The full property ascription
Pieter E. Vermaas
The different modal interpretations all advance a core property ascription {〈P j , C α j 〉} j . This chapter is about how this core property ascription fixes the full property ascription. I start with some logic and algebra. I then present two existing proposals for determining the full property ascriptions as well as four conditions one can impose on them. Lastly I give my own proposal and end by discussing how the full property ascription leads to a value assignment to magnitudes. Some logic and algebra To prepare the ground for discussing the full property ascription, I firstly define the logical connectives (negation, conjunction and disjunction) for properties. Then because, as discussed in Section 4.1, all the modal interpretations which I consider give up on the idea that thefull property ascription assigns definite values to all properties, I secondly define two types of subsets of properties: Boolean algebras and faux-Boolean algebras. I have already assumed that every property Q α pertaining to a system α is represented by one and only one projection Q α defined on the Hilbert space ℋα associated with α. Each projection Q α in its turn corresponds one-to-one to the subspace of ℋα, denoted by 2α, onto which it projects. One thus has a bijective mapping from a property Q α to a projection Q α to a subspace 2α. For the set of subspaces of a Hilbert space one can in a natural way define an orthocomplement, a meet and a join. I now choose 45 to define the logical connectives for properties pertaining to a system by means of this orthocomplement, meet and join for subspaces and the bijective mapping between properties and subspaces (by means of an isomorphism, more shortly).
Cambridge University Press eBooks•Feb 5, 2010•0 citations