When “pure thought” tells you that 1 + 1 = 2, “independently of any experience or observation”, you are, in effect, observing your own brain as evidence.
I mean, yeah? You can still do that in your armchair, without looking at anything outside of yourself. Mathematical facts are indeed “discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe,” if you modify the statement a little to say “anywhere else existent” in order to acknowledge that the operation of thought indeed exists in the universe. Do mathematical facts exist independently of the universe? Maybe, maybe not, it probably depends what you mean by “exist” and it doesn’t really matter to anyone since either way, you can’t discover any mathematical facts without using your brain, which is in the universe. So there’s no observable difference between whether Platonic math exists or not.
“free will” is a useful concept which should be kept, even though it has been used to refer to nonsensical things. Just because one can’t will what he wills, doesn’t mean we shouldn’t be able to talk about willing what you do. Similarly, just because you can’t get knowledge without thinking, doesn’t mean we shouldn’t be able to use “a priori knowledge” to talk about getting knowledge without looking.
I mean, yeah? You can still do that in your armchair, without looking at anything outside of yourself. Mathematical facts are indeed “discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe,” if you modify the statement a little to say “anywhere else existent” in order to acknowledge that the operation of thought indeed exists in the universe. Do mathematical facts exist independently of the universe? Maybe, maybe not, it probably depends what you mean by “exist” and it doesn’t really matter to anyone since either way, you can’t discover any mathematical facts without using your brain, which is in the universe. So there’s no observable difference between whether Platonic math exists or not.
“free will” is a useful concept which should be kept, even though it has been used to refer to nonsensical things. Just because one can’t will what he wills, doesn’t mean we shouldn’t be able to talk about willing what you do. Similarly, just because you can’t get knowledge without thinking, doesn’t mean we shouldn’t be able to use “a priori knowledge” to talk about getting knowledge without looking.