Understanding Indeterminacy
Parsons (Terence)
Source: Parsons - Indeterminate Identity, 2000, Chapter 7
Paper - Abstract

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Analytic TOC1

  1. The terminology used in explaining indeterminate identity2 is meant to be ordinary; 'identical' is not intended in a special sense. 'Indeterminate' may be definable within certain world views (such as idealism), but is otherwise taken as a primitive.
  2. The biggest impediment to understanding views that invoke indeterminate identity3 is our tendency to reason bivalently; this has nothing special to do with identity. One can picture situations involving indeterminacy using Venn-like diagrams in which objects are represented by images with finite size. An object is pictured as being indeterminately P if its image lies partly inside of and partly outside of the region representing property P; objects are pictured as being indeterminately identical if their images properly overlap.
  3. Simple constraints on the picturing conventions entail that Leibniz's definition of identity in terms of coincidence of properties is built into the picturing. Picturings of the paradigm identity puzzles are given.
  4. A more general notion of picturing can be defined that is not necessarily two-dimensional; a simple condition yields a kind of principle of plenitude for properties and the Leibnizian account of identity.
  5. A process is given to refine pictures into more determinate ones; under certain general conditions these refinements picture the resolutions discussed earlier in giving super-resolutional readings of sentences.

In-Page Footnotes

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

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