From: rickert@mp.cs.niu.edu (Neil Rickert)
Newsgroups: comp.ai.philosophy
Subject: Re: syntax and semantics
Date: 9 Apr 92 01:15:49 GMT
Organization: Northern Illinois University

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:
>>
>>In article <92098.170625JPE1@psuvm.psu.edu> JPE1@psuvm.psu.edu writes:
>>>    Are you suggesting that such computations are _not_ syntactic?  In what
>>>manner would they not be?  From what I understand, whatever the computer does
>>>_is_ "formal" and "precise", although we may interpret its output as
>>>_meaning_ something imprecise.
>>
>> 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

>     The point is not that what computers do is _necessarily_ meaningless, just
>that, at the machine level, there is no inherent meaning (or reference).  It

 There is no inherent meaning or reference at the chemical level in your
brain either.

>is we who come along and project reference upon the formal manipulations that
>the computer has carried out.   I can't say that I know or understand enough
>(about either math or computers) to follow your floating point arithmetic
>example, but in the case of my bank account, the point would be something
>like this: the bank's computer need not "know" anything about money or
>buying meals in order to carry out the mechanical functions that it performs
>as a matter of is causal operation.  However, this activity of the computer

  Simply this:

	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.

  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.

-- 
=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=*=
  Neil W. Rickert, Computer Science               <rickert@cs.niu.edu>
  Northern Illinois Univ.
  DeKalb, IL 60115                                   +1-815-753-6940
Newsgroups: comp.ai.philosophy