On Mon, May 15, 2017 at 7:06 PM, David Nyman <da...@davidnyman.com> wrote:
>> 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? > Because there is no mathematical reason time or space or anything else can't be continuous , nor can mathematics find anything special about the numbers 1.6*10^-35 or 5.4*10^-43 , but physics can. And mathematics can produce paradoxes but physics never can. > > > 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. > It makes sense to me that Information is physical because non-reversible computation uses energy and increases entropy . C omputationalism says the human mind is a information processing system and thinking is a form of computation , and that makes sense to me too . > > > Roger Penrose, for example, has defended very robustly the view of the > "discovery" rather than the invention of mathematical truths. > In mathematics you start with certain axioms and agree to follow certain rules on how to manipulate those axioms, and if you follow those rules without error then we say the result is mathematically true, but all we're really saying is that in the language of mathematics the result is grammatically correct. Noam Chomsky famously gave an example of a sentence in another language, the English language, that was correct grammatically but meant nothing: "*The c* *olorless green ideas sleep furiously* **" 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.
