  This paper is the second in a series whose goal is to develop a fundamentally
new way of constructing theories of physics. The motivation comes from a desire
to address certain deep issues that arise when contemplating quantum theories
of space and time. Our basic contention is that constructing a theory of
physics is equivalent to finding a representation in a topos of a certain
formal language that is attached to the system. Classical physics arises when
the topos is the category of sets. Other types of theory employ a different
topos. In this paper, we study in depth the topos representation of the
propositional language, PL(S), for the case of quantum theory. In doing so, we
make a direct link with, and clarify, the earlier work on applying topos theory
to quantum physics. The key step is a process we term `daseinisation' by which
a projection operator is mapped to a sub-object of the spectral presheaf--the
topos quantum analogue of a classical state space. In the second part of the
paper we change gear with the introduction of the more sophisticated local
language L(S). From this point forward, throughout the rest of the series of
papers, our attention will be devoted almost entirely to this language. In the
present paper, we use L(S) to study `truth objects' in the topos. These are
objects in the topos that play the role of states: a necessary development as
the spectral presheaf has no global elements, and hence there are no
microstates in the sense of classical physics. Truth objects therefore play a
crucial role in our formalism.
