Metaphysical Vagueness Without Vague Objects

Abstract

Elizabeth Barnes and Robert Williams have developed a theory of metaphysical indeterminacy, via which they defend the theoretical legitimacy of vague objects. In this paper, we argue that while the Barnes-Williams theory supplies a viable account of genuine metaphysical vagueness, it cannot underwrite an account of genuinely vague objects. First we clarify the distinction between these two key theses. Then we argue that the Barnes-Williams theory of metaphysical vagueness not only fails to deliver genuinely vague objects, it in fact provides grounds for rejecting them.

1. Introduction

In a series of papers,1 Elizabeth Barnes and Robert Williams have developed a theory of metaphysical indeterminacy, which they present as offering—among other things—a defence of the theoretical legitimacy2 of vague objects. On this account, vague objects such as Mount

Kilimanjaro are metaphysically indeterminate in that the source of their vagueness is worldly (not

1 See Barnes 2009, 2010a, 2010b, 2013 and 2014; Barnes and Williams 2009 and 2011a; and Williams 2006, 2008a, and 2008b.

2 Serious doubts about this date back at least to Dummett 1975, where it is claimed that ‘the notion that things might actually be vague, as well as vaguely described, is not properly intelligible’ (p. 314).

1 representational or epistemic), and vagueness is a species of indeterminacy.3 Barnes and Williams clarify that a commitment to metaphysical indeterminacy is not per se a commitment to vague objects.4 However, a defence of the legitimacy of vague objects appears to be among the intended applications of their theory.5

In this paper, we argue that while the Barnes-Williams theory is a viable account of genuine metaphysical vagueness, i.e. vagueness with a metaphysical source, it cannot serve to underwrite an account of genuinely vague objects. First we clarify the distinction between these two key theses. Then we argue that the Barnes-Williams theory of metaphysical vagueness does not simply fail to be committed to genuinely vague objects, it in fact provides grounds for rejecting them.

A terminological note: we here avoid using the phrase ‘ontic vagueness’, as it blurs over the distinction between metaphysical vagueness and vague objects. (Its popularity has plausibly been partly responsible for some confusions and conflations; see Williams 2008a for more on this.)

3 Barnes and Williams do not argue that either metaphysical indeterminacy or vague objects are real aspects of our world, only that both are at least intelligible. See Barnes 2006, pp. 196-7 and Barnes and Williams 2011b, p. 173.

4 See e.g. Barnes 2010b, p. 605, and Barnes and Williams 2011a, p. 111. In Barnes and Williams 2011a, they say that their theory is silent about vague objects. However, in other papers, they commit to vague objects explicitly. In Barnes and Williams 2009 (in response to Weatherson’s 2003 argument against vague objects), they claim that their theory preserves vague objects within classical logic and standard mereology. Williams 2008b is also explicit about the commitment to vague objects (such as surviving amoebas after fissions). It’s also important that other philosophers take the Barnes-Williams theory to be a defense of vague objects (see e.g. Akiba 2015a and 2015b, Paganini 2017).

5 See Williams 2008a, p. 768, and Barnes and Williams 2009, p. 182.

2. Metaphysical Vagueness And Vague Objects

Vagueness is associated with three principal characteristic features: a lack of sharp boundaries,

Sorites-susceptibility (tolerance to small changes but not to large ones), and borderline cases.6

Many ordinary objects appear to possess these features. Consider Mount Kilimanjaro.7 Mount

Kilimanjaro appears to have no sharp boundaries. It also seems tolerant to small changes: if we remove one electron from Mount Kilimanjaro, it does not become a different object. But it is not tolerant to large changes: if we remove all but one of its electrons, we no longer have the same object. There are associated borderline cases: an electron near the edge of the mountain seems to be a borderline case of being included in or part of Mount Kilimanjaro.

Let’s say that a vague object is an object that genuinely possesses the three characteristic properties of vagueness: lack of sharp boundaries, Sorites-susceptibility of something like the above kind, and borderline cases of inclusion or parthood. Following Barnes and Williams, let’s say that metaphysical vagueness is vagueness with a metaphysical source.8

Metaphysical vagueness does not commit us to vague objects, even if that vagueness concerns objects. Saying that the source of vagueness is metaphysical does not entail that any object possesses the three characteristic properties of vagueness. (Maybe it’s only facts or states of affairs that are metaphysically vague.) In fact, the Barnes-Williams theory enables a very clear explanation of how metaphysical vagueness and vague objects can come apart.

6 See e.g. Keefe 2000, p. 6, and Williamson 1994.

7 This example was introduced in McGee and McLaughlin 1994.

8 See Barnes 2010b, p. 603-5, and Barnes and Williams 2011a, p. 108. Unlike Barnes and Williams, we do not assume here that vagueness is a kind of indeterminacy: there is no reference to indeterminacy in the characteristic features of vagueness.

3. The Barnes-Williams Theory

Theories of vagueness attempt to account for the appearance of three main symptoms of vagueness.

Those who do not believe in metaphysical vagueness typically hold that vagueness is generated by, and/or a feature of, modes of representation or cognitive faculties. Until recently, the orthodox position was that all vagueness is generated by, and/or a feature of, representation.

Supervaluationism (see e.g. Dummett 1975, Fine 1975, Lewis 1982 and 1986, and Keefe 2000) is perhaps the best known representational theory of vagueness, and might be understood as attempting to explain away any appearance of metaphysical vagueness and/or vague objects.9

Supervaluationists account for vagueness as a consequence of semantic indeterminacy or unsettledness.10 The phenomena of vagueness associated with objects are due, not to objects genuinely lacking sharp boundaries (etc.), but to the indeterminacy of reference. When a singular term is vague, it fails to pick out a unique referent from among the many similar precise objects that are all “good enough” candidates to be that term’s referent.

The Barnes-Williams theory provides a serious metaphysical alternative. Like the supervaluationists, they understand vagueness as a kind of indeterminacy in reference, but for them the ultimate source of this indeterminacy is not semantic but metaphysical. Recall the case of

Mount Kilimanjaro, and consider electron e which is a borderline case for inclusion in the mountain. For the sake of simplicity, let’s pretend that e is the only electron that is borderline in this way. Now consider precise objects Kilimanjaro+ and Kilimanjaro-, which are exactly like

9 More recently, Williamson (1994) and Sorensen (1988 and 2001) have developed epistemic accounts.

10 More precisely, for Fine (1975) vagueness is a consequence of ‘semantic deficiency’ and for Lewis (1986) it is a consequence of ‘semantic indecision’.

Kilimanjaro except that they are non-vague: e is (determinately) included in Kilimanjaro+ but

(determinately) not included in Kilimanjaro-. On the Barnes-Williams theory, ‘Kilimanjaro’ is referentially indeterminate between precise objects Kilimanjaro+ and Kilimanjaro-, and the source of this indeterminacy is the world, not language.

Like the supervaluationists, Barnes and Williams hold that there exist a number of similar precise objects, all of them “good enough” to be referent of ‘Kilimanjaro’, and vagueness happens because there is nothing to select a unique referent for ‘Kilimanjaro’ from among these candidates.

However, whereas supervaluationists argue that this is a matter of our language failing to be precise enough to determine a referent, Barnes and Williams hold the world is responsible. By their lights, reality is indeterminate: unsettled between a (possible) world where e is included in Mount

Kilimanjaro and one where it isn’t.

This is a theory of metaphysical vagueness. It is not yet, however, a theory of vague objects.

4. Evading Evans

A classic objection to genuinely vague objects is found in Evans 1978. The argument is based on a controversial background assumption:11 that vague objects must have indeterminate identities. It starts with an explicit assumption for reductio: that it is indeterminate whether a=b, where a and b are vague objects. From this we are to derive, by property abstraction, that b has the property of being indeterminately identical with a. However, a does not have the property of being indeterminately identical with a.12 By Leibnitz’s Law ~(a=b) is then derived, which contradicts

11 For rejections of this assumption see Sainsbury 1989 and Paganini 2011.

12 It is assumed that a is determinately identical with a.

5 the starting assumption. We are invited to conclude that indeterminate identities—and hence vague objects—are incoherent.

To be successful, a theory of vague objects must block Evans’s argument.13

Supervaluationists can block Evans’s argument by rejecting the step from the indeterminacy of a=b (where ‘a’ and ‘b’ refer to vague objects) to a having the property of being indeterminately identical with b (or to b having the property of being indeterminately identical with a). Details may be found in Lewis 1988.14

In virtue of its structural similarities to supervaluationism, the Barnes-Williams theory can block Evans in the same way. This is explained in Barnes and Williams 2009 (p. 180-3).15

However, its structural resemblance to the mechanics of supervaluationism is also exactly why the

Barnes-Williams theory cannot really underwrite a theory of vague objects. The objects Barnes and Williams posit are precise objects, just like those that appear in the supervaluationist’s account. Vagueness—according to Barnes and Williams—arises only because the world hasn’t settled which of the candidate precise objects is the referent of ‘Kilimanjaro’.16 According to the

13 For different defenses of vague objects from Evans’s argument see also Sainsbury 1989, Akiba 2000, Parsons 2000,

Wilson 2013, and AUTHOR.

14 We should emphasize that Lewis agrees with Evans that there cannot be vague objects. Lewis’s point is that when vagueness is attributed to semantic indeterminacy, vague identity statements are meaningful.

15 See also Williams 2008b.

16 One might posit a further candidate referent—a vague object, Kilimanjaro*—that is (partly) responsible for the indeterminacy of reference for the name ‘Kilimanjaro’. However, if there is such a vague object, a theory must be appended to account for its vagueness. If this is a new theory of vague objects, it risks rendering the Barnes-Williams theory unnecessary (and, of course, the work of accounting for vague objects begins again). However, if it is the same theory, we are going around in theoretical circles. Thanks to a Thought referee for pressing us on this.

Barnes-Williams theory, these objects exhibit none of the symptoms of vagueness: they do not lack sharp boundaries, tolerate small changes, or come with borderline cases of inclusion and parthood. In fact, according to Barnes and Williams it is determinate that Kilimanjaro is identical with one of the precise candidate objects although it is indeterminate which one.17

So while Barnes and Williams propose a theory of metaphysical vagueness, it is one that does not posit any vague objects, and in fact offers a way to account for metaphysical vagueness without requiring that we posit any vague objects. For this reason, the Barnes-Williams theory stands ready to be pressed into service as part of an argument against vague objects, alongside a commitment to qualitative ontological parsimony.

5. Concluding Remarks

As far as we can see, the only reason the Barnes and Williams theory might have been understood as potentially underwriting a theory of vague objects is that it is a theory of metaphysical vagueness that concerns objects. But these two theoretical goals are distinct—and importantly so.

We conclude with a slightly more general moral: no theory of vagueness that attributes vagueness to unsettledness of reference, while maintaining that all worldly candidate referents are perfectly precise, can deliver a theory of vague objects. Such a theory locates vagueness at the interface between representation and reality, whether it goes on to place the blame on representation (like the supervaluationists) or reality (like Barnes and Williams). To commit to vague objects, by contrast, a theory must somehow manage to locate vagueness in objects themselves, not at this interface.

17 Barnes and Williams 2009, p. 185; see also Williams 2008b.

References

Authors’ works removed from list

Akiba, K. 2000. ‘Vagueness as a Modality’, in Philosophical Quarterly 50, pp. 359–70.

------2015a. ‘Referential Indeterminacy with an Ontic Source? A Criticism of Williams’s

Defense of Vague objects’, in Metaphysica 16, pp. 167–78.

------2015b. ‘How Barnes and Williams Have Failed to Present an Intelligible Ontic Theory

of Vagueness.’ in Analysis 75, pp. 565-73.

Barnes, E. 2006. ‘Conceptual Room for Ontic Vagueness’, PhD thesis, University of St Andrews.

------2009. ‘Indeterminacy, Identity, and Counterparts: Evans Reconsidered’, in Synthese

168, pp. 81-96.

------2010a. ‘Arguments Against Metaphysical Indeterminacy’, in Philosophy Compass 5,

pp. 953-64.

------2010b. ‘Ontic Vagueness: A Guide for the Perplexed’, in Noûs 44, pp. 601-27.

------2013. ‘Metaphysically Indeterminate Existence’, in Philosophical Studies 166, pp. 495-

510.

------2014. ‘Fundamental Indeterminacy’, in Analytic Philosophy 55, pp. 339-62.

Barnes, E. and Williams, R. 2009. ‘Vague Parts and Vague Identity’, in Pacific Philosophical

Quarterly 90, pp. 176-87.

------2011a. ‘A Theory of Metaphysical Indeterminacy’, in K. Bennett & D. Zimmerman

(ed.s), Oxford Studies in Metaphysics Volume 6, Oxford: Oxford University Press, pp. 103-

48.

------2011b. ‘Reply to Eklund’ in K. Bennett & D. Zimmerman (ed.s), Oxford Studies in

Metaphysics Volume 6, Oxford: Oxford University Press, pp. 173-82.

Dummett, M. 1975. ‘Wang’s Paradox’, in Synthese 30, pp. 301-24.

Evans, G. 1978. ‘Can There Be Vague Objects?’, in Analysis 38, p. 208.

Fine, K. 1975. ‘Vagueness, Truth and Logic’, in Synthese 54, pp. 235-59.

Keefe, R. 2000. Theories of Vagueness. Cambridge: Cambridge University Press.

Lewis, D. 1982. ‘Logic For Equivocators’, in Noûs 16, pp. 431-41.

------1986. On the Plurality of Worlds. Oxford: Blackwell.

------1988. ‘Vague Identity: Evans Misunderstood’, in Analysis 48, pp. 128-30.

McGee, V. and McLaughlin, B. 1994. ‘Distinctions Without a Difference’, in Southern Journal of

Philosophy 30 (supp. 1), pp. 203-51.

Paganini, E. 2011. ‘Vague Objects without Ontically Indeterminate Identity’, in Erkenntnis 74, pp.

351-62

------2017. ‘Vague Objects Within Classical Logic and Standard Mereology, and Without

Indeterminate Identity’, in Journal of Philosophical Logic, 46, pp. 457-65.

Parsons, T. 2000. Indeterminate Identity: Metaphysics and Semantics. Oxford: Oxford University

Press.

Sainsbury, M. 1989. ‘What is a Vague Object?’, in Analysis 49, pp. 99-103.

Sorensen, R. 1988. Blindspots. Oxford: Oxford University Press.

------2001. Vagueness and Contradiction. Oxford: Oxford University Press.

Weatherson, B. 2003. ‘Many Many Problems’, in The Philosophical Quarterly 53, pp. 481-501.

Williams, R. 2006. ‘An Argument for the Many’, in Proceedings of the Aristotelian Society 106,

pp. 409-17.

------2008a. ‘Ontic Vagueness and Metaphysical Indeterminacy’, in Philosophy Compass 3,

pp. 763-88.

------2008b. ‘Multiple Actualities and Ontically Vague Identity’, in The Philosophical

Quarterly 58, pp. 134-54.

Williamson, T. 1994. Vagueness. London: Routledge.

Wilson, J. 2013. ‘A Determinable-Based Account of Metaphysical Indeterminacy’, in Inquiry 56,

pp. 359-85.