In 610 BCE, Anaximander declared the fundamental principle of reality to be the boundless, the infinite. No argument established it. No observation confirmed it. It was posited, and from that positing a trajectory began that would run for 2,500 years without interruption. This book questions the assumption. It traces the commitment to infinity from Anaximander through Zeno, Aristotle, Leibniz, Cantor, and Zermelo. It identifies the grammatical mechanism by which infinity enters every logical framework since Frege. It shows that all actual mathematical practice is finite: every proof assistant is a bounded system claiming to implement an unbounded logic. It develops the ceiling resolution that makes bounded foundations coherent, demonstrates that the paradoxes dissolve and the mathematics survives, and ends by shifting the burden of justification to the defender of infinity. The forced-move argument demonstrates that when infinity is genuinely rejected, bounded finitude is the only coherent position. The bounded programme constructs the complete number chain, full analysis with constructive gains, and a unified physics on a single finite simplicial complex. The paradoxes dissolve not by clever resolution but by the absence of the objects they require. It concedes what honesty requires: the boundary between finite knowledge and infinite assertion is real, and the book states exactly where it falls. Its central claim: There is no infinity. And there is an upper bound.
