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Article 1377 of comp.ai.philosophy:
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>From: markrose@spss.com (Mark Rosenfelder)
Subject: Re: Chinese Room Variant
Message-ID: <1991Nov18.171828.7975@spss.com>
Date: Mon, 18 Nov 1991 17:18:28 GMT
References: <1991Nov12.131428.4850@osceola.cs.ucf.edu> <1991Nov14.163630.20597@spss.com> <1991Nov17.163705.5540@husc3.harvard.edu>
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Thomas Clarke writes:
>>>That is, the bare rules of computation plus any finite set of additional 
>>>usage/correspondence rules are not sufficient for an understanding of number. 
to which I respond:
>>What is sufficient, then?  An infinite set of rules?  Or, if something else
>>entirely is needed, what is it?

and Mikhail Zeleny comments:
>In effect, on the syntactical level, infinitely many rules are required in
>order to characterize the standard model of the natural numbers.  This is a
>direct consequence of G\"odel's Second Incompleteness Theorem.

Interesting, perhaps, but completely irrelevant to this thread, which was
about what it takes for a child or a robot to know arithmetic.  A child does
not need an infinite set of rules, or an understanding of Godel, to be said
to understand arithmetic.  A definition of understanding that excludes robots
but also the vast majority of human beings is not very useful. 

Since Mr. Clarke did not respond to my question, I will make a stab at it
myself: a child or a robot will understand arithmetic when it can perform the
operations, knows a large number of correspondences with their uses in the
real world, and is capable of constructing new uses in new situations.


