From: Lester Zick on
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
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
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
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
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~~
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