  In this paper we attempt to discuss what has Kochen-Specker (KS) theorem to
say about physical invariance and quantum individuality. In particular, we will
discuss the impossibility of making reference to objective physical properties
within the orthodox formalism of quantum mechanics. Through an analysis of the
meaning of physical invariance and quantum contextuality we will derive a
Corollary to KS theorem that proves that a vector in Hilbert space cannot be
interpreted coherently as an object possessing (objective) physical properties.
As a consequence, the notion of quantum object can be only defined in terms of
nomological properties. We conclude the paper by analyzing the consequences of
this Corollary to KS theorem for the ongoing debate about quantum
individuality.
