How does the concept of indiscernibility (abbreviated ‘INDS’) relate to the concept of identity?
Even though this topic may seem unimportant, eliminating confusion about more fundamental topics removes an important source of confusion about less fundamental topics. [See also the posts ‘Define Understanding’ and ‘Define Identity.’]
Surprisingly, this issue holds an important lesson about how to live our lives.
What is INDS?
Two objects have INDS if and only if whatever quality one has the other also has.
Leibniz is the western philosopher most closely associated with this topic; it seems to have been him who spawned discussion of the principle of the INDS of identicals (“identicals are indiscernible”) and the principle of the identity of indiscernibles (“indiscernibles are identical”).
Is it even possible to conceive of discernible identicals or nonidentical indiscernibles? No.
What really matters is the relation between the concept of INDS and the concept of identity. In particular, do we ground identity judgments on using the concept of INDS?
Think about this using a standard example. If you agree that the Morning Star is the Evening Star, is that because you found “them” to have all their qualities in common? No.
In fact, understood as pure objects, they are not indiscernible. They are discernible. Even if they share all their monadic qualities, they certainly do not share all their relational qualities. [A monadic quality is had by one object, whereas a relational quality is had by two or more objects. Being red and being square are monadic qualities; being to the left of and being between are relational qualities.] The point of the identity judgment about them is that, even though they appear to be two, they are really one; i.e., simplification is the purpose of identity.
So, it’s false that INDS is the criterion of identity.
Actually, as Panayot Butchvarov argues in Being Qua Being, it’s the other way around: Identity is the (only) criterion of INDS.
When we judge that two objects are one entity, we do so without appealing to the INDS of the objects of its application.
When we judge them identical, we enforce their INDS. If the Morning Star is the Evening Star and the Morning Star is made out of a certain kind of rock, then the Evening Star is also made out of that kind of rock. This occurs so naturally that we may not even be aware that we are enforcing anything.
The interesting point is that we never discover the INDS of two objects.
This is interesting because it is an excellent example of the important thesis that ordinarily we perceive what we think is there, in other words, our perceivings are contaminated with our understandings. Putting it colloquially, it is not generally true that seeing is believing; rather, believing is seeing. We see what we believe is there.
This explains why many disputes remain intractable even though the disputants may be experiencing the same event or sequence of events: because their understandings are different, their perceptions are different.
What can be done to resolve disputes? There is no simple procedure that, even in theory, could resolve many disputes.
The only general procedure that provides any genuine hope of success is the enterprise of philosophy, which is the practice of living examined lives, the practice of pursuing wisdom. Hope arises only when we are willing to challenge our own understandings.
Sadly, and foolishly, most people are not philosophers.