Re: Am I a crank?

On Thu, 31 Aug 2006 12:20:55 -0600, Virgil <virgil@xxxxxxxxxxx> wrote:

In article <1157024892.614341.149030@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
schoenfeld.one@xxxxxxxxx wrote:

Lester Zick wrote:
On 30 Aug 2006 05:01:52 -0700, schoenfeld.one@xxxxxxxxx wrote:


Han de Bruijn wrote:
schoenfeld.one@xxxxxxxxx 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.

Arbiter dicta are often difficult to fulfill but we do the best we can
anyway.

~v~~
.

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