Sortal Predicates and Cardinality in Quantum Context

Abstract

Based on the indistinguishability of the identical particles in the quantum statistics, French and Krause have proposed the existence of a new class of predicates: the ‘Quantum sortal’. The peculiar behavior of such predicates is that, besides establishing criterion of application, they assign a criterion of (quasi) cardinality that does not require the individuality of the items that fall on their extension. Such non-individual items are called m-atoms and their lack of individuality formally results in syntactic rule: ‘x = x’ is not a well-formed formula (being x a variable for m-atoms). The obvious problem with the posing of French and Krause is that the usual definition of cardinal presupposes the notion of identity, so to talk about how many non-individuals are in the extension of a quantum sortal is necessary to develop a notion of cardinality different from that used in the classical sets theory and perhaps common sense. In this paper, I will try to argue that this task faces two problems: 1) that the proposals that deviate from the classical notion of cardinal do not allow to answer the question ‘How many?’ in any intelligible sense; and 2) even if the above is not a problem (because in quantum contexts people often say things that nobody understands with quite impunity) cardinal definitions applicable to sortal do not achieve become independent of the identity. From the above, I suggest, in conclusion, that the peculiarity of quantum sortal is due to the primitive individuality of quantum objects.