What about Steven Landsburg’s frequent crowing on the Platonicity of math and how numbers are real because we can “directly perceive them”? How does this relate to it?
While I greatly sympathize with the “Platonicity of math”, I can’t shake the idea that my reasoning about numbers isn’t any kind of direct perception, but just reasoning about an in-memory representation of a model that is ultimately based on all the other systems that behave like numbers.
I find the arguments about how not all true statements regarding the natural numbers can be inferred via first-order logic tedious. It doesn’t seem like our understanding of the natural numbers is particularly impoverished because of it.
What about Steven Landsburg’s frequent crowing on the Platonicity of math and how numbers are real because we can “directly perceive them”? How does this relate to it?
EDIT: Well, he replies here.
I was wondering what he thought about this!
While I greatly sympathize with the “Platonicity of math”, I can’t shake the idea that my reasoning about numbers isn’t any kind of direct perception, but just reasoning about an in-memory representation of a model that is ultimately based on all the other systems that behave like numbers.
I find the arguments about how not all true statements regarding the natural numbers can be inferred via first-order logic tedious. It doesn’t seem like our understanding of the natural numbers is particularly impoverished because of it.