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Comment by svat | Hacker News Reader

This is from the Stanford Encyclopedia of Philosophy; see also the corresponding article in the Internet Encyclopedia of Philosophy: https://iep.utm.edu/mathplat/

Also, frequently quoted (by me at least): from an interview with Yuri Manin (http://www.ams.org/notices/200910/rtx091001268p.pdf):

> I must explain to you how I imagine mathematics. I am an emotional Platonist (not a rational one: there are no rational arguments in favor of Platonism). Somehow or other, for me mathematical research is a discovery, not an invention. I imagine for myself a great castle, or something like that, and you gradually start seeing its contours through the deep mist, and begin to investigate something.

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I wonder why he thinks there are no rational arguments in favor of Platonism. I think there have been a lot of convincing ones over the last few thousand years.

You may want to review Russell's A History of Western Philosophy. Bertrand pretty effectively shredded most of the fantastical precepts Platonism relies on in his analysis in the chapter on Theory of Ideas (15 in the Audible audio book).

The basic gist is that the basis of Platonism is metaphysical more than logical. Mysticism is the key bedrock of the form of the Good. Plato's ideal of Ultimate Truth is self-contradictory when reconciled with Geometry. Plato's lack of subtlety with syntax causes a lot of his arguments to fall flat, such as "beauty is beautiful." The analysis of the Parmenides is beautiful, highly recommended.

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Although he may not be convinced by the rational arguments, I took the quote as mostly expressing the emotional/irrational draw of it; the dismissal as hyperbole to support that as a rhetorical device.

Yeah, the physicist Tegmark has arguments for a mathematical multiverse. Sean Carole has a podcast interviewing Justin Clark-Doane who argues that at least arithmetic must be real if the world is to be understood as consistent.

https://www.preposterousuniverse.com/podcast/2021/03/08/137-...

Flat Earth is sort of consistent somewhere too. But platonism isn't an idea on the level "looks like that somewhere", it aspires to be a deeper fundamental view of reality.

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