Composition as identity is the thesis that a thing is identical to its parts.

For example, the bicycle is identical to the wheels, frame, seat, gears, pedals, brakes, and chain. (You could break the bicycle down into smaller parts, and the identity claim would hold.) Note what the view is not: It is not that a composite object is identical to the sum or set of its parts. Rather, a composite is identical to its parts, plural.

Philosophers who believe in four-dimensionalism understand composition (and thus composition as identity) to include temporal as well as spatial parts (more precisely, composition includes spatiotemporal parts). On the four-dimensionalists’ view, the bicycle is not wholly present at any time; it has spatiotemporal parts such as Monday parts (e.g., Monday wheels, Monday brakes), which are distinct from Tuesday parts. Composition as identity is then the claim that an object is identical to its spatiotemporal parts taken together over the lifetime of the object.

Table of Contents

Passages Motivating Composition as Identity

Suppose a man owned some land which he divides into six parcels. Overcome with enthusiasm for [the denial of Composition as Identity] he might perpetrate the following scam. He sells off the six parcels while retaining ownership of the whole. That way he gets some cash while hanging on to his land. Suppose the six buyers of the parcels argue that they jointly own the whole and the original owner now owns nothing. Their argument seems right. But it suggests that the whole was not a seventh thing. ¹

David Lewis motivates the thesis in his book, Parts of Classes:

To be sure, if we accept mereology, we are committed to the existence of all manner of mereological fusions. But given a prior commitment to cats, say, a commitment to cat-fusions is not a further commitment. The fusion is nothing over and above the cats that compose it. It just is them. They just are it. Take them together or take them separately, the cats are the same portion of Reality either way. Commit yourself to their existence all together or one at a time, it’s the same commitment either way. If you draw up an inventory of Reality according to your scheme of things, it would be double counting to list the cats and then also list their fusion. In general, if you are already committed to some things, you incur no further commitment when you affirm the existence of their fusion. The new commitment is redundant, given the old one. ²

Challenges for Composition as Identity

• The indiscernibility of identicals (one of the theses commonly called Leibniz’s Law): For all x and y, if x=y, then x and y have the same properties.³
  If composition as identity is true, then we have a counterexample to the indiscernibility of identicals, for as David Lewis pointed out, the composite is one and the parts are many.



• Classical logic does not allow flanking an identity symbol with a singular term on one side and a plural term on the other. To say that x equals the ys requires revisionary logic and new apparatus to represent it.

Annotated Bibliography (with links to papers available online)

Baxter, Donald L. M. “Many-One Identity.” Philosophical Papers XVII (1988): 193–216.

Baxter, a philosopher at the University of Connecticut, argues that there is more than one ’count’ of what exists. In part-whole relationships, the parts exist in one count, and the whole exists in another count. (For example, the whole parcel of land and the six parts that it has been sold off in do not exist in the same count. However, both the parcel and its parts exist: the parcel in one count and the six parts in another.) Composition as identity, on Baxter’s account, is a cross-count identity relation.

Baxter attempts to solve the identity problem raised by Lewis in Parts of Classes: composition as identity must explain how things can be identical yet have disparate properties (Lewis’ example of a difference: the one is one and the many are many). In this endeavor, Baxter argues for the discernibility of identicals. He thinks that qualitative difference is insufficient for numerical difference. In contrast, David Lewis (see below) tries to solve the problem by attributing to composition a broader, non-traditional sense of identity that allows for one-many identity, and of which one-one numerical identity is a special case (that does not hold in composition).

Lewis, David. Parts of Classes. Cambridge, Massachusetts: Basil Blackwell, 1991.

See pages 81 through 87 for the heart of Lewis’s discussion of composition as identity. The late David Lewis is considered by some to be the leading analytic philosopher of the late 20th century; he is also known for his modal realism, which is famous for being both crazy and philosophically fruitful. Here Lewis endorses a qualified composition as identity. He writes that composition is importantly analogous to the identity relation, but he stops short of attributing identity. Lewis writes that composition as identity is the key to making mereology (which he takes to include unrestricted composition) “ontologically innocent.” In other words, he thinks that any two or more things compose a third thing (his example: a trout and a turkey compose a trout-turkey), but he thinks that this is not positing too many entities because of composition as identity. If the composition relation is like the identity relation, then counting the trout-turkey among the things that are after we have counted the trout and the turkey is like counting Superman after we have already counted Clark Kent. In contrast, Baxter attributes strict identity to the composition relationship.

McDaniel, Kris. "Against Composition as Identity." Analysis 68, no. 2 (April 2008): 128–133.

McDaniel, a philosopher at Syracuse University, argues that if composition as identity were true, then strongly emergent properties would be metaphysically impossible. McDaniel thinks that strongly emergent properties are possible, so composition as identity cannot be true. The classic examples of strong emergent properties are mental properties, such as the property of being conscious or the property of having qualia (e.g., the experience of what-it-is-like to smell coffee). This article is significant for offering a new argument against composition as identity and for connecting the literature about composition as identity with the more longstanding literature on emergence in the philosophy of mind (which includes the work of C. D. Broad and David Chalmers). McDaniel's argument targets both the strict form of composition as identity (à la Baxter) and the qualified form (à la Lewis and Sider).

Merricks, Trenton. “Composition as Identity, Mereological Essentialism, and Counterpart Theory.” Australasian Journal of Philosophy 77, no. 2 (June 1999): 192–195.

Merricks, a philosopher at the University of Virginia, argues that composition as identity entails mereological essentialism. (Mereological essentialism is the view that a thing has its parts essentially; that is, it cannot lose a part and still be the same thing. For example, if the bumper fell off of a car, it would no longer be the same car.) Many philosophers reject mereological essentialism, so Merricks argues that such philosophers should reject composition as identity as well. In contrast, Donald Baxter (see above) argues that advocates of composition as identity should reject the indiscernibility of identicals, which is one of Merricks’s premises. Merricks’s article is important to extending the consequences of composition as identity.

Merricks, Trenton. “Composition and Vagueness.” Mind 114 (July 2005): 615–637.

Merricks argues against the claim (by David Lewis, Ted Sider) that restricted composition entails cases of vague existence. The paper includes a discussion of composition as identity (see pp. 629–631). Merricks argues that if composition is restricted, then composition as identity must be false.

Sider, Theodore. “Parthood.” Articles. <http://tedsider.org/papers/parthood.pdf>.

This paper is available on Sider’s Web page. Under the Articles heading, click on “Parthood” to read it as a PDF: http://tedsider.org/.

Note: This annotation refers to an earlier draft dated January 31, 2005.
Like David Lewis, Ted Sider advocates a qualified composition as identity. Both philosophers stop short of attributing strict identity to the parts-whole relation, but both insist that the whole is nothing over and above its parts. Sider, a philosopher at New York University, rejects the stronger thesis on the grounds that it would require giving up plural quanification.⁴ He thinks that the idea that the whole is nothing more than its parts can be expressed by seven principles about parthood and composition. From these principles, Sider then argues against colocationism (the view that two distinct objects can be located in the same place at the same time) and against endurantism (the view that objects continue wholly through time and do not have temporal parts).

Van Inwagen, Peter. “Composition as Identity.” Philosophical Perspectives, Vol. 8, Logic and Language (1994): 207–220.

Available on JSTOR.org (subscription required; your academic library may have one): http://links.jstor.org/sici?sici=1520-8583%281994%298%3C207%3ACAI%3E2.0.CO%3B2-7

Van Inwagen, a philosopher at the University of Notre Dame, critically examines David Lewis’s thesis of composition as identity as put forth in Lewis’s Parts of Classes. Van Inwagen’s arguments center around two overarching points: (1) Lewis’s claim that composition as identity makes mereology “ontologically innocent” is dubious (especially to colocationists and those who do not believe in composition) and (2) What Lewis means by some of his assertions is elusive, and those assertions about composition as identity might be meaningless. He develops the second point by considering specific claims one by one and considering proposed meanings of those claims.

Yi, Byeong-Uk. “Is Mereology Ontologically Innocent?” Philosophical Studies 93 (1999): 141–160.

Available on kluweronline.com (subscription required; your academic library may have one): http://springerlink.metapress.com/openurl.asp?genre=article&issn=0031-8116&volume=93&issue=2&spage=141

Yi, a philosopher at the University of Toronto, argues against David Lewis’s claim in Parts of Classes (see entry above) that composition as identity makes Lewis’s mereology “ontologically innocent.” (Yi thinks that Lewis’s mereology [which includes unrestricted composition] is innocent if one need not make new ontological commitments in order to accept it.) Yi argues that the strong version of composition as identity, which attributes the identity relation to the parts-whole relation, is false. The weak version is Lewis’s version, according to which composition is importantly analogous to identity. Yi argues that on the weak version, when one posits a fusion of things, one makes a new ontological commitment, and mereology loses its ontological innocence.