> On 8 May 2018, at 01:32, John Clark <[email protected]> wrote: > > On Mon, May 7, 2018 at 12:58 PM, Bruno Marchal <[email protected] > <mailto:[email protected]>> wrote: > > > in some model CH is true (Gödel) and in some model CH is false (Cohen). > > That is incorrect. Godel showed that if the CH is false it would not produce > any contradictions in Zermelo–Fraenkel set theory plus the Axiom Of Choice > (ZFC), but that does not prove that the CH is false.
OK, but that is prove by building a model where CH is false, like we can prove the independence of Euclid postulate by building a model satisfying all axioms + the negation of the parallel postulate. The notion of truth is always relativised to a model, in logic. Bruno > And Cohen proved that if the CH is true it would not produce any > contradiction in ZFC, but that doesn't prove its true either. What the two of > them did prove is that ZFC has nothing to say about Continuum Hypothesis, it > just doesn't know if its true or not. > > And I think you're confused about the difference between what a model says > and what reality says. One model may say you can safely march across that > bridge and another model might say the bridge will collapse, but it makes no > difference which model you believe when you cross that bridge, it will > either fall down or it won't. > > John K Clark > > > > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] > <mailto:[email protected]>. > To post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <https://groups.google.com/d/optout>. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
