The Necessity and Determinacy of Distinctness
Williamson (Timothy)
Source: Lovibond & Williams - Identity, Truth & Value: Essays for David Wiggins
Paper - Abstract

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Author’s Introduction

  1. Any metaphysical caprice can be indulged in some more or less deviant formal system. The work of David Wiggins is a reminder of the depth to be gained in metaphysics from the constraints of orthodoxy in logic. His writing on the metaphysics of identity is a salient case in point. Consider four claims:
    • (NI) If things are identical, they are necessarily identical.
    • (ND) If things are distinct, they are necessarily distinct.
    • (DI) If things are identical, they are determinately identical.
    • (DD) If things are distinct, they are determinately distinct.
    NI and DI proclaim the necessity1 and determinacy2 of identity, ND and DD the necessity and determinacy of distinctness. NI is provable with a modicum of fairly orthodox logic. A formally parallel proof can be given of DI. Similar proofs of ND and DD can be given only in an extended logic.
  2. Wiggins has endorsed NI and DI but not ND or DD, and considered sympathetically a view combining DI with the denial of DD. A parallel view would combine NI with the denial of ND.
  3. This paper assembles some considerations relevant to the assessment of such views. An alternative proof will be given of ND that is almost as compelling as the proof of NI. This result is quite consistent with Wiggins's position in "Wiggins (David) - Sameness and Substance" and elsewhere; his defence of NI against supposed counterexamples can be extended to ND. On a common view of determinacy, the alternative proof of ND can be adapted as an alternative proof of DD, contrary to the view that accepts DI and rejects DD. This result would be consistent with the main lines of Wiggins's position; his defence of DI against supposed counterexamples can be extended to DD.
  4. If these considerations point in the right direction, identity is a metaphysically rigid relation. Either it necessarily and determinately relates a given pair of individuals, or it necessarily and determinately fails to relate them. In that sense, the facts about it form part of the necessary and determinate structure of reality. Any alternative to them is epistemic, not metaphysical. In what follows, the question of necessity will be discussed first; ideas from that discussion will then be applied to the question of determinacy.


See "Wiggins (David) - Reply to Williamson (The Necessity and Determinacy of Distinctness)" for a reply.

In-Page Footnotes

Footnote 1:
  • Necessity is understood as metaphysical necessity, although the arguments of the paper would extend to weaker kinds, such as natural necessity.
Footnote 2:

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  1. Blue: Text by me; © Theo Todman, 2019
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