 If one maintains that the projectors \(\Pi^{\alpha}\) and \(\Pi^{\alpha} \otimes I^{\beta}\) must represent the same property, the violation of Property Composition and Property Decomposition is a serious problem. Thus, Arntzenius (1990) finds the violation of Property Composition bizarre, since different truth values are assigned to propositions like ‘the left-hand side of a table is green’ and ‘the table has a green left-hand side’; a similar argument is put forward by Clifton (1996, see also Clifton 1995c).