A project examining the foundational assumptions embedded in mathematics, physics, and thought itself — and the consequences of taking them seriously.
Explore the Topics →Every system of thought begins somewhere. Those starting points — often unstated, rarely examined — determine not just what conclusions are reachable, but which questions can even be asked. Shaky Foundation is an attempt to go back before the beginning and look at the ground itself.
This is not a project of demolition. It is a project of honest examination. Some foundations, examined closely, turn out to be solid. Others turn out to be declarations that calcified into axioms — assumed because they were useful, forgotten because they were old, never questioned because they were everywhere.
"The assumption did not become more justified by becoming more precise. It became harder to question."
The Axiom of Infinity was declared, not proved. What happens when you negate it on its own epistemic terms — and follow the consequences through ZFC, physics, and 2,600 years of thought?
A companion to the Axiom of Finite Bounds. Ten Parts from classical mechanics through the Standard Model — every partition function a finite sum, every spectrum computable, every claim grounded in experiment.
75 named paradoxes from mathematics, logic, physics, and philosophy — each stated, diagnosed, and classified. Banach-Tarski, Hilbert's Hotel, Zeno, Thomson's Lamp. Four mechanisms. One axiom. Most cannot even be stated.
Pain still hurts. The self still coheres. What dissolves is not the phenomena but the unnecessary category imposed on top of them. "Consciousness" does not name a natural kind — and retiring it costs nothing that was real.
There is no public, cross-cultural account of what AI is actually being aligned to. This investigation builds one from the ground up — from human rights conventions, environmental law, animal welfare standards, and the literature on AI moral consideration.
"Brilliant mathematicians spend careers on problems that exist only as artifacts of the infinite assumption — problems that would not arise, and do not need solving, if the foundational postulate were different." — The Axiom of Finite Bounds, Working Paper 2026