Abstract
The general composition question asks “what are the necessary and jointly sufficient conditions any xs and any y must satisfy in order for it to be true that those xs compose that y?” Although this question has received little attention, there is an interesting and theoretically fruitful answer. Namely, strong composition as identity (SCAI): necessarily, for any xs and any y, those xs compose y iff those xs are identical to y. SCAI is theoretically fruitful because if it is true, then there is an answer to one of the most difficult and intractable questions of mereology (The Simple Question). In this paper, I introduce the identity account of simplicity and argue that if SCAI is true then this identity account of simplicity is as well. I consider an objection to the identity account of simplicity. Ultimately, I find this objection unsuccessful.
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Notes
This question was first introduced by van Inwagen (1990). In a short section of Material Beings, van Inwagen clearly distinguished the General Composition Question from the much more widely discussed Special Composition Question. My formulation of the General Composition Question is slightly different from van Inwagen’s and conforms to the formulation of the Simple Question found below.
It might be easy to answer this question if we were allowed to employ mereological vocabulary. We could just say that necessarily, for any xs and any y, those xs compose y iff each of those xs is a part of y and everything that is a part of y shares a part with one of those xs. Similarly, we may be able to give an infinitely long answer if we are able to list any possible xs and any possible y and say which xs compose which y in any given possible world. However, even though these answers may be easy or straightforward, they are not proper.
Hawley (2006) claims that headway can be made on the GCQ if we give up on the constraints given. Moreover, she argues that answers to other mereological questions, such as the Special Composition Question, are not held to such high standards. Whether or not Hawley is correct, I am going to proceed to discuss the GCQ under the assumption that a proper answer must meet the constraints given above.
See, in particular, van Inwagen (1990, 51). It is unclear to me why van Inwagen thinks that open question style arguments are problematic for answers to the General Composition Question but not to answers to the Special Composition Question.
Strong Composition as Identity is rejected by van Inwagen (1995) on just this ground.
This may make the individual constants logically redundant. However, it is sometimes more perspicuous to present ideas with the individual constants rather than the plural constants.
If SCAI is true, then there will be some surprising examples of true statements involving ‘is/are among’.
Since the plural variables can be satisfied by individuals as well as pluralities, any statement of the form (∀xs)(ϕxs) entails a statement for the form (∀x)(ϕx). Hence, Strong Leibniz’s Law entails the standard version of Laibniz’s Law which employs only individual variables.
Some people who endorse SCAI may choose to reject Strong Leibniz’s Law in response to the argument that I consider in Sect. 3 below. However, at least for the moment, I will assume that Strong Leibniz’s Law is true.
Of course, if SCAI is true, then there will also be some very surprising examples of true statements involving ‘is/are identical to’.
Given SCAI it may be that we need not take this relation as primitive. It may be that the following claim is true:
Necessarily (∀x) (∀y) (x is a part of y iff (∃zs) (x is among those zs and those zs are identical to y))
If the above claim is true, then we may choose to eliminate the primitive ‘is/are part(s) of’ relation in favor of a relation defined in terms of ‘is/are among’ and ‘is/are identical to’.
Again, if SCAI is true, then there will be some surprising examples of true statements involving ‘is/are part(s) of’.
The Simple Question was first introduced in Markosian (1998).
See Markosian (1998), Tognazzini (2006) and McDaniel (2007) for formulations of several answers to the SQ. Markosian (1998) and Hudson (2001) both endorse spatial occupancy accounts of simplicity according to which objects are simples iff they occupy regions of space that have certain features. McDaniel endorses a brutal account of simplicity according to which there is no finitely long and informative answer to the SQ.
Another way to formalize the intuitive idea is as follows:
The Identity Account of Simplicity 2 Necessarily (∀x) (x is a simple iff (∀ys) (if those ys are among x, then x is among those ys)).
I have chosen to focus on The Identity Account of Simplicity rather than The Identity Account of Simplicity 2 because the proof that SCAI logically entails The Identity Account of Simplicity is far more intuitive than the proof that SCAI logically entails the Identity Account of Simplicity 2. The proof of the latter requires the highly counterintuitive idea that a proper part of an object is among that object (e.g. my hand is among me). Although highly counterintuitive, this seems to follow from SCAI. I leave it to the reader to reconstruct the proof.
Or to the General Composition Question or to the long standing Special Composition Question.
It is obvious that a similar problem will plague answers to the General Composition Question and the Special Composition Question.
References
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Spencer, J. Strong Composition as Identity and Simplicity. Erkenn 78, 1177–1184 (2013). https://doi.org/10.1007/s10670-012-9387-2
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DOI: https://doi.org/10.1007/s10670-012-9387-2