Announcement: Chris Langan has published a new paper, "An Introduction to Mathematical Metaphysics", in the journal Cosmos and History.
A duality principle expresses a duality, or situation where there are two aspects of a process going on where each aspect is in a certain sense opposite or contrasting to the other aspect. The duality principle allows the process to be viewed from either of these dual aspects, and by merging the symmetric halves of the resulting picture, meaningful implications can be extracted.
The most famous example of a duality principle in the CTMU is that of conspansive duality. This duality describes the two opposite ways in which the same process (the evolution of the universe) can be viewed. From the local vantage, the universe expands as a function of time. From the global vantage the universe remains constant in size and matter contracts into itself (along with all intrinsic measurement scales) as a function of time. Expansion and contraction are dual aspects of the same process and so form a conspansive duality. (The reason the universe can't "actually" be expanding into nothing is precisely because there is nothing outside of reality for it to expand into.)