Skip to main content
SpringerLink
Log in

Against the Modal Argument

  • Critical Discussion
  • Published:
Erkenntnis Aims and scope Submit manuscript

Abstract

The relationship between alethic modality and indeterminacy is yet to be clarified. A modal argument—an argument that appeals to alethic modality—against vague objects given by Joseph Moore offers a potential clarification of the relationship; it is proposed that there are cases for which the following holds: if it is indeterminate whether A = B then it is possible that it is determinate that A = B. However, the argument faces three problems. The problems remove the argument’s threat against vague objects and prompt a fuller scrutiny of Moore’s proposed relationship between alethic modality and indeterminacy. Such a scrutiny offers valuable lessons concerning the justification for claims of indeterminate identity, appeals to identity principles in contexts involving both alethic modality and indeterminacy, and how to identify the form of Gareth Evans’s argument against vague objects in other arguments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Notes

  1. See Moore (2008).

  2. Throughout, I freely interchange the identity predicate ‘is’ for ‘=’ and the negation of the identity predicate ‘distinct’ for ‘≠’.

  3. For example, Parsons (2000) and Van Inwagen (1995).

  4. I adopt the canonical view of the ‘that’/‘whether’ distinction for indeterminacy and determinacy;

    it is indeterminate whether ϕ iff it is not determinate that ϕ and not determinate that \(\neg \phi, \)

    it is indeterminate that ϕ iff it is not determinate that \(\neg \phi, \)

    it is determinate whether ϕ iff it is determinate that ϕ or determinate that \(\neg \phi\) (iff it is not indeterminate whether ϕ), and

    it is determinate that ϕ iff (it is determinate whether ϕ) and (ϕ).

  5. See Unger (1980).

  6. See Benacerraf (1965).

  7. It may be denied that unrestricted mereological composition holds in this instance. This is a response that rivals the positing of vague objects to account for the situation. Since Moore’s argument is intended to motivate a rejection of the positing of vague objects and so requires the assumption that there are vague objects, let us ignore the rival responses.

  8. Sometimes known as the Indiscernibility of Identicals.

  9. See Benacerraf (1965).

  10. Benacerraf’s original conclusion was to bite the bullet in this fashion by claiming that numbers are not objects (1965). He later recanted; any old ω-sequence would do for the natural numbers after all (Benacerraf 1996).

  11. Moore also claims that instances of the Ship of Theseus problem are analogous to the Problem of the Many case and Benacerraf case (2008: 2). For simplicity I ignore the Ship of Theseus problem and do not commit to whether it is analogous or not.

  12. The epistemicist response is a notable exception.

  13. This is merely application of the equivalences in fn. 4.

  14. Thank you to an anonymous referee who pointed out the controversial nature of this.

  15. See Evans (1978).

  16. See Salmon (1981).

  17. ‘Parsimony’ is a potentially misleading name for the assumption, as admitted by Moore (2008: 3), since it does not concern shaving away the number of objects, just the number of kinds.

  18. On the assumption that the progression of the natural numbers begins at zero.

  19. The Barnes-Williams theory of vague objects relies on their compatibility (Williams 2007; Barnes and Williams 2011; Barnes 2009). Since the theory rejects Referential Determinacy it is not subject to the modal argument.

  20. I have altered the argument slightly from the original. In Moore’s original version (*) does not explicitly contain ‘it is determinate whether’. Without it may be though that (*) would not be a contradiction. But once it is acknowledged that the assumptions for the argument are assumed to be determinately true, A ≠ C is secured a determinate truth-value. For if Necessary Distinctness is determinately true then B ≠ C is determinately true. Hence the use of Leibniz’s law to obtain (PN) will secure the determinate truth of A ≠ C just as long as we take it that Leibniz’s Law is determinately true. I have added the redundant ‘determinate’ to sentences in the argument just to make the application of determinacy apparent.

  21. The claim that if C didn’t exist then A would be B is taken on intuition: consider if C didn’t exist yet A and B did - what prevents A = B?

  22. See Moore (2008: 9).

  23. See Moore (2008: 10).

  24. See Moore (2008: 11–15).

  25. See Lowe (2005).

  26. Thank you to an anonymous referee for diagnosing a fallacy in the initial rendering of this objection.

  27. A mix of Democracy and Parsimony, (Moore 2008: 9).

  28. An appeal to it being indeterminate whether A and B share a property invites a version of Evans’s argument against vague objects; if the property of indeterminately sharing a property with A is had by B (C) then it distinguishes A from B (C). There are several responses to Evans’s argument (such as Lowe’s, which we note in Sect. 3.3) that serve to preserve the appeal to A and B′s (C′s) properties in order to justify that it is indeterminate whether A = B (indeterminate whether A = C). In any case, the modal argument disregards Evans’s argument since if it did not then the reductio of the modal argument could be blocked by Evans’s reductio. For if the latter is applied to (P1) then a contradiction from ‘it is indeterminate whether A = B′ and from ‘it is indeterminate whether A = C′ is derivable, thus blocking the modal argument at (P1).

  29. See Moore (2008: 8).

  30. See Moore (2008: 11).

  31. Thank you to an anonymous referee to pointing this out.

  32. If you think that there are no objects that are necessarily (self-)identical then you may think that \({\hat x} (\square x = A)\) cannot be instantiated since it does not exist. If so, then replace talk of \({\hat x} (\square x = A)\) with talk of \({\hat x} (\nabla x = B)\) (where ‘∇’ is ‘it is contingent whether’). On this diagnosis of a fallacy, A has the property (of being contingently identical to B) in w 1 whereas B does not (since there is no possible world in which any object is distinct from itself).

  33. Thank you to an anonymous referee for pointing out the need to make this clearer.

  34. This requires the assumption that it is determinate whether (E1). This needs to be assumed for every premise for otherwise the argument would be neither valid nor invalid (indeterminate truth is not sufficient to secure validity and not sufficient to secure invalidity). Hence it is legitimate to prefix (E5) with ‘it is determinate whether’ since each premise (E1)-(E4) needs to be prefixed with ‘it is determinate whether’ in order to ensure that the argument is either valid or invalid.

  35. See Lowe (2005). What follows is my take on Lowe’s response since my explanation differs slightly; Lowe claims that it is indeterminate whether \({\hat x} [\blacktriangledown (x = a)]\) is distinct from \({\hat x} [\blacktriangledown (x = b)]\) (Lowe 2005: 299) whereas I remain silent on this, instead I rely on the judgment that it is not determinate that \({\hat x}[\blacktriangledown (x = a)]\) is distinct from \({\hat x} [\blacktriangledown (x = b)]\) . I do not know whether Lowe would endorse my interpretation of his response. For a defence of vague objects against Evans’s argument and a defence against other arguments against vague objects see Barnes and Williams (2009).

  36. For otherwise identity would not be an equivalence relation since it would not be be symmetric. If it is assumed that it is determinate that \({\hat x}[\blacktriangledown(x = a)]\) is distinct from \({\hat x}[\blacktriangledown(x = b)]\) then since it is determinate that \({\hat x}[\blacktriangledown(x = a)]\) is distinct from \({\hat x}[\blacktriangledown(x = b)], a\) has \({\hat x}[\blacktriangledown(x = b)]\) iff b does not and b has \({\hat x}[\blacktriangledown(x = a)]\) iff a does not. So either it would be indeterminate whether a is identical to b but not indeterminate whether b is identical to a, or it would be indeterminate whether b is identical to a but not indeterminate whether a is identical to b.

  37. I have omitted consideration of the Salmon argument (1981) for simplicity.

  38. For

    1. (iv)

      \(\diamondsuit\,[\forall \Upphi (\Upphi(A) \equiv \Upphi(B))]\)    [modus ponens on I(b) from (iii)] depends upon (iii).

  39. This objection was provided by an anonymous referee.

  40. This is nothing new; Lowe states this (2005: 300–301).

References

  • Barnes, E. (2009). Ontic vagueness: A guide for the perplexed. Noûs, 44(4), 601–627

    Google Scholar 

  • Barnes, E., Williams, R. (2009). Vague parts and vague identity. Pacific Philosophical Quarterly, 90(2), 176–187

    Article  Google Scholar 

  • Barnes, E., & Williams, R. (2011) A theory of metaphysical indeterminacy. In Oxford studies in metaphysics (Vol. 6). Karen Bennett and Dean Zimmerman.

  • Benacerraf, P. (1965). What numbers could not be. The Philosophical Review, 74, 47–73

    Article  Google Scholar 

  • Benacerraf, P. (1996). Recantation or any old ω-sequence would do after all. Philosophia Mathematica, 4(2), 184–189

    Article  Google Scholar 

  • Evans, G. (1978). Can there be vague objects? Analysis, 38, 208

    Article  Google Scholar 

  • Lowe, E. J. (2005). Identity, vagueness, and modality. In Bermúdez, J., (Ed.), Thought, reference, and experience. Oxford: Clarendon Press.

    Google Scholar 

  • Moore, J. G. (2008). A modal argument against vague objects. Philosophers’ Imprint, 8(12), 1–17.

    Google Scholar 

  • Parsons, T. (2000). Indeterminate identity: Metaphysics and semantics. New York: Oxford University Press

    Book  Google Scholar 

  • Salmon, N. (1981). Reference and essence. Princeton: Princeton University Press.

    Google Scholar 

  • Unger, P. (1980). The problem of the many. Midwest Studies in Philosophy, 5, 411–467

    Article  Google Scholar 

  • Van Inwagen, P. (1995). Material beings. Ithaca, New York: Cornell University Press

    Google Scholar 

  • Williams, R. (2007). Multiple actualities and ontically vague identity. The Philosophical Quarterly, 58(230), 134–154

    Google Scholar 

Download references

Acknowledgments

Thank you to Anthony Everett, \({\O}\)ystein Linnebo, and Stuart Presnell for comments and suggestions on drafts of this paper.

Author information

Authors and Affiliations

  1. Department of Philosophy, University of Bristol, 9 Woodland Road, Bristol, BS8 1TB, UK

    Christopher S. Gifford

Authors
  1. Christopher S. Gifford
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christopher S. Gifford.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gifford, C.S. Against the Modal Argument. Erkenn 78, 627–646 (2013). https://doi.org/10.1007/s10670-012-9366-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10670-012-9366-7

Keywords

Search

Navigation