Re: what makes it true?
Ittay Weiss wrote:
I don't know this theorem. I do know however the soundness theorem
that states that if a statement has a proof from a set of axioms
then it is true in any model where the axioms hold. Thus if something
can be proved it is true. I would appreciate it if you explain more
about this Goodstein theorem, or explain how can it be that what you
claim doesn't contradict the soundness theorem
Better Google it up (just by: "Goodstein's Theorem") than asking *me*
for an explanation.
Han de Bruijn
.
Relevant Pages
- Re: Goedel - interesting problem?
... >> might be true both within and without the set of axioms, ... theorem will need the explanation we are discusssing, ... use, reliability, intended reader, context, context, and context. ... >> reader is not a logician, but from any of a large variety of fields. ...
(sci.logic) - Re: Goedel applied to the real-world
... Torkel Franzen wrote: ... Kent Paul Dolan posts. ... Goedel proved that any set of axioms at least as rich as the ... The above explanation can be confirmed with reasonable ...
(sci.logic) - Re: Deep Thoughts # 17: Liar Paradox is a Formal Metamathematical Theorem
... axioms are all of the true sentences, ... Once again you use the word "ignorance" and once ... the rules must be sound, that would indicate ignorance rather than ... the Soundness Theorem. ...
(sci.logic) - Re: Goedel - interesting problem?
... >>axioms at least as rich as the axioms of arithmetic has ... which is out of the use context. ... and "language of the formal theory" is also too technical and not ... try to apply "true/false" to the explanation, you may go out of context. ...
(sci.logic) - Re: Uncountable sets in CZF?
... > requires more than a single sentence or two is overcomplex, ... If you won't enumerate the axioms clearly and completely, ... rather than explicitly stating your axioms. ... If I understood David's explanation, ...
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