I don't understand the comment relating the equation to the continuum hypothesis so apologies if I'm missing a fundamental part of your question, but you do say:
> I have an intuition that arithmetical statements are true or false independently of my ability to prove or disprove them.
When I ask myself the question about the meaning/truth of mathematical statements, I usually end up convinced that mathematical statements are all tautologies. Or in other words, when I say "1 + 1 = 2", what I mean to say is that "Peano => (1 + 1 = 2)", the former just be... (read more)
I don't understand the comment relating the equation to the continuum hypothesis so apologies if I'm missing a fundamental part of your question, but you do say:
> I have an intuition that arithmetical statements are true or false independently of my ability to prove or disprove them.
When I ask myself the question about the meaning/truth of mathematical statements, I usually end up convinced that mathematical statements are all tautologies. Or in other words, when I say "1 + 1 = 2", what I mean to say is that "Peano => (1 + 1 = 2)", the former just be... (read more)