| Title | Puzzles about Identity. Aristotle and his Greek Commentators |
| Type | Book Section |
| Language | English |
| Date | 1985 |
| Published in | Aristoteles - Werk und Wirkung. Paul Moraux gewidmet. Bd. 1: Aristoteles und seine Schule |
| Pages | 57-97 |
| Categories | no categories |
| Author(s) | Mignucci, Mario |
| Editor(s) | Wiesner, Jürgen |
| Translator(s) |
| Aristotle’s conception of identity is too large a subject to be analyzed in a single article. I will try to discuss here just one of the many problems raised by his views on sameness. It is not, perhaps, the most stimulating question one could wish to see treated, but it is a question about logic, where I feel a little more at ease than among the complicated and obscure riddles of metaphysics. My subject will be Aristotle’s references to what is nowadays called ‘Leibniz’s Law’ (LL): if two objects x and y are the same, they both share all the same properties. A formal version of it could be: (1) x=y ⟹ ∀F(F(x) ⟺ F(y))x=y⟹∀F(F(x)⟺F(y)) It is perhaps worth remembering that (LL) must be distinguished from what is normally called the ‘principle of substitutivity’ (SP), according to which substitution of expressions that are said to be the same is truth-preserving. As has been shown, (LL) does not entail (SP), since there are counterexamples to (SP) that do not falsify (LL). Not only (SP), but also (LL) has been doubted by some modern logicians. The question is far from being settled, and it is perhaps of interest to examine how ancient logicians tried to manage this problem. First, I will consider Aristotle’s statements about (LL) and the analyses he gives of some supposed counterexamples to this principle. Secondly, the interpretations of his view among his Greek commentators will be taken into account, and their distance from the position of the master evaluated. As Professor Moraux has taught us, the study of the Aristotelian tradition often gives us the opportunity of understanding Aristotle’s own meaning better. [introduction p. 57-58] |
| Online Resources | https://uni-koeln.sciebo.de/s/VYZdFzrmNGSDth4 |
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| Title | Puzzles about Identity. Aristotle and his Greek Commentators |
| Type | Book Section |
| Language | English |
| Date | 1985 |
| Published in | Aristoteles - Werk und Wirkung. Paul Moraux gewidmet. Bd. 1: Aristoteles und seine Schule |
| Pages | 57-97 |
| Categories | no categories |
| Author(s) | Mignucci, Mario |
| Editor(s) | Wiesner, Jürgen |
| Translator(s) |
Aristotle’s conception of identity is too large a subject to be analyzed in a single article. I will try to discuss here just one of the many problems raised by his views on sameness. It is not, perhaps, the most stimulating question one could wish to see treated, but it is a question about logic, where I feel a little more at ease than among the complicated and obscure riddles of metaphysics. My subject will be Aristotle’s references to what is nowadays called ‘Leibniz’s Law’ (LL): if two objects x and y are the same, they both share all the same properties. A formal version of it could be:
(1) x=y ⟹ ∀F(F(x) ⟺ F(y))x=y⟹∀F(F(x)⟺F(y))
It is perhaps worth remembering that (LL) must be distinguished from what is normally called the ‘principle of substitutivity’ (SP), according to which substitution of expressions that are said to be the same is truth-preserving. As has been shown, (LL) does not entail (SP), since there are counterexamples to (SP) that do not falsify (LL). Not only (SP), but also (LL) has been doubted by some modern logicians. The question is far from being settled, and it is perhaps of interest to examine how ancient logicians tried to manage this problem.
First, I will consider Aristotle’s statements about (LL) and the analyses he gives of some supposed counterexamples to this principle. Secondly, the interpretations of his view among his Greek commentators will be taken into account, and their distance from the position of the master evaluated. As Professor Moraux has taught us, the study of the Aristotelian tradition often gives us the opportunity of understanding Aristotle’s own meaning better. [introduction p. 57-58] |
| Online Resources | https://uni-koeln.sciebo.de/s/VYZdFzrmNGSDth4 |
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