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Composition as identity: pushing forward

  • S.I. : Mereology and Identity
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Abstract

In this paper, I present the thesis of Composition as Identity (CAI) as I think it should be understood (Sects. 1, 2), and reply to some objections to it (Sects. 3, 4). My aim is not to argue that CAI is true, but to show how CAI can be true, and push the debate forward in the direction I think it must and should go in light of some new objections.

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Notes

  1. Whenever I say that plural variables range over pluralities of objects, I take them to range over one or more objects, not plural objects (whatever that means). A plurality of objects is just those objects. In other words, singular quantification and plural quantification are just two different ways of quantifying over the same objects. It is not committed to quantifying over different domains, or different kinds of objects. Cf. Boolos (1984).

  2. One might, on the one hand, reject HII as ungrammatical and incoherent, or one might, on the other hand, accept HII as grammatical and coherent, but hold that it only has vacuously true instance where the antecedent is false (except when the value of ‘xx’ is singular). A CAI-fan like myself thinks it is both coherent and has non-vacuously true instances.

  3. Deriving classical mereology from GI and CAI is tedious, and not something I can do here. But note that we can and should add a syntactic restriction so that the composition predicate C doesn’t behave symmetrically, like identity does. For example, ‘xCyy’ should not come out well-formed, even though ‘x = yy’ and ‘xCx’ do (and are true). I want to derive classical mereology from GI and CAI, not revise classical mereology.

  4. I take it to be pretty obvious that it is not a lexical definition.

  5. Where f(xx) is the unique fusion of xx. Proof: Right-to-Left: assume y is part of ƒ(xx). The fusion ƒ(xx) is composed of xx as well as y,ƒ(xx); so given CAI, ƒ(xx) = xx and ƒ(xx) = y,ƒ(xx); and hence, by HII, xx = y,ƒ(xx). But y is one of y,ƒ(xx); hence, by HII, y is one of xx. Left-to-Right: assume y is one of xx. It is obvious that z = ƒ(xx) iff each one of xx is a part of z and each part of z overlaps at least one of xx (this is usually part of the definition of fusion). But if each one of xx is a part of z, then since y is one of xx, y is a part of z; hence, y is a part of ƒ(xx). Q.E.D.

  6. I treat’mode of presentation’ and’concept’ interchangeably.

  7. A set of a,b,c has only one ultimate decomposition, namely into its members a, b and c; a composite fusion of a,b,c on the other hand might have a further ultimate decomposition into parts of a, b and c. The properties involved in the objections above are more like sets than fusions in this respect; hence the characterization set-like.

  8. For what it is worth, the relativity I suggest is not Frege’s view. While I hold cardinal properties to be relative to concepts, Frege holds cardinal properties to be properties of concepts.

  9. Note that CAI is, by Necessitation, a thesis that holds of necessity, so the mere possibility of emergent properties is enough to get the problem. The same goes for the other problematic properties we’ll discuss below.

  10. These problems are greatly inspired by a talk Philip Bricker gave at the conference Mereology and Identity in Pisa, Italy, July 2017. But, of course, all confusions are mine.

  11. Note that I am here talking about plural and mereological metaphysical structure in fundamental reality, not merely structures as a matter of linguistics or semantics.

  12. For a similar use of distributional properties, to be compared to the way I use it here, see Schaffer (2010). A distributional property is not a structural property a la Armstrong (1978), because a structural property is a logical construct of other properties.

  13. The bubbling up principle (but without the mentioning of the distributivity or directionality) has come up at least once during Q&A in various talks I have given on the trickling down principle over the last couple of years, but I cannot now remember where and when it first came up.

  14. Thanks to the audience at the conference Mereology and Identity in Pisa, Italy, July 2017, and the anonymous referees for this journal.

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  1. University of Agder, Kristiansand, Norway

    Einar Duenger Bohn

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Bohn, E.D. Composition as identity: pushing forward. Synthese 198 (Suppl 18), 4595–4607 (2021). https://doi.org/10.1007/s11229-019-02193-x

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