A comprehensive theory of induction and abstraction

I present a solution to the epistemological problem of induction. A universal theory of meaning is developed whereby meaning of a proposition is separated from the proposition and how it is represented. The theory has most similarity with Wittgenstein's early picture theory of meaning but with fundamental differences: (1) Meaning of a proposition is characterised by necessary conditions for truth and falsity as opposed to sufficient ones. In this way propositions are not reduced to atomic ones. (2) Certain assumptions form logical reference frames for which meaning is relative to. (3) Meaning is not found through analysis of language, rather it is formed, with language providing a mould that shapes meaning. (4) There is no unique association between a proposition, the sign used to express it and meaning. Inductive inference is explicated by logical probabilities using logic construed in this way. Spaces of hypotheses and the version of Bayes' theorem that utilises them emerge from first principles. The problems of uniqueness of probabilities, representation of other logics and logical omniscience are solved and other salient problems potentially solved. A theory of abstract hypothesis formation--similar to the notion of inference to the best explanation--is simultaneously developed and unified with induction. Notions of explanatory force, falsifiability and incommensurability emerge as a consequence