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Article 3120 of comp.ai.philosophy:
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>From: jeff@aiai.ed.ac.uk (Jeff Dalton)
Newsgroups: comp.ai.philosophy
Subject: Re: Intelligence Testing
Message-ID: <1992Jan24.161425.5929@aisb.ed.ac.uk>
Date: 24 Jan 92 16:14:25 GMT
References: <11819@optima.cs.arizona.edu> <42196@dime.cs.umass.edu>
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In article <42196@dime.cs.umass.edu> orourke@sophia.smith.edu (Joseph O'Rourke) writes:
>In article <11819@optima.cs.arizona.edu> gudeman@cs.arizona.edu (David Gudeman) writes:
>>In article  <42139@dime.cs.umass.edu> Joseph O'Rourke writes:
>>]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.

Wait a minute.  One can't from the truth of the consequent,
but one can from the flasehood.  If p -> q, and ~q, we can
conclude ~p.  Just think of proof by contradiction.  If we
have ~q, we can assume p, put in ~q, and get p -> ~q.  From
that and p -> q, we get p -> (q & ~q); hence ~p.  (Actually,
this explanation may be more obscure than what it's trying
to explain; but if it's not clear directly any explanation
may have that problem.)

>I thought that ~P => Q is logically equivalent to ~Q => P, so that
>from ~P => Q and ~Q, P follows.  Or in other words, if I believe
>~P => Q is true, and I gain evidence that Q is false, then I should
>conclude that ~P is false, so P is true.

That looks reasonable to me (see above).  But you're also switching
between "there is a series of questions" and "a long series of
quesitons is answered".  So you switch from saying there is _some_
series of questions (which perhaps one no one has found) to
considering _one_ long series of questions.  So you need something
to justify that.

Now, the idea that seeing a lot of questions successfully answered
increases our confidence may be true (though I don't know about
increasing it _without bound_).  But it's wrong to suppose that
any old series of questions will do.  Teachers presumably try to
ask the right sorts of questrions, and they can get it wrong.
Feynman's story about Brazilian physics is often used as an example.

And if we consider the Turing Test applied to programs, the right
question might be one about how the program works.  And we answer
it by looking at how the program is written, not by _asking_ it.

-- jd


