what makes it true?



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

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