Organization: Penn State University
Date: Thursday, 9 Apr 1992 12:32:28 EDT
From: <JPE1@psuvm.psu.edu>
Newsgroups: comp.ai.philosophy
Subject: Re: syntax and semantics
 <1992Apr8.215800.18021@mp.cs.niu.edu> <92099.194744JPE1@psuvm.psu.edu>
 <1992Apr9.011549.15678@mp.cs.niu.edu>

In article <1992Apr9.011549.15678@mp.cs.niu.edu>, rickert@mp.cs.niu.edu (Neil
Rickert) says:
>
>In article <92099.194744JPE1@psuvm.psu.edu> <JPE1@psuvm.psu.edu> writes:
>>In article <1992Apr8.215800.18021@mp.cs.niu.edu>, rickert@mp.cs.niu.edu (Neil
>>Rickert) says:
>>> [Rickert:]
>>> It is of course possible to view floating point arithmetic as formal and
>>>precise.  If you view it that way the floating point numbers satisfy some
>>>very strange and quite complex algebraic properties.  Moreover the
>>>algebra of floating point numbers as implemented on one machine is quite
>>>different from the algebra as implemented on a different machine.  All in
>>>all, when viewed this way floating point numbers are useless curiosities.
>>>However if view as approximations to real numbers then we have a much
>>>simpler algebra (the algebra of real numbers), we have consistency between
>>>different machines, but the numbers are no longer precise, since they are
>   [Emmer:]
>>     The point is not that what computers do is _necessarily_ meaningless,   t
>jus
>>that, at the machine level, there is no inherent meaning (or reference).  It
>   [Rickert:]
> There is no inherent meaning or reference at the chemical level in your
>brain either.
>
  [Emmer:]   I agree.  See my reply to your other comments.

  [Rickert:]
>
>        Floating point arithmetic, when viewed as precise symbolic
>manipulations, does not satisfy the associative law:
>
>        (10^20 + (-10^20) ) + 1 is 1
>        10^20 + ((-10^20) + 1)  is 0  on most machines.
>
> The square root of 2 computed on various machines is likely to be different,
>both due to different floating point representations, different numbers
>of digits of precision, different rounding assumptions.
>
>  Viewed as precise symbol manipulators, these machines are total
>disasters.  Viewed as computing approximate real values, they are very
>useful and the minor discrepancies are insignificant.
>
>  This discussion started with your comment that all computers do is
>syntax, and my response that syntax is usually considered precise and
>doesn't fit with floating point computation.  If you still wish to hold
>that, even when doing floating point arithmetic, computers should only be
>interpreted as performing syntactic manipulations, you are a victim
>of self deception.
>
[Emmer:]
      I think there is some confusion here over what is meant by 'precise'.
When someone else first used this term in this discussion, I took it to be
just another way to state the fact that computers are formal systems.  You
you seem to be saying that the formal systems instantiated by various
computers only approximate the task of performing floating point computations,
and that even this approximation differs from machine/system to machine/system.
In other words, the computer's "precise" formal manipulations are used by us
as an "imprecise" approximation of some task we wish to achieve.  I'm sorry
if I am responsible for this equivocation.  I hope this clears it up.

[Rickert:]
>  Whether there is actually semantics in the floating point unit is a
>different question.  I don't suggest there is - the semantics would be in
>the data.  But I am not currently making a case that computers are capable
>of semantics.  I am making the case that the reasoning you use to convince
>yourself that they are not is seriously flawed.

[Emmer:]
     This I don't understand.  In my earlier post, I suggested that, if
semantics has a 'where' it's in the pragmatic context.  When you say
semantics is not "in the floating point unit" but perhaps "in the data",
what are you sugsuggesting?  I don't know what you intend to refer tloatinge "f
point unit" - is this the state of the computer?  Are you saying that
the state of the computer does not 'contain' semantics but that the marks
on a piece of paper do?   And, once again, I have not yet made the claim
the computers are 'incapable of semantics' - perhaps they could understand
the pragmatic context, and gain meaning from it, however it is that we
manage this.



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 John Emmer               "...reason has no dictatorial authority; its verdict
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 Penn. State University                   - Immanuel Kant, CPR, A738/B765
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