悖论简史英文版.doc

1
A BRIEF HISTORY
of the
Paradox
2
This page intentionally left blank
3
ONE
Anent yesterday, -2 the day before yesterday, and so on. For us, the fact that there are infinitely many numbers before 0 does not raise a mystery about how 0 can be reached. Why should an infinite past be any more puzzling than the infinite sequence of negative integers?
This mathematical model seems apt for an infinite future. +1 could be tomorrow, +2 could represent the day after tomorrow, and so on. You can imagine encountering an immortal destined to count forever. Each positive integer will be counted by this number god.
5
ANAXIMANDER AND THE RIDDLE OF ORIGIN 3
But negative numbers are not enough to solve the paradox of origin. There is a “something from nothing” feel about the claim to have recited infinitely many digits.
WHAT IS A PARADOX?
When discussing whether the barbarians originated philosophy, Diogenes Laertius reports, “As to the Gymnosophists and Druids we are told that they uttered their philosophy in riddles . . . “ I take paradoxes to be a species of riddle. The oldest philosophical questions evolved from folklore and show vestiges of the verbal games that generated them.
Seduction riddles are constructed to make a bad answer appear as a good answer. How much dirt is in a hole two meters wide, two meters long, and two meters deep? This question entices us to answer, eight cubic meters of dirt. The riddler then reminds us that no dirt is in a hole.
Mystery riddles, in contrast, appear to have no answer. One way to achieve this aura of insolubility is by describing an object in an apparently contradictory way. As a boy, Anaximander must have been asked the ancient Greek riddle, “What has a mouth but never eats, a bed but never sleeps?” (Answer: A river.) Literary riddles elaborate the genres found in folklore. Anaximander probably learned of the riddle of the Sphinx from Hesiod’s Theogony. We know it best from