> On 7 May 2018, at 16:38, John Clark <johnkcl...@gmail.com> wrote: > > If the Real numbers exist then the Continuum Hypothesis is either true or it > is not.
That does not follow. Cunter-exemple: Intuitionist analysis admit Real Numbers, but certainly not with the CH being true or false. You assume classical logic, on some first order axiomatisation of set theory. Other counterexample. All models of ZF have real numbers; but in some model CH is true (Gödel) and in some model CH is false (Cohen). Bruno > But are the Real numbers really real? No less a mathematician than Gregory > Chaitin (of Chaitin's Omega fame) is on record as saying the real numbers do > not exist. If he's right and they don't exist then the Continuum Hypothesis > is neither true nor false, its gibberish. Perhaps a better example would be > "is the Goldbach Conjecture either true or not true?" because we know > integers exist and unlike the Continuum Hypothesis we can at least conceive > of experimental evidence proving that it is wrong; tomorrow a computer > grinding through ever larger integers could find some huge even number that > is not the sum of two prime numbers. > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
