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Jan Burse
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 Posted: Fri Jul 25, 2008 2:14 am Post subject: Re: completeness what is it exactly |
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translogi schrieb:
[quote]But how do you call a theory that can prove true facts but cannot
disprove false facts?
[/quote]
Nope, if it were so easy.
PA cannot prove all true facts.
PA actually can disprove some false facts.
[quote]
PA is half complete but it not negation complete.
[/quote]
PA is incomplete, yes.
not negation complete = not complete = incomplete.
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herbzet
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| Posted: Fri Jul 25, 2008 7:09 am Post subject: Re: completeness what is it exactly |
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translogi wrote:
[quote]But how do you call a theory that can prove true facts but cannot
disprove false facts?
[/quote]
The term of art here is "refutes". If a theory T proves formula A
then it refutes ~A.
Whether formula A is true or false depends on the model in which
it is interpreted (unless it is a pure validity or a contradiction).
If all of the theorems of some theory T are true in some model then
T is sound in that model. T cannot fail to refute falsehoods in
that model, since to prove a formula is to refute its negation.
--
hz |
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