On Sun, May 19, 2019 at 6:00 PM Russell Standish <li...@hpcoders.com.au> wrote:
> On Sun, May 19, 2019 at 05:11:20PM +1000, Bruce Kellett wrote: > > On Sun, May 19, 2019 at 4:45 PM Russell Standish <li...@hpcoders.com.au> > wrote: > > > > > > > > That remains to be proved. Church-Turing is about calculable > numbers, not about > > > reification. It also works in a purely nominalist account. > > > > > > > Hmm - possibly I went too fast here. The existence of a running > > universal dovetailer is sufficient for the whole numbers to be > > reified, as the abovementioned constructive program will eventually > be > > run for all such whole numbers. > > > > > > For the dovetailer to run on all numbers, it must be run "in > arithmetic", as > > Bruno claims. If you do not assume arithmetical realism, the dovetailer > cannot > > get off the ground unless it is implemented in a physical computer. But > that is > > always necessarily finite, so the argument again collapses. > > > > > > In order for the dovetailer to fail to > > generate all whole numbers, it must be starved of some resources, > > which is an ultrafinitist move. > > > > > > Or the necessary involvement of a finite physical computer.... > > > > That is an assumption. There are proposed cosmologies that allow for > an infinite number of computational steps to occur - IIRC, the "big > rip" is one such. I don't think so -- the "big rip" would simple tear the physical computer to pieces..... > Once multiverses get into the picture, there is > almost assuredly sufficient computational resources to go around. > No so fast. The multiverse is an assemblage of disjoint universes -- what happens in one universe does not affect any other universe. So that doesn't get you any more computing power. > Nevertheless, it is an interesting question as to whether insufficient > resources to support the full reality of the integers makes any damn > difference at all to mathematics or even observable reality. Norm > Wildberger is one of the few people championing this sort of work. > If the dovetailer has only limited resources, does it actually get you anything at all? > > > > I think that the CT thesis requires that all possible programs can be > > run in order for a machine to be considered truly > > universal. > > > > > > That might be the case, in which case the argument works only on the > realist > > assumption. Since there is no necessity to make such an assumption, we > can > > safely ignore the whole shebang.... > > > > There's a lot of plausible arguments in favour of a multiversal > reality - indeed it tends to be the prevalent background assumption of > this mailing list. > This list is a very small sample of the scientific community, much less of humanity as a whole. Multiverse ideas are around, but unless seriously constrained, they are definitely suspect. > My gut feeling is that if there really is an ultrafinitist limit to > the amount of computation available in the universe, then there ought > to be some measureable consequence of this in our observable universe. > Why? That might be the case if the computationalist/arithmetical realist thesis has some basis. But there is no evidence for that. Physicalism is still safer bet...... Bruce -- 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/CAFxXSLSak7WKaUphQgiox%3DmwNQrSUWD2wKgGiGWHGv8908MZAw%40mail.gmail.com.
