philosophy discussion 3
Valerielee
GrellingsParadox.pdf
2/8/2018
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Phil 2: Puzzles and Paradoxes
Prof. Sven Bernecker
University of California, Irvine
Grelling‘s Paradox
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Kurt Grelling (1886 – 1942)
Grelling was a German
logician and philosopher and
member of the Berlin Circle.
Grelling‘s Paradox
Grelling’s Paradox is similar to the liar paradox. To begin with,
let’s consider a principle like Disquotation:
“F” applies to x = x is F
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Autological and Heterological
The analogue of the liar statement in Grelling’s paradox is the new
term “heterological” defined as follows:
And we can define autological, as follows:
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x is heterological = x does not apply to x
x is autological = x does apply to x
2/8/2018
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Examples of autological terms:
“Short” is short
“Red” is red
“Unhyphenated” is unhyphenated
“English” is English
“Adjectival” is adjectival
“Polysyllabic” is polysyllabic
Examples of heterological terms:
“Monosyllabic” is not monosyllabic
“Long” is not long
“Spanish” is not Spanish
“Nominal” is not nominal
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Question: Is “heterological” heterological?
If “heterological” is heterological, then the term must describe
itself, and therefore not be heterological.
If “heterological” isn’t heterological, then the term must not
describe itself, and therefore be heterological.
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1) “H” applies to “H” Assumption
2) “H” is H (1) Disquotation
C) “H” does not apply to “H” (2) Def of H
1) “H” does not apply to “H” Assumption
2) “H” is H (1), Def of H
C) “H” applies to “H” (2), Disquotation
We are led into a contradiction.
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