Re: Cantorian pseudomathematics

david petry wrote:
> A statement has observable content if it makes predictions about the
> results of a computational experiment.

Same as last post:

Suppose I give you two natural numbers such that the second natural
number is the Godel number of the string of symbols that mathmaticians
point to as the theorem that the set of real numbers is uncountable.
You put both natural numbers into your computer and let your computer
compute whether the first natural number is the Godel number of a proof
of the formula whose Godel number is the second natural number.

If a mathematician claims to have proven a theorem from the axioms of
set theory, then the claim can be decided (either confirmed or
falsified) by sticking the numbers into your computer and letting it
compute.

If a mathematician makes the statement, "It is a theorem of set theory
that the set of real numbers is uncountable, and the following is a
proof: [fill in purported proof]" then just run the Godel numbers and
you have your computational experiment. You'll always get an answer,
yes or no.

MoeBlee

MoeBlee

.

Relevant Pages

  • Re: Cantorian pseudomathematics
    ... >> A statement has observable content if it makes predictions about the ... >> results of a computational experiment. ... > compute whether the first natural number is the Godel number of a proof ... > If a mathematician makes the statement, "It is a theorem of set theory ...
    (sci.math)
  • Re: Cantorian pseudomathematics
    ... >>> A statement has observable content if it makes predictions about the ... >>> results of a computational experiment. ... >> compute whether the first natural number is the Godel number of a proof ... uncountability of reals". ...
    (sci.math)
  • Re: an important set theory post
    ... taken to be undefined in set theory. ... Strange, since everyone knows what it means. ... about mathematics as it is. ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
  • Re: Godel Contradiction
    ... OK Godel Says: ... ... for all consistent systems T there exists a true unprovable ... Z set theory is such a formal theory in which we may prove ... In the case of Z set theory, Tis not an axiom, since Tis not ...
    (sci.logic)
  • Re: -- g o g = f
    ... that f is 1-1 then it's nothing but simple set theory. ... since 0 < k-j < n this contradicts the fact that ... "Understanding Godel isn't about following his formal proof. ...
    (sci.math)
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