Are a material object, such as a statue, and its constituting matter, the clay, parts of one another? One wouldn't have thought so, and yet a number of philosophers have argued that they are. I review the arguments for this surprising claim showing how they all fail. I then consider two arguments against the view concluding that there are both pre-theoretical and theoretical considerations for denying that the statue and the clay are mutual parts.

Standard principles of mereology, such as the transitivity and asymmetry of proper parthood, have been questioned, using various multi-location scenarios. The most famous of these is Borges’s Aleph, although the literature is rife with other examples that allegedly show that some mereological principle is at odds with some form of multi-location. However, the scenarios only support this conclusion given various bridge principles that link location to parthood. I argue that the bridge principles that guarantee the desired conclusion are controversial partly (...) because they give the wrong result in other situations, in particular cases of co-location. Moreover, less controversial bridge principles do not provide an incompatibility result between standard mereological principles and multi-location. Hence, multi-location does not threaten any standard mereological principles. (shrink)

Classical mereology is a particularly strong theory about the part–whole relation. Not only does it ensure that any collection of entities composes a whole, or ‘fusion’, it also states that this object is unique: no two entities have the same parts. Recently, Claudio Calosi (dialectica 68(1):121–139, 2014) has argued that this extensional aspect makes classical mereology incompatible with multilocated entities. Calosi’s argument is arguably the most precise one from a whole battery of arguments to the effect that some mereological principle (...) is at odds with multilocation. Still, I show that Calosi’s arguments fail and that classical mereology is a safe space for multilocation. Moreover, I argue that the question of extensionality is orthogonal to the question of multilocation. (shrink)

Classical mereology is a particularly strong theory about the part–whole relation. Not only does it ensure that any collection of entities composes a whole, or ‘fusion’, it also states that this object is unique: no two entities have the same parts. Recently, Claudio Calosi (dialectica 68(1):121–139, 2014) has argued that this extensional aspect makes classical mereology incompatible with multilocated entities. Calosi’s argument is arguably the most precise one from a whole battery of arguments to the effect that some mereological principle (...) is at odds with multilocation. Still, I show that Calosi’s arguments fail and that classical mereology is a safe space for multilocation. Moreover, I argue that the question of extensionality is orthogonal to the question of multilocation. (shrink)

The doctrine of the immaculate conception, which is a dogma binding on all Roman Catholics and also held by members of some other Christian denominations, holds that Mary the mother of Jesus Christ was conceived without the stain of original sin as a result of the redeeming effects of Christ’s later life, passion, death, and resurrection. In this paper I argue first that, even on an orthodox reading of this doctrine, the immaculate conception seems to result in a kind of (...) causal time loop. I then consider several common philosophical objections to causal time loops, showing how each is either not a serious problem for causal time loops in general or is not a serious problem for the immaculate conception time loop in particular because of some particular features of that particular loop. The upshot of this discussion is that it shows that anyone who is committed to the dogma of the immaculate conception is also committed to the possibility, and, indeed, the actuality, of at least one causal time loop, but also that this is no reason to reject the dogma, since all of the major worries for causal time loops can be resolved in one way or another. (shrink)

Core principles of mereology have been questioned by appealing to time travel scenarios. This paper questions the methodology of employing time travel scenarios to argue against mereology. We show some time travel scenarios are structurally equivalent to more standard ones not involving time travel; and that the three main theories about persistence through time can each solve both the time travel scenario as well as the structurally similar classical scenario. Time travel scenarios that are not similar to more standard arguments (...) are instead problematic because they are open to different, incompatible interpretations. We conclude that compared to the classical arguments against mereological principles, time travel scenarios do not add anything new. (shrink)

We contribute to the ongoing discussion on mathematical structuralism by focusing on a question that has so far been neglected: when is a structure part of another structure? This paper is a first step towards answering the question. We will show that a certain conception of structures, abstractionism about structures, yields a natural definition of the parthood relation between structures. This answer has many interesting consequences; however, it conflicts with some standard mereological principles. We argue that the tension between abstractionism (...) about structure and classical mereology is an interesting result and conclude that the mereology of abstract structures is a subject that deserves further exploration. We also point out some connections between our discussion of the mereology of structures and recent work on non-well-founded mereologies. (shrink)

Some philosophers defend the possibility of synchronic multilocation, and have even used it to defend other substantive metaphysical theses. But just how strong is the case for the possibility of synchronic multilocation? The answer to this question depends in part on whether synchronic multilocation is wedded to other controversial metaphysical notions. In this paper, I consider whether the possibility of synchronic multilocation depends on the possibility of time travel, and I conclude that the answer hinges on the nature of time (...) and persistence. (shrink)

One objection to the thesis that multilocation is possible claims that, when combined with a preference for parsimonious theories, it leads to the absurd result that we ought to believe the material universe is composed of just one simple particle. I argue that this objection fails.

Multilocation and Minimal Mereology do not mix well. It has been pointed out that Three-Dimensionalism, which can be construed as multilocation-friendly, runs into trouble with Weak Supplementation. But in fact, regardless of one’s theory of persistence, if someone posits the possibility of any one of several kinds of multilocation, he or she will not be able to maintain the necessity of any of the three axioms of Minimal Mereology: the Transitivity of Proper Parthood, the Asymmetry of Proper Parthood, and Weak (...) Supplementation. In fact, positing even the mere conceivability of cases involving multilocation will require the denial of the analyticity of Minimal Mereology. In response to this, some have claimed that we ought to relativise parthood, either to one region or to two. Unfortunately, if we replace the axioms of Minimal Mereology with region-relativised counterparts, we will not be able to capture the intuitions that supported the original axioms. The only adequate solution, I maintain, is to restrict multilocation to a domain outside the scope of the rules we intuitively take to govern the parthood relation. For those who take Minimal Mereology to be necessary and universal, that will mean relinquishing the possibility of multilocation. (shrink)

The relation of being more fundamental than, as well as the Finean notion of partial grounding, are widely taken to be irreflexive, transitive, and asymmetric. However, certain time-travel cases that have been used to raise worries about the irreflexivity, transitivity, and asymmetry of proper part of can also be used to argue that more fundamental than and partially grounds do not have these formal properties. I present this worry and discuss several responses to it, with the aim of showing that (...) the problem is harder to address when applied to fundamentality and partial grounding than it was when merely applied to proper parthood. (shrink)

This paper argues that, assuming properties exist and must be located in spacetime, the prevailing view that they are exactly located where their instances are is false. Instead a property is singularly located at just one region, namely the union of its instance's locations. This bears not just on issues in the metaphysics of properties, but also on the debate over whether multi-location is conceivable and/or possible.

This paper argues that, in light of certain scenarios involving time travel, Sider’s definition of ‘instantaneous temporal part’ cannot be accepted in conjunction with a semantic thesis that perdurantists often assume. I examine a rejoinder from Sider, as well as Thomson’s alternative definition of ‘instantaneous temporal part’, and show how neither helps. Given this, we should give up on the perdurantist semantic thesis. I end by recommending that, once we no longer accept such semantics, we should accept a new set (...) of definitions, which are superior in certain respects to Sider’s original set. (shrink)

Cook argues that impure sets are not located. But ‘location’ is an ambiguous word and when we resolve those ambiguities it turns out that on no resolution is Cook's argument compelling.

Endurantists have recently faced a mereological puzzle in various forms. Here I argue that, instead of presenting a genuine worry, the puzzle actually reveals a common misunderstanding about the endurantist ontology. Furthermore, through this discussion of the alleged problem and the misunderstanding which motivates it, I reveal metaphysical commitments the endurantist has that may not be widely recognized. For instance, she is committed to interesting and perhaps controversial views about shape and location. I highlight these commitments and what they mean (...) for the endurantist. (shrink)

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. (shrink)

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. (shrink)

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, 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. (shrink)

An overview of contemporary part-whole theories, with reference to both their axiomatic developments and their philosophical underpinnings.

Material objects extend through space by having different spatial parts in different places. But how do they persist through time? According to some philosophers, things have temporal parts as well as spatial parts: accepting this is supposed to help us solve a whole bunch of metaphysical problems, and keep our philosophy in line with modern physics. Other philosophers disagree, arguing that neither metaphysics nor physics give us good reason to believe in temporal parts.

An introduction to the theories of endurantism and perdurantism, and persistence more broadly.

An overview of the way I picture the amorphous world we live in, built around my comments and responses to nine festschrift essays by A. Borghini (on the Fedro metaphor and the art of butchery), F. Calemi (on the predication principle and metalinguistic nominalism), C. Calosi (on the argument from mereological universalism to extensonality), E. Casetta (on the role of “monsters” in the realism/antirealism debate), V. Giardino (on inductive reasoning, spatial representation, and problem solving), P. Graziani (on mereological notation), P. (...) Pedrini (on the distinction between natural and artificial boundaries), D. Santoro (on causation by omission), and G. Torrengo (on absolute vs. relational space and the problem of incongruent counterparts). (shrink)