Lmao
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Replying to @AnarchicEvolist
I suppose Guenon is against the infinite at a conceptual level? Differential calculus is formally equivalent to an algebraic theory (nonstandard analysis) if one accepts the real numbers, and a real number is just an infinite set of rational numbers (Dedekind cuts).
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Replying to @ungeometer @AnarchicEvolist
Thus the only objection I can see is to sets with infinitely many elements (and then one can't even accept that the natural numbers exist as a set). I know mathematicians had long debates about this stuff 100 years ago. It all seemed like autism-overdrive to me.
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Replying to @ungeometer
Guenon argues that "infinite" is not a quality you can ascribe to anything, including not to a set. Basically the Infinite is that which is absolutely not limited by anything, thus it can never be ascribed a certain determination, nor be used in this way, e.g an "infinite number"
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Replying to @AnarchicEvolist
I don't think I disagree with anything there. Mathematicians don't assign an 'infinite number' to an infinite set as a size. Sets are infinite by virtue of the fact that they aren't in bijective correspondence with any finite set, and that's it.
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Replying to @ungeometer
Understood, but Guénon would say that the concept of an "infinite set" is a contradiction in terms, because infinite means not limited, and by saying it is a set you are limiting it to a specific kind of thing. I suppose he would propose using "indefinite set" instead
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Replying to @AnarchicEvolist
So what would Guénon say about the set of natural numbers? That it's not proper to conceptualize it in totality (because that would delimit it in some sense)?
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Replying to @ungeometer
"The finite, even if capable of indefinite extension, is always strictly nil with respect to the Infinite" I think Guénon would affirm the conceptualising of the set in its totality, able of indefinite extension, while also affirming its limit, thus not being an absolute totality
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Replying to @AnarchicEvolist
To me, being capable of conceptualizing the natural numbers in their totality is sufficient license to begin the logical inquiries that constitute mathematics with them, so perhaps this is where Guénon and I part company (a bit unsure though).
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Maybe so, I must admit that I may not have done a perfect job of representing his position accurately, so if you wish to get it from the source I would recommend reading the first chapter of his book on the subject, it deals with the principles if I recall correctly
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