Re: what makes it true?

In article <1125682794.213992.12360@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
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

That's a philosophical question that people still disagree on.

One school of thought says that something is only true if we can prove
it's true.

The other school says that mathematical objects have an existence
independent of our description of them, and that statements about them
can be true or false even if we can never have a proof.

A good current example is the Continuum Hypothesis. It's known to be
independent of the standard axioms of set theory. You can call it true
or call it false, and either way you can do consistent mathematics.

Some would say that CH therefore has no definite truth value. Others
would say that we simply don't understand the real numbers well enough,
and that someday when we do, we'll see that CH is actually true or false.
.

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