A core idea that I am exploring is the context principle. Traditionally, this states that a philosopher should always ask for a word's meaning in terms of the context in which it is being used, not in isolation.

I've redefined this to make it more general: Context creates meaning and in its absence there is no meaning.

And I've added the corollary: Domains can only be connected if they have contexts in common. Common contexts provide shared meaning and open a path for communication between disparate domains.

Some examples: In programming, an argument or message can be passed only if sender and receiver agree on the datatype of the argument (i.e. on how the bits should be interpreted). In Bayesian inference, all probabilities are conditional on background knowlege. In natural deduction (logic), complex sentences in simple contexts are decomposed into simple sentences in complex contexts.

In all cases, there are rules for transferring information between context and "content". But you can never completely eliminate the context. You are always left with a residual context which may take the form of assumed axioms, rules of inference, grammars, or alphabets. That is, the residual is our way of representing the simplest possible context. I think that it is an interesting research program to examine how more complex contexts can be specified using the same core machinery of axioms, alphabets, grammars, and rules.