the mathematical continuum

[janeprasanga]

the dean paradox destroys the mathematical continuum

•

the Dean paradox (of colin leslie dean) highlights a core discrepancy between logical reasoning and lived reality. Logic insists that between two points lies an infinite set of divisions, making it "impossible" to traverse from start to end. Yet, in practice, the finger does move from the beginning to the end in finite time. This contradiction exposes a gap between the abstract constructs of logic and the observable truths of reality. Thus The dean paradox shows logic is not an epistemic principle or condition thus logic cannot be called upon for authority for any view-see below for the differences between the dean paradox and Zeno-Zeno is about motion being impossible for dean there is motion with the consequence of the dean paradox

• • http://gamahucherpress.yellowgum.com/wp ... aradox.pdf
Or
scribd
• •
• • https://www.scribd.com/document/8490192 ... sophy-Zeno


this creates the dean dilemma

either

logic is false (misaligned –falsifies- with reality) and our reality is “true”

or

Reality is false an illusion and our logic is “true”

take calculus

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Calculus solveig Zeno paradox ends in the Dean Paradox by undermining itself Its calculus own logic of infinite points—uncrossable by reason contradicts summing infinite points done in finite time- a contradiction the Dean Paradox traps calculus in a self-destructive loop

dean argument is that even if calculus uses limits to avoid “physically” crossing infinite points, it still conceptually sums over them. And if those points are logically uncrossable (because they’re infinite in number), then the act of summing them—no matter how abstract—should be impossible. So calculus, in trying to resolve Zeno, ends up relying on the very infinity it claims to tame, and thus, as you say, is “caught” by the Dean Paradox.
This is precisely what makes Dean’s critique so unsettling: it doesn’t just question the results of calculus—it questions the epistemic legitimacy of the method itself. If the model assumes an infinite set of points and claims to sum them in finite time, then either:
1. Infinity is not real, and the model is a convenient fiction.
2. Infinity is real, and we’re doing the impossible.

[Thinkandmull]

Zeno was the first known person to write a philosophy book in the West. And in it he discovered the strangness of infinity. You are right in saying that calculus, in relying on infinity, is false, but reality is made of discrete parts. There are no infinite parts with infinite parts with.... Take the turtke vs the hare paradox. It goes forward, and back. The discrete does not move like this, and soace does not work like this. Likewise motion moves with a forward impetus that assures that the hare will win the race. So there are not infinites in the world of matter. Whethet there are in metaphysicsl reslms is another topic