MOTION MOUNTAIN

concepts, lies and patterns of nature 287
Ref. 260
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Challenge 285 s
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Challenge 284 s
Challenge 286 s
terms such as ‘calculable’, ‘provable’ and ‘deducible’.
In fact, self-referential statements are undecidable because they are meaningless. If
theusual definitionof ‘true’, namelycorrespondingtofacts,issubstitutedintothesentence
‘This statementisnottrue’, wequickly seethatithasnomeaningful content.The
most famous meaningless sentence of them all was constructed by the linguist Noam
Chomsky:
Colorless greenideas sleepfuriously.
It is often used as an example for the language processing properties of the brain, but
nobodysensibleelevates it to the status of a paradox and writes philosophical discussions
about it. To do that with the title of this section is a similar waste of energy.
The main reason for the popular success of self-referenceisthedifficultyinperceiving
the lack of meaning.* A good example is the statement:
This statementis false oryou areanangel.
We can actually deduce from it that ‘you are an angel.’ Can you see how? If you want,
you can change the second half and get even more interesting statements. Such examples
show that statements referring to themselves have to be treated with great care when
under investigation. In short, whenever you meet somebody who tries to use the selfreferential
construction by Kurt Gödel to deduce another statement, take a step back,
or better, a few more. Self-reference, especially the type defined by Gödel, is a hard but
commonpath–especiallyamongstwannabe-intellectuals–tothink,tellandwritenonsense.Nothing
useful can be deduced from nonsense.Well, not entirely; it does help to
meetpsychiatristsonaregular basis.
In physics, in the other natural sciences, and in legal trials these problems do not
emerge,because self-referentialstatementsarenotused.**Infact,theworkoflogicians
confirms,oftenratherspectacularly,thatthereisnowaytoextendtheterm ‘truth’ beyondthedefinitionof
‘correspondencewithfacts.’
“EinSatzkannunmöglich vonsichselbst
aussagen,daßerwahr ist.***
LudwigWittgenstein, Tractatus, 4.442”
Curiosities and fun challenges about lies and nonsense
“Aman ishisowneasiestdupe,forwhathe
wishestobetruehegenerally believestobe
true.
Demosthenes,349bce.”
*Awell-knownvictimofthisdifficultyisPaulusofTarsus.TheparadoxoftheCretanpoetEpimenedes(6th
century bce) who said ‘All Cretans lie’ is too difficult for the notoriously humour-impaired Paulus, who
in his letter to Titus (chapter 1, verses12 and 13, in the christian bible) calls Epimenedes a ‘prophet’, adds
some racist comments, and states that this ‘testimony’ is true.But wait! There is a final twist to this story.
The statement ‘All Cretans lie’ is not a paradox at all; a truth value can actually be ascribed to it, because
thestatement is not really self-referential.Can you confirmthis? Theonly genuineparadox is ‘Iamlying’,
towhichit isindeedimpossibletoascribeatruth value.
**Whyarecircular statements,like thoseofGalilean physics,not self-referential?
*** ‘Itisquite impossibleforaproposition tostatethat ititselfistrue.’
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net