Am I a crank?
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From: Virgil on 31 Aug 2006 14:20 In article <1157024892.614341.149030(a)e3g2000cwe.googlegroups.com>, 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"). That definition is not false, as it does not say that any such thing exists. Nor is it true. It is merely impossible to fulfill.
From: Virgil on 31 Aug 2006 14:49 In article <m46ef2d4qb8agbn0id2r7efu60ivv2lvcq(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > 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. Zick's 'sour grapes' rejection of what he has not the wit to understand.
From: Virgil on 31 Aug 2006 14:52 In article <v66ef29p15baruaor8s3o848vk04o8prek(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > 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. Zick again attempts to speak authoritatively about modern mathematics from the depths of his almost total ignorance of it. Proclaiming 'sour grapes' about what he cannot have.
From: Virgil on 31 Aug 2006 14:55 In article <v76ef2tt99t6kfnltkss0pjl1he46ndppf(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > >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. If one had said that there is an odd even, that would be declarative and a false declaration, bit "Let x be an even odd" is not a declaration of presumed fact but a request, which can be denied but not falsified.
From: Virgil on 31 Aug 2006 14:57
In article <5a6ef2t2gn4qosrje5q55uoihf5r76fkmc(a)4ax.com>, Lester Zick <dontbother(a)nowhere.net> wrote: > 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? He is right, in the sense that definitions are requests to let one thing represent another, and while one can refuse a request, it is silly to call a request either true or false. |