- The Identity of Indiscernibles2 is expressible in a Wittgensteinian language which lacks a sign for identity, and does not appear to be logically necessary.
- The Indiscernibility of Identicals3, on the other hand, if stated in a non-trivial form in such a language, splits into two theses which are provable as theorems of the predicate calculus with variables exclusively interpreted.
- Apparent failure of substitutivity of identicals is to be explained by making appropriate scope distinctions.
- Contradictory beliefs seem to be attributable to people on a large scale if we allow unlimited substitution of identicals for identicals.
- Introduction of the Xi-operator allows us to distinguish clearly, by means of scope-distinctions, what it is to hold incompatible beliefs about what is in fact one and the same thing from what it is to hold that one and the same thing has incompatible properties.
- The same distinctions can be made with the use of the reflection operator. Contexts which are opaque with respect to reflection are transparent with respect to proper names. Reflection makes a difference to the conceptual content of thoughts, but names do not.
- The role of a proper name is simply to indicate the subject of discourse. Names do not have separately significant parts,
- One name, one object, and vice versa. 'London', as the name of a city in Ontario, is a different name from 'London' as used to refer to the capital of England. There are two names (at least) spelled 'Cato', whereas 'Dubrovnik' and 'Ragusa' are semantically the same name.
- Any name of an object will serve to identify a thought about that object, but will not constitute any part of that thought. An expression like '— thinks that......' forms an n-place predicable out of an (n — 1)-place predicable. 'John thought that Peter struck Malchus' is not of the form 'John thought that p'.
- This justifies the claim that there is mutual entailment between (1A) and (2A), and makes sense of the Wittgensteinian principle, earlier ignored, 'one object, one name'.
- The content of (1A) and (2A) is identical, but different from that of (6A).
- Metalinguistic version of the Principle of the Indiscernibility of Identicals4.
- Summary of the chapter.
Photocopy of complete Book filed in "Various - Papers on Identity Boxes: Vol 19 (W)".
Footnote 1: Taken from "Williams (Christopher) - What Is Identity?: Introduction and Analytical Table of Contents". The numbering corresponds to Williams’s section-numbering.
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