you might find this interesting proven Kant’s antinomies unsolvable-due to the dean paradox-of colin leslie dean
Dean’s paradox highlights a core discrepancybetween logical reasoning and lived reality. Logic insists that between two points lies an infinite set ofdivisions, 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 andthe observable truths of reality.The dean paradox doesn’t just question philosophy, mathematics, or science—it kills their authorityoutright, forcing us into an intellectual void where no structured system holds absolute truth. If Nietzsche’s “God is dead” crisis left us searching for new values, Dean’s paradox leaves us with no way to think— confronting a universe where no stable framework exists at all
Example
Kant’s Antinomies and TheirResolution
Kant’s second antinomy posits a contradiction:
1. Thesis:All composite things are made of simple, indivisible parts.
2. Antithesis:Nothing is simple; everything is infinitely divisible.
Kant resolved this by distinguishing between phenomena(appearances, governed by human categories) and noumena (things-in-themselves,unknowable).
For phenomena, infinite divisibility applies potentiallybut not actually-a conceptual compromise
The Dean Paradox’s Challenge
The Dean Paradox amplifies Zeno’s motion paradox but with abiological twist:·
Logical Abstraction: Infinitedivisibility implies traversing infinite points to move from A to B (logicallyimpossible).·
Empirical Reality: Motionoccurs in finite time (e.g., moving a finger across a line)
This creates an unsolvable antinomy:1. Thesis:Logic demands infinite steps, making motion impossible.2. Antithesis:Empirical observation confirms motion happens.
Unlike Zeno’s paradox (resolved by calculus), the Dean Paradoxargues this gap is irreducible because human cognition(“monkey-brain” biology) cannot reconcile abstract logic with sensoryexperience- Motion occurs in finite time (e.g., moving a finger across a line)but crossing an infinite number of points
Unsolvable Antinomies: Kant’s resolution—that divisibility isphenomenal, not noumenal—relies on logic’s a priori categories (space, time)structuring experience. The dean paradox’s proof, by falsifying infinitedivisibility empirically, shows these categories misalign with reality, asmotion defies logical infinity. This makes Kant’s antinomies unsolvable, because reason’s framework—whether positing finite or infinitedivisibility—fails when logic itself is flawed, collapsing hisphenomena-noumena distinction
Implications for PhilosophyPhilosophy’s Collapse:
The paradox’s proof kills rational systems, as argued. Kant’s transcendental idealism, relying on logic’s categories, crumbles when infinite divisibility fails empirically, rendering his antinomies—meant to limit reason’s metaphysical overreach—unresolvable, echoing “philosophy is dead”.
Other systems (Hume’s empiricism, Plato’s metaphysics) also fall, as logic’s “painted veil”
publisher-free
http://gamahucherpress.yellowgum.com/wp-content/uploads/The-dean-paradox.pdf
Scribd
https://www.scribd.com/document/849019262/The-Dean-Paradox-science-mathematics-philosophy-Zeno
