## Church's Descendants ### Or: The Transitive Closure of Church's Students 1: What's a reverse begat list? 0: Well picking up where we left off: - That book was by Jeff Hirst. - Jeff Hirst's advisors were: - Harvey Friedman (who we saw up above in The Sigmas) and - Stephen Simpson (the other founder of The Sigmas) - And The Sigmas are the culture of Reverse Mathematics. - And Reverse Mathematics is the same "All of mathematics is equivalent to one of five sentences" research program mentioned earlier.) - Harvey Friedman and Stephen Simpson both had the same advisor, Gerald Sacks. - Gerald Sacks's advisor was John Barkley Rosser. (Another one of Rosser's students was Elliott Mendelson, who was mentioned above, as the author of the book that does foundations formally but less "frighteningly technical" than Kleene.) - And John Barkley Rosser's advisor was Alonzo Church. (Who was also the advisor of Stephen Kleene.) - That's a reverse begat list. 1: Damn, that was good! 0: And here's Steve Kleene talking to Gerald Sacks about Alonzo Church and J. B. Rosser. 1: Ok nevermind this was pretty well planned after all. --- > John Crossley: What did you do Steve? When you first started learning logic. You didn't have books did you? > > Steve Kleene: We didn't have books. > > Gerald Sacks: You had _Principia Mathematica._ > > _(Everyone laughs)_ 1: Why did everyone laugh there? 0: Nobody reads _Principia Mathematica._ 1: Why not? 0: It's impossible. Takes like over 300 pages to prove 1+1=2. So basically at this point in history, logic exists but it's a massive pain to do anything with it. So Church starts in standard foundations. He's like "Wow this sucks." So then fast forward, Church goes to work on foundations. Real foundations. Stuff that feels a lot more like programming. 1: Show me. --- The document ends here, abruptly in the middle. ---