> On 18 Dec 2018, at 21:28, Brent Meeker <[email protected]> wrote: > > > > On 12/18/2018 4:29 AM, Bruno Marchal wrote: >>> But mathematical objects are completely defined by their axioms. >> >> No, they are not. All theories containing a bit of arithmetic have an >> infinity of non isomorphic models/realities. >> >> >> > OK. Then how do you judge the truth of unprovable propositions? You can't > rely on a model when there are an infinity of different ones.
Of course. It is *because* I have a good intuition, like you, of what the standard model is, that I can dismiss the non standard model, and the no-standard numbers. Addition and multiplication are no more computable in the non standard model. Your question is really, where do our intuition of the natural numbers come from? That is a deep philosophical question. It comes probably from the consciousness of the Löbian machine, but that requires some intuition of the infinities, Hilbertt spaces, complex analysis, etc… As I said, after Gödel, we know that our intuition of the natural numbers comes from a deeper intuition of the infinities, and then, with mechanism, we can explain that such an intuition is already capture by the very concept of “universal machine”. That one cannot be justified by less, only by equivalent. Bruno > > Brent > > -- > 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. -- 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.
