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Single Idea 13427

[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic ]

Full Idea

In 'a = b' either 'a' and 'b' are names of the same thing, in which case the proposition says nothing, or of different things, in which case it is absurd. In neither case is it an assertion of a fact; it only asserts when a or b are descriptions.

Gist of Idea

Either 'a = b' vacuously names the same thing, or absurdly names different things

Source

Frank P. Ramsey (The Foundations of Mathematics [1925], §1)

Book Ref

Ramsey,Frank: 'Philosophical Papers', ed/tr. Mellor,D.H. [CUP 1990], p.179

A Reaction

This is essentially Frege's problem with Hesperus and Phosphorus. How can identities be informative? So 2+2=4 is extensionally vacuous, but informative because they are different descriptions.

The 16 ideas with the same theme [logical assertions that that two objects are identical]:

13427 Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
18759 Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee]
18154 The sign of identity is not allowed in 'Tractatus' [Wittgenstein, by Bostock]
13429 The identity sign is not essential in logical notation, if every sign has a different meaning [Wittgenstein, by Ramsey]
10012 Quantification theory can still be proved complete if we add identity [Quine]
18897 Predicate logic has to spell out that its identity relation '=' is an equivalent relation [Sommers]
13800 |= α=α and α=β |= φ(α/ξ ↔ φ(β/ξ) fix identity [Bostock]
13803 If we are to express that there at least two things, we need identity [Bostock]
13799 The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock]
10697 Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos]
3299 In logic identity involves reflexivity (x=x), symmetry (if x=y, then y=x) and transitivity (if x=y and y=z, then x=z) [Baillie]
6051 In 'x is F and x is G' we must assume the identity of x in the two statements [McGinn]
6055 Both non-contradiction and excluded middle need identity in their formulation [McGinn]
6059 Identity is unitary, indefinable, fundamental and a genuine relation [McGinn]
10011 Identity is a level one relation with a second-order definition [Hodes]
13851 Unlike most other signs, = cannot be eliminated [Engelbretsen/Sayward]