When some objects are the parts of another object, they compose that object and that object is composite. This article is intended as an introduction to the central questions about composition and a highly selective overview of various answers to those questions. In §1, we review some formal features of parthood that are important for understanding the nature of composition. In §2, we consider some answers to the question: which pluralities of objects together compose something? As we will see, the (...) dominant answers are all of them and none of them. In §§3-4, we examine one of the main arguments that has driven philosophers to these extreme answers: the argument from vagueness. In §5, we turn to the question of whether composition is unique: is it sometimes the case that some things compose more than one thing? Finally, in §6, we turn from the question of which composites exist to the question of which composites exist fundamentally. (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)

A variety of relations widely invoked by philosophers—composition, constitution, realization, micro-basing, emergence, and many others—are species of what I call ‘building relations’. I argue that they are conceptually intertwined, articulate what it takes for a relation to count as a building relation, and argue that—contra appearances—it is an open possibility that these relations are all determinates of a common determinable, or even that there is really only one building relation.

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

A critical survey of the fundamental philosophical issues in the logic and formal ontology of space, with special emphasis on the interplay between mereology (the theory of parthood relations), topology (broadly understood as a theory of qualitative spatial relations such as continuity and contiguity), and the theory of spatial location proper.

The discovery of the importance of mereology follows and does not precede the formalisation of the theory. In particular, it was only after the construction of an axiomatic theory of the part-whole relation by the Polish logician Stanisław Leśniewski that any attempt was made to reinterpret some periods in the history of philosophy in the light of the theory of parts and wholes. Secondly, the push for formalisation - and the individuation of mereology as a specific theoretical field - arise (...) from several particular theories, first from biology and then from psychology. Mereological considerations were explicitly developed within the school of Brentano, by Brentano himself- starting from the problem of the unity of consciousness - and by his students, particularly Stumpl, Twardowski and the Gestaltists. The most complete result of this tradition is undoubtedly the third of Husserl's Logical Investigations, called "the single most important contribution to realist (Aristotelian) ontology in the modern period". (shrink)

Atomism denies that complexes exist. Common-sense metaphysics may posit masses, composite individuals and sets, but atomism says there are only simples. In a singularist logic, it is difficult to make a plausible case for atomism. But we should accept plural logic, and then atomism can paraphrase away apparent reference to complexes. The paraphrases require unfamiliar plural universals, but these are of independent interest; for example, we can identify numbers and sets with plural universals. The atomist paraphrases would fail if plurals (...) presuppose complexes: but an Appendix shows that reference to complexes is not required in the semantics of plurals. (shrink)

Peter Simons has argued that the expression ‘the universe’ is not a genuine singular term: it can name neither a single, completely encompassing individual, nor a collection of individuals. (It is, rather, a semantically plural term standing equally for every existing object.) I offer reasons for resisting Simons’s arguments on both scores.

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, 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 distinguisher between the ways in which different sorts of stuffs are sums of their subportions. (shrink)

Classical mereology is a formal theory of the part-whole relation, essentially involving a notion of mereological fusion, or sum. There are various different definitions of fusion in the literature, and various axiomatizations for classical mereology. Though the equivalence of the definitions of fusion is provable from axiom sets, the definitions are not logically equivalent, and, hence, are not inter-changeable when laying down the axioms. We examine the relations between the main definitions of fusion and correct some technical errors in prominent (...) discussions of the axiomatization of mereology. We show the equivalence of four different ways to axiomatize classical mereology, using three different notions of fusion. We also clarify the connection between classical mereology and complete Boolean algebra by giving two "neutral" axiom sets which can be supplemented by one or the other of two simple axioms to yield the full theories; one of these uses a notion of "strong complement" that helps explicate the connections between the theories. (shrink)

In this paper, using a propositional modal language extended with the window modality, we capture the first-order properties of various mereological theories. In this setting, $\Box \varphi $ reads all the parts (of the current object) are $\varphi $, interpreted on the models with a whole-part binary relation under various constraints. We show that all the usual mereological theories can be captured by modal formulas in our language via frame correspondence. We also correct a mistake in the existing completeness proof (...) for a basic system of mereology by providing a new construction of the canonical model. (shrink)

The notions of part and whole play an important role for ontology and in many areas of the semantics of natural language. Both in philosophy and linguistic semantics, usually a particular notion of part structure is used, that of extensional mereology. This paper argues that such a notion is insufficient for ontology and, especially, for the semantic analysis of the relevant constructions of natural language. What is needed for the notion of part structure, in addition to an ordering among parts, (...) is the notion of integrated whole. In the context of semantics, the notion of an integrated whole needs to be relativized to a situation, or so it is argued. (shrink)

Speaking of dental floss contaminated with bacteria, I may separate the dental floss that is sterile from the dental floss that isn’t sterile. The definite description “the dental floss that isn’t sterile” contracts its reference to just the dental floss near bacteria, although it, the dental floss whole, isn’t sterile. To accommodate the definite descriptions that contract their reference, received definitions for ⌜the Φ⌝ are amended from to read as in : ⌜the Φ⌝ refers to that which any Φ is (...) part of and is the least such. ⌜the Φ⌝ refers to that which any Φ overlaps and is the least such. If definite description is to be based on a purely logical notion of plural and mass predication, it is further amended. Like overt demonstratives—⌜this/these Φ⌝, ⌜that/those Φ⌝—any definite description in natural language is also perspectival, scanning everywhere the description Φ is satisfied:⌜the Φ⌝ refers to the least Φ that overlap Φ anywhere there is Φ. (shrink)

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. (shrink)