Schopenhauer gets a sad/10 from me. Very interesting stuff, but his distaste for math displays both a misunderstanding of mathematics (in my view) and a clear underlying...unreasonable judgment of mathematics lol.
I suppose where I think he really goes wrong is in thinking of the axiomatization of math as enforcing the PSR? You can only have correct intuition about mathematical objects after spending a ton of hours learning about all of the weird nonsense that can happen. It can't just be "well this feels right so it is", which seems to be what Schopenhauer argues for. I've put together a list at the bottom of YouTube videos which should be accessible to most anyone that display some deeply *unintuitive but true* facts about math. The last two in particular are geometric in nature, so Schopenhauer doesn't have any excuses for those objects being "wholly the realm of the PSR" or whatever.
Thanks for adding these videos! Schopenhauer is a really interesting guy to me. I don't think his view of reality accords with what's real, but I find his system to be an impressive feat. He says he's committed to articulating only one idea and carrying it through his entire book, and what's intriguing about his view on math is that it forces him to say that all of this really could be intuitive (since intuition is the best/true way of knowing). He has this convenient escape valve of assuming everyone who disagrees with him just lacks genius, of course, and I think that's where he'd go here.
In the end, I don't think he's right about math or most things for that matter, but he's such a fun thinker to wrestle with (in my opinion).
Mathematics operates in the same foundational way as philosophy, premises and reasoning both evaluated for their coherence with reality based on intuition. It's just that the premises are of a certain sort and the reasoning a particular flavor. His rejection of mathematics seems to instead be a cope for not being able to handle abstractions. And since all is representation except for the genius who pierces the veil to The Force (oh, I'm sorry The Will), either I'm the genius, he's the genius, or neither of us are geniuses. But we also have no way of evaluating that either. Seems like a real solid system that is virtuous instead of vicious. No way it eats itself at all.
Although I have a minor in mathematics, I don't particularly like math. But the reason is practical: mathematics (especially higher math) is generally taught without any reference to application. They never really explain in class why you want to do differentials or integrations, they just teach how to do it.
Nevertheless, I came to your substack to comment about your recent video on how Anglican denominational apologetics is losing online. I just thought, well of course it is, because how can you convince Catholics to join the Anglican church when you can't even tell them they're probably gonna be damned for worshiping Mary (which unless they are convicted of they will continue to believe their church is the "one true church" and thus never consider Anglican as viable at all). The constant trajectory towards papism in modern Anglicanism, and your own personal distaste for the truth that Catholics do verily worship Mary (for her supposed ability to save from purgatory, of course) means your denominational apologetics are doomed to accomplish nothing but making you look silly.
And when you try to convince Baptists to accept infant baptism, transubstantiation, calling Mary "Mother of God", and apostolic succession, you either fail because they say "bro, that's papism" and then end up being against Anglicans (especially if they watch your channel in particular and see that you say the reformation has an expiration date and we must go back under the pope some day), OR you convince the biblically illiterate among them of your Romish doctrines and they say, "Why not just bypass Anglican and become a full blown Roman Catholic?" so your denominational apologetics for Anglicanism fails there too, as they skip you and follow the papist track of your argument to full papism.
Yeah its funny how he wants to say all Protestants are losing, when its just that he himself is a loser Anglo-Papist who wants to trick Protestants to going back under the Pope.
"The genius always interprets his own limitations as universal characteristics." Fixed it.
Two sweeping refutations:
1) Leibniz
2) This claim is simply nonsensical: "In other words, we already know intuitively what Euclid labors to demonstrate empirically." You might as well say, "The artist already knows intuitively all about paint colors, so we have no such need for specialists who understand the methods and compounds used in making paint." No one "intuitively knows" the Pythagorean theorem.
Schopenhauer gets a sad/10 from me. Very interesting stuff, but his distaste for math displays both a misunderstanding of mathematics (in my view) and a clear underlying...unreasonable judgment of mathematics lol.
I suppose where I think he really goes wrong is in thinking of the axiomatization of math as enforcing the PSR? You can only have correct intuition about mathematical objects after spending a ton of hours learning about all of the weird nonsense that can happen. It can't just be "well this feels right so it is", which seems to be what Schopenhauer argues for. I've put together a list at the bottom of YouTube videos which should be accessible to most anyone that display some deeply *unintuitive but true* facts about math. The last two in particular are geometric in nature, so Schopenhauer doesn't have any excuses for those objects being "wholly the realm of the PSR" or whatever.
https://www.youtube.com/watch?v=uvMGZb0Suyc
https://www.youtube.com/watch?v=n7GYYerlQWs
https://www.youtube.com/watch?v=wKV0GYvR2X8
Thanks for adding these videos! Schopenhauer is a really interesting guy to me. I don't think his view of reality accords with what's real, but I find his system to be an impressive feat. He says he's committed to articulating only one idea and carrying it through his entire book, and what's intriguing about his view on math is that it forces him to say that all of this really could be intuitive (since intuition is the best/true way of knowing). He has this convenient escape valve of assuming everyone who disagrees with him just lacks genius, of course, and I think that's where he'd go here.
In the end, I don't think he's right about math or most things for that matter, but he's such a fun thinker to wrestle with (in my opinion).
Ok, just watched the last video and my brain is fried. That's so interesting.
Yeah math is full of wild and wacky things like that, it’s why I love math so much
Mathematics operates in the same foundational way as philosophy, premises and reasoning both evaluated for their coherence with reality based on intuition. It's just that the premises are of a certain sort and the reasoning a particular flavor. His rejection of mathematics seems to instead be a cope for not being able to handle abstractions. And since all is representation except for the genius who pierces the veil to The Force (oh, I'm sorry The Will), either I'm the genius, he's the genius, or neither of us are geniuses. But we also have no way of evaluating that either. Seems like a real solid system that is virtuous instead of vicious. No way it eats itself at all.
Sorry Schopenhauer, the representation of you I intuit is of a madman raving
Although I have a minor in mathematics, I don't particularly like math. But the reason is practical: mathematics (especially higher math) is generally taught without any reference to application. They never really explain in class why you want to do differentials or integrations, they just teach how to do it.
Nevertheless, I came to your substack to comment about your recent video on how Anglican denominational apologetics is losing online. I just thought, well of course it is, because how can you convince Catholics to join the Anglican church when you can't even tell them they're probably gonna be damned for worshiping Mary (which unless they are convicted of they will continue to believe their church is the "one true church" and thus never consider Anglican as viable at all). The constant trajectory towards papism in modern Anglicanism, and your own personal distaste for the truth that Catholics do verily worship Mary (for her supposed ability to save from purgatory, of course) means your denominational apologetics are doomed to accomplish nothing but making you look silly.
And when you try to convince Baptists to accept infant baptism, transubstantiation, calling Mary "Mother of God", and apostolic succession, you either fail because they say "bro, that's papism" and then end up being against Anglicans (especially if they watch your channel in particular and see that you say the reformation has an expiration date and we must go back under the pope some day), OR you convince the biblically illiterate among them of your Romish doctrines and they say, "Why not just bypass Anglican and become a full blown Roman Catholic?" so your denominational apologetics for Anglicanism fails there too, as they skip you and follow the papist track of your argument to full papism.
Yeah its funny how he wants to say all Protestants are losing, when its just that he himself is a loser Anglo-Papist who wants to trick Protestants to going back under the Pope.
Yeah, Austin's a joke and probably gay.
“I’ve recently signed up to spend a semester studying Euclid. Prayers appreciated.”
I’ve got you covered.
"The genius always interprets his own limitations as universal characteristics." Fixed it.
Two sweeping refutations:
1) Leibniz
2) This claim is simply nonsensical: "In other words, we already know intuitively what Euclid labors to demonstrate empirically." You might as well say, "The artist already knows intuitively all about paint colors, so we have no such need for specialists who understand the methods and compounds used in making paint." No one "intuitively knows" the Pythagorean theorem.