I 218
Identity/GeachVsFrege: identity is not a relation - "Is an A" does not mean "has identity with A" - (whereby "A" is a name).
VsFrege: (in Frege, basic principles of artihmetics) instead of "There are just as many Fs as Gs": "Either any given object F iff it is a G, or there is a relation that is a one-to-one correspondence between the Fs and Gs". But this must not be an identity.
I 226
Identity/Geach: only objects can be strictly identical. - In terms, there is only analogous identity: if they are coextensive.
>
Coextensive.
I 238
Identity/GeachVsQuine: Thesis: Identity is relative. - If someone says "x is identical to y", this is an incomplete expression. - It is an abbreviation for "x is the same as y". - (Weird, that Frege did not represent this).
>
Identity/Quine.
Identity/tradition/Geach: can be expressed by a single schema.
(1) l- Fa (x)(Fx u x = a) - everyday-language: whatever is true of something which is identical with an object y is true of a and vice versa.
From this we derive the law of self-identity:
"l-a = a".
Because we take "Fx" for "x unequal a", then schema (1) gives us:
(2) l- (a unequal a) Vx(y unequal a u x = a) - this,of course, gives "l-a = a"
I 240
Identity/Geach: if we demand strict identity, regardless of the theory in which we move, we get into the semantic paradoxes such as Grelling's or Richard's
>
Grelling's paradox.
Solution: relative identity on theory or language, indissibility/"indiscernibility"/Quine ->
Partial identity.
1. Frege, G. (1893). Grundgesetze der Arithmetik. Jena: Hermann Pohle.
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Tugendhat I 37
Identity/Dummett/Geach: "=" can only be used with reference to objects.
>
Equal sign.
- - -
Habermas IV 158
Identity/Geach/Habermas: Peter Geach argues that identity predicates can only be used meaningfully in connection with the general characterization of a class of objects.
(1) (See also
Criteria/Henrich, HenrichVsGeach).
E.g. Person/Identification/Habermas: Persons cannot be identified under the same conditions as observable objects. In the case of persons, spatiotemporal identification is not sufficient.
Also see >
Identity/Henrich.
1.P.Geach, Ontological Relativity and Relative Identity, in: K. Munitz, Logic and Ontology, NY. 1973
