> On 15 Dec 2018, at 10:02, Philip Thrift <[email protected]> wrote: > > > > On Friday, December 14, 2018 at 10:36:29 PM UTC-6, Brent wrote: > > > On 12/14/2018 10:41 AM, Philip Thrift wrote: > > One type of objection might be that matter is a mystery, but math > > isn't. But I think complexity theorists (like Chaitin) have shown that > > math is a mystery too. > > Actually the argument has been made the other way. Math is not a > mystery, it is completely known as are fictional stories like "Moby > Dick". What is written down in all there is. If you ask what was the > beam of the Pequod there is no corresponding fact. But if you ask what > was the beam of the Pinta, there was such a value, even if you can't > find what it was. So real things are more complex and are not > completely definable. > > Brent > > > When I think of "math is a mystery" I'm going mainly back to > > The Limits of Reason > Ideas on complexity and randomness originally suggested by Gottfried W. > Leibniz in 1686, combined with modern information theory, imply that there > can never be a “theory of everything” for all of mathematics. > By Gregory Chaitin > - http://www.cs.virginia.edu/~robins/The_Limits_of_Reason_Chaitin_2006.pdf
It his just Gödel’s theorem. But it is not that a theory of everything in math does not exist, but that a *complete* theory of everything in math does not exist. (Complete means that we can *prove* all truth). It makes the mathematical truth into a god in the sense of the platonism. All this is also said by all universal machine, which is what the logicians discovered a long time ago. All this is in favour of mathematical realism. With mechanism we need only a weak form of arithmetical realism, which is accepted by all scientists, even Nelson and even ultrafinitist. Bruno > > - pt > > -- > 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.
