Online research in philosophy

Do mereological fusions have their parts essentially? None of the axioms of non-modal formulations of classical mereology appear to speak directly to this question, and yet a great many philosophers who take the part-whole relation to be governed by these axioms seem to assume they do. Curiously, dissenters tend to depart from non-modal formulations of classical mereology at least when it comes to the uniqueness of composition: no two mereological fusions ever fuse exactly the same objects. I would like to argue that this is more than a remarkable coincidence; there are reasons of principle why one’s adherence to classical mereology should exert some pull towards the hypothesis that fusions have their parts essentially. There is, however, no direct route from non-modal classical mereology to the hypothesis that fusions have their parts essentially, and the reason for this is not merely the expressive limitations of the language of classical mereology; there is no direct route from the combination of classical mereology and propositional modal logic to the hypothesis that fusions have their parts essentially.

If ordinary objects have temporal parts, then temporal predications have the following truth conditions: necessarily, ( a is F) at t iff a has a temporal part that is located at t and that is F. If ordinary objects have temporal counterparts, then, necessarily, ( a is F) at t iff a has a temporal counterpart that is located at t and that is F. The temporal-parts account allows temporal predication to be closed under the parthood relation: since all that is required to be F at t is to have a temporal part, a t , that is located at t and that is F, every object that has a t as a temporal part is F at t . Similarly for the temporal-counterparts account. Both closure under parthood and closure under counterparthood are shown to have unacceptable consequences. Then strategies for avoiding closure are considered and rejected.

E. J. Lowe and others argue that there can be 'uncountable' things admitting of no numerical description. This implies that there can be something without there being at least one such thing, and that things can be identical without being one or nonidentical without being two. The clearest putative example of uncountable things is portions of homogeneous stuff or 'gunk'. The paper argues that there is a number of portions of gunk if there is any gunk at all, and that the possibility of uncountable things is inadequately supported.

Sometimes mereologists have problems with counting. We often don't want to count the parts of maximally connected objects as full-fledged objects themselves, and we don't want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes "full-fledged object" to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look counterintuitive to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View . The Minimalist View may be summarized in the slogan: "Count x as an object iff it does not overlap with any y you have already counted as an object". The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting "conceptually salient" entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects.

A picture of the world as chiefly one of discrete objects, distributed in space and time, has sometimes seemed compelling. It is however one of two main targets of this work; for it is seriously incomplete. The picture leaves no space for stuff like air and water. With discrete objects, we may always ask "how many?," but with stuff the question has to be "how much?" Within philosophy, stuff of certain basic kinds is central to the ancient pre-Socratic world-view; but it also constitutes the field of modern chemistry and is a major factor in ecology. Philosophers these days are unlikely to deny that stuff exists. But they are very likely to deny that it is ("ultimately") to be contrasted with things, and it is on this account that logic and semantics figure largely in the framework of the book. Elementary logic is a logic which takes values for its variables; and these values are precisely distinct individuals or things. Existence is then symbolized in just such terms; and this, it is proposed, creates a pressure for "reducing" stuff to things. Non-singular expressions, which include words for stuff, "mass" nouns, and also plural nouns, are "explicated" as semantically singular. Here then is the second target of the work, only the first chapter of which is here included. The posit that both mass and plural nouns name special categories of objects (set-theoretical "collections" of objects in the one case, mereological "parcels" or "portions" of stuff in the other) represents the imposition of an alien logic upon both the many and the much.

I examine the implications of positing stuff (which occupies an ontological category distinct from things) as a way to avoid colocation in the case of the statue and the bronze that constitutes it. When characterising stuff, it’s intuitive to say we often individuate stuff kinds by appealing to things and their relations (e.g., water is water rather than gold because it is entirely divisible into subportions which constitute or partially constitute H2O molecules). I argue that if this intuition is correct, there are important restrictions on how we can characterise stuff in order to avoid colocated portions of stuff.

Milk, sand, plastic, uranium, wood, carbon, and oil are kinds of stuff. The sand in Hawaii, the uranium in North Korea, and the oil in Iraq are portions of stuff. Not everyone believes in portions of stuff.1 Those who do are likely to agree that, whatever their more specific natures, portions of stuff can at least be identified with mereological sums of their subportions.2 It seems after all trivial that a given portion of stuff just is all of its subportions combined—not by a spatiotemporal or any other substantive unifying relation, but by a mere principle of summation, a principle requiring that, if some things exist, there exists the sum, or collection, of those things.

Naive mereology studies ordinary conceptions of part and whole. Parts, unlike portions, have objective boundaries and many things, such as dances and sermons have temporal parts. In order to deal with Mark Heller's claim that temporal parts "are ontologically no more or less basic than the wholes that they compose," we retell the story of Laplace's Genius, here named "Swifty." Although Swifty processes lots of information very quickly, his conceptual repertoire need not extend beyond fundamental physics. So we attempt to follow Swifty's progress in the acquisition of ordinary concepts such as 'table'. (Puzzles of precision and intrusion appear along the way.) Swifty has to understand what tables are before understanding what temporal portions of tables are. This is one reason for regarding tables as ontologically prior to table portions. intrusion appear along the way.).

According to the prevalent ‘sum view’ of stuffs, each portion of stuff is a mereological sum of its subportions. The purpose of this paper is to re-examine the sum view in the light of a modal temporal mereology which distinguishes between different varieties of summation relations. While admitting David Barnett’s recent counter-example to the sum view (Barnett, Philos Rev 113:89–100, 2004), we show that there is nonetheless an important sense in which all portions of stuff are sums of their subportions. We use our summation relations to develop, as an alternative to the sum view, an analysis of stuffs that distinguishes between the ways in which different sorts of stuffs are sums of their subportions.

I claim that, if persisting objects have temporal parts, then there are non-supervenient relations between those temporal parts. These are relations which are not determined by intrinsic properties of the temporal parts. I use the Kripke-Armstrong 'rotating homogeneous disc' argument in order to establish this claim, and in doing so I defend and develop that argument. This involves a discussion of instantaneous velocity, and of the causes and effects of rotation. Finally, I compare alternative responses to the rotating disc argument, and consider the implications of my arguments for the doctrines of Humean Supervenience and unrestricted mereology.