Combining Philosophers

Ideas for Peter Geach, Gottfried Leibniz and Yuval Noah Harari

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12 ideas

9. Objects / F. Identity among Objects / 1. Concept of Identity
Inequality can be brought infinitely close to equality [Leibniz]
     Full Idea: Equality may be considered as an infinitely small inequality, and we may make inequality approach equality as much as we wish.
     From: Gottfried Leibniz (A General Principle to Explain Laws of Nature [1687], p.67)
     A reaction: An interesting response to David Lewis's brusque dismissal of the problem of identity, as all-or-nothing...end of story.
9. Objects / F. Identity among Objects / 3. Relative Identity
Denial of absolute identity has drastic implications for logic, semantics and set theory [Wasserman on Geach]
     Full Idea: Geach's denial of absolute identity has drastic implications for logic, semantics and set theory. He must deny the axiom of extensionality in set theory, for example.
     From: comment on Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6
     A reaction: I'm beginning to think we have two entirely different concepts here - the logicians' and mathematicians' notion of when two things are identical, and the ordinary language concept of two things being 'the same'. 'We like the same music'.
Identity is relative. One must not say things are 'the same', but 'the same A as' [Geach]
     Full Idea: Identity is relative. When one says 'x is identical with y' this is an incomplete expression. It is short for 'x is the same A as y', where 'A' represents some count noun understood from the context of utterance.
     From: Peter Geach (Reference and Generality (3rd ed) [1980], p.39), quoted by John Perry - The Same F I
     A reaction: Perry notes that Geach's view is in conscious opposition to Frege, who had a pure notion of identity. We say 'they are the same insofar as they are animals', but not 'they are the same animal'. Perfect identity involves all possible A's.
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
Two eggs can't be identical, because the same truths can't apply to both of them [Leibniz]
     Full Idea: It isn't possible to have two particulars that are similar in all respects - for example two eggs - for it is necessary that some things can be said about one of them that cannot be said about the other, else they could be substituted for one another.
     From: Gottfried Leibniz (works [1690]), quoted by David Wiggins - Sameness and Substance 2.2
     A reaction: [from a 'fragment' for which Wiggins gives a reference] This quotation doesn't rest the distinctness of the eggs on some intrinsic difference, but on the fact that we can say different things about the two eggs.
No two things are totally identical [Leibniz]
     Full Idea: By virtue of insensible variations, two individual things can never be perfectly alike.
     From: Gottfried Leibniz (New Essays on Human Understanding [1704], Pref)
     A reaction: This sounds a bit like the 'discernibility of non-identicals', except that he says that the differences may not be 'sensible'. He has to be talking of physical things, since I presume that, say, the symmetry of two circles is perfectly identical.
Things in different locations are different because they 'express' those locations [Leibniz]
     Full Idea: Things that differ in place must express their place, that is, they must express the things surrounding, and thus they must be distinguished not only by place, that is, not by an extrinsic denomination alone, as is commonly thought.
     From: Gottfried Leibniz (Letters to Burcher De Volder [1706], 1703.06.20)
     A reaction: This is an unusual view, which has some attractions, as it enables the relations of a thing to individuate it, while maintaining that this is a real difference in character.
In nature there aren't even two identical straight lines, so no two bodies are alike [Leibniz]
     Full Idea: In nature any straight line you may take is individually different from any other straight line you may find. Accordingly, it cannot come about that two bodies are perfectly equal and alike.
     From: Gottfried Leibniz (Letters to Burcher De Volder [1706], 1703.06.20)
     A reaction: Leibniz was very good at persuasive examples! It remains unclear, though, why he takes the Identity of Indiscernibles to be a necessary truth, when he seems to have only observed it from experience. This is counter to his other principles.
If two bodies only seem to differ in their position, those different environments will matter [Leibniz]
     Full Idea: If two bodies differ only in their position, their individual relations to the environment must be taken into account, so that more is involved in their distinguishability than just position.
     From: Gottfried Leibniz (Letters to Burcher De Volder [1706], 1703.06.20)
     A reaction: This seems to allow that two bodies could be intrinsically type-identical (though differing in extrinsic features), which is contrary to his normal view. I suppose a different location in the gravitational field will make an intrinsic difference.
There must be some internal difference between any two beings in nature [Leibniz]
     Full Idea: There are never two beings in nature that are perfectly alike, two beings in which it is not possible to discover an internal difference, that is, one founded on an intrinsic denomination.
     From: Gottfried Leibniz (Monadology [1716], §09)
     A reaction: From this it follows that if two things really are indiscernible, then we must say that they are one thing. He says monads all differ from one another. People certainly do. Leibniz must say this of electrons. How can he know this?
9. Objects / F. Identity among Objects / 8. Leibniz's Law
Leibniz's Law is incomplete, since it includes a non-relativized identity predicate [Geach, by Wasserman]
     Full Idea: Geach rejects the standard formulation of Leibniz's Law as incomplete, since it includes a non-relativized identity predicate.
     From: report of Peter Geach (Reference and Generality (3rd ed) [1980]) by Ryan Wasserman - Material Constitution 6
     A reaction: Not many people accept Geach's premiss that identity is a relative matter. I agree with Wiggins on this, that identity is an absolute (and possibly indefinable). The problem with the Law is what you mean by a 'property'.
9. Objects / F. Identity among Objects / 9. Sameness
Things are the same if one can be substituted for the other without loss of truth [Leibniz]
     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').
     From: Gottfried Leibniz (works [1690]), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §65
     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'.
Being 'the same' is meaningless, unless we specify 'the same X' [Geach]
     Full Idea: "The same" is a fragmentary expression, and has no significance unless we say or mean "the same X", where X represents a general term. ...There is no such thing as being just 'the same'.
     From: Peter Geach (Mental Acts: their content and their objects [1957], §16)
     A reaction: Geach seems oddly unaware of the perfect identity of Hespherus with Phosphorus. His critics don't spot that he was concerned with identity over time (of 'the same man', who ages). Perry's critique emphasises the type/token distinction.