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The nature of number

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The nature of number
Categories+Sheaves Offline
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#63
The nature of number
September 5, 2012 at 5:47 am (This post was last modified: September 5, 2012 at 5:49 am by Categories+Sheaves.)
(September 3, 2012 at 7:20 pm)jonb Wrote: Quick thought though, what if individual numbers do not have integrity of themselves, but are only created from the series by the observation. Is that a possible line of enquiry?
I mean, what do we count "observation" as? There's a very old discussion about whether the mathematical structures we play with exist in their own right, or just through our intuition/visualization/understanding. Finitism/Ultrafinitism is also a thing; if I prove that some formula works when I plug in '1', and then (abstractly) prove "if the formula works for some integer n, then the formula must work for n+1 as well" I've proven this formula for all natural numbers, right? It's common practice in math to say "yes, of course!" but some folks aren't so sure (e.g. Ed Nelson from Princeton tried to prove that the Peano Axioms weren't consistent about a year ago). It's not like I'll ever "observe" all the integers out there (given a finite brain and a finite lifespan, anyway) so how can I intelligently make statements about all the integers? The phenomenology of math is pretty weird.
So these philosophers were all like, "That Kant apply universally!" And then these mathematicians were all like, "Oh yes it Kan!"
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Atheist Forums › Science › Mathematics v
The nature of number

Messages In This Thread
The nature of number - by jonb - July 10, 2012 at 8:02 am
RE: The nature of number - by Cato - July 10, 2012 at 12:17 pm
RE: The nature of number - by jonb - July 10, 2012 at 12:58 pm
RE: The nature of number - by Tobie - July 10, 2012 at 1:57 pm
RE: The nature of number - by Whateverist - August 24, 2012 at 10:49 am
RE: The nature of number - by jonb - July 10, 2012 at 2:06 pm
RE: The nature of number - by Cato - July 10, 2012 at 2:20 pm
RE: The nature of number - by Categories+Sheaves - July 10, 2012 at 6:25 pm
RE: The nature of number - by jonb - July 10, 2012 at 8:17 pm
RE: The nature of number - by Categories+Sheaves - July 12, 2012 at 6:15 am
RE: The nature of number - by Whateverist - August 26, 2012 at 10:11 am
RE: The nature of number - by jonb - July 12, 2012 at 6:02 am
RE: The nature of number - by jonb - July 12, 2012 at 8:10 am
RE: The nature of number - by Categories+Sheaves - July 12, 2012 at 3:02 pm
RE: The nature of number - by jonb - July 16, 2012 at 8:30 am
RE: The nature of number - by CliveStaples - July 16, 2012 at 2:14 pm
RE: The nature of number - by jonb - July 16, 2012 at 2:37 pm
RE: The nature of number - by CliveStaples - July 16, 2012 at 6:47 pm
RE: The nature of number - by jonb - July 16, 2012 at 7:00 pm
RE: The nature of number - by CliveStaples - July 16, 2012 at 7:17 pm
RE: The nature of number - by jonb - July 16, 2012 at 7:23 pm
RE: The nature of number - by CliveStaples - July 17, 2012 at 1:24 am
RE: The nature of number - by Categories+Sheaves - July 17, 2012 at 1:41 am
RE: The nature of number - by CliveStaples - July 17, 2012 at 1:51 am
RE: The nature of number - by Categories+Sheaves - July 17, 2012 at 3:14 am
RE: The nature of number - by CliveStaples - July 17, 2012 at 10:49 am
RE: The nature of number - by jonb - July 17, 2012 at 6:39 am
RE: The nature of number - by Angrboda - July 16, 2012 at 2:06 pm
RE: The nature of number - by jonb - July 16, 2012 at 6:15 pm
RE: The nature of number - by Angrboda - July 16, 2012 at 8:07 pm
RE: The nature of number - by Categories+Sheaves - July 17, 2012 at 7:56 pm
RE: The nature of number - by jonb - July 18, 2012 at 9:59 am
RE: The nature of number - by Angrboda - July 17, 2012 at 11:25 pm
RE: The nature of number - by jonb - July 18, 2012 at 10:40 am
RE: The nature of number - by Cato - July 18, 2012 at 12:59 am
RE: The nature of number - by Categories+Sheaves - July 18, 2012 at 1:21 am
RE: The nature of number - by jonb - July 18, 2012 at 6:13 am
RE: The nature of number - by Categories+Sheaves - July 18, 2012 at 10:05 am
RE: The nature of number - by jonb - July 19, 2012 at 11:44 am
RE: The nature of number - by Categories+Sheaves - July 28, 2012 at 3:22 am
RE: The nature of number - by jonb - July 28, 2012 at 8:17 am
RE: The nature of number - by Categories+Sheaves - July 28, 2012 at 12:52 pm
RE: The nature of number - by jonb - July 29, 2012 at 4:04 am
RE: The nature of number - by Categories+Sheaves - July 29, 2012 at 4:18 pm
RE: The nature of number - by CliveStaples - July 29, 2012 at 8:54 pm
RE: The nature of number - by Categories+Sheaves - July 29, 2012 at 9:17 pm
RE: The nature of number - by CliveStaples - July 30, 2012 at 2:39 am
RE: The nature of number - by Categories+Sheaves - July 30, 2012 at 5:33 am
RE: The nature of number - by jonb - August 1, 2012 at 11:26 am
RE: The nature of number - by Categories+Sheaves - August 1, 2012 at 4:53 pm
RE: The nature of number - by jonb - August 8, 2012 at 8:41 am
RE: The nature of number - by Categories+Sheaves - August 8, 2012 at 11:41 am
RE: The nature of number - by jonb - August 8, 2012 at 11:50 am
RE: The nature of number - by CliveStaples - August 9, 2012 at 8:23 am
RE: The nature of number - by jonb - August 24, 2012 at 7:43 am
The nature of number - by Categories+Sheaves - August 24, 2012 at 12:51 pm
RE: The nature of number - by jonb - August 26, 2012 at 4:30 pm
The nature of number - by Categories+Sheaves - August 26, 2012 at 5:13 pm
RE: The nature of number - by jonb - August 26, 2012 at 5:27 pm
RE: The nature of number - by jonb - September 3, 2012 at 10:47 am
RE: The nature of number - by Categories+Sheaves - September 3, 2012 at 6:52 pm
RE: The nature of number - by jonb - September 3, 2012 at 7:20 pm
The nature of number - by Categories+Sheaves - September 5, 2012 at 5:47 am
RE: The nature of number - by jonb - September 5, 2012 at 6:00 am
The nature of number - by Categories+Sheaves - September 5, 2012 at 6:19 am
RE: The nature of number - by jonb - September 5, 2012 at 6:29 am
RE: The nature of number - by Categories+Sheaves - September 7, 2012 at 12:12 am
RE: The nature of number - by jonb - September 7, 2012 at 1:31 am
RE: The nature of number - by Categories+Sheaves - September 11, 2012 at 2:32 pm
RE: The nature of number - by jonb - September 11, 2012 at 11:11 pm
RE: The nature of number - by Categories+Sheaves - September 12, 2012 at 4:19 am
RE: The nature of number - by jonb - October 4, 2012 at 7:56 am
RE: The nature of number - by Categories+Sheaves - October 5, 2012 at 5:26 am
RE: The nature of number - by jonb - October 10, 2012 at 6:07 am
The nature of number - by Categories+Sheaves - October 12, 2012 at 11:22 pm
RE: The nature of number - by CliveStaples - October 17, 2012 at 7:01 pm
RE: The nature of number - by Categories+Sheaves - October 18, 2012 at 1:31 am
RE: The nature of number - by jonb - October 12, 2012 at 11:30 pm
The nature of number - by Categories+Sheaves - October 13, 2012 at 3:27 am
The nature of number - by Categories+Sheaves - October 13, 2012 at 7:54 am
RE: The nature of number - by jonb - October 13, 2012 at 11:22 am
RE: The nature of number - by Categories+Sheaves - October 22, 2012 at 3:21 pm
RE: The nature of number - by jonb - October 28, 2012 at 11:02 pm

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