Hard agree on the computing system schema - it's always there, whether in a bag of brains or as a XSD file.
The usefulness of these concepts lie on a spectrum, with user behavior located in one part of that spectrum. Numbers occupies a broad spectrum that overlies most human experience, although not all. Type systems have overhead that occlude some aspects of computing, and by itself the phrase "type system" has fuzzy edges. Somewhat - although less so - same thing with functions - is a function a callable unit or is it an explicit method? Platonists - I think - would definitely agree that these things have the inherent quality of existence as a consequence of their nature; Anselm's Ontological Argument is sort of the Final Evolution of dire Platonism.
The world, though, as it exists in nature? Functions, types, even numbers are not primary observables. Our experience of reality is probably more akin to the observed experience of a rainbow, where the observer stands 138 degrees to the sun precisely . . or the rainbow doesn't exist. We're in a 138 degree arc to reality, living on a rainbow, counting the bands. But honestly? Who knows? Probably some learned cosmologist. I am but a MilStdJunkie on the internet.
The usefulness of these concepts lie on a spectrum, with user behavior located in one part of that spectrum. Numbers occupies a broad spectrum that overlies most human experience, although not all. Type systems have overhead that occlude some aspects of computing, and by itself the phrase "type system" has fuzzy edges. Somewhat - although less so - same thing with functions - is a function a callable unit or is it an explicit method? Platonists - I think - would definitely agree that these things have the inherent quality of existence as a consequence of their nature; Anselm's Ontological Argument is sort of the Final Evolution of dire Platonism.
The world, though, as it exists in nature? Functions, types, even numbers are not primary observables. Our experience of reality is probably more akin to the observed experience of a rainbow, where the observer stands 138 degrees to the sun precisely . . or the rainbow doesn't exist. We're in a 138 degree arc to reality, living on a rainbow, counting the bands. But honestly? Who knows? Probably some learned cosmologist. I am but a MilStdJunkie on the internet.