Is _Brave New World_ really science fiction?
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From: Jesse F. Hughes on 10 Apr 2010 20:02 Jonathan Schattke <wizwom(a)gmail.com> writes: > On 4/10/2010 5:50 PM, Bill Snyder wrote: >> On Sat, 10 Apr 2010 17:33:25 -0500, Jonathan Schattke >> <wizwom(a)gmail.com> wrote: >> >>> On 4/7/2010 10:27 PM, Transfer Principle wrote: >>>> Those posters who >>>> believe in a smallest real number, such as AP and MR, may be >>>> included with the "discrete mathematicians" as well. >>> >>> For any proposed smallest real, I can come up with a smaller number ;-) >> >> >> Then I pick "The real number that's smaller than any you can ever >> come up with." Better yet, I pick the largest such number. This >> is why kooks so often prefer text to math. > > It actually points to the failure of "constructivist" mathematicians > over "platonic" ones - the refusal to accept the trichotomy theorem and > infinity leads to strange results. Such as saying there is a concrete > minimum real. > How's that? Do constructivists really believe there is a concrete minimum real? -- Jesse F. Hughes "Mistakes are big part of the discovery process. I make lots of them. Kind of pride myself on it." -- James S. Harris
From: Quadibloc on 10 Apr 2010 21:35 On Apr 10, 6:02 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: > Jonathan Schattke <wiz...(a)gmail.com> writes: > > It actually points to the failure of "constructivist" mathematicians > > over "platonic" ones - the refusal to accept the trichotomy theorem and > > infinity leads to strange results. Such as saying there is a concrete > > minimum real. > > How's that? Do constructivists really believe there is a concrete > minimum real? Considering that all the rationals can be constructed, and there is no smallest rational number greater than zero, I would have thought that even if constructivism does lead to absurdities, this wouldn't be one of them. John Savard
From: Jesse F. Hughes on 10 Apr 2010 23:26 Quadibloc <jsavard(a)ecn.ab.ca> writes: > On Apr 10, 6:02 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Jonathan Schattke <wiz...(a)gmail.com> writes: > >> > It actually points to the failure of "constructivist" mathematicians >> > over "platonic" ones - the refusal to accept the trichotomy theorem and >> > infinity leads to strange results. Such as saying there is a concrete >> > minimum real. >> >> How's that? Do constructivists really believe there is a concrete >> minimum real? > > Considering that all the rationals can be constructed, and there is no > smallest rational number greater than zero, I would have thought that > even if constructivism does lead to absurdities, this wouldn't be one > of them. M3 T0000! -- Jesse F. Hughes "You're terrified of your daughters dreaming about me." -- James S. Harris, on why mathematicians fear him
From: Mike Schilling on 11 Apr 2010 00:22 Quadibloc wrote: > On Apr 10, 6:02 pm, "Jesse F. Hughes" <je...(a)phiwumbda.org> wrote: >> Jonathan Schattke <wiz...(a)gmail.com> writes: > >>> It actually points to the failure of "constructivist" mathematicians >>> over "platonic" ones - the refusal to accept the trichotomy theorem >>> and infinity leads to strange results. Such as saying there is a >>> concrete minimum real. >> >> How's that? Do constructivists really believe there is a concrete >> minimum real? > > Considering that all the rationals can be constructed, The lifetime of the universe is finite; how can you construct an infinite amount of number in a finte time? Talk about absurdities...
From: Brian M. Scott on 11 Apr 2010 00:59
On Sat, 10 Apr 2010 20:02:06 -0400, "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote in <news:87ljcu6em9.fsf(a)phiwumbda.org> in rec.arts.sf.written,sci.math: > Jonathan Schattke <wizwom(a)gmail.com> writes: [...] >> It actually points to the failure of "constructivist" >> mathematicians over "platonic" ones - the refusal to >> accept the trichotomy theorem and infinity leads to >> strange results. Such as saying there is a concrete >> minimum real. > How's that? Do constructivists really believe there is a > concrete minimum real? 'Constructivist' isn't well-defined, but no flavor of constructivism that I've encountered allows that conclusion. Brian |