On 2025. Aug 30., Sat at 12:04, John Clark <[email protected]> wrote:
> On Fri, Aug 29, 2025 at 3:09 PM Alan Grayson <[email protected]> > wrote: > > *>>> Actually, sometimes even in pure mathematics we can't always reach >>>> absolute conclusions, a good example of which is the CONTINUUM HYPOTHESIS. >>>> AG * >>> >>> > *>> But it has been proven you can assume that the continuum hypothesis >> is true or you can assume that the continuum hypothesis is not true, but >> neither assumption will produce a contradiction to existing mathematics. It >> doesn't matter, so to my mind that indicates that the continuum hypothesis >> is just not very important. * > > >> *> What's "important" here is in the mind of mathematicans. And IMO >> you've misstated the result. AG* > > > *In 1940 Kurt Gödel proved that the truth of the Continuum Hypothesis is > consistent with existing mathematics, that is to say if it's true then it > would not change anything. In 1963 Paul Cohen proved that the NEGATION of > the Continuum Hypothesis is ALSO consistent with existing mathematics. As a > result of these developments I don't think the Continuum Hypothesis is > meaningless but I do think it's unimportant. I say that because, if neither > the truth nor the falsehood of a conjecture would change anything and if > the word has any meaning then that conjecture is "unimportant". * > > *And we can't just add the Continuum Hypothesis as an axiom because an > axiom needs to be simple and self-evidently true, and the Continuum > Hypothesis is neither of those things. And the same thing could be said > about its negation.* > Doesn’t seem unimportant to me, quite the contrary. I guess we haven’t found yet a good set of axioms. > *John K Clark See what's on my new list at Extropolis > <https://groups.google.com/g/extropolis>* > aoc > > > -- > 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 view this discussion visit > https://groups.google.com/d/msgid/everything-list/CAJPayv0PSeikr%2BABO2kVzGAupGQyGtaCHtZeEh86q-KytT3uKw%40mail.gmail.com > <https://groups.google.com/d/msgid/everything-list/CAJPayv0PSeikr%2BABO2kVzGAupGQyGtaCHtZeEh86q-KytT3uKw%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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 view this discussion visit https://groups.google.com/d/msgid/everything-list/CAKTCJydW6-%2BF_Y4%3DnO8PJqk1y9UxzMarNz%2Bdju-dRo%2BH4piSvQ%40mail.gmail.com.
