Identity of Indiscernibles - Indiscernibility of Identicals

Indiscernibility of Identicals

As stated above, the principle of indiscernibility of identicals – that if two objects are in fact one and the same, they have all the same properties – is mostly uncontroversial. However, one famous application of the indiscernibility of identicals was by René Descartes in his Meditations on First Philosophy. Descartes concluded that he could not doubt the existence of himself (the famous cogito argument), but that he could doubt the existence of his body.

This argument is criticized by some modern philosophers on the grounds that it allegedly derives a conclusion about what is true from a premise about what people know. What people know or believe about an entity, they argue, is not really a characteristic of that entity. Numerous counterexamples are given to debunk Descartes' reasoning via reductio ad absurdum, such as the following argument based on a secret identity:

1. Entities x and y are identical if and only if any predicate possessed by x is also possessed by y and vice versa.
2. Clark Kent is Superman's secret identity; that is, they're the same person (identical) but people don't know this fact.
3. Lois Lane thinks that Clark Kent cannot fly.
4. Lois Lane thinks that Superman can fly.
5. Therefore Superman has a property that Clark Kent does not have, namely that Lois Lane thinks that he can fly.
6. Therefore, Superman is not identical to Clark Kent.

1. Since in proposition 6 we come to a contradiction with proposition 2, we conclude that at least one of the premises is wrong. Either:
   • Leibniz's law is wrong; or
   • A person's knowledge about x is not a predicate of x; or
   • The application of Leibniz's law is erroneous; the law is only applicable in cases of monadic, not polyadic, properties; or
   • What people think about are not the actual objects themselves; or
   • A person is capable of holding conflicting beliefs.

Any of which will undermine Descartes' argument.

A response may be that the argument in the Meditations on First Philosophy isn't that Descartes cannot doubt the existence of his mind, but rather that it is beyond doubt, such that no being with understanding could doubt it. This much stronger claim doesn't resort to relational properties, but rather presents monadic properties, as the foundation for the use of Leibniz's law. One could expound an infinite list of relational properties that may appear to undermine Leibniz's law (i.e. Lois Lane loves Clark Kent, but not Superman. etc.) but nonetheless any approach focused on monadic properties will always produce accurate results in support of Descartes' claim.