@hue-man,

Can one doubt a hypothesis? Does that even make sense to say? Is not a hypothesis fallible by definition? Then what is the point of doubting what doesn't profess to be the truth to begin with?

But can one doubt 1+1=2? If I say there is lightning and rain because there are storm clouds about, in what sense can my proposition be known or doubted?

For there is a difference between geometric constructions and calculations. Namely, one learns how to use the latter by way of the answers. One is taught how to solve 1+1 by being told the answer is 2.

But suppose we used a different mathematical system, something base 4 or base 20 instead of base 10. Wouldn't the base unit added to itself still be equal to the next sequential unit? At least, if it did not, I would not call the calculus addition.

And so it is with our logical scaffolding; the logic of our language; the limits of propositions.

But surely logic is not a theory. No more than blue is a theory. Or 3.