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### 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

#### [logical assertions that that two objects are identical]

16 ideas
 13427 Either 'a = b' vacuously names the same thing, or absurdly names different things [Ramsey]
 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]
 18759 Identity is invariant under arbitrary permutations, so it seems to be a logical term [Tarski, by McGee]
 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]
 13799 The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b) [Bostock]
 13803 If we are to express that there at least two things, we need identity [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]