As a consequence of Proposition 2.2, the agents' private information systems determine an a priori structure of propositions over the space of possible worlds regarding what they can know, including what mutual and common knowledge they potentially have.
On this reading, the Dream Theory claims that simple, private objects of experience are the elements of the proposition; thus, the Dream Theory is both a theory about the structure of propositions and a theory about simple and complex objects.
This fits well with the asymmetries we have noted between analysis and construction, with analysis aimed at the discovery of the constituents and structure of propositions which are given to us, and construction which is more a matter of choice, with the goal being the recovery of particular "neat" features of the construction in a formal theory.
In the fundamental idiom, which approximates closely the structure of propositions, "A is the father of B" should be translated as "The whole which contains A and B has the following property: the first element is the father of the second".
(i) Assume that (mathcal {C}_0), (mathcal {C}_1) are model categories, L is left-derivable, and M is right-derivable, and equip (mathsf{L}(L)), (mathsf{R}(M)) with the model structures of Proposition 3.8.
There is, of course, no problem about incompatible theories, as structures of propositions, co-existing.
The structure of the proposition, and particularly the unity of the proposition as well as the use of language to create a social and institutional reality have, I believe, profound biological bases.
However, in a properly analyzed proposition, there is a clear isomorphism between the structure of the proposition and the structure of the fact that would make it true (PLA, 197); hence a precise and analyzed proposition is capable of being true in one and only one way (Vag, 219).
It helps solve the problem of the unity of the proposition (see the previous section), insofar as the structure of a proposition derives from the syntactic structure of a corresponding sentence.
Since the things a term stands for are not established a priori but dependent on propositional context, the analysis of the structure of a proposition in terms of the identity relation requires a correspondence theory of truth.
First, the structure of the proposition must conform to the constraints of logical form, and second, the elements of the proposition must have reference (bedeutung).
