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Full Idea
When the identity relation is vague, it may seem intransitive; a claim of apparent identity may yield an apparent non-identity. Some sort of 'counterpart' notion may have some utility here.
Gist of Idea
A vague identity may seem intransitive, and we might want to talk of 'counterparts'
Source
Saul A. Kripke (Naming and Necessity notes and addenda [1972], note 18)
Book Ref
Kripke,Saul: 'Naming and Necessity' [Blackwell 1980], p.51
A Reaction
He firmly rejects the full Lewis apparatus of counterparts. The idea would be that a river at different times had counterpart relations, not strict identity. I like the word 'same' for this situation. Most worldly 'identity' is intransitive.
| 12266 | 'Same' is mainly for names or definitions, but also for propria, and for accidents [Aristotle] |
| 12287 | Two identical things have the same accidents, they are the same; if the accidents differ, they're different [Aristotle] |
| 12288 | Numerical sameness and generic sameness are not the same [Aristotle] |
| 8650 | Things are the same if one can be substituted for the other without loss of truth [Leibniz] |
| 21315 | A tree remains the same in the popular sense, but not in the strict philosophical sense [Butler] |
| 15826 | There is 'loose' identity between things if their properties, or truths about them, might differ [Chisholm] |
| 11910 | Being 'the same' is meaningless, unless we specify 'the same X' [Geach] |
| 16999 | A vague identity may seem intransitive, and we might want to talk of 'counterparts' [Kripke] |
| 16494 | We want to explain sameness as coincidence of substance, not as anything qualitative [Wiggins] |