On Sunday, May 12, 2019 at 9:40:12 PM UTC-5, Jason wrote: > > > >> > Incompleteness disproves nominalism. Arithmetical truth was proven not > only to be not human defined, but to be not human definable. >
(This is something I posted a few days ago in another forum.) >From Joel David Hamkins @JDHamkins - http://jdh.hamkins.org/ "Truths" in the set-theoretic multiverse (slides from a talk last week): http://jdh.hamkins.org/wp-content/uploads/Is-there-more-than-one-mathematical-universe.pdf The final slides: ---- *The Continuum Hypothesis is settled* On the multiverse perspective, the CH question is settled. It is incorrect to describe it as an open question. The answer consists of our detailed understanding of how the CH both holds and fails throughout the multiverse, of how these models are connected and how one may reach them from each other while preserving or omitting certain features. Fascinating open questions about CH remain, of course, but the most important essential facts are known. Ultimately, the question becomes: do we have just one mathematical world or many ---- Mathematics is a language - with multiple dialects. * Each dialect of mathematics has its own syntax *(to some extent)* and semantics!* There is no settled "truth" in mathematics. For example (as Hamkins shows) the CH is true in one dialect (of set theory) and false in another. @philipthrift -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/06ca3480-cdf1-426b-9f38-404bc2fa1550%40googlegroups.com.
