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Article 3088 of comp.ai.philosophy:
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>From: gudeman@cs.arizona.edu (David Gudeman)
Newsgroups: comp.ai.philosophy
Subject: Re: Intelligence Testing
Message-ID: <11819@optima.cs.arizona.edu>
Date: 24 Jan 92 00:10:11 GMT
Sender: news@cs.arizona.edu
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In article  <42139@dime.cs.umass.edu> Joseph O'Rourke writes:
]The point is that it is not necessary to establish self-awareness to
]establish understanding:  we only need evidence for grasping.
]And I believe this:
]
]	[*] If a subject does not fully grasp the meaning of X,
]	then there are a series of questions about X that will 
]	reveal this.
]
]Every teacher who has composed an exam believes this.  The flip side
]of [*] is that if a long series of such questions are answered
]correctly, our confidence that the subject does indeed grasp X
]increases without bound.

That is a logical fallacy in that you are starting with a sentence of
the form "(not P) implies Q" and are drawing conclusions based on a
sentence of the form "(not Q) implies P".  As any freshman in a logic
class can tell you, you cannot make logical inferences about the
antecedent from the truth or falsehood of the consequent.

To get your "flip side", you need to start with a statement of the
form "If there is no series of questions about X that show the subject
does not understand X, then the subject understands X."  This is a
reasonable position to take _until someone demonstrates a syntactic
way to simulate understanding.  For that amounts to a proof of the
statement:

  There is a syntactic transformation S for X such that there is no
  series of questions about X that cannot be transformed by S to give
  the impression that the subject understands X.

This contradicts the statement

  If there is no series of questions about X that show the subject
  does not understand X, then the subject understands X.

And leaves you with no reason to believe it.

Of course, you can retreat to a completely empty definition of
understanding, something like

  A subject understands X just in case there is no series of
  questions about X that it cannot answer.

But then take the claim above and replace "understands" with its
definition.  You get

  If there is no series of questions about X that a subject cannot
  answer, then there is no series of questions about X that the
  subject cannot answer.

Hardly an interesting thing to say.
--
					David Gudeman
gudeman@cs.arizona.edu
noao!arizona!gudeman


