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We can see mereology as a theory of parthood and topology as a theory of wholeness. How can these be combined to obtain a unified theory of parts and wholes? This paper examines various non-equivalent ways of pursuing this task, with specific reference to its relevance to spatio-temporal reasoning. In particular, three main strategies are compared: (i) mereology and topology as two independent (though mutually related) chapters; (ii) mereology as a general theory subsuming topology; (iii) topology as a general theory subsuming mereology. Some more speculative strategies and directions for further research are also considered.

SURVEYS (a) David Lewis, Parts of Classes (Blackwell, Oxford, 1991), §§3.4–3.6 (pp. 72–87) (b) Achille Varzi, ‘Mereology’, Stanford Encyclopedia of Philosophy, http:// plato.stanford.edu/entries/mereology/. (c) Michael C. Rea (ed.), Material Constitu- tion (Rowman & Littlefield, Lanham, MD, 1997), esp. the introduction. (d) van Cleve and Markosian, ‘Mereology’, Theodore Sider, John Hawthorne, and Dean W. Zimmerman (eds.), Contemporary Debates in Metaphysics (Blackwell, Oxford, 2007), ch. 8, pp. 319–63. (e) Peter M. Simons, Parts: A Study in Ontology (Oxford University Press, Oxford, 1987).

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.

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.

Mereology is the logic of part—whole concepts as they are used in many different contexts. The old chemical metaphysics of atoms and molecules seems to fit classical mereology very well. However, when functional attributes are added to part specifications and quantum mechanical considerations are also added, the rules of classical mereology are breached in chemical discourses. A set theoretical alternative mereology is also found wanting. Molecular orbital theory requires a metaphysics of affordances that also stands outside classical mereology.

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.

Mereology is the logic of part—whole concepts as they are used in many different contexts. The old chemical metaphysics of atoms and molecules seems to fit classical mereology very well. However, when functional attributes are added to part specifications and quantum mechanical considerations are also added, the rules of classical mereology are breached in chemical discourses. A set theoretical alternative mereology is also found wanting. Molecular orbital theory requires a metaphysics of affordances that also stands outside classical mereology.

Mereology (from the Greek μερος, ‘part’) is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratic atomists and continuing throughout the writings of Plato (especially the Parmenides and the Thaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium ), and Boethius (especially In Ciceronis Topica ). Mereology has also occupied a prominent role in the writings of medieval ontologists and scholastic philosophers such as Garland the Computist, Peter Abelard, Thomas Aquinas, Raymond Lull, and Albert of Saxony, as well as in Jungius's..

0. Introduction: Mereology, Metaphysics, and Speculative Grammar 0.1 Mereology, Ancient and Contemporary 0.11 Mereology is, strictly speaking, the theory of ...