Mathematics 1

“There is no such thing as types — it’s all terms, and terms in relation to terms that stand in relation to terms that reflect upon relationships!” Thus declaims the RDF Ontologist. But also, curiously, the classical model theorist of the 1950s; Henkin’s approach to type hierarchies, one of the first papers to appear in that sadly no irrelevant Journal of Symbolic Logic; and Martin-Lof’s foundation of computing. For that latter Swedish philosopher had the intent to frame mathematics as computation over data, and computation as a mathematics of data, but wherein, crucially, both types and terms are merely impredicative datapoint. 

In my middle age, my own PhD and research in this topic now a distant memory, I find myself reflecting more emotionally upon that statement, those theorists. The domain aside, they each address the dialectic of thing/categorization versus thing/thing, of Plato versus pragmatism, and this dialectic is, in other places, something deadly, potentially. The mathematicians and philosophers: their statements are a turn, of thought, of the dialectic, and imbued fully with the triumphant  revolutionary emotions of any such turn.

I draw on that kind of emotion, these days, increasingly. So even though, as a practically religious type theorist, it might sound strange: I say now “The ‘category:Thing’ is nothing more than data, so in many ways, I’d prefer to say ‘thing:(thing:Thing)’, predicatively.”


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