On Sun, May 19, 2019 at 6:00 PM Russell Standish <[email protected]> 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 <[email protected]> > 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 [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLSak7WKaUphQgiox%3DmwNQrSUWD2wKgGiGWHGv8908MZAw%40mail.gmail.com.
