From newshub.ccs.yorku.ca!ists!helios.physics.utoronto.ca!news-server.csri.toronto.edu!psych.toronto.edu!michael Tue Mar 24 09:54:57 EST 1992
Article 4399 of comp.ai.philosophy:
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>From: michael@psych.toronto.edu (Michael Gemar)
Subject: Re: Definition of understanding
Organization: Department of Psychology, University of Toronto
References: <1992Mar10.143639.10130@neptune.inf.ethz.ch> <1992Mar10.171755.7458@psych.toronto.edu> <1992Mar11.122705.22342@neptune.inf.ethz.ch>
Message-ID: <1992Mar11.185921.10347@psych.toronto.edu>
Date: Wed, 11 Mar 1992 18:59:21 GMT

In article <1992Mar11.122705.22342@neptune.inf.ethz.ch> santas@inf.ethz.ch (Philip Santas) writes:
>
>In article <1992Mar10.171755.7458@psych.toronto.edu> michael@psych.toronto.edu (Michael Gemar) writes:
>>In article <1992Mar10.143639.10130@neptune.inf.ethz.ch> santas@inf.ethz.ch (Philip Santas) writes:
>>>michael@psych.toronto.edu (Michael Gemar) writes:
>>>>
>>>>PE = 1/2 k x^2
>>>>
>>>>where PE = potential energy
>>>>       k = spring constant
>>>>       x = displacement from equilibrium
>>>>
>>>>You do so as a purely mechanical operation.  If asked, he would answer
>>>>that he knows nothing about potential energy, or spring constants, or
>>>>the like.
>>>>
>>>>You then say, "Aha, but the *system* that calculates potential energy
>>>>in a spring does!"  However, someone who knows electrostatics says,
>>>>"But wait!  That's also the formula for calculating the electrostatic
>>>>energy *in a capacitor*.  Simply *interpret* k as C (capacitance) and
>>>>x as V (potential across the capacitor plates)."  *Now* what does the
>>>>system "understand"?  Only pendulums?  Only capacitors?  Pendulums *and*
>>>>capacitors?  I'd vote for neither, myself.
>>>
>>>If the system has as input only the mathematical formula, it is
>>>possible that you get a variety of solutions according to the input.
>>>k can be number of number of cars, and x anything else.
>>>The human or the computer needs the definitions that you add after the
>>>formula. This means that we talk about mechanical and not electrical
>>>energy.
>>
>>How do you give definitions that have semantic content to a computer?
>>How does it know that when you respond to the request "Please input
>>the capacitance constant => " that you are talking about capacitance,
>>and not number of cars?  The problem of generating "definitions" with
>>semantic content for a computer *is* the central problem under discussion.
>
>You can do type checking even statically in this example:
>
>  PE GivePE(Distance displacementFromEquilibrium)
>          {
>           Distance x = displacementFromEquilibrium;
>           SpringConstantType k = SpringConstant;    // this is global variable 
>           return (1/2) * k * power(x,2);
>          };
>
>Relevant things you can do for capacitances, by changing the type
>of the argument displacementFromEquilibrium.

This does *not* ground the meaning of these terms.  How do these variables
know that the numbers input are spring constant and displacement, rather
than capacitance and potential.  Merely typing 
  
Distance x = displacmentFromEquilibrium

does not tell the computer what "distance" and "displacement from equilibrium"
*is*!  I could have just as easily typed:

Qaatlus x = GwornsBleebArack

and the program would *still* compute *both* Potential *and* electrostatic
energy.

>>>Your formula itself does not refer to capacitors either. It is the set
>>>of definitions of the variables that clear things up
>>
>>Agreed.  But I do not see a way of providing variable definitions that would
>>"clear things up" from the point of view of the computer.
>
>Notice that EVEN languages like C++ have such abilities...

C++ may have the ability to distinguish between different variables.  It
does *not* have the ability to provide semantics for those variables.

- michael 


