Philosophy Now Forum

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

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.