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This paper is the second in a series whose goal is to develop a fundamentallynew way of constructing theories of physics. The motivation comes from a desireto address certain deep issues that arise when contemplating quantum theoriesof space and time. Our basic contention is that constructing a theory ofphysics is equivalent to finding a representation in a topos of a certainformal language that is attached to the system. Classical physics arises whenthe topos is the category of sets. Other types of theory employ a differenttopos. In this paper, we study in depth the topos representation of thepropositional language, PL(S), for the case of quantum theory. In doing so, wemake a direct link with, and clarify, the earlier work on applying topos theoryto quantum physics. The key step is a process we term `daseinisation' by whicha projection operator is mapped to a sub-object of the spectral presheaf--thetopos quantum analogue of a classical state space. In the second part of thepaper we change gear with the introduction of the more sophisticated locallanguage L(S). From this point forward, throughout the rest of the series ofpapers, our attention will be devoted almost entirely to this language. In thepresent paper, we use L(S) to study `truth objects' in the topos. These areobjects in the topos that play the role of states: a necessary development asthe spectral presheaf has no global elements, and hence there are nomicrostates in the sense of classical physics. Truth objects therefore play acrucial role in our formalism.Comment: 34 pages, no figure

A topos foundation for theories of physics: II. Daseinisation and the liberation of quantum theory