Proposed new syntax

[Rustom Mody]

On Sunday, August 20, 2017 at 11:00:22 AM UTC+5:30, Paul Rubin wrote:
> Rustom Mody writes:
> > Specifically the term 'comprehension' used today as a programming construct
> > traces somewhat tenuously to an axiom that Zermelo/Fraenkel formulated
> > in the 1920s
> 
> I thought went back to Frege.  Also, it appears in Zermelo set theory Z.
> ZF is Z with the Axiom of Replacement added, but Z was somewhat earlier
> than ZF.

Do you mean Frege or Cantor?

No I am not an historian, not even amateur, so my data may be quite screwed up
What I know [open to correction!]

- Cantor invented naive¹ Set Theory — late 19th century
- He was the first to discover paradoxes — Cantor's paradox — which were not
taken too seriously
- Russel discovered his paradox — generally regarded as a bigger problem
- Frege — inventor of predicate calculus — was, like Russel, interested in a
  sound and complete foundation of math
- Russell's paradox dashed Frege's hope and put him into depression

- This is about what (I know of) the relation between Frege and set theory
- From beginning 20th century upto 1930 uncovering paradoxes became a cottage industry
- While at the same time people like Hilbert were rebelling against the attempts
  'to expel us from the paradise created by Cantor'
- Zermelo-Fraenkel and Gödel-Bernays-Neumann were two of the principa lattempts
  at formalizing systems (called axiomatization then) so as to avoid the
  contradictions.  At the risk of over-simplification, the Gödel-Bernays system
  is haskell-like (typed) and the Zermelo-Fraenkel system is python-like
  (untyped)
- All this cottage-industry got decimated by Gödel's (2nd)² theorem showing
  that a single unitary axiomatization is impossible
  Today maybe we should say systematization? Or programming language ? 😇 

Many people seem to think that all this is not related to computer science… Amusing!
[For Turing a 'computer' was a (dumb) mathematician doing a computation]


¹ If such anachronism is permissible. But then much of this thread is anachronistic!
² http://mathworld.wolfram.com/GoedelsSecondIncompletenessTheorem.html