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Full Idea
Insofar as identity seems vague, it is provably mistaken. If it is vague whether x and y are identical (as in the Ship of Theseus), then x,y is definitely not the same as x,x, since the first pair is indeterminate and the second pair isn't.
Gist of Idea
It can't be indeterminate whether x and y are identical; if x,y is indeterminate, then it isn't x,x
Source
Nathan Salmon (Reference and Essence: seven appendices [2005], App I)
Book Ref
Salmon,Nathan: 'Reference and Essence (2nd ed)' [Prometheus 2005], p.243
A Reaction
[compressed; Gareth Evans 1978 made a similar point] This strikes me as begging the question in the Ship case, since we are shoehorning the new ship into either the slot for x or the slot for y, but that was what we couldn’t decide. No rough identity?
| 21594 | Stoics applied bivalence to sorites situations, so everyone is either vicious or wholly virtuous [Stoic school, by Williamson] |
| 14742 | It can't be indeterminate whether x and y are identical; if x,y is indeterminate, then it isn't x,x [Salmon,N] |
| 9050 | A third truth-value at borderlines might be 'indeterminate', or a value somewhere between 0 and 1 [Keefe/Smith] |
| 9061 | People can't be placed in a precise order according to how 'nice' they are [Keefe/Smith] |
| 9062 | If truth-values for vagueness range from 0 to 1, there must be someone who is 'completely tall' [Keefe/Smith] |
| 9063 | How do we decide if my coat is red to degree 0.322 or 0.321? [Keefe/Smith] |
| 8946 | We could make our intuitions about heaps precise with a million-valued logic [Fisher] |