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Single Idea 13799
[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
]
Full Idea
We shall use 'a=b' as short for 'a is the same thing as b'. The sign '=' thus expresses a particular two-place predicate. Officially we will use 'I' as the identity predicate, so that 'Iab' is as formula, but we normally 'abbreviate' this to 'a=b'.
Gist of Idea
The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b)
Source
David Bostock (Intermediate Logic [1997], 8.1)
Book Ref
Bostock,David: 'Intermediate Logic' [OUP 1997], p.323
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]
|
13429
|
The identity sign is not essential in logical notation, if every sign has a different meaning
[Wittgenstein, by Ramsey]
|
18154
|
The sign of identity is not allowed in 'Tractatus'
[Wittgenstein, by Bostock]
|
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]
|
13799
|
The sign '=' is a two-place predicate expressing that 'a is the same thing as b' (a=b)
[Bostock]
|
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]
|
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]
|