Abstract
Proponents of linguistic accounts of vagueness generally trace vagueness in mereological claims to imprecision in singular terms. The purpose of this chapter is to develop an alternative linguistic account of vague mereological claims. I propose that vagueness in ordinary mereological claims is typically due, not to imprecision in singular terms, but to imprecision in mereological terms such as the relational predicate “is part of.” Though my account is not problem-free, I think it is preferable to the standard linguistic account because it preserves important ordinary intuitions about objects. Moreover, my account is supported by the evident lack of rigor and specificity in our actual use of mereological vocabulary. I further suggest that my linguistic account of mereological vagueness might accommodate some intuitions motivating ontic accounts of vagueness while avoiding a troublesome commitment to indeterminacy in the world.
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Notes
- 1.
Of course, the singular term “X” may lack a unique referent as well. Strictly speaking, the account which traces all mereological vagueness to imprecision in singular terms says that the sentence “X is part of Y” is vague iff, on some admissible interpretations of singular terms, the referent of “X” is a part of the referent of “Y,” while on other admissible interpretations, the referent of “X” is not part of the referent of “Y.” However, in typical parthood claims, variation in the referent of the first term (here, “X”) would not seem to create any additional fluctuation in truth value beyond that already due to variation in the referent of the second term. Thus, I focus in my example parthood claims only on the purported imprecision of the second term.
- 2.
van Inwagen discusses a similar example at (1990, pp. 94–96, 217–218) in support of his claim that the parthood relation is vague.
- 3.
- 4.
See also Peter Unger’s presentation of the problem of the many in Unger (1980).
- 5.
Notice that in the case of a prosthetic implant, unlike that of the digested carbon atom or the loose hair, the question is not when the implant becomes, or ceases to be, part of the organism, but whether it is ever part of the organism.
- 6.
- 7.
See Smith (2007) for an extended criticism this consequence of VST.
- 8.
Lewis and other proponents of VST may nonetheless hold that it is supertrue—that is, true on each admissible interpretations of our language—that exactly one object on the mat is Tibbles. See, for example, Lewis (1993, pp. 172–173). However, supertruth is not truth. Lewis himself points out that within the supervaluationist framework, we cannot even state the initial puzzle—that there appear to be many equally admissible ways delineating Tibbles’ boundaries—much less Lewis’ own VST-style solution to that puzzle. Thus, Lewis admits (as he must) that, supervaluationism aside, it is true that singular terms like “Tibbles” have multiple equally eligible referents. See, for example, Lewis (1993, p. 173): “Under the supervaluationist rule, it’s right to say that there’s only one cat, and so the candidates have unequal claim. Suspending the rule it’s right to say the candidates have equal claim, and that all of them alike are not definitely not cats. Suspending the rule, it’s even right to say that they are all cats!”
- 9.
I think it is helpful to compare VST to other philosophical claims which, though also highly unintuitive, are nonetheless much easier to accommodate than is VST. As one example, consider the “universal fusion principle” stating that, for any arbitrary plurality of objects, some object is composed of just that plurality of objects. Clearly the universal fusion principle counterintuitive—we normally assume that no object is composed of just Tibbles and the Empire State Building. Nonetheless, there seems to be no substantial barrier to altering ordinary thought and speech to accommodate the universal fusion principle. We can do so as long as we are willing to admit that, in addition to ordinary integral objects, there are also many scattered objects which we usually ignore. In contrast to the universal fusion principle, VST does not merely require that we countenance additional objects outside of the realm of ordinary concerns. VST implies that our thoughts and speech drastically misrepresent objects at the center of our practical lives.
- 10.
See Lewis (1993, pp. 172–173) and note 8 above. However, Lewis never explains what is supposed to be the basis of a restriction of admissible interpretations of our language to those which assign exactly one cat-like object on Tibbles’ mat to the extension of the “…is a cat” predicate. Note that it is not a requirement of our concept of cathood that distinct cats cannot overlap—we allow that they do in cases of Siamese twins and can imagine fictional circumstances in which overlapping cats are commonplace. It is thus not clear what supports Lewis’ assumption that any interpretation which assigns more than one of the overlapping Tibbles-candidates to the extension of “…is a cat” must be inadmissible.
- 11.
Toward the end of the next section, I briefly discuss the sort of alternative position advocated in Lowe (1982, 1995). Lowe allows that there are many cat-shaped lumps of feline tissue on Tibbles’ mat, but (in opposition to Lewis) claims that there is exactly one (candidate) cat on Tibbles’ mat. I take it that Lowe’s position is much more intuitively acceptable than is Lewis’. The difficulty with Lewis’ position lies not so much in his claim that there are many cat-shaped and cat-sized things on Tibbles’ mat but in his claim that all of these many things equally qualify as cats.
- 12.
A terminological clarification: if interpretation I assigns relation R to the relational predicate R and the pair <x, y> is in the extension of R, I will say that <x, y> is in the extension of R under interpretation I.
- 13.
Alternatively, we might dispense with properties and relations altogether and just talk about predicates and the (determinate or fuzzy) extensions assigned to them under different interpretations.
- 14.
Of course, the proponent of the VMT-style account of mereological vagueness must admit that some singular terms lack unique referents. For example, “the nicest man in the room” may designate different men under different interpretations of “nicest.” Moreover, a proponent of VMT could hold that certain types of ordinary singular terms—for example, terms for geographical entities like mountains—never succeed in designating unique objects. Even with this more limited rejection of VST, VMT is required for a linguistic account of vague mereological claims involving whatever singular terms do succeed in picking out unique referents.
- 15.
See Simons (1987) for a discussion of alternative formal mereologies. The VMT account of mereological vagueness will be discussed in relation to classical mereology at the end of this section.
- 16.
See, for example, van Inwagen (1990, pp. 43–44) for additional rules along these lines.
- 17.
In fact, although (Loc-In) is relatively noncontroversial, we might interpret the parthood predicate in such a way that locational inclusion is necessary but not sufficient for parthood. For example, Lowe holds that a lump of clay constituting a statue does not have the statue—or the statue’s arms, legs, etc.—as parts even though these objects are all located within the lump. See Lowe (2003). Doepke (1982) endorses a similar position. Thus, even if all material objects had precise locations, (Loc-In) would still not fix a unique interpretation for the parthood predicate, since it leaves room for variation among interpretations in which objects count as parts of wholes they are (spatially) included in.
- 18.
Thus, for example, <Tibbles’ tail, Tibbles> is assigned to the extension of the parthood predicate on every precisification, <Tibbles’ tail, the Empire State Building> is excluded from the extension of the parthood predicate on every precisification, and any precisification which assigns <H, Tibbles> to the extension of the parthood predicate also assigns <H, Tibbles> to the extension of the “located within” predicate.
- 19.
A caveat: although we ordinarily assume that (Mass) is generally true, it is not at all clear that it applies in case the x’s are extremely small. If each of the x’s is a minimal particle and if minimal particles have no mass, then x’s mass cannot be the sum of the separate masses of the x’s (unless of course x also has no mass). But we may at least assume that (Mass) holds in cases involving only objects with positive mass.
- 20.
See Rosen and Smith (2004) for a similar suggestion.
- 21.
Note that unlike the parthood predicate, the borderline parthood predicate is not assigned different extensions on different (first-order) precisifications of our language. Nonetheless, the borderline parthood predicate may be vague if it is vague which interpretations of a language qualify as precisifications of that language (i.e., if the metalinguistic term “precisification” is vague). The same points apply to the predicates defined in (Dprec), (Dprec*), and (Dvague).
- 22.
Note that the presence of an organism, planet, or table is not determined by the mere presence of any particular plurality of particles. On the one hand, such objects are not tied to any specific plurality of particles (since they change parts over time). On the other hand, for an organism, planet, or table to be in the world, it is not sufficient that any particles merely exist. What is required is that certain kinds of particles stand in particular spatial or functional relations to one another.
- 23.
See Donnelly (2009) for more details on the relation between classical mereology and a VMT-style account of mereological vagueness.
- 24.
Note that (*) does not require that the same object is the fusion of the x’s on all precisifications. In other words, (*) does not require that some object z is such that for every precisification j, z stands in the fusion j relation to the x’s.
- 25.
Recall that according to the definition of the fusion predicate (Dfus), if z is a fusion of the x’s, then each of the x’s is a part of z.
- 26.
Note that, despite the similarities between T and Tibbles, there is no temptation to claim that their identity relations are indeterminate. T is definitely distinct from Tibbles since the two objects stand in different relations to the particle y.
- 27.
Of course, the problem described here compounded by the fact that Tibbles has a multitude of other borderline parts besides y. Thus, it seems that the VMT-er who endorses (*) must admit a multitude of other “Tibbles doubles” besides T.
- 28.
Again, there is no reason to think that identity relations are indeterminate. Since M and Tibbles stand in different relations to the particles x 1, … x n , y (M, but not Tibbles, stands in fusion j to x 1, … x n , y), M and Tibbles are definitely distinct.
- 29.
See Lowe (1995) for a response to Lewis (1993) which endorses a position roughly along these lines. However, Lowe does not here explicitly endorse either a purely linguistic account of vagueness or the strong principle (Pfusion). He does, however, assume that there are many precise lumps of cat tissue in Tibbles’ vicinity, each of which is definitely distinct from Tibbles.
- 30.
One additional advantage of the VMT account is that it offers more ontological flexibility than the VST account. Because the VST account requires multiple candidate referents for each ordinary singular term, the VST account is committed to an ontology which includes many overlapping complex objects wherever there is any complex object. As we have just seen, the VMT account is compatible with either a somewhat sparse ontology or an ontology abundant enough to include arbitrary portions of matter in addition to ordinary objects.
- 31.
- 32.
See Williamson (1994) for an influential recent defense of an epistemic account of vagueness.
- 33.
See Keefe (2000, pp. 62–84).
- 34.
In fact, Smith (2005) uses two different parthood relations, only one of which (concrete parthood) holds to intermediate degrees. The other parthood relation (notional parthood) is a crisp relation. However, I take Smith’s comments in Section 4 of his paper to indicate that he takes only the vague relation (concrete parthood) to correspond to the ordinary notion of parthood.
Also, Smith’s concrete parthood relation is represented as a mapping that assigns a real number in [0, 1] to each pair of objects at a given time in a given possible world. I do not consider variation across possible worlds in this chapter.
- 35.
See, for example, Keefe (2000).
- 36.
I leave open the possibility that vague properties and relations may be better suited for accounts of other forms of vagueness.
- 37.
By an “indeterminately obtaining” maximal state of affairs I mean a maximal state of affairs S such that it is indeterminate whether S obtains. If I understand correctly, the Kripke models introduced in Barnes and Williams (2010) are intended to represent alternative indeterminately obtaining (maximal) states of affairs.
- 38.
See, for example, Smith (2007) for an explicit statement of this assumption.
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Donnelly, M. (2014). A Linguistic Account of Mereological Vagueness. In: Akiba, K., Abasnezhad, A. (eds) Vague Objects and Vague Identity. Logic, Epistemology, and the Unity of Science, vol 33. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7978-5_3
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