Re: what makes it true?

lhlhsand@xxxxxxxxxxx wrote:
> Are mathematical statements considered true (or false) independent of
> whether or not they've been proven? If so, then what exactly is it
> that makes them true (or false), if not the proof? I know it's kind of
> a weird question but it makes me curious. Like for instance take the
> statement "There are exactly 4 primes between 1 and 10." I know this
> is true because if I divide each number between 1 and 10 I find that
> only 2, 3, 5, and 7 don't have integral factors other than 1 and
> themselves. And by resorting to the definition of prime number, I
> conclude that the statement is true. But isn't this method in itself a
> kind of "proof"? I'm confused!
>
> L

I personally call it proof by demonstration. It is perfectly valid if
you have used valid procedures, and you have. Mathematicians do it all
the time. They start doing it with quadratic equations by demostrating
the two roots, equal or distinct, and keep on doing it without too much
explanation. There is a saying in my language that can be translated to
the modern context as, "You do not need a mirror to check your
wrist-watch". I do have an anecdote about it but some folks will not
like it.
Muhammad Zafrullah

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