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It pains me to repeatedly see debates which were decidedly answered in the 1700s by Kant in the Critique of Pure Reason--with such persuasion to even turn Hume.
by ethn 6y ago
It pains me to repeatedly see debates which were decidedly answered in the 1700s by Kant in the Critique of Pure Reason--with such persuasion to even turn Hume. Transcendental idealism is more or less non-controversial in mainstream philosophy. Especially without even a mention of idealism from the author of the article.
Math is a synthetic a priori judgment, a transcendental object.
I can only believe that this fashion of thought is from the unwarranted development of the nihilist project which came nearly 100 years later.
Bertrand Russell wrote in his historical treatment of philosophy that much of philosophy is forgotten and rediscovered throughout history. I'm skeptical of the argument but less so everyday.
>Roger Penrose, the renowned British mathematical physicist, is a staunch Platonist...
Roger Penrose states in his book "The Road To Reality" that he is a light Platonist.
- curuinor 6y agoIf you state that philosophers mostly have a consensus on anything, you'd be brutally wrong. That's not how philosophy is, or can be. Consensuses is not what they do.
- ethn 6y agoIndeed this is precisely the unwarranted nihilism I'm criticizing, where if we were to believe that consensus in philosophy is impossible, so would philosophical progress--and therefore knowledge. This is a libelous claim that all philosophers are engaging in intellectual masturbation explicitly aware that their exercises are to be of no progress. The Pyrrhonists, Diogenes, Descartes and others famously believed in this; but Kant fixes this, making the discipline of philosophy possible by proving the scope of reason.
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- btilly 6y agoIt pains me to see people who are blithely unaware of the philosophical challenges that mathematics faced from repeatedly falling apart in the 1800s and therefore believe that the real challenges were already solved before that happened. If only.
- ethn 6y agoIt's a straw man to argue that math has brought new philosophical challenges, no one has posited against that. I've only stated that math is readily understood by transcendental idealism, disproving the false dilemma presented by the author of the article. A more mature comment would be to point out an instance where there is some philosophical challenge to transcendental idealism that came from 'new mathematics'. Though I find the possibility of this to be impossible. I would expect at least the German-Idealist Godel to write about it. If you're talking about Gauss's non-Euclidean geometry, that's completely compatible with transcendental idealism, in fact Gauss took his non-euclidean geometry from the second chapter of The Critique of Pure Reason. He read Kant's passage on the triangle and the line in respect to the sum of angles obsessively.
- btilly 6y agoI'm talking the collapse of infinitesmals as a basis for Calculus, the development of a more rigorous foundation, the rise of axiomatization, debates around the validity of pure existence proofs, the failure of naive set theory, and so on. On pure existence proofs, mathematicians have generally agreed that something can be proven to exist by proof by contradiction on an infinite set. The result is that we say that it exists even though there is no way to find it, and no way to verify that you have found it if you are presented with it. Nothing in Kant's philosophy had anything useful to say about the debate about whether to accept this kind of proof.
- ethn 6y agoThanks for your reply. The first part, although mostly true (axiomatization isn't new and Kant was well aware of Euclid), is wholly irrelevant so I'll comment on the second part. None of this contradicts the synthetic apriori of mathematics, in fact Kant's critique strictly tells you that analysis IS possible and guarantees its legitimacy. I would look to Wittgenstein and Godel for that expounded application of the transcendental idealism.
- mensetmanusman 6y agoPhilosophy is definitely rediscovered by every generation. Nothing can be proven, but you can look for evidence of whether any improve people’s lives.
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