The category of categories as a model for the Platonic World of Forms by David A Edwards & Marilyn L Edwards
- Thales (7th cent. BC) made the first universal statement (proof w/o regard to the gods or mythology, just from pure reason)
- pre-Greek mathematics was essentially engineering maths.
- I owe ya a post on the illiterates in chapter 2 of James Gleick’s The Information. He tells the story of some illiterates in outer Soviet Union. According to the tale, they basically do not abstract at all. No abstract reasoning, no properties ascribed to members of a class, and so on.
It sounds kind of idyllic in the way of NYT tales of the Pirahã or Jill Bolte Taylor’s story of losing the logical half of her brain. I’m not sure if Thales set us on the path to Hell or Heaven.
- “Plato set for himself the [goal] of extending geometry [beyond] triangles and circles and such, to all of human thought. He failed, but his vision has come to pass.”
- Why did Lawvere succeed where Plato and Whitehead failed?
- He had Descartes’ already-abstract notion of a function, along with
- Eilenberg & Mac Lane’s notions of category and functor.
- The definition of function for infinite sets is already implicit in the choice of “which set theory”.
- Category theory, unlike earlier formalisations (think Peano arithmetic and Goedel’s proof), is stable to the “meta” step: you do 2-categories, you do n-categories … the abstraction is ultimately a
k → k+1kind of deal rather than a “And this is the ultimate finality!” kind of deal.