Every system of thought begins with assumptions. Some of those assumptions are explicit — clearly stated postulates that a reader can inspect and dispute. Most are not. They arrive embedded in notation, baked into definitions, invisible in the grammar of a discipline. They are not argued for because they are not recognized as assumptions at all.
Shaky Foundation is a personal project dedicated to finding those assumptions, making them explicit, and examining them honestly. The goal is not to tear down what has been built. It is to know what the building is actually standing on — and, where the ground turns out to be less solid than it looked, to ask whether a better foundation can be found.
The method is simple: take a foundational assumption seriously enough to examine it on its own terms. Ask what justification exists for it. Then ask what happens when you try a different starting point.
The first topic is infinity. The Axiom of Infinity — the formal assertion that completed infinite sets exist — was introduced in 1908 as an unargued postulate. It has never been demonstrated true of anything in physical reality. The working paper on this site proposes a replacement: the Axiom of Finite Bounds, and traces its consequences through mathematics, physics, and intellectual history.
Subsequent topics are planned. The questions are large, the answers are uncertain, and the project makes no claim to finality. It is an attempt at honest examination, conducted in public, with working papers made freely available.