Re: what makes it true?


Ittay Weiss wrote:
> so what is Goedel's incompleteness theorem? please answer this question informativly since for the rest of my questions you gave no information at all. How can we have a discussion if you dont even bother to give me some information?

Wikipedia states: Gödel's most famous works were his incompleteness
theorems, the most famous of which states that any self-consistent
recursive axiomatic system powerful enough to describe integer
arithmetic will allow for "true" propositions about integers that can
not be proven from the axioms.

> and just for clarity: I am claiming that if a statement can be proved from a set of axioms then the statement holds in any model where the axioms hold. If I am wrong please explain why

You are right.

--
Ron

.

Relevant Pages

  • Re: Question regarding incompleteness in formal systems without sufficient power for arithmetic.
    ... Before Godel proved the incompleteness theorem, ... The answer to that question is A RECURSIVE SET OF AXIOMS. ... FOL *is not* a recursive set of axioms. ... Scandinavian School of Truth as founded by Torkel Franzen ...
    (sci.logic)
  • System P is Godels meta theory not his object theory
    ... PM as an example of his incompleteness theorem. ... Godels meta-theory and not his object theory as it is based upon system P ... The general result as to the existence of undecidable propositions reads: ... the class of axioms and the riles of inference- note these axioms ...
    (sci.logic)
  • Re: Set Theory: Should you believe?
    ... "inequivalent versions" of Godel's 1st Incompleteness Theorem, ... More to the point, eliminating all functors will ... force of the Peano Axioms. ...
    (sci.logic)
  • Re: Goedel - interesting problem?
    ... >related to e.g. the Liar Paradox, but is developed as a formalized version ... >problems like e.g. the Liar Paradox, assuming later formalization? ... axioms at least as rich as the axioms of arithmetic has ... Goedel's incompleteness theorem only shows that some true ...
    (sci.logic)