On Mar 13, 11:35 pm, Transfer Principle <david.l.wal...@lausd.net> wrote: > On Mar 13, 3:06 pm, Curlytop <pvstownsend.zyx....@ntlworld.com> wrote: > > > Peter Moylan set the following eddies spiralling through the space-time > > continuum: > > > I'm in the Cantor camp myself. If you can't conceive of uncountable > > > infinities then measure theory has to be re-done from the bottom up, and > > > things like integration become conceptually harder. Not to mention > > > concepts like continuity, limits, and so on. Yes, I'll concede that you > > > can build a mathematics on treating everything as countable, but as a > > > believer in Ockham's razor I prefer not to multiply complexity like that. > > Here Moylan appeals to Occam's Razor -- don't multiply complexities > unnecessarily, the simplest argument is usually the best. > > But what makes an argument or theory the "simplest"? Here's a common > trick sometimes used by ZFC users -- they a priori assume that the > "simplest" theory is ZFC or standard theory, then go back to show > why this is the case. > > For example, let's bring up analysis, since Moylan does so here. An > opponent of ZFC states that they'd rather do analysis over some > countable set X (where X may be, say, the computable reals) rather > than standard R. So the majority counters by arguing that analysis > over X is much, much harder than classical analysis over R, since, > for example, to find the limit of a Cauchy sequence, one has to > divide into cases where the limit is in X or not in X, whereas the > limit is always in R. So, by Occam's Razor, we should do analysis > only in R, not some countable subset like X.
No. The problem is that you and your darlings claim to want to "do analysis over some countable set" but none of you ever actually do anything except whine about being persecuted. None of you has ever done so much as show us how to find the area of a triangle in such a system.