On 15 May 2017 at 21:35, John Clark <johnkcl...@gmail.com> wrote: > On Mon, May 15, 2017 at 6:38 AM, David Nyman <da...@davidnyman.com> wrote: > > > >> I've been thinking a bit about physical supervenience in the >> computationalist context and have come to the conclusion that I don't >> really understand it. >> > > If X superveniens Y then there can NOT be a change in X without a change > in Y; but if you changed mathematics (by changing one of the fundamental > axioms for example) it would not change the physical world, therefore > mathematics can not supervene physics. Furthermore it is physics that > rescues us from paradox that mathematics alone would otherwise produce. > > Suppose you had a lamp and made it flash in a Zeno like manner, it was on > for one minute, off for 30 seconds, on for 15 sec and so on, after 2 > minutes would the lamp be on or off? It can't be off because on ALWAYS > follows off, and it can't be on because off ALWAYS follows on. > > Or suppose you had a infinite number of balls each with a unique integer > printed on it and decided to place all of them in a box in a accelerated > Zeno way. In step 1 (which takes one minute) you place balls 1 through 10 > in the box but remove ball 1, in step 2 (which takes half as long as step > 1) you place balls 11 through 20 in the box but remove ball 2, in step 3 > (which takes half as long as step 2) you place balls 21 through 30 in the > box but remove ball 3 etc . At the end of 2 minutes how many balls are in > the box? If might seem that there are a infinite many since each step adds > 9 balls (10-1=9) and there are a infinite number of steps, but for any > integer you care to name I can name the step where that integer was > removed; one was removed at step 1, 10 was removed at step 10, a trillion > was removed at step trillion and so on. So the number of balls grows > without limit during the task but after it is completed there are no balls > in the box at all. Zero. > > In what would seem to be a slight variation on the previous procedure lets > add 9 balls in each step just as we did before, in step 1 we put in balls 1 > through 9 but this time we write a zero after the 1 on ball number 1 with a > magic marker. In step 2 we put in balls 11 through 19 and draw a zero after > the 2 on ball number 2. In step 3 we put in balls 21 through 29 and draw a > zero after the 3 on ball number 3 etc. Now at the end of 2 minutes it is > revealed that the magic marker must have really been magical because now we > have a infinite number of balls in the box as opposed to zero because every > integer is written on one of the balls followed by a infinite number of > zeros. > > Physics prevents the above paradoxes because all of these > thought experiments assume that space or time or both are infinitely > divisible, but quantum physics says there is a smallest length (1.6*10^-35 > meter) and a smallest time (5.4*10^-43 seconds). >
Yes indeed. But why in your view wouldn't this merely imply that whatever mathematics we invoke in explicating physics cannot thereby in the limit be continuous? I know you take the view, which you reiterate above, that mathematics should be conceived exclusively in terms of the formalised mathematical intuitions we derive from observation of a physical externality. And if you find you cannot in the last analysis accept a viable distinction between mathematics defined in this way and its more abstract generalisation then of course computationalism in the sense I'm discussing it here can make no sense to you. I have no quarrel with that view, if it is indeed your own, but it is simply incompatible with my argument. So mathematics must be a language, the best language Homo Sapiens has ever > found to describe the physical world > Well, it certainly is at least that in the intuitionist sense, but as I've said many if not most mathematicians find that they conceive it in its more generalised or platonic form as distinct from any such partial or finite symbolic formulation. Roger Penrose, for example, has defended very robustly the view of the "discovery" rather than the invention of mathematical truths. I'm in no position to insist on any such view, but on the other hand the arguments I outline here will make little sense to you on any other principle. Possibly you could entertain the notion on an "as if" basis if you are in any way curious to see where it might lead. But if not, go in peace. David but like any language it can tell both fictional and non fictional stories, > and it can even tell fictional stories with logical plot holes. > We can certainly agree on that. David > > > John K Clark > > > > > > > > > > > > > > -- > 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 post to this group, send email to everything-list@googlegroups.com. > 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
