Side-stepping Grelling's Paradox
I probably misunderstand something, but I took a crack at Grelling's Heterological Paradox.
I was diving into philosophy and mathematics, more particularly set theory and the like, when I came across Grelling's Paradox which roughly states:
I've seen Russell's version involving sets that do not contain themselves, but I had not really thought about Grelling's version before in much depth. For some reason while reading tonight, something sparked in my brain and I noticed something which would dismiss his paradox altogether.
The heterological paradox (as it's also called), feeds off the Schrödinger's Cat 'paradox' in my opinion - the answer is not known until you examine the scenario. First, some frequent examples for this paradox: 'long' and 'monosyllabic' are heterological while 'short' and 'pentasyllabic' are both autological. An adequate test to figure out whether or not a word is heterological or autological is to form the question: 'Does '[word]' describe [word]?' If it does, it's autological, if not, it's heterological.
So, does 'heterological' describe heterological? Only in the instances in which it's describing other words. The key I think is to introduce 'instances' or 'references'. Think about variables in a programming language using references or memory pointers. In evaluating whether or not a word is heterological, you would try to evaluate whether or not the instance in which the word is being used is heterological (words by themselves do very little). For example: "The word 'long' is heterological" is an instance of 'heterological' not describing itself, so in this particular instance it would be heterological. The introduction of instances or references also side-steps Russell's problems of a set which contains all sets that do not contain themselves, but I have other issues with Russell's paradox anyway ('the set of all sets that do not contain themselves' is ill-defined in my mind).
Grelling's Heterological Paradox only arrises when using ambiguous parameters. If you introduce a reference or instance constraint, you'll see the problems disappear, I think.
comments
1
molotov
Thursday, March 29, 2007
And as a side thought: autological words can only be words that are physically descriptive in nature. For example 'short', 'pentasyllabic', or even 'divine'*. Does 'easter' describe 'easter'? Sure, in some sense it does, but it would seem that in the scope of auto/heterologicallity it would be a bit absurd. Does 'the' describe 'the'? Sure, it's the definite article, but how else does 'the' relate to itself? The whole paradox is obviously created to form a paradox, and doing so is not hard. Russell's set paradox is more condemning.
*devine - Here's an interesting idea: if you break down words and use the described 'test', all words would be in some degree autological, based on pure identity and equality laws. If there are 'degrees' of application for the descriptions of autological and heterological, then I'll let the author draw the lines more concretely before playing in to this 'paradox' trap.
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ava
Monday, April 2, 2007
All words (except onomatopoeia) are heterologic, in that they are completely arbitrary in what they describe. The autologic examples ("pentasyllabic" etc) seem to have ended up as self-descriptive by chance rather than by intention. No word truly "describes itself", because no word has an a priori meaning; it simply seems that way because we have grown up using the language, and it seems perfectly natural to us to see to the word as inseparable from its object.
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molotov
Monday, April 2, 2007
What about 'noun'?
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ava
Tuesday, April 3, 2007
Still heterologic; the word "noun" has no a priori meaning - we could call nouns anything, use the word noun to describe something completely different from what it currently describes, etc. The word "noun" is no more autological than the words "adjective" or "predicate".
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molotov
Wednesday, April 4, 2007
Ah, I see. I think that you and I have (or could) take extremes in both directions; you saying that all words are heterological, me saying that all words are autological. If there is an argument for either case, then the paradox is crappily constructed.
However, I think that Grelling would say that we're 'over analyzing' and missing his point (regardless of how poorly his paradox was constructed).