To Exist and to Count: a Note on the Minimalist Viewdltc_1198

Sometimes mereologists have problems with counting. We often don’t want to count the parts of maximally connected objects as full-fledged objects themselves, and we don’t want to count discontinuous objects as parts of further, full-fledged objects. But whatever one takes “fullfledged object” to mean, the axioms and theorems of classical, extensional mereology commit us to the existence both of parts and of wholes – all on a par, included in the domain of quantification – and this makes mereology look counterintuitive to various philosophers. In recent years, a proposal has been advanced to solve the tension between mereology and familiar ways of counting objects, under the label of Minimalist View. The Minimalist View may be summarized in the slogan: “Count x as an object iff it does not overlap with any y you have already counted as an object”. The motto seems prima facie very promising but, we shall argue, when one looks at it more closely, it is not. On the contrary, the Minimalist View involves an ambiguity that can be solved in quite different directions. We argue that one resolution of the ambiguity makes it incompatible with mereology. This way, the Minimalist View can lend no support to mereology at all. We suggest that the Minimalist View can become compatible with mereology once its ambiguity is solved by interpreting it in what we call an epistemic or conceptual fashion: whereas mereology has full metaphysical import, the Minimalist View may account for our ways of selecting “conceptually salient” entities. But even once it is so disambiguated, it is doubtful that the Minimalist View can help to make mereology more palatable, for it cannot make it any more compatible with commonsensical ways of counting objects. 1. The Minimalist View as a count policy Classical, extensional mereology (from now on just “mereology”, for short) faces a “tension between countenancing and counting” (Varzi 2000, 284). If a given object x has parts, classical mereology treats the parts as objects in the domain of quantification, on a par with the object x itself. This seems to fall foul of our intuition that many objects have parts that do not count as full-fledged objects themselves, because they are undetached, cognitively irrelevant, and to a large extent arbitrary: the middle third of a baseball bat, for instance, or the southern half of the Empire State Building. † Francesco Berto, Department of Philosophy, University of Venice-Ca’Foscari, Dorsoduro, 3246, 30123 Venice, Italy; E-mail: [email protected]. Massimiliano Carrara, Department of Philosophy, University of Padua, P.zza Capitaniato 3, 351339 Padova, Italy; E-mail: [email protected] 1 By which we mean: a mereology including (a) some version of the Extensionality Principle, to the effect that for any (non-atomic) x and y, if x and y have the same (proper) parts, then x = y, and (b) some version of Unrestricted Composition, to the effect that given any x and y, there is a (unique) mereological fusion or sum z = x + y. dialectica Vol. 63, N° 3 (2009), pp. 343–356 DOI: 10.1111/j.1746-8361.2009.01198.x © 2009 The Authors. Journal compilation © 2009 Editorial Board of dialectica. Published by Blackwell Publishing Ltd., 9600 Garsington Road, Oxford, OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA On the other hand, given any two objects x and y, mereology treats their mereological sum z = x + y as an object in the domain of quantification, on a par with x and y themselves, because of its principle of Unrestricted Composition. This flies in the face of another pervasive intuition, according to which many mereological sums or fusions do not count as full-fledged objects, because they are discontinuous, irrelevant, and to a large extent arbitrary: the fusion of the southern half of the Empire State Building and the middle third of our bat, for instance. As ontologists, we may not want to count undetached parts and disconnected wholes of these kinds. In a word: we need a count policy. Otherwise, mereology is liable of providing an implausible ontology, to say the least (see Chisholm 1987; van Inwagen 2002). The Minimalist View, proposed by Achille Varzi in order to provide the required count policy, goes as follows: We should not include [in our inventory of the world] entities that overlap, i.e., share common parts. If we include the table we should not include its top and legs. If we include its top and legs we ought to disregard the whole table as well as every other table part. For instance, we ought to disregard the right half of the table, consisting of the two right legs and the right half of the top. Call this the Minimalist View. The Minimalist View says nothing specific about mereology, about what entities are parts of what. But given a mereological theory and a corresponding domain of quantification, the view tells us how to weigh our ontological commitments: (M) An inventory of the world is to include an entity x if and only if x does not overlap any other entity y that is itself included in that inventory (Varzi 2000, 285). This passage includes not only a concise statement of the Minimalist View, but also what we take to be its basic ambiguity – an ambiguity that threatens to make it unsuitable for mereology. In order to disclose the trouble, we will make a couple of assumptions concerning identity. Assumption (1): it is not the case that identity is only relative to a sortal term. It is not the case, that is, that there is no such thing as identity tout-court, but only non-Leibnizian relations of the form “x is the same F as y”, which do not entail congruence with respect to all properties. Assumption (2): there is no such thing as worldly vague identity, that is to say: for no x and y can it be indeterminate de re whether x = y. These two assumptions are shared by most mereologists – including Varzi. As for (1), for instance, David Lewis rejects the doctrine of relative identity by deeming it “incredible”, and “not [the real] identity, as may be seen from the fact that it sometimes holds between things that differ in their other relative identities” (Lewis 1986, 249). Varzi (2001, 93–94) also appears to follow Lewis’s position. As for (2) – the de re vagueness of identity – “the only intelligible account of vagueness locates it in our thought and language”, that is to say, “vagueness is semantic indecision” (Lewis 1986, 212); and this, too, is apparently maintained by Varzi (2001, 146–148). Moreover, precisely this denial of de re vagueness works Francesco Berto and Massimiliano Carrara 344 © 2009 The Authors. Journal compilation © 2009 Editorial Board of dialectica. as a key assumption in Lewis’s argument for Unrestricted Composition in On the Plurality of Worlds. Let us stick, then, to Assumptions (1) and (2): there is such a thing as identity simpliciter, and it admits no de re indeterminacy. Next, let us assume as our sample world a “restricted model”: there are just two non-overlapping objects Out There, x and y. Let us also straightforwardly assume that they have no proper parts (we may also take them as having proper parts, but this would just complicate the calculation without changing the point of the argument). The Minimalist View tells us that, in order to “weigh our ontological commitments”, we should count either the parts, or the whole. We can do exactly one of two things: we can count as items in our “inventory of the world” x and y; or, we can count only z (that is, x + y); for the formers overlap the latter and, according to Principle (M), mentioned in Varzi’s quotation above, we should not include overlapping entities. The Minimalist View does not tell us which option(s) should be favored: “one mereologist may go for a fine-grained inventory including x and y but not x + y; another mereologist may go for a coarser inventory including x + y but not x or y” (Varzi 2000, 287): x and y may be too disconnected and independent to count x + y as a full-fledged object (in this case, calling x and y “parts” may sound odd to begin with – parts of what?). Or the z = x + y may be too self-connected to count x and y as full-fledged objects (in this case, calling the one relevant object around, namely, z, “x + y” may sound odd to begin with – a fusion of what?). But whatever we choose, neither one nor two is three. And so the Minimalist View is incompatible with mereology. The latter asserts the existence of three objects, which the former denies. To be “included in the inventory of the world” – a general catalogue of all that is Out There – is nothing more and nothing less than to exist. But then, to claim that, if one has already “included in the inventory of the world” x and y, one should not include x + y, and vice versa, is to claim that if one is committed to the existence of x and of y, one should not concede an existence ticket also to x + y – and vice versa. But this is precisely what mereology does. 2. Against innocent mereology and double existence The Minimalist View avoids one problem of mereology at the cost of getting a new one. The problem it avoids concerns the ontological innocence of mereology. The cost is the introduction of a double notion of existence. Let us see how. 2 The argument, roughly, goes as follows: our restrictions on composition depend on vague intuitions and admit of degrees. But the issue whether, given that x and y are Out There, their mereological sum z = x + y is Out There, too, can be formulated in a (fragment of) language in which nothing is vague. Therefore (given that there is no de re vagueness), it cannot have a vague answer: either there is such a thing as x + y, or there isn’t. So “no restriction on composition can be vague. But unless it’s vague, it cannot fit the intuitive desiderata” (Lewis 1986, 213). Consequently, any restriction on composition would be unmotivated. To Exist and to Count: a Note on the Minimalist View 345 © 2009 The Authors. Journal compilation © 2009 Editorial Board of dialectica. If it is true that mereology is ontologically innocent, as Lewis has argued, then once we are committed to the existence of x and y, our commitment to z, i.e., x + y, is, in a sense, not a further commitment. In Lewis’s own words: Given a prior commitment to cats, say, a commitment to cat-sums is not a further commitment. The sum 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 is the same commitment either way . . . I say that composition . . . is like identity. The ‘are’ of composition is, so to speak, the plural form of the ‘is’ of identity. Call this the Thesis of Composition as Identity. It is in virtue of this thesis that mereology is ontologically innocent: it commits us only to things that are identical, so to speak, to what we were committed to before (Lewis 1991, 81–82). At least prima facie, the view of composition as identity could make mereology’s unrestricted composition more palatable, by advocating its ontological innocence. Lewis’s argument for the innocence of mereology can be summarized in the following way: (P1) Composition – a many-one mereological relation – is like identity. (P2) Nothing could be considered more ontologically innocent than the request to accept something identical to things already accepted. (C) Therefore, mereology is ontologically innocent. For Lewis, the sum z of certain objects x and y is the very same objects: the sum z is those things, x and y, and nothing more. Lewis’s argument rests on the thesis (P1) of composition as identity. What does the claim that composition is like identity mean? The answer depends on the reading of (P1) one accepts. In fact, there are two of them: a strong reading (StrongCom) and a weak one (WeakCom). The former goes as follows: (StrongCom) The predicate “are” used for the composition relation is literally the plural form of the “is” of identity.