So with rational calculus on the way in about a month (confirmed

no, I already know calculus and am studying higher level stuff.

>>8836240

How can any self-respecting mathematician continue to work with the reals and infinite sets and not be bothered by the issues that Wildberger brings to the table

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You can't refute him.

>>8836262
He didn't bring the issues to the table. Everything he says about existing math has already been extensively debated.

How come any self respecting person who wants to think about the foundations of math obses over this one obscure professor's YouTube channel and ignore everything else?

Also, his concerns are only problematic for a diehard realist who thinks mathematics refers to the tangible objective reality. This is not a common position.

>>8836409
>Also, his concerns are only problematic for a diehard realist who thinks mathematics refers to the tangible objective reality.
Some mathematicians and logicians care about the legitimacy of applying mathematics to solve problems in the tangible objective reality. We know well enough that "cuz it works" is not an acceptable answer due to its circular logic.

>we don't even have a proper definition of what a set means

But drawing fucking lines on the board is legit?

>>8836416

t. brainlet

Under wildberger,
The reals are not complete
The natural numbers are bounded

Limits of sequences,continuity of functions, all of this stuff has to be redefined because even a simple sequence like 1/x is not convergent under this system.

I'm interested to see what he uses to justify these problems but I bet it'll be cringeworthy

>>8836415
Yes indeed, some are concerned with this, and with the nature of Mathematical objects. But I think pure mathematicians rarely are. You can like or dislike this, but apparently it doesn't matter for the debate.

Also, 'because it works' is perfectly fine as last explanation. I personally think it's the only reasonably one. Remember that all such thinking must end either in a circle, or in unfounded principles and undefined terms, or be an infinite regression.

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>tfw we discover the universe is a quantized cellular automata
>tfw wildberger and wolfram are both simultaneously justified after decades of being laughed at
>mfw

>>8836423
>'because it works' is perfectly fine as last explanation.
It is not because it has no support, it falls under Hume's criticism of the induction argument. Questioning does need to come to an end, but the end point needs justification as well.

>>8836433
Yes and the justification 'it works' is OK. In fact, I believe Wittgenstein made a convincing argument that it's the only one there is.

>>8836433
Also, I've always read Hume's remarks on induction as a description of why certain and universal knowledge about the external world is principally impossible, not as a prescription for solid first principles as e.g. Descartes

>>8836442
I did have Wittgenstein in mind when I wrote the last comment. He considers the matters in On Certainty, but it would be promptly dismissed by most scientist, and a good numbers of philosophers, because if we are to take Wittgenstein point then the certain concepts fall beyond the scope of true/false since we've reached a point where no knowledge nor doubt is possible. "It works" in Wittgenstein's context does not cast any meaning of truth upon the legitimacy of application of mathematics, which would render mathematics and physics a matter of faith - hence his mystical side which shows in his late tractarian phase.

>>8836432
What if it's a cellular automaton with an infinite number of cells between any two cells?

>>8836452
I don't think that accepting something like his hinge propositions amounts to declaring math and physics as a matter of faith. Quite the opposite: to me faith would me something you now you don't have rational argument for but choose to believe nonetheless. Hinge propositions is inarticulated knowledge, believed involuntarily, needed for the rational mind to work.

But anyway, my point was that only after agreeing with Wild Burger on some philosophy of mathematics, do his concerns become relevant. And in a discussion about these first principles, it would be silly to ignore the very rich history if the subject, as his fanboys seem to do.

>>8836432
even if our universe was particular then it wouldn't make wildberger any more correct, mathematics is its own universe independent of our universe that can be continuous if it wants to

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>>8836485
>3084
>transdimensionally travelling through wildberger-wolfram rational quandrance fields
>mfw normies still think "mathematics is its own universe"

>>8836238
>So with rational calculus on the way in about a month (confirmed by Wildberger himself),
I was happy to hear this