Personally, I think that pointing out the self defeating nature of skepticism in the way it’s described here is indeed a good argument against it
“This statement is a false”—is a paradox.
“This statement is unprovable”—is not.
We can say that both are self-defeating if we want to, but that doesn’t really change anything.
We can say with confidence that they are curved and that our experience of them depends on our velocity and position.
Let’s just say that Kant didn’t see that coming. He essentially made a very confident prediction about the nature of space an time that was later shown wrong.
This seems unfair to philosophers because the very nature of their subject matter precludes, or at least makes far more difficult, the precise articulation of what they’re talking about in a way which might allow for mathematical levels of rigour.
I think this is exactly fair. It’s true that philosophy has some excusable complications preventing it from achieving the same rigor as math. But then one shouldn’t claim this rigor for philosophy and be very careful when comparing philosophy to math.
This presupposes that mathematics is not the real world. If we lived in a Tegmark-like platonic mathematical universe, and knew this for certain, then mathematics could indeed prove things about the real, physical world.
I don’t need to presuppose that some elaborate theory like platonic mathematical universe is wrong, when I have a simpler account for it’s evidence.
Even if we don’t, I would still consider mathematics to be real, just not physical, and therefore to be possible to use to prove things about the real world. I object to the use of the word ‘merely’ here, even if it wouldn’t be possible to prove we lived in a mathematical universe if we did.
And what exactly do you mean by real here?
I think it’s fair for me to point out that the fact that mathematics requires the assumption of axioms does not show that it can’t provide justification for knowledge, because the axioms themselves can be included in statements about what follows from the axioms.
It means that it’s conditional knowledge, exactly what I’m talking about.
“This statement is a false”—is a paradox.
“This statement is unprovable”—is not.
We can say that both are self-defeating if we want to, but that doesn’t really change anything.
Let’s just say that Kant didn’t see that coming. He essentially made a very confident prediction about the nature of space an time that was later shown wrong.
I think this is exactly fair. It’s true that philosophy has some excusable complications preventing it from achieving the same rigor as math. But then one shouldn’t claim this rigor for philosophy and be very careful when comparing philosophy to math.
I don’t need to presuppose that some elaborate theory like platonic mathematical universe is wrong, when I have a simpler account for it’s evidence.
And what exactly do you mean by real here?
It means that it’s conditional knowledge, exactly what I’m talking about.
Comment withdrawn.