[BLML] Cheshire cat [SEC=UNOFFICIAL]

Robert Park bpark56 at comcast.net
Thu Sep 9 15:54:12 CEST 2010


  On 9/9/10 9:27 AM, Alain Gottcheiner wrote:
>    Le 9/09/2010 15:09, Thomas Dehn a écrit :
>> Alain Gottcheiner<agot at ulb.ac.be>   wrote:
>>>     Le 9/09/2010 7:43, richard.hills at immi.gov.au a écrit :
>>>> Richard Hills, 11th April 2005:
>>>>
>>>>> It is easy for apparently "simple logic" to conceal invalid
>>>>> logical operations.
>>>>>
>>>>> For example:
>>>>>
>>>>> (Axiom 1) Nothing is better than eternal happiness.
>>>>> (Axiom 2) A ham sandwich is better than nothing.
>>>>> (Conclusion) Therefore, a ham sandwich is better than
>>>>> eternal happiness.
>>> AG : it's not logic that we should consider the culprit here ; it's the
>>> extreme ambiguity of words, especially English words.
>> One would also have to prove mathematically that "is better than"
>> is a transitive operation.
>>
>>
>>
> It is usually considered that preferences are transitive.
> For example, all of votation theory and 90% of economics and marketing
> fall down if one uses a non-transitive preference relation (NB :
> relation, not operation)
>
> It is an axiom, rather than a theorem, so no proof, sorry.

Wrong. See, for example, "Mathematical Games," by Martin Garner, 
Scientific American, Oct 1974.

As a simple example, he demonstrates an asymetrical dice game with 4 
dice (either there of in a related article) where we play for a dollar a 
point and I let you choose your die first. Whichever die you choose, I 
can choose a better one.

   --Bob Park


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