and suggest a natural fix.
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Mind, 125:500, 959--965, 2016.
I reply to Hawthorne and Uzquiano’s arguments for the incompatibility between mereological universalism and plenitudinous co-location. I argue that a mereology in which antisymmetry for parthood fails is independently motivated, and allows for both universalism and plenitudinous co-location. There can be as many angels in a place as there are cardinalities.
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Nous, 50:1, 121--132, 2016.
Does a commitment to mereological universalism automatically bring along a commitment to the controversial doctrine of mereological extensionalism—the view that objects with the same proper parts are identical? A recent argument suggests the answer is ‘yes’. This paper attempts a systematic response to the argument, considering nearly every available line of reply. It argues that only one approach—the mutual parts view—can yield a viable mereology where universalism does not entail extensionalism.
NB: I no longer agree with some of the conclusions of this paper. See Loss (2022), and Calosi & Giordani (2023).
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Logic & Logical Philosophy, Special Issue: Mereology & Beyond, (eds.) A. C. Varzi and R. Gruszczynski, 24:4, 429--447, 2015.
In classical extensional mereology, composition is idempotent: if x is part of y, then the sum of x and y is identical to y. In this paper, I provide a systematic and coherent formal mereology for which idempotence fails. I first discuss a number of purported counterexamples to idempotence that have been put forward in the literature. I then discuss two recent attempts at sketching non-idempotent formal mereology due to Karen Bennett and Kit Fine. I argue that these attempts are incomplete, however, and there are many open issues left unresolved. I then construct a class of models of a non-idempotent mereology using multiset theory, consider their algebraic structure, and show how these models can shed light on the open issues left from the previous approaches.
LINK
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Synthese, 192.5: 1267--1294, 2015.
Mereotopology is a theory of connected parts. The existence of boundaries, as parts of everyday objects, is basic to any such theory; but in classical mereotopology, there is a problem: if boundaries exist, then either distinct entities cannot be in contact, or else space is not topologically connected. In this paper we urge that this problem can be met with a paraconsistent mereotopology, and sketch the details of one such approach. The resulting theory focuses attention on the role of empty parts, in delivering a balanced and bounded metaphysics of naive space.
For developments of this formal system, see Casati & Fujikawa (2019).
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Australasian Journal of Philosophy, 4:92, 649--664, 2014.
Those who accept the necessity of mereological universalism face what has come to be known as the ‘junk argument’ due to Bohn (2009), which proceeds from (i) the incompatibility of junk with universalism and (ii) the possibility of junk, to conclude that mereological universalism isn't metaphysically necessary. Most attention has focused on (ii); however, recent authors have cast doubt on (i). This paper undertakes a defence of premise (i) against three main objections. The first is a new objection to the effect that Bohn's defence of that premise presupposes far too much. I show that one can defend premise (i) from a much weaker set of assumptions. The second objection, due to Contessa (2012), is that those who accept unrestricted composition should only accept the existence of binary sums (which are compatible with junk) rather than infinitary fusions. I argue that this conception of unrestricted composition is problematic: it is in conflict with an intuitive remainder principle. The final objection is due to Spencer (2012). His view is that there is no absolutely unrestricted plural universal quantifier; so any statement of the unrestricted fusion axiom will simply not rule out the existence of junky worlds. I argue that the failure of unrestricted quantification will not be enough by itself to establish the existence of junk. Furthermore, it is not clear whether this view counts as a form of mereological universalism. As a result, I suggest that if one wants to reject the junk argument, premise (ii) is the only viable option.
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Thought, Special Issue: Time & Modality, 2:3, 228--241, 2013.
Mereological nihilists are faced with a difficult challenge: explaining ordinary talk about material objects. Popular paraphrase strategies involve plurals, arrangements of particles, or fictions. In this paper, a new paraphrase strategy is put forward that has distinct advantages over its rivals: it is compatible with gunk and emergent properties of macro-objects. The only assumption is a commitment to a liberal view of the nature of simples; the nihilist must be willing to accept the possibility of heterogeneous extended simples. I suggest reinterpreting the parthood and composition relations as modal. According to this paraphrase, composition is a kind of counterpart relation. I show that one can accept that mereological nihilism is metaphysically necessary, while endorsing all the claims of classical mereology. As a result, the nihilists are in exactly the same position as the classical mereologist when it comes to explaining talk about ordinary objects, but without the additional ontology.
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Thought, 2:1, 67--72, 2013.
Contemporary metaphysicians have been drawn to a certain attractive picture of the structure of the world. This picture consists in classical mereology, the priority of parts over wholes, and the well-foundedness of metaphysical priority. In this short note, I show that this combination of theses entails superatomism, which is a significant strengthening of mereological atomism. This commitment has been missed in the literature due to certain sorts of models of mereology being overlooked. But the entailment is an important one: we must either accept superatomism or reject one (or other) of the most widespread theses of contemporary metaphysics.
NB: I no longer accept the conclusions in this paper. See Uzquiano (2017) and Dixon (2020).
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Philosophy Compass, 8:9, 834--845, 2013.
The dominant theory of parts and wholes – classical extensional mereology – has faced a number of challenges in the recent literature. This article gives a sampling of some of the alleged counterexamples to some of the more controversial principles involving the connections between parthood and identity. Along the way, some of the main revisionary approaches are reviewed. First, counterexamples to extensionality are reviewed. The ‘supplementation’ axioms that generate extensionality are examined more carefully, and a suggested revision is considered. Second, the paper considers an alternative approach that focuses the blame on antisymmetry but allows us to keep natural supplementation axioms. Third, we look at counterexamples to the idempotency of composition and the associated ‘parts just once’ principle. We explore options for developing weaker mereologies that avoid such commitments
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Oxford Studies in Metaphysics, vol. 8, (eds.) D. Zimmerman and K. Bennett, OUP, 295--322, 2013.
There are three main challenges for defenders of composition as identity: the syntactic challenge, the semantic challenge, and the discernibility challenge . In this chapter, the author claims all three challenges can be met. The first — van Inwagen’s — is that the view cannot be expressed grammatically in English. The author responds by appealing to free relatives as operators that shift syntactic number while leaving semantic number fixed. The second — Lewis’s — is that no generalization of standard notions of identity can be put in service of composition as identity. The author responds by giving full set-theoretic models of a generalized identity relation that preserves standard singular and plural identity. The author also derives a generalization of the parthood relation that preserves classical extensional mereology, and shows that standard features of plural logic are preserved. The third — Lewis’s — is that one cannot account for apparent failures of Leibniz’s Law. This challenge is met by utilizing two different cover-based semantics for predication in plural logic involving no restrictions on Leibniz’s Law for general identity.
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Composition as Identity, (eds.) A. J. Cotnoir and D. L. M. Baxter, OUP, 3--23, 2014.
Composition is the relation between a whole and its parts—the parts are said to compose the whole; the whole comprises the parts. But is a whole anything over and above its parts taken collectively? Are the many parts identical to the one whole? This chapter traces the motivations, varieties, and problems with the view that has come to be known as composition as identity. It also provides an introduction and background in formal mereology and plural logic that is necessary for understanding the contemporary debate.
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Review of Symbolic Logic, 5.2: 187--204, 2012.
This paper is a systematic exploration of non-wellfounded mereology. Motivations and applications suggested in the literature are considered. Some are exotic like Borges’ Aleph, and the Trinity; other examples are less so, like time traveling bricks, and even Geach’s Tibbles the Cat. The authors point out that the transitivity of non-wellfounded parthood is inconsistent with extensionality. A non-wellfounded mereology is developed with careful consideration paid to rival notions of supplementation and fusion. Two equivalent axiomatizations are given, and are compared to classical mereology. We provide a class of models with respect to which the non-wellfounded mereology is sound and complete.
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Philosophical Quarterly, 60 (239): 396--405, 2010.
I examine the link between extensionality principles of classical mereology and the anti‐symmetry of parthood. Varzi's most recent defence of extensionality depends crucially on assuming anti‐symmetry. I examine the notions of proper parthood, weak supplementation, and non‐well‐foundedness. By rejecting anti‐symmetry, the anti‐extensionalist has a unified, independently grounded response to Varzi's arguments. I give a formal construction of a non‐extensional mereology in which anti‐symmetry fails. If the notion of ‘mereological equivalence’ is made explicit, this non‐anti‐symmetric mereology recaptures all of the structure of classical mereology.
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Handbook of Mereology, (eds.) H. Burkhardt , J. Seibt, S. Gerogiorgakis, and G. Imaguire, Philosophia Verlag, 385--390, 2017.
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Notre Dame Philosophical Reviews, 2015.
Papers in Philosophical Logic
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Pluralisms in Truth and Logic, (eds.) N. Kellen, N.J.L.L. Pedersen, J. Wyatt, Palgrave Macmillan, 301--329, 2018.
Much of the discussion in the philosophy of logic over the last decade has been devoted to the debate between logical monism and logical pluralism. But logical nihilism hasn’t been given nearly as much attention, even though the view has historical roots and is philosophically defensible. I present and defend a number of arguments in favor of logical nihilism. These arguments are grouped into two main families: arguments from diversity (§2) and arguments from expressive limitations (§3). These arguments are often simple syllogisms pointing to fundamental differences between natural languages and formal consequence relations. Many of the arguments involve familiar problems in the philosophy of logic. The arguments, taken individually, are interesting in their own right; they each highlight an important way in which the formal methods of logic can be seen to be inadequate to modeling natural language inference. But the arguments taken jointly are more significant; by presenting all the arguments together, we can build something of a cumulative case for logical nihilism. Of course, if any of these arguments are sound, then logical nihilism is correct. But the arguments reinforce one another, such that logical nihilism presents us with a unified view across a broad range of issues in philosophy of logic. I conclude (§4) by considering related philosophical issues and sketching a general outlook on logic and formal methods that is nihilist-friendly. -
Journal of Philosophy, 3:112, 113--140, 2015.
Ontological pluralism holds that there are different ways of being. Truth pluralism holds that there are different ways of being true. Both views have received growing attention in recent literature, but so far there has been very little discussion of the connections between the views. The authors suggest that motivations typically given for truth pluralism have analogue motivations for ontological pluralism; they argue that while neither view entails the other, those who hold one view and wish to hold the other will find natural routes by which to do so. The authors additionally identify some disanalogies between the views, by considering whether certain “mixed” problems commonly pressed against truth pluralism have analogues for ontological pluralism.
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The Moon Points Back, (eds.) Y. Deguchi, J. Garfield, G. Priest, and K. Tanaka, OUP, 176--188 2015.
Jay Garfield and Graham Priest have attempted to make sense of Nagarjuna’s apparently paradoxical uses of the catuskoti, or “four corners of truth”—according to which, a sentence may be true, false, both, or neither—by presenting a series of lattices. This chapter argues that Garfield and Priest’s lattices cannot ground the logic at play in Nagarjuna’s MMK; their semantic analysis cannot be an accurate analysis of Nagarjuna’s arguments. The chapter argues for a new semantic interpretation that places greater emphasis on the suggestion that the positive catuskoti requires disambiguation between the conventional and ultimate perspectives, whereas the negative catuskoti does not.
For recent discussion, see Wang & Wen-Fang (2024)
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Philosophy and Phenomenological Research, 83:3, 563--579, 2013.
Truth pluralists accept that there are many truth properties. But truth pluralists disagree over whether any of these truth properties apply generally across the whole class of propositions, or whether their application is in some way restricted. Weak truth pluralists accept that there is at least one general truth property. Strong pluralism is the view that does not accept a general truth property. I think that strong pluralism has not recieved sufficient attention. Perhaps this is due in large part to strong pluralists’ difficulties in solving some formal problems faced by truth pluralists, such as Tappolet’s Problem of Mixed Inferences. In this paper, I argue that the strong pluralist’s prospects for solving this problem are not as hopeless as it might first appear; the Problem of Mixed Inferences can be solved.
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Truth and Pluralism: Current Debates, (eds.) N.J.L.L. Pedersen and C.D. Wright, OUP, 339--350, 2013.
The semantic paradoxes are as much of a problem for pluralists about truth as they are for any other theory of truth. Alethic pluralists, however, have generally set discussion of the paradoxes aside. In what follows, I argue that considerations involving the paradoxes have direct implications for alethic pluralism. More specifcally, alethic pluralism has bifurcated into two main types: strong and weak . Weak theories accept a truth predicate that applies to every true sentence (a universal truth predicate) in addition to the many other truth predicates. Strong theories reject a universal truth predicate in favor of the many. is chapter has two parts. The negative part (§2) shows that both types of theories suffer from paradox-generated inconsistency given certain plausible assumptions. The positive part (§3) outlines a new, consistent way to be a strong alethic pluralist. The trick to avoiding paradox is rejecting infinitary disjunction, something we already have pluralism-independent (but paradox-motivated) reasons to reject. In §4, I conclude by comparing this theory with a Tarskian hierarchical view and discuss some directions for future research.
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Analysis, 69.3: 473--479, 2009.
Christine Tappolet (1997) posed a problem for alethic pluralism: either deny the truth of conjunctions whose conjuncts are from distinct domains of inquiry, or posit a generic global truth property thus making other truth properties redundant. Douglas Edwards (2008) has attempted to solve the problem by avoiding the horns of Tappolet’s dilemma. After first noting an unappreciated consequence of Edwards’ view regarding a proliferation of truth properties, I show that Edwards’ proposal fails to avoid Tappolet’s original dilemma. His response is not successful as it lets in a generic truth property through the ‘back door’. I conclude by briefly offering a new solution to the problem, and an alternative diagnosis of Tappolet’s dilemma.
I now think the mixed inference problems have been solved by Yu (2017).
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Analysis, 68.3: 238--244, 2008.
Jenkins (2007) charges that the language advanced in Beall (2007) is either expressively impoverished, or inconsistent. We argue that Jenkins’ objections are based on unreasonably strong constraints on formal theories of truth. Our primary concern is not to defend the ‘paranormal’ framework advanced in Beall, but to respond to a common – and implausible – ‘revenge’-style charge directed at a certain class of formal theories of truth and paradox.
Papers in Philosophy of Religion
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Oxford Handbook of Omnipresence, (eds.) A. Marmodoro, D. Migliorini, B. Page, Oxford University Press, 2025.
Recently analytic metaphysicians have been concerned with carefully examining the interaction between theories of location and theories of parthood. Mereological ‘Harmony’ or ‘Mirroring’ principles often necessitate that any entity occupying a complex location must have parts located there. On some understandings, these principles can come into conflict with the traditional view of an omnipresent yet mereologically simple God. This chapter lists the potential sources of conflict, showing how most occupation-based accounts of omnipresence (including the popular ‘ubiquitous entension’ view) must reject metaphysically important mirroring principles. I then outline a new occupation-based theory of omnipresence which avoids these conflicts. The central idea, motivated by considerations of divine transcendence and divine immensity, is that God is weakly located everywhere but lacks any exact location in spacetime.
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Religious Studies, 58(1):258—265, 2022.
Philosophers and theologians have long recognized apparent contradictions in the Christian doctrine of the incarnation wherein Jesus is both fully divine and fully human and thereby exemplifies all properties essential to being divine and all properties essential to being human, including, respectively, immutability and mutability. In this article, we outline a new account of such apparent contradictions, wherein each such pair of (modal) properties involves different modal operators.
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Journal of Analytic Theology, 17: 508--528, 2019.
What is the proper role of logic in analytic theology? This question is thrown into sharp relief when a basic logical principle is questioned, as in Beall’s ‘Christ – A Contradiction.’ Analytic philosophers of logic have debated between exceptionalism and anti-exceptionalism, with the tide shifting towards anti-exceptionalism in recent years. By contrast, analytic theologians have largely been exceptionalists. The aim of this paper is to argue for an anti-exceptionalist view, specifically treating logic as a modelling tool. Along the way I critically engage with Beall on the role of logic in theology, maintaining that theological inquiry is in some ways disanalogous with other theoretical enterprises.
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Australasian Journal of Philosophy, 96:3, 592--609, 2018.
The divine attributes of omniscience and omnipotence have faced objections to their very consistency. Such objections rely on reasoning parallel to semantic paradoxes such as the Liar or to set-theoretic paradoxes like Russell's paradox. With the advent of paraconsistent logics, dialetheism—the view that some contradictions are true—became a major player in the search for a solution to such paradoxes. This paper explores whether dialetheism, armed with the tools of paraconsistent logics, has the resources to respond to the objections levelled against the divine attributes.
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Analysis, 77:4, 681--689, 2017.
Traditional monotheism has long faced logical puzzles. We argue that such puzzles rest on the assumed logical truth of the Law of Excluded Middle, which we suggest there is little theological reason to accept. By way of illustration we focus on God's alleged stone problem, and present a simple but plausible ‘gappy’ framework for addressing this puzzle. We assume familiarity with the proposed logic but an appendix is offered as a brief review.
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Faith & Philosophy, 34:2, 123--151, 2017.
Perichoresis, or “mutual indwelling,” is a crucial concept in Trinitarian theology. But the philosophical underpinnings of the concept are puzzling. According to ordinary conceptions of “indwelling” or “being in,” it is incoherent to think that two entities could be in each other. In this paper, I propose a mereological way of understanding “being in,” by analogy with standard examples in contemporary metaphysics. I argue that this proposal does not conflict with the doctrine of divine simplicity, but instead affirms it. I conclude by discussing how mutual indwelling relates to the concepts of unity and identity.