> On 3 Jul 2018, at 00:50, Russell Standish <[email protected]> wrote: > > On Mon, Jul 02, 2018 at 05:31:33PM +0200, Bruno Marchal wrote: >> >>> On 1 Jul 2018, at 19:27, John Clark <[email protected]> wrote: >>> >>> On Sun, Jul 1, 2018 at 6:42 AM, Bruno Marchal <[email protected] >>> <mailto:[email protected]>> wrote: >>> >>>> But you should not confuse the arithmetical reality with a book, be it >>>> virtual or relatively material. >>> One of us is very confused that much is certain. You think arithmetical >>> reality is the only reality there is >>> >> >> I have never said what I think. That is private. But I can prove that if >> mechanism is true, then we cannot assume more than arithmetic (or Turing >> equivalent) without being inconsistent. > > That is surprising. Why would assuming the existence of real numbers > make one inconsistent? Otiose, perhaps, but not inconsistent, surely.
Not sure what you mean by Otiose. And OK, I should have said “inconsistent with the facts”. Obviously, you can add an infinity axioms, or the induction axioms, to RA without bringing any formal contradictions, but this leads, I begin to suspect, to reintroducing to much white rabbits in the phenomenologies. Once you have an axiom of infinity, it will be true in all models, and it will have to be taken account all real oracles in the phenomenology. G and G* might remains valid, so it might be that physics is still recovered, but that remains to be seen, and it would violate mechanism. The fact is that with mechanism, anything you add to RA must be either redundant, or explains in a phenomenology which do not presuppose those things in the ontology. I thought for long that we could already add the induction axioms in the ontology, but even that leads to problem, not far away of the reason why Nelson think (wrongly, I think) that PA is inconsistent. But with mechanism, RA + infinity, or RA + induction should lead to predict white rabbits . I am not yet entirely confident of this. The reason are technical, and involve much more model theory, which is even less known than recursion theory. So I do not insist too much on this, and should do some some work before. Bruno > > > -- > > ---------------------------------------------------------------------------- > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders > Visiting Senior Research Fellow [email protected] > Economics, Kingston University http://www.hpcoders.com.au > ---------------------------------------------------------------------------- > > -- > 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.
