Am I a crank?
in [Math]
|
Prev: Any coordinate system in GR?
Next: Euclidean Spaces
From: Lester Zick on 31 Aug 2006 13:13 On Thu, 31 Aug 2006 02:26:36 -0600, Virgil <virgil(a)comcast.net> wrote: >In article <8746c$44f690ea$82a1e228$18104(a)news2.tudelft.nl>, > Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: > >> Virgil wrote: >> >> > Let's see Zick empirically establish the axiom of infinity, then. >> >> Nobody can. Therefore it does not correspond to (part of an) implicit >> definition of some real world thing. Therefore it will do no harm if >> we throw it out. >> >> Han de Bruijn > >By that argument, it will do no harm to throw out every axiom of every >set theory or geometry theory or any other mathematical theory since >none of them refer to anything that exists in the "real world". Collective angst projection. >If Han wishes to do entirely without any mathematics, he is free to do >so, but he cannot compel anyone else to join him. ~v~~
From: Lester Zick on 31 Aug 2006 13:14 On Thu, 31 Aug 2006 09:22:15 +0200, Han de Bruijn <Han.deBruijn(a)DTO.TUDelft.NL> wrote: >Lester Zick wrote: > >> In physics a hypothesis is either contradictory or not. > >Likewise, in biology, a piece of fruit is an apple or not. But apparently not in modern math. ~v~~
From: Lester Zick on 31 Aug 2006 13:15 On 31 Aug 2006 04:48:12 -0700, schoenfeld.one(a)gmail.com wrote: > >Lester Zick wrote: >> On 30 Aug 2006 05:01:52 -0700, schoenfeld.one(a)gmail.com wrote: >> >> > >> >Han de Bruijn wrote: >> >> schoenfeld.one(a)gmail.com wrote: >> >> >> >> > Then there is no experiementation. Mathematics is not an experimental >> >> > science, it is not even a science. The principle of falsifiability does >> >> > not apply. >> >> >> >> Any even number > 2 is the sum of two prime numbers. Now suppose that I >> >> find just _one_ huge number for which this (well-known) conjecture does >> >> _not_ hold. By mere number crunching. Isn't that an application of the >> >> "principle of falsifiability" to mathematics? >> > >> >Falsifiability does not _need_ to apply in mathematics. In math, >> >statements can be true without their being a proof of it being true. >> >Likewise, they can be false. >> >> Except apparently for definitions. > >Definitions can be false too (i.e. "Let x be an even odd"). Except that Virgil maintains that definitions in modern math are neither true nor false. >> >In physics, a hypothesis is never true only verified xor false. >> >> In physics a hypothesis is either contradictory or not. >> >> ~v~~ ~v~~
From: Lester Zick on 31 Aug 2006 13:16 On Thu, 31 Aug 2006 09:58:27 -0400, "Jesse F. Hughes" <jesse(a)phiwumbda.org> wrote: >schoenfeld.one(a)gmail.com writes: > >> Definitions can be false too (i.e. "Let x be an even odd"). > >That is not what one usually means when he says "mathematical >definition". A mathematical definition is a stipulation that a >particular phrase means such-and-such. > >Like: A /group/ is a set S together with a distinguished element e and >an operation *:S x S -> S such that blah blah blah > >But what you're doing is different. You are specifying that a >variable should be interpreted as a certain kind of number, namely an >even odd. Even though there is no such thing as an even odd, however, >this is not false. How could it be false? It's an imperative, >telling the reader to do something (namely, assume that x names an >even odd). > >If I tell you to find integers a, b such that a/b = sqrt(2), I haven't >said something false. I've given you a command that is impossible to >fulfill, but it isn't false. Imperatives don't have truth values. > >I'm not sure that "Let x be an even odd," is impossible to do in the >same sense that finding a rational equal to sqrt(2) is impossible. I >think that this imperative just means: Assume that x satisfies certain >conditions. And as far as I can see, I can assume impossible facts >willy nilly. So is Virgil right or wrong that definitions in modern math can be neither true nor false? ~v~~
From: Lester Zick on 31 Aug 2006 13:17
On Thu, 31 Aug 2006 09:59:35 EDT, fernando revilla <frej0002(a)ficus.pntic.mec.es> wrote: >schoenfeld.one(a)gmail.com wrote: > > > Definitions can be false too (i.e. "Let x be an even >> odd" > >That is not a definition. See ( 7 is an even and 7 >is odd ) --> ( All the elephants are yellow ) it is a >proposition, by the way, a true proposition. So how exactly do definitions differ from propositions? ~v~~ |