@19:00 I'd count myself a platonist and Fregeian, but the idea here is that arithmetic truths certainly do have something to do with the way people think about quantity, but that this is not a foundation for mathematics. It is a precursor. You get dirty and beaten up, then you learn the rules of Rugby properly. (OK, I'm a Kiwi, so cannot resist the our religion analogy.) Once you are done piddling around in the baby waters of experience and empiricism your thought matures then you realize mathematics is indeed properly independent of our minds. You also don't have to give up on the notion we use our minds to probe the structures of mathematics. There is a distinction between what mathematics *_is_* and how we go about exploring the thing. By the way, this was one of the best intros to Frege on youtube. Patricia kept it simple but no simpler than necessary.
@19:00 I'd count myself a platonist and Fregeian, but the idea here is that arithmetic truths certainly do have something to do with the way people think about quantity, but that this is not a foundation for mathematics. It is a precursor. You get dirty and beaten up, then you learn the rules of Rugby properly. (OK, I'm a Kiwi, so cannot resist the our religion analogy.) Once you are done piddling around in the baby waters of experience and empiricism your thought matures then you realize mathematics is indeed properly independent of our minds. You also don't have to give up on the notion we use our minds to probe the structures of mathematics. There is a distinction between what mathematics *_is_* and how we go about exploring the thing.
By the way, this was one of the best intros to Frege on youtube. Patricia kept it simple but no simpler than necessary.
huh, I guess Patricia said this more or less @23:00. :)