Hi you might find this paper interesting
Blowing the Cover Off Mathematics by colin leslie dean
http://gamahucherpress.yellowgum.com/wp-content/uploads/Blowing-the-Cover-Off-Mathematics.pdf
or
scribd
mathematics —"being trapped in their own logic and contradiction
mathematics simultaneously holds two definitions that generate deep tension:
Infinity as defined by mathematicians: a never-ending process with no last element (the infinite decimal expansion is never completed and never terminates).
Infinity used as a completed object: the infinite decimal notation 0.999... is interpreted as the completed limit of that never-ending process—a single, finished number.
Dean’s critique slices through this with precision:
· You can’t define infinity as never-ending, then use it as a completed set.
· You can’t claim motion is infinitely divisible, then say we move through it.
· You can’t invoke limits to resolve paradoxes, when the very concept of a limit presupposes the contradiction.
The original definition of infinity is that it is unending, incomplete, and never fully attainable.
So when mathematics treats infinity as a completed object, or even ∞\infty in extended real analysis), it violates its own conceptual foundation
The Unspoken Truth: Real Numbers as a Construct
The equation 0.999 = 1 is more than a quirky identity—it’s a crack in the foundation. It reveals that:
· Real numbers are not “real” in any ontological sense. They’re abstract constructs built on infinite processes.
· Decimal representation is not neutral. It encodes assumptions about convergence, identity, and completeness.
· Infinity is domesticated—turned into a tool, stripped of its wildness, and made to serve precision.
This isn’t just math. It’s ideology.
The contradiction isn’t a bug. It’s a feature.
Mathematics thus tolerates "convenient fictions" or formal maneuvers that mask contradictions to maintain functional efficacy, at the cost of foundational truth
Dean Critique: Declares that if foundational contradictions cannot be resolved, the very basis of knowledge, reason, and reality "caves in" — a radical epistemic and ontological crisis akin to "epistemic extinction."
Mathematics as a Social Institution:
Mathematical practice is embedded in human culture and power structures. Foundational "inconsistencies" may be tolerated because the practical utility and social authority of mathematics outweigh metaphysical purity
The contradiction isn’t a bug. It’s a feature.
Mathematics works because it contradicts itself—and because it continues to feed prediction, control, and profit. That’s why the paradox is buried. To question it is heresy, not just against logic, but against the entire institutional structure that depends on it.
This is Dean’s real power move. He’s not just showing a flaw—he’s exposing a political technology:
· Mathematics is political.
· Truth is negotiated.
· Infinity is a suppressed rebellion.
This kind of thinking doesn’t just shift a theorem—it sets fire to the altar of rationalism. It unearths the fact that our deepest systems—scientific, philosophical, economic—depend on contradictions they refuse to acknowledge. And it invites us to ask what happens when reality breaks the rules of logic we use to contain it.
Dean’s paradox doesn’t merely break a model.
It breaks the spell.
It opens the door to revolution—not just in mathematics, but in how we understand truth, power, and reality itself.
