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Full Idea
Leibniz's definition is as follows: Things are the same as each other, of which one can be substituted for the other without loss of truth ('salva veritate').
Gist of Idea
Things are the same if one can be substituted for the other without loss of truth
Source
Gottfried Leibniz (works [1690]), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §65
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.76
A Reaction
Frege doesn't give a reference. (Anyone know it?). This famous definition is impressive, but has problems when the items being substituted appear in contexts of belief. 'Oedipus believes Jocasta (his mother!) would make a good wife'.
| 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] |