My interest in using notation in logic (e.g., ~ for “not,” strictly defined) is in part a result of often finding it useful to keep track of how I would notate the logical skeleton of what’s fleshed out as natural prose. For example, in natural prose the word “not” doesn’t always mean ~. In natural prose, there’s no 1-to-1 correspondence between the linguistic form and the logical substance. With the symbol ~ strictly defined, you can, whenever doing so would be useful, ask yourself: “Is the present usage of the word ‘not’ equivalent to ~?”

When I’m reading or writing, my internal experience is often such that I visualize ~ and other symbols as furigana. That is, I often ask myself whether I could justifiably put a certain logical symbol above a given word or phrase.

When writing, that technique helps you get the best of both worlds of the artificial and the natural: the artificiality of scientific writing and the naturalness of artistic writing. It helps you keep track of the logic without there being any need for you to artificially limit or regiment how you use natural language.