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Single Idea 6051
[filed under theme 5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic
]
Full Idea
If we say 'for some x, x is F and x is G' we are making tacit appeal to the idea of identity in using 'x' twice here: it has to be the same object that is both F and G.
Clarification
F and G stand for properties
Gist of Idea
In 'x is F and x is G' we must assume the identity of x in the two statements
Source
Colin McGinn (Logical Properties [2000], Ch.1)
Book Ref
McGinn,Colin: 'Logical Properties' [OUP 2003], p.8
A Reaction
This may well be broadened to any utterances whatsoever. The only remaining question is to speculate about whether it is possible to think without identities. The Hopi presumably gave identity to processes rather objects. How does God think?
The
16 ideas
with the same theme
[logical assertions that that two objects are identical]:
13427
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Either 'a = b' vacuously names the same thing, or absurdly names different things
[Ramsey]
|
18759
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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]
|