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Ideas for 'works', 'Grundlagen der Arithmetik (Foundations)' and 'Critique of Pure Reason'

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6 ideas

9. Objects / F. Identity among Objects / 1. Concept of Identity

16022	The idea of a criterion of identity was introduced by Frege [Frege, by Noonan]
	Full Idea: The notion of a criterion of identity was introduced into philosophical terminology in Frege's 'Grundlagen', and was strong emphasised in Wittgenstein's 'Philosophical Investigations'.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Harold Noonan - Identity §4
	A reaction: For Frege a thing can only have an intrinsic identity if it can participate in an equality relation. For abstract objects (such as directions or numbers) the relation is an equivalence. The general idea is that identical objects must relate in some way.

11100	Frege's algorithm of identity is the law of putting equals for equals [Frege, by Quine]
	Full Idea: Frege's algorithm of identity is the law of putting equals for equals.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Willard Quine - Identity, Ostension, and Hypostasis 4
	A reaction: Quine, and most modern philosophers, seem to accept universal substitutivity as a sufficient condition for identity. But you then get the problem of coextensionality (renate/cordate), which can only be solved by introducing modality.

9. Objects / F. Identity among Objects / 3. Relative Identity

12153	Geach denies Frege's view, that 'being the same F' splits into being the same and being F [Perry on Frege]
	Full Idea: Frege's position is that 'being the same F as' splits up into a general relation and an assertion about the referent ('being the same' and 'being an F'). This is what Geach denies, when he says there is no such thing as being 'just the same'.
	From: comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by John Perry - The Same F I
	A reaction: It looks as if you can take your pick - whether two things are perfectly identical, or whether they are identical in some respect. Get an unambiguous proposition before you begin the discussion. Identify referents, not kinds of identity, says Perry.

9. Objects / F. Identity among Objects / 6. Identity between Objects

9853	Identity between objects is not a consequence of identity, but part of what 'identity' means [Frege, by Dummett]
	Full Idea: Part of Frege's profound new idea of identity is that the criteria for identity of objects of a given kind is not a consequence of the way that kind of object is characterised, but has to be expressly stipulated as part of that characterisation.
	From: report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.13
	A reaction: This makes identity a relative concept, rather than an instrinsic concept. Does a unique object have an identity? Do properties have intrinsic identity conditions, making them usable to identify two objects. Deep waters. Has Frege muddied them?

9. Objects / F. Identity among Objects / 7. Indiscernible Objects

7576	The Identity of Indiscernibles is true of concepts with identical properties, but not of particulars [Kant, by Jolley]
	Full Idea: Kant said that the principle of the Identity of Indiscernibles is true only at the level of concepts; two concepts having identical properties are the same concept; the principle is not true at the level of particulars given in sensory experience.
	From: report of Immanuel Kant (Critique of Pure Reason [1781]) by Nicholas Jolley - Leibniz Ch.8
	A reaction: Good. I would think that should be the last word on that particular subject. ...Suppose, though, that two people had identical concepts with identical properties, but believed that the extensions (application to particulars) were different?

14509	If we ignore differences between water drops, we still distinguish them by their location [Kant]
	Full Idea: In the case of two drops of water one can completely abstract from all inner difference (of quality and quantity), and it is enough that they be intuited in different places at the same time in order for them to be held to be numerically different.
	From: Immanuel Kant (Critique of Pure Reason [1781], B319/A263)
	A reaction: Adams points out that this is the same idea as Max Black's famous two spheres thought experiment. We assume that all the water drops are distinct from one another, even if we are unable to perceive the fact. Best explanation.