Berkeley CSUA MOTD:2011:April:26 Tuesday <Wednesday>
Berkeley CSUA MOTD
2011/4/26-7/13 [Politics/Domestic/Election, Politics/Domestic/President/Bush] UID:54094 Activity:nil
4/26    "IMF Bombshell: Age of America Nears End" (
        "According to the latest IMF official forecasts, China's economy will
        surpass that of America in real terms in 2016 -- just five years from
        \_ We can turn them into a economy of smoking glass in 5 minutes.
2011/4/26-7/13 [Computer/Theory, Health/Women] UID:54095 Activity:nil
4/26    Is it correct to say that Godel's work on the incompleteness thm
        proved the Principia Mathematica wrong?
        \_ It didn't exactly prove it wrong; it proved that the true goal of
           PM (a complete and consistent set of mathematical truths)
           is unattainable.  -tom
           \_ Ah cool, no this is good. See ok yeah so the main goal of PM
              was to "be complete" but obGodel so that fails.  However as a
              piece of logic, that is, a system build up from first principles
              is PM is still valid, inspite of Godel?
              etc.) --OP
              \_ What Godel showed is that you can use PM's language (or any
                 other complete mathematical language) to create a paradoxical
                 statement.  That means that you can't assert that any
                 statement described by PM's language is true.  But in
                 practice it doesn't change much.  (Although why you would
                 use PM's language in practice is unclear; it's rather a
                 theoretical exercise).  -tom
                 \_ Would you use it to teach logic to a someone?  Is it at
                    least good for that?
                    \_ Sure, it could work for that, but it's pretty complex.
                       \_ Would it be correct to say, "If you studied logic
                          and understand how to follow logic, then you should
                          be able to read the PM." (as a milestone marker)?
        \_ It proved that PM is incomplete. DUH!!!
           \_ Well, more precisely, it proved that a symbolic logic cannot
              be both complete and consistent.  It would be more accurate to
              say that PM is inconsistent than that it's incomplete.  -tom
Berkeley CSUA MOTD:2011:April:26 Tuesday <Wednesday>