Identity of Indiscernibles

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3-2 What does discernibility mean?

One way to define the concept of discernibility, which is to be distinct from other objects, is

understood in terms of the differences between the properties of an object and those of other objects.

Accordingly, the definition of discernibility involves the properties of an object and its differences with

the properties of other objects. For example, two objects are discernible from each other iff when they

are not identical they do not share their properties.

According to the PII, if two objects share all their properties then they are identical. If the PII is

true, then its contrapositive is also true, that is if two objects are not identical, then they do not share all

their properties, that is they are discernible. That is how traditionally discernibility was described.

However, as we have seen in French’s counterexample to the PII, two bosons that are not numerically

identical might share all their properties. Since the PII is not true its contrapositive, sentence (5) below,

is not true either. Therefore, it is not the case that every two objects that are identical are discernible.


On the other hand, if there is at least one property that two objects do not share, the objects are

not identical. This is the contrapositive of LL which is a logical truth, and its logical formulation is as



In other words, for every two objects if there is at least one property which is not in common between

the objects we can say the objects are discernible.

Accordingly, since all objects are individual, individuality means that all objects are

self-identical and for every pair of them if there is at least one property that is not in common, they are

not identical. A...

... middle of paper ...

...hat have properties like mass are not objects anymore.

Similar to the case of all boson's, except photons.

5. If there is a universe with only one Boson, that Boson would be an object since it does not share all its properties with another object. But, in the same universe with two bosons, bosons are not objects anymore.

6. If something is penetrable and co-exists with something else it would not be an object, but if it

accidentally does not co-exist with something else, it is an object.


7. According to 5 and 6 object-hood is context dependent that seems counter-intuitive.

Works Cited

Black, Max (1952). The identity of indiscernibles. Mind 61 (242):153-164.

Décio Krause(2009), The mathematics of non-individuality.

Tugendhat, Ernst (1982). Traditional and Analytical Philosophy: Lectures on the Philosophy of

Language. Cambridge University Press.
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