The “trinity of computation”

I never thought of it this way

Logic tells us what propositions exist (what sorts of thoughts we wish to express) and what constitutes a proof (how we can communicate our thoughts to others). Languages (in the sense of programming) tells us what types exist (what computational phenomena we wish to express) and what constitutes a program (how we can give rise to that phenomenon). Categories tell us what structures exist (what mathematical models we have to work with) and what constitutes a mapping between them (how they relate to one another). In this sense all three have ontological force; they codify what is, not how to describe what is already given to us.

In this sense they are foundational; if we suppose that they are merely descriptive, we would be left with the question of where these previously given concepts arise, leading us back again to foundations.

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