On Apr 1, 10:59 pm, david petry <david_lawrence_pe...@yahoo.com> wrote: > On Monday, April 1, 2013 12:17:22 PM UTC-7, Dan wrote: > > On Apr 1, 9:58 pm, david petry <david_lawrence_pe...@yahoo.com> wrote: > > > On Monday, April 1, 2013 11:38:05 AM UTC-7, Dan wrote: > > > > Falsifiability only comes into consideration when you have something > > > > apparently 'external' against which to test your mathematical models . > > > Precisely. The "external" reality underlying mathematics is computation. > > > A very good way of thinking about this stuff is to think of the computer as the mathematicians' microscope [...] > > You've never actually seen a "real computer" , nor will you ever do > > so . The Turing machine requires an infinite tape . > > That's what this "debate" is all about. > > I'm suggesting that mathematics should have meaning within the context of real-world computers which have arbitrarily large but finite memories, and you insist that "real" computers have an actually infinite memory capacity, and then (I think) you insist that mathematics itself deals with even larger infinities than that actually infinite memory of the "real" computer. > > I believe my view is superior for the mathematics of the real world. > > > "What Turing disregards completely is the fact that mind, in its use, > > is not static, but constantly developing" -Godel > > Mind boggling.
Finitism? Really ? What about induction? And more importantly ,who gets to decide how large a number is 'enough'?And by what criteria? This is the most important question regarding finitism . You can't just wish it away . Should we play "who can think of the largest number"?
If reality were finite , then our infinite mathematics would certainly be enough to model it , as it includes all finite models . On the other hand , if reality were infinite , only an infinite mathematics would suffice for it .
"If the doors of perception were cleansed every thing would appear to man as it is, infinite. For man has closed himself up, till he sees all things through narrow chinks of his cavern." -William Blake