A material simple is a material object that has no proper parts. Some philosophers have argued for the possibility of extended simples. Some have even argued for the possibility of heterogeneous simples or simples that have intrinsic variations across their surfaces. There is a puzzle, though, that is meant to show that extended, heterogeneous simples are impossible. Although several plausible responses have been given to this puzzle, I wish to reopen the case against extended, heterogeneous simples. In this paper, I (...) briefly canvass responses to this puzzle which may be made in defense of extended, heterogeneous simples. I then present a new version of this puzzle which targets simples that occupy atomic yet extended regions of space. It seems that none of the traditional responses can be used to successfully save this particular kind of extended simple from the new puzzle. I also consider some non-traditional defenses of heterogeneous extended simples and argue that they too are unsuccessful. Finally, I will argue that a substantial case can be made against the possibility of extended heterogeneous simples of any kind. (shrink)

It is widely believed that shapes are intrinsic properties. But this claim is hard to defend. I survey all known theories of shape properties, and argue that each theory is either incompatible with the claim that shapes are intrinsic, or can be shown to be false.

I argue that the assumptions that physically basic things are either mereologically atomic, or that they are continuous and there are no atoms, both face difficult conceptual problems. Both views tend to presuppose a largely unquestioned assumption, that things have parts corresponding to the geometric parts of the regions they occupy. To avoid these problems I propose a third view, that physically simple things occupy a finite volume without themselves having parts. This view is examined enough to tease out some (...) of its consequences and show that it withstands the obvious questions it faces. I conclude by mentioning some precedents for this view in Democritus, Kant, and Whitehead, with close variants in Boscovich, Harré, and Markosian. (shrink)

I argue that the assumptions that physically basic things are either mereologically atomic, or that they are continuous and there are no atoms, both face difficult conceptual problems. Both views tend to presuppose a largely unquestioned assumption, that things have parts corresponding to the geometric parts of the regions they occupy. To avoid these problems I propose a third view, that physically simple things occupy a finite volume without themselves having parts. This view is examined enough to tease out some (...) of its consequences and show that it withstands the obvious questions it faces. I conclude by mentioning some precedents for this view in Democritus, Kant, and Whitehead, with close variants in Boscovich, Harré, and Markosian. (shrink)

I argue that extended simples are possible. The argument given here parallels an argument given elsewhere for the claim that the shape properties of material objects are extrinsic, not intrinsic as is commonly supposed. In the final section of the paper, I show that if the shape properties of material objects are extrinsic, the most popular argument against extended simples fails.

The problem of qualitative heterogeneity is to explain how an extended simple can enjoy qualitative variation across its spatial or temporal axes, given that it lacks both spatial and temporal parts. I discuss how friends of extended simples should address the problem of qualitative heterogeneity. I present a series of arguments designed to show that rather than appealing to fundamental distributional properties one should appeal to tiny and short-lived tropes. Along the way, issues relevant to debates about material composition, persistence (...) over time and existence monism are discussed.  . (shrink)

Here is a question about mereological simples that I raised in a recent paper.

Since the publication of Peter van Inwagen's book, Material Beings,1 there has been a growing body of philosophical literature on the topic of composition. The main question addressed in both van Inwagen's book and subsequent discussions of the topic is a question that van Inwagen calls "the Special Composition Question." The Special Composition Question is, roughly, the question Under what circumstances do several things compose, or add up to, or form, a single object? For the purposes of formulating a more (...) precise version of the Special Composition Question, we can adopt the following technical terms. (shrink)

A number of philosophers have recently claimed that intrinsicality can be analysed in terms of the metaphysical notion of grounding. Since grounding is a hyperintensional notion, accounts of intrinsicality in terms of grounding, unlike most other accounts, promise to be able to discriminate between necessarily coextensive properties that differ in whether they are intrinsic. They therefore promise to be compatible with popular metaphysical theories that posit necessary entities and necessary connections between wholly distinct entities, on which it is plausible that (...) there are such properties. This paper argues that this promise is illusory. It is not possible to give an analysis of intrinsicality in terms of grounding that is consistent with these theories. Given an adequate analysis should be compatible with these theories, it follows that it is not possible to analyse intrinsicality in terms of grounding. (shrink)

A number of philosophers have recently claimed that intrinsicality can be analysed in terms of the metaphysical notion of grounding. Since grounding is a hyperintensional notion, accounts of intrinsicality in terms of grounding, unlike most other accounts, promise to be able to discriminate between necessarily coextensive properties that differ in whether they are intrinsic. They therefore promise to be compatible with popular metaphysical theories that posit necessary entities and necessary connections between wholly distinct entities, on which it is plausible that (...) there are such properties. This paper argues that this promise is illusory. It is not possible to give an analysis of intrinsicality in terms of grounding that is consistent with these theories. Given an adequate analysis should be compatible with these theories, it follows that it is not possible to analyse intrinsicality in terms of grounding. (shrink)

All of the current leading theories of location are parsimonious: they have at most one locative primitive, and the definitions of all of the other locative relations appeal to nothing beyond that primitive, mereological properties and relations, and basic logic. I argue that if we believe there can be extended, mereologically simple regions, we can construct cases that are incompatible with every possible parsimonious theory of location. In these cases, an object is contained within a simple region that is larger (...) than the object; that is, there is some region, r, and some object, x, are such that every subregion of r fails to be completely free of x, yet x fails to fill r. I argue that we ought to respond to this incompatibility by rejecting the analytic possibility of extended, simple regions. (shrink)

The notion of multiple location plays an important role in the characterization of endurantism. Several authors have recently offered cases intended to demonstrate the incoherence of multiple location. I argue that these cases do not succeed in making multiple location problematic. Along the way, several crucial issues about multiple location and its use by endurantists are clarified.

The idea that there could be spatially extended mereological simples has recently been defended by a number of metaphysicians (Markosian 1998, 2004; Simons 2004; Parsons (2000) also takes the idea seriously). Peter Simons (2004) goes further, arguing not only that spatially extended mereological simples (henceforth just extended simples) are possible, but that it is more plausible that our world is composed of such simples, than that it is composed of either point-sized simples, or of atomless gunk. The difficulty for these (...) views lies in explaining why it is that the various sub-volumes of space occupied by such simples, are not occupied by proper parts of those simples. Intuitively at least, many of us find compelling the idea that spatially extended objects have proper parts at every sub-volume of the region they occupy. It seems that the defender of extended simples must reject a seemingly plausible claim, what Simons calls the geometric correspondence principle (GCP): that any (spatially) extended object has parts that correspond to the parts of the region that it occupies (Simons 2004: 371). We disagree. We think that GCP is a plausible principle. We also think it is plausible that our world is composed of extended simples. We reconcile these two notions by two means. On the one hand we pay closer attention to the physics of our world. On the other hand, we consider what happens when our concept of something—in this case space—contains elements not all of which are realized in anything, but instead key components are realized in different features of the world. (shrink)

Endurantism, the view that material objects are wholly present at each moment of their careers, is under threat from supersubstantivalism, the view that material objects are identical to spacetime regions. I discuss three compromise positions. They are alike in that they all take material objects to be composed of spacetime points or regions without being identical to any such point or region. They differ in whether they permit multilocation and in whether they generate cases of mereologically coincident entities.