 However, Vermaas (1998) argues that the observational indistinguishability of the magnitudes represented by \(\Pi^{\alpha}\) and \(\Pi^{\alpha} \otimes I^{\beta}\) does not force one to consider these two projectors as representing the same property: in fact, they are different from a theoretical viewpoint, since they are defined on different Hilbert spaces. Moreover, he argues that the examples developed by Arntzenius and Clifton sound bizarre precisely in the light of Property Composition and Property Decomposition. But in the quantum realm we must accept that the questions of which properties are possessed by a system and which by its subsystems are different questions: the properties of a composite system \(\alpha\beta\) don’t always fix the properties of subsystem \(\alpha\), and vice versa. Vermaas concludes that the tenet that \(\Pi^{\alpha}\) and \(\Pi^{\alpha} \otimes I^{\beta}\) do represent the same property can be viewed as an addition to quantum mechanics, which can be denied as, for instance, van Fraassen (1991) did.