Abstract:
The Greek philosopher Zeno presented for the first time in history the problems
derived from assuming (or rejecting) the infinite divisibility of space and time.
He showed that knowledge of the physical world is dependent on what axioms
concerning reality are admitted: either space ant time are atomic or dividable ad
infinitum. Aristotle, differential calculus, Einstein’s relativity, nonstandard
mathematics, and modern philosophers such as Heidegger, all tried to cope with
this problem. However, their “solutions” always imply adding controversial new
axioms. Thus, a fundamental aspect of how humans understand Nature or,
equivalently, the problem of determining which of the possible but indispensable
axioms should be given pre-eminence, is reflected in the study of this famous
paradox. Finally, a recently characterised subset of the real numbers called
“Lexicons” adds a surprising twist to this notorious paradox.
