Counting Objects
Parsons (Terence)
Source: Parsons - Indeterminate Identity, 2000, Chapter 8
Paper - Abstract

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Analytic TOC1

  1. If we try to count objects in the face of indeterminacy, we sometimes get no determinate answer; this is due to indeterminacy of predication (producing indeterminacy regarding which objects are supposed to be counted), or indeterminacy of identity (producing indeterminacy regarding whether an object has already been counted), or both.
  2. Familiar formulas are given for making cardinality claims; e.g. "there are at least two φ's" is written as '∃x∃y (¬x = y & φx & φy)'.
  3. It is shown how to get the "right" answers; e.g. that in the ship case it is true that there are at least two ships, false that there are more than three, and indeterminate whether there are exactly two (or exactly three).
  4. Sometimes a question can be formulated in two ways: either austerely, or with a determinacy connective ('!') added; these formulations correspond to two natural "right" answers.
  5. Super-resolutional readings also explain certain of our intuitions.

In-Page Footnotes

Footnote 1: Taken from "Parsons (Terence) - Indeterminate Identity: Analytical Table of Contents".

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