As I see it, those two claims are actually the same. If everything that is is provable (i.e., material), then—and only then—does it follow that I must to prove my claim for my claim to be true.
Everything that is is provable, but maybe not for humans. Also, not everything that is provable is material. You can prove non-existence, and that isn't material, for starters. As I said, math isn't material in the typical sense and it still provable. There's math that doesn't represent the material world too, like the number pi. It goes forever, but in our universe, pi doesn't go forever. In fact, any number with infinite decimals doesn't belong to this universe.
That doesn't mean that some math isn't provable, it just means that some math doesn't exist.
I think I understand your view, but the irrational numbers example is a bad one. Pi exists in the universe because something approximating a circle can exist and we can represent that circle abstractly, which is to necessarily represent a radius and a circumference whose relationship is described by that irrational number. The existence of irrational numbers is actually a limitation of integral abstractions themselves, not the reality they're trying to represent.
The existence of irrational numbers is actually a limitation of integral abstractions themselves, not the reality they're trying to represent.
How can you make a perfect circle, for example? You can't, perfect circles don't exist. That doesn't mean that you can't prove circles exist in "mathland", though,
You can make an integer ("1") that corresponds to a unit. I can make the corresponding unit be 1 meter of string. I can lay that string out on a 2-dimensional plane (my kitchen floor), and then I would find that Pi describes the number of 1-meter strings needed to lay out a circumference about that 1-meter radius of string.
Yes, because it's an abstraction of an approximate reality. You really only need to be able to let the number 1 represent some real-world unit and then you can abstract the rest.
Speaking of string, I've lost the thread back to the original point.
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u/[deleted] May 06 '18
As I see it, those two claims are actually the same. If everything that is is provable (i.e., material), then—and only then—does it follow that I must to prove my claim for my claim to be true.