On 3/15/07, Brent Meeker <[EMAIL PROTECTED]> wrote:

> > Torgny Tholerus wrote: > > Stathis Papaioannou skrev: > >> On 3/14/07, *Torgny Tholerus* <[EMAIL PROTECTED] > >> <mailto:[EMAIL PROTECTED]>> wrote: > >> > >> Stathis Papaioannou skrev: > >>> How can you be sure? Maybe space is discrete. > >> Yes, space (and time) is discrete. Everything in the universe is > >> finite, and the universe itself is finite. Infinity is a > >> logically impossible concept. > >> > >> > >> I don't see that "discrete" and "finite" necessarily go together. The > >> integers are discrete, but not finite. > > No, the integers are finite. There exists only a finite numer of > > integers. There exists a biggest integer N. It is true that you can > > construct the integer N+1, but this integer is not a member of the set > > of all integers. > > This must be computer arithmetic (modulo N?) - not Peano's. :-) > > > > > Because everything is finite, you can conclude that the space-time is > > discrete. > > That doesn't follow. The universe could be finite and closed, like the > interval [0,1] and space could still be a continuum. > > But these ideas illustrate a problem with "everything-exists". Everything > conceivable, i.e. not self-contradictory is so ill defined it seems > impossible to assign any measure to it, and without a measure, something to > pick out this rather than that, the theory is empty. It just says what is > possible is possible. But if there a measure, something picks out this > rather than that, we can ask why THAT measure? Isn't that like arguing that there can be no number 17 because there is no way to assign it a measure and it would get lost among all the other objects in Platonia? Stathis Papaioannou --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---