Individuality and Non-Individuality in Quantum Mechanics
You cannot mark an electron, you cannot paint it red. Indeed, you must not even think of it as marked.
E. Schrödinger 1953
Let us recall our discussion from Chap 22422u2021w ter 1 of the Principle of Individuality. The following broad positions were set out: on the one hand there are those views which strive for a kind of metaphysical economy by advocating a Principle which serves double-duty in grounding both individuality and distinguishability; on the other, there are those positions which are rooted in the insistence that the two must be kept distinct, at least conceptually. Of the former, perhaps the most straightforward, at least initially, is the view that attempts to ground both distinguishability and individuality in the properties of objects. This requires a kind of 'guarantor' of individuality such as the Principle of the Identity of Indiscernibles (PII) which, we recall again, states that two things simply cannot possess the same set of (relevant) properties. The debate then shifts to the status of this Principle-whether it is necessarily true or only contingently so, and so on. As we saw, certain forms of PII can be maintained in classical mechanics. In particular, if we assume some form of impenetrability-as Newton did, for example-then no two things can have exactly the same spatio-temporal properties and if the latter are included in our set, then PII(1) appears to hold. Spatio-temporal location then performs a nice unifying role in our metaphysics: it allows us to distinguish even those things which share all their other properties-and in terms of which these things are indistinguishable-and it acts as a Principle of Individuality.
The alternative tradition insists that distinguishability and individuality must be kept distinct. Accordingly, what makes a thing an individual cannot be any multiply instantiable property-these relate to distinguishability only-but rather something else, over and above or transcending such properties. According to some, this something else is what the Scholastics called a thing's 'haecceity', reincarnated in modern times as its 'primitive thisness' which has been further explicated in terms of self-identity ('a = a'). According to others, it is substance, famously characterized as 'something we know not what'. Those of a broadly empiricist persuasion have not taken too kindly to such notions, as we indicated, but they have proven notably resilient and hard to do away with.
Our intention in this chapter is to further examine the impact of quantum mechanics on these positions. We have already indicated how this impact was understood historically, by those engaged in the elaboration of the new statistics, namely that quantum particles, unlike their classical counterparts, cannot be regarded as individuals. As we shall see, this conclusion does not necessarily follow from the physics.
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