I’ll emphasize with the following analogy: you need to observe the sun to know of it. However, you can nevertheless be certain—as certain as you are of anything at all—that the sun exists independently of observation. You need to define the Peano axioms and observe the deductions that lead to the tautologies to know of them, but they are mathematically true independent of your observation.
I’ll emphasize with the following analogy: you need to observe the sun to know of it. However, you can nevertheless be certain—as certain as you are of anything at all—that the sun exists independently of observation. You need to define the Peano axioms and observe the deductions that lead to the tautologies to know of them, but they are mathematically true independent of your observation.