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.
-tom
\_ 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 |