There will be a few themes. One to get us going: expansion versus contraction. About an object, o, and the region, R, of space(time) in which o is exactly located,1 we may ask: i) must there exist expansions of o: objects in filled superregions2 of R? ii) must there exist contractions of o: objects in filled subregions of..

According to Composition is Identity, a whole is literally identical to the plurality of its parts. According to Mereological Nihilism, nothing has proper parts. In this note, it is argued that Composition is Identity can be shown to entail Mereological Nihilism in a much more simple and direct way than the one recently proposed by Claudio Calosi.

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)

This paper provides new arguments for the following claim: either strong composition as identity cannot retain the full strength of both the logical principles of one-one identity and its semantical principles or it only delivers cases of boring composition in that it entails mereological nihilism.

Composition as Identity is the thesis that a whole is, strictly and literally, identical to its parts, considered collectively. McDaniel [2008] argues against CAI in that it prohibits emergent properties. Recently Sider [2014] exploited the resources of plural logic and extensional mereology to undermine McDaniel’s argument. He shows that CAI identifies extensionally equivalent pluralities – he calls it the Collapse Principle – and then shows how this identification rescues CAI from the emergentist argument. In this paper I first give a (...) new generalized version of both the arguments. It is more general in that it does not presuppose an atomistic mereology. I then go on to argue that the consequences of CP are rather radical. It entails mereological nihilism, the view that there are only mereological atoms. I finally show that, given a mild assumption about property instantiation, namely that there are no un-instantiated properties, this argument entails that CAI and emergent properties are incompatible after all. (shrink)

Composition is Identity is the thesis that a whole is, strict and literally, its parts considered collectively. Mereological Nihilism is the thesis that there are no composite objects whatsoever instead. This paper argues that they are equivalent, at least insofar as Composition is Identity is phrased in a particular way. It then addresses some consequences of such equivalence.

David Lewis famously takes mereology ‘to be perfectly understood, unproblematic, and certain". In this chapter, the author proceeds by articulating four theses that Lewis holds about composition. Three of them are familiar; Lewis himself explicitly articulates and relies upon them. The fourth remains implicit, but it is nonetheless important. The four theses include: composition is unique (the same things cannot have two different fusions); composition is unrestricted (any two things whatsoever have a fusion); composition is ontologically innocent (composed entities do (...) not "count" beyond their parts); and composition is unmysterious (it is not problematic to treat it as primitive, and can function in demystifying explanations). The author devotes a section to each thesis: explaining what it says, pointing to the texts that illustrate that Lewis believes it, and explaining why Lewis believes it. Lewis uses the label ‘uniqueness’ and explicitly endorses the thesis. (shrink)

Ordinary English contains different forms of quantification over objects. In addition to the usual singular quantification, as in 'There is an apple on the table', there is plural quantification, as in 'There are some apples on the table'. Ever since Frege, formal logic has favored the two singular quantifiers ∀x and ∃x over their plural counterparts ∀xx and ∃xx (to be read as for any things xx and there are some things xx). But in recent decades it has been argued (...) that we have good reason to admit among our primitive logical notions also the plural quantifiers ∀xx and ∃xx. More controversially, it has been argued that the resulting formal system with plural as well as singular quantification qualifies as ‘pure logic’; in particular, that it is universally applicable, ontologically innocent, and perfectly well understood. In addition to being interesting in its own right, this thesis will, if correct, make plural quantification available as an innocent but extremely powerful tool in metaphysics, philosophy of mathematics, and philosophical logic. For instance, George Boolos has used plural quantification to interpret monadic second-order logic and has argued on this basis that monadic second-order logic qualifies as “pure logic.” Plural quantification has also been used in attempts to defend logicist ideas, to account for set theory, and to eliminate ontological commitments to mathematical objects and complex objects. (shrink)

Mereological nihilism says that there do not exist (in the fundamental sense) any objects with proper parts. A reason to accept it is that we can thereby eliminate 'part' from fundamental ideology. Many purported reasons to reject it - based on common sense, perception, and the possibility of gunk, for example - are weak. A more powerful reason is that composite objects seem needed for spacetime physics; but sets suffice instead.

"Composition as identity" is the radical claim that the whole is identical to the parts - radical because it implies that a single object can be identical to many objects. Composition as identity, together with auxiliary assumptions, implies the principle of "collapse": an object is one of some things if and only it is part of the fusion of those things. Collapse has important implications: the comprehension principle of plural logic must be restricted, plural definite descriptions such as "the Cheerios (...) in the bowl" are empty, Composition as identity does not preclude emergent properties (contrary to what McDaniel has argued), and drastic simplifications of mereological and logical ideology are extensionally available. (shrink)

In this chapter, I examine Lewis's ideas about ontological innocence, ontological commitment and double-counting, in his discussion of composition as identity in Parts of Classes. I attempt to understand these primarily as epistemic or methodological claims: how far can we get down this route without adopting radical metaphysical theses about composition as identity?

I endorse Composition as Identity, broadly and loosely understood as the thesis that a composite whole is nothing over and above its parts, and the parts nothing over and above the whole. Thus, given an object, x, composed of n proper parts, y1, ..., yn, I feel the tension between my Quinean heart and its Lewisian counterpart. I feel the tension between my obligation to countenance n+1 things, x and the y’s, each of which is a distinct portion of reality, (...) and my inclination to count just 1 thing, x, or just n things, the y’s, the former encompassing the same amount of reality as the latter. This paper is an attempt to reconstruct this tension and to explain it away without forgoing the intimate link between counting and countenancing. (shrink)

A plurality or plural object is a single object that is also many, and pluralitism is the thesis that there is such an object. This paper argues that pluralitism and closely related theses (e.g., the many-one identity thesis and the composition as identity thesis) violate logic. To do so, it formulates an approach to the logic and semantics of plural constructions that results in plural logic and relates treatments of plural constructions to accounts of natural number. And it gives a (...) critical examination of Frege’s views of numbers and plural constructions, and sketches the view of plural constructions as devices for talking about the many (as such), and an account of natural numbers as properties of a special kind, plural properties. (shrink)