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Single Idea 13702
[filed under theme 9. Objects / F. Identity among Objects / 7. Indiscernible Objects
]
Full Idea
The identity of indiscernibles (∀x∀y(∀X(Xx↔Xy)→x=y) is necessarily true, provided that we construe 'property' very broadly, so that 'being a member of such-and-such set' counts as a property.
Gist of Idea
The identity of indiscernibles is necessarily true, if being a member of some set counts as a property
Source
Theodore Sider (Logic for Philosophy [2010], 5.4.3)
Book Ref
Sider,Theodore: 'Logic for Philosophy' [OUP 2010], p.125
A Reaction
Sider's example is that if the two objects are the same they must both have the property of being a member of the same singleton set, which they couldn't have if they were different.
The
38 ideas
with the same theme
[objects between which no differences are detectable]:
489
|
Each thing must be in some way unique
[Diogenes of Apollonia]
|
13788
|
If we made a perfect duplicate of Cratylus, there would be two Cratyluses
[Plato]
|
17175
|
There cannot be two substances with the same attributes
[Spinoza]
|
17554
|
There must be some internal difference between any two beings in nature
[Leibniz]
|
5055
|
No two things are totally identical
[Leibniz]
|
13178
|
Things in different locations are different because they 'express' those locations
[Leibniz]
|
19411
|
In nature there aren't even two identical straight lines, so no two bodies are alike
[Leibniz]
|
19412
|
If two bodies only seem to differ in their position, those different environments will matter
[Leibniz]
|
16504
|
Two eggs can't be identical, because the same truths can't apply to both of them
[Leibniz]
|
7576
|
The Identity of Indiscernibles is true of concepts with identical properties, but not of particulars
[Kant, by Jolley]
|
14509
|
If we ignore differences between water drops, we still distinguish them by their location
[Kant]
|
12033
|
An object is identical with itself, and no different indiscernible object can share that
[Russell/Whitehead, by Adams,RM]
|
11849
|
It at least makes sense to say two objects have all their properties in common
[Wittgenstein on Russell]
|
14107
|
Terms are identical if they belong to all the same classes
[Russell]
|
11095
|
We should just identify any items which are indiscernible within a given discourse
[Quine]
|
10195
|
If the universe just held two indiscernibles spheres, that refutes the Identity of Indiscernibles
[Black]
|
5477
|
One thing can look like something else, without being the something else
[Ellis]
|
12034
|
If the universe was cyclical, totally indiscernible events might occur from time to time
[Adams,RM]
|
14510
|
Two events might be indiscernible yet distinct, if there was a universe cyclical in time
[Adams,RM]
|
16455
|
Black's two globes might be one globe in highly curved space
[Adams,RM]
|
12130
|
a and b share all properties; so they share being-identical-with-a; so a = b
[Brody]
|
16453
|
The bundle theory makes the identity of indiscernibles a necessity, since the thing is the properties
[Stalnaker]
|
16505
|
By the principle of Indiscernibility, a symmetrical object could only be half of itself!
[Wiggins]
|
7566
|
The Identity of Indiscernibles is really the same as the verification principle
[Jolley]
|
4033
|
Two pure spheres in non-absolute space are identical but indiscernible
[Campbell,K]
|
3145
|
The Indiscernibility of Identicals is a truism; but the Identity of Indiscernibles depends on possible identical worlds
[Rey]
|
13379
|
If two objects are indiscernible across spacetime, how could we decide whether or not they are the same?
[Jubien]
|
13730
|
The Indiscernibility of Identicals has been a big problem for modal logic
[Fitting/Mendelsohn]
|
4203
|
Identity of Indiscernibles (same properties, same thing) ) is not Leibniz's Law (same thing, same properties)
[Lowe]
|
13702
|
The identity of indiscernibles is necessarily true, if being a member of some set counts as a property
[Sider]
|
4476
|
Most philosophers think that the identity of indiscernibles is false
[Moreland]
|
10198
|
If only two indiscernible electrons exist, future differences must still be possible
[Zimmerman,DW]
|
10199
|
Discernible differences at different times may just be in counterparts
[Zimmerman,DW]
|
5746
|
The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities
[Melia]
|
4639
|
Leibniz's Law is about the properties of objects; the Identity of Indiscernibles is about perception of objects
[Baggini /Fosl]
|
7927
|
At different times Leibniz articulated three different versions of his so-called Law
[Macdonald,C]
|
7928
|
The Identity of Indiscernibles is false, because it is not necessarily true
[Macdonald,C]
|
18764
|
The notion of 'property' is unclear for a logical version of the Identity of Indiscernibles
[Anderson,CA]
|