- A curious omission in the burgeoning philosophical literature on vague objects and vague identity has been the absence of much serious discussion of the bearing of quantum indeterminacy upon this issue. Standard quantum-theoretical treatments of certain types of particle-interaction suggest that we can intelligibly countenance ontically indeterminate identity statements, contrary to the widespread philosophical opinion that vagueness must reside in our linguistic representations rather than in the world.
- Before commenting on the best-known argument for this philosophical opinion, let me illustrate the sort of quantum-theoretical situation I have in mind. Suppose (to keep matters simple) that in an ionization chamber a free electron a is captured by a certain atom to form a negative ion which, a short time later, reverts to a neutral state by releasing an electron b. As I understand it, according to currently accepted quantum-mechanical principles there may simply be no objective fact of the matter as to whether or not a is identical with b. It should be emphasized that what is being proposed here is not merely that we may well have no way of telling whether or not a and b are identical, which would imply only an epistemic indeterminacy. It is well known that the sort of indeterminacy presupposed by orthodox interpretations of quantum theory1 is more than merely epistemic - it is ontic. The key feature of the example is that in such an interaction electron a and other electrons in the outer shell of the relevant atom enter an 'entangled' or 'superposed' state in which the number of electrons present is determinate but the identity of any one of them with a is not, thus rendering likewise indeterminate the identity of a with the released electron b.
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