The concept of individuality in quantum mechanics shows radical differences
from the concept of individuality in classical physics, as E. Schroedinger
pointed out in the early steps of the theory. Regarding this fact, some authors
suggested that quantum mechanics does not possess its own language, and
therefore, quantum indistinguishability is not incorporated in the theory from
the beginning. Nevertheless, it is possible to represent the idea of quantum
indistinguishability with a first order language using quasiset theory (Q). In
this work, we show that Q cannot capture one of the most important features of
quantum non individuality, which is the fact that there are quantum systems for
which particle number is not well defined. An axiomatic variant of Q, in which
quasicardinal is not a primitive concept (for a kind of quasisets called finite
quasisets), is also given. This result encourages the searching of theories in
which the quasicardinal, being a secondary concept, stands undefined for some
quasisets, besides showing explicitly that in a set theory about collections of
truly indistinguishable entities, the quasicardinal needs not necessarily be a
primitive concept.Comment: 46 pages, no figures. Accepted by Foundations of Physic