Banach-Tarski. Hilbert's Hotel. Thomson's Lamp. Zeno's Achilles. Russell's set. The ultraviolet catastrophe. 75 named paradoxes from mathematics, logic, physics, and philosophy — each stated, diagnosed, and classified. Four mechanisms. One axiom. Most of them simply cannot be stated when completed infinity is removed.
Note. This is a survey and working paper. It is intended as a demonstration of what happens to a broad class of named paradoxes when the Axiom of Infinity is replaced by the Axiom of Finite Bounds. The classifications are the author's assessment, made in good faith, and are open to challenge. Individual entries may be revised as the analysis deepens. The paper does not claim to have resolved any paradox — it claims to have shown that most of them depend on a specific foundational assumption, and that a different assumption dissolves them. The seven that survive point to genuine open problems — in self-reference, epistemology, ethics, and decision theory — that may require new tools beyond what BST or any current foundational system provides.
The Axiom of Finite Bounds replaces the Axiom of Infinity with a single bound: every set is finite. The paradoxes catalogued here all depend — in whole or in part — on the assumption that completed infinite sets, processes, or totalities exist. Remove the assumption. Watch what happens.
What happens is not a collection of cheap victories. Many of these paradoxes are deep. Their dissolution reveals what they were actually about once the infinite scaffolding is removed. The mathematical content survives. The pathology does not.
Completed infinities do not exist in BST. Every dissolution traced in this paper follows from that single fact, expressed through one of four mechanisms.
Dissolved means it cannot be stated. Tamed means the pathology disappears. Transformed means it becomes a different question. Preserved means it survives — because it was never about infinity.
Each of these has generated decades of literature. Each depends on a single assumption.
A paper that dissolved every paradox would be dishonest. These 7 survive because they were never about infinity. They are about self-reference, epistemology, ethics, and decision theory. Their survival confirms that BST is dissolving artefacts, not sweeping real problems under the rug.
"The paradoxes are not inevitable features of mathematical reality. They are artefacts of a foundational choice. A different choice dissolves them." — The Paradox Dividend, 2026
Nine sections. 75 paradoxes. Each one stated in its classical form, diagnosed, and classified. From Zeno through Banach-Tarski through the black hole information paradox. Four mechanisms, one axiom, and an honest accounting of what survives.
"The result is not a weakening of mathematics. It is a clarification of what mathematics is actually doing." — The Paradox Dividend, 2026