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Single Idea 6049
[filed under theme 9. Objects / F. Identity among Objects / 8. Leibniz's Law
]
Full Idea
Leibniz's Law says 'x = y iff for all P, Px iff Py'.
Clarification
'Iff' means if and only if; Px means x has the property P
Gist of Idea
Leibniz's Law says 'x = y iff for all P, Px iff Py'
Source
Colin McGinn (Logical Properties [2000], Ch.1)
Book Ref
McGinn,Colin: 'Logical Properties' [OUP 2003], p.7
A Reaction
That is, two things are the same if when we say that one thing (x) has a property (P), then we are saying that the other thing (y) also has the property. A usefully concise statement of the Law.
The
18 ideas
with the same theme
[identical objects must have identical features or truths]:
11840
|
Only if two things are identical do they have the same attributes
[Aristotle]
|
16768
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Two things are different if something is true of one and not of the other
[Duns Scotus]
|
17255
|
Two bodies differ when (at some time) you can say something of one you can't say of the other
[Hobbes]
|
17173
|
Two substances can't be the same if they have different attributes
[Spinoza]
|
16073
|
Leibniz's Law is incomplete, since it includes a non-relativized identity predicate
[Geach, by Wasserman]
|
4942
|
The indiscernibility of identicals is as self-evident as the law of contradiction
[Kripke]
|
11839
|
Do both 'same f as' and '=' support Leibniz's Law?
[Wiggins]
|
11845
|
Substitutivity, and hence most reasoning, needs Leibniz's Law
[Wiggins]
|
14065
|
Two identical things must share properties - including creation and destruction times
[Gibbard]
|
14074
|
Leibniz's Law isn't just about substitutivity, because it must involve properties and relations
[Gibbard]
|
16019
|
Leibniz's Law must be kept separate from the substitutivity principle
[Noonan]
|
16018
|
Indiscernibility is basic to our understanding of identity and distinctness
[Noonan]
|
6049
|
Leibniz's Law says 'x = y iff for all P, Px iff Py'
[McGinn]
|
6050
|
Leibniz's Law presupposes the notion of property identity
[McGinn]
|
6048
|
Leibniz's Law is so fundamental that it almost defines the concept of identity
[McGinn]
|
12236
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Leibniz's Law is an essentialist truth
[Oderberg]
|
14754
|
If you say Leibniz's Law doesn't apply to 'timebound' properties, you are no longer discussing identity
[Sider]
|
16225
|
If two things might be identical, there can't be something true of one and false of the other
[Hawley]
|