shinoteki

• shinoteki 8 Sep 2011 21:51 UTC

  3 points

  in reply to: Normal_Anomaly’s comment on: Pri­soner’s Dilemma Tour­na­ment Results

  A piece of code that runs a piece of source code does not thereby become that piece of source code.

• shinoteki 7 Sep 2011 18:19 UTC

  5 points

  in reply to: JoshuaZ’s comment on: Harry Pot­ter and the Meth­ods of Ra­tion­al­ity dis­cus­sion thread, part 8

  It’s not clear to me that ZFC without regularity, replacement, infinity, choice, power set or foundation with a totally ordered field with the LUB property does allow you to talk about most things you want to do with the reals : without replacement or powerset you can’t prove that cartesian products exist, so there doesn’t seem to be any way of talking about the plane or higher-dimensional spaces as sets. If you add powerset back in you can carry out the Hartogs number construction to get a least uncountable ordinal

• shinoteki 5 Sep 2011 21:06 UTC

  5 points

  in reply to: [deleted]’s comment on: Harry Pot­ter and the Meth­ods of Ra­tion­al­ity dis­cus­sion thread, part 8

  You don’t need Z, third-order arithmetic is sufficient. Every set of ordinals is well-ordered by the usual ordering of ordinals.

• shinoteki 5 Sep 2011 15:23 UTC

  6 points

  in reply to: Psy-Kosh’s comment on: Harry Pot­ter and the Meth­ods of Ra­tion­al­ity dis­cus­sion thread, part 8

  It is basically the main point of the definition of ordinals that for any property of ordinals , there is a first ordinal with that property. There are, however, foundational theories without uncountable ordinals , for instance Nik Weaver’s Mathematical Conceptualism.