MOTION MOUNTAIN

286 9 concepts, lies and patterns of nature
Ref. 259
we chose an increase in precision as a guide for our mountain ascent: we want to avoid
lies completely. (And, besides, we do not look for money in this trip either.) By the way,
the same method is used in criminal trials. To discover the truth, investigators typically
ask all the witnesses a large number of questions, allowing as many details as possible
come to light. When sufficient details are collected, and the precision is high enough, the
situation becomes clear. Telling ‘good’ lies is much more difficult than telling the truth;
it requires an excellent imagination.
Democritus”
“Truthisanabyss.
“Toteachsuperstitions astruth isamostterrible
thing.
Hypatia ofAlexandria (c.355–415)”
CharlesPeirce”
“[Absolutetruth:] Itiswhatscientistssayitis
whentheycometotheendoftheirlabors.
Is this statement true? – A bit about nonsense
“Therearethree typesofpeople:thosewho
believeinFatherChristmas,thosewhodonot
believeinFatherChristmas,andthosewhoare
FatherChristmas.
Anonymous” “Truthisarhetorical concept.
PaulFeyerabend”
Not all statements can be categorized as true or false.There is a third option: statements
can simply makenosense.There are even such statements in mathematics, where they are
called undecidable. However, ‘undecidable’ and ‘nonsense’ is really the same thing! An
example is the continuum hypothesis.This hypothesis is undecidable because it makes
a statement that depends on the precise meaning of the term ‘set’; in standard mathematical
usagethe term is not defined sufficiently precisely so that a truth value can be
assigned to the continuum hypothesis. In short, statements can be undecidable because
the concepts contained in them are not sharply defined.
Statements can also be undecidable for other reasons. Phrases such as ‘This statementisnottrue’
illustrate thesituation.Thephraseisundecidable becauseitreferences
to itself. Kurt Gödel* has even devised a general way of constructing such undecidable
statements in the domain of logic and mathematics.The different variations of theseselfreferential
statements, especially popular both in the field of logic and computer science,
have captured a large public.** Similarly undecidable statements can be constructed with
*KurtGödel(b.1906Brünn,d.1978Princeton),famouslogician.
** A general introduction is given in the beautiful books by Raymond Smullyan: Satan, Cantor and
InfinityandOtherMind-bogglingPuzzles,Knopf,1992;WhatistheNameofThisBook?TheRiddleofDracula
and Other Logical Puzzles, Touchstone, 1986, and The Lady or the Tiger? And Other Puzzles, Times Books,
1982. Also definitions can have no content, such as David Hilbert’s ‘smallest number that has not been
mentioned this century’ or ‘the smallest sequence of numbers that is described by more signs than this
sentence’.
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net