March 26, 2023
infinite regress of arguments, of definitions, of causes, axioms, inductive laws, primitive concepts, origins, Münchhausen Trilemma, Agrippan Trilemma, Theorem of Formal Dependence, Theorem of the First Element.
Paper 8 of this series of papers on discrete cosmology examines the Aristotelian infinite regress of arguments, and extends it to definitions and causes. Infinite regress then becomes a very serious limitation of human knowledge, much more serious than Gödel's famous incompleteness theorems. But at the same time, and also considering the inconsistency of the actual infinity and the infinite divisibility, it suggests the way we should go to explain the physical world by clearly setting out what can and cannot be explained in formal terms. In particular, it is proved here that any history either has an initial instant or it is inconsistent.