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In <Bx5KKt.HA5@unx.sas.com>
sasghm@theseus.unx.sas.com (Gary Merrill) writes:

>In article <1992Nov3.162733.18079@dcs.qmw.ac.uk>,
>arodgers@dcs.qmw.ac.uk (Angus H Rodgers) writes:
>|> In <Bx5AKy.4C3@unx.sas.com>
>|> sasghm@theseus.unx.sas.com (Gary Merrill) writes:
>|> 
>|> >[...] (just as mathematics is not science,
>|> >though it is considered by many to be "the same kind of thing").
>|> 
>|> If maths isn't science, than there's something wrong with the 
>|> definition of "science", so it's nothing to worry about if
>|> computing fails to qualify as well - it's in good company.

>On the other hand, if *you* think that math *is* a science, this
>is an indication of the depth of your understanding of what "science"
>means.

I once made a list of meanings commonly attributed to the word
"science"; I think it ran off the page. If *you* think that there
is a great Dictionary in the sky, in which every English word
is assigned a unique and precise and uncontroversial definition,
then this is an indication of the depth of your understanding of
natural language! But I don't mean to flame you, and I'm sure you
don't think that.

I was hoping to appeal to one commonly-accepted meaning of the
word "science", as a field of study in which there are widely-agreed 
rational procedures for establishing truths. In this sense, 
mathematics is a science. It is also a science by virtue of its
links to other sciences.

"Science" means (among other things) "trustworthy knowledge".
I believe mathematical knowledge is trustworthy. Lots of people
certainly do trust it, as a reliable basis for their work in
(other) sciences.

I'm not saying that this isn't controversial; I am saying that
to categorically *deny* mathematics the status of a science is to
employ the word "science" in an indefensibly narrow way. Of
course, if you take care to define your terms first, it's OK; but
you can't justify the denial on the basis of ordinary usage.

I'm quite happy to admit that I am engaging in rhetoric rather than
logic. That seems appropriate when terms are hard to define, and
there are no axioms.

>I in fact gave a number of respects in which mathematics
>fails many of the standard criteria for being a science. 

No quarrel there.

>The
>distinction is also enshrined in traditional and common usage.
>For example, consider the "North Carolina School of Math and Science".
>If math is a science, why the distinction?

Presumably (this is only a guess) because the word "science" also
has a commonly-accepted meaning (which you seem to take to be the
only one), in which, in order to qualify as a "science", a discipline
must allow the settlement of disagreements by appeal (however
indirect) to observations via the senses; and it very much a
minority view that maths is a science in this sense. (It is not
an "empirical" or a "natural" science.) So if you want to make
it quite clear that your institution teaches maths, you'd better
mention it explicitly; hence the appellation.

Perhaps we should use German. Can anyone supply the definitions
of the German nouns "Wissenschaft", "Naturwissenschaft", "Geistes-
wissenschaft"? (Spelling?) They just might help to clarify the
argument.

>Do not mistake "precise and formal" as being equivalent to "science".

I don't.

>You could think of mathematics as a "formal science".

Ugh!

>Then logic would count too.  So, perhaps, would music.

No, I would not want to admit music as a science. For one thing,
It does not employ widely-agreed rational procedures for arriving 
at truths. (This is not to say that it is not a discipline for
arriving at truths! -- I worship Beethoven, and it is no insult to
him to say that he is not a scientist. -- But it *would* be an
insult to Eudoxus or Dedekind or Hilbert to deny them that title.)

>However, it is still the case that "computer science" is quite
>different from such disciplines.

You've lost me now. Which group of disciplines have you identified,
and by what criterion?

>|> >Computer "science" is more like mathematics than empirical science
>|> >(even the theoretical aspects of empirical science).

My feeling (it is little more than that) is that computer science
is roughly equally (un)like both. I think of it as being a branch
of applied maths; and applied maths is not maths, but maths in the
making.

>|> A propos of which, are algorithms mathematical objects?

>Well, they may be thought of as *formal* objects.

What does this mean?

>But I don't see the point of the question.

I don't have a clear concept of "algorithm", so it seems helpful 
to ask what kind of object an algorithm is. I don't think it is a
mathematical object like a number, or a group: mainly because I
think that physical time enters into it in an essential way. But
it has the kind of "exactness" which only mathematical objects have.
Does this make any sense? (Never mind if it doesn't; I was more
concerned to ask a thought-provoking question than to make any
statement. -- Just so long as the question makes some sense! I'm
disappointed that it didn't.)

>|> [...] every engineering discipline is supported by a science.
>|> Where is the "software science" to support "software engineering"?
>|> Or is this form of engineering a unique exception?

>The notion of "supported by" is pretty unclear clear.  However, it
>is clear that software engineering is "supported by" at least
>logic and mathematics (several flavors thereof).  I don't see any
>identifiably distinct "software science" that needs to be appealed
>to in addition to this.

What is the *ontology* of software engineering? Neither mathematics
nor logic provides any convincing (to me) answer to the question
of what the *objects* are which software engineers work with.
Whereas physics has a lot to say about the materials with which
civil engineers work; chemistry describes the materials with
which chemical engineers work; and so on. It is for this reason
that I think of computer science as a discipline sui generis. It
is immature as a science, but what else do you expect?

>|> >Whatever computer science is, it is a discipline terribly difficult
>|> >to characterize (and to distinguish from parts of other more
>|> >well established disciplines).
>|> 
>|> What other disciplines pose such a difficulty of definition? 
>|> It may not be a very unusual phenomenon. Mathematics immediately
>|> springs to mind as another example; followed by statistics,
>|> philosophy and psychoanalysis (and psychology in general, given
>|> that for many years it was fashionable to exclude consciousness
>|> from it altogether!).

>It is interesting that *none* of the examples you give are *sciences*.

This begs the question. (Also it shifts the ground, because you were
discussing "disciplines", not "sciences".)

>I don't see that mathematics poses a similar difficulty.

Great news! You've cracked the problem of the foundations of maths!
Tell me all about it! :-)
--
Angus H. Rodgers  (PhD student), | arodgers@dcs.qmw.ac.uk  
Dept. of Computer Science, Queen | [ +44 | 0 ] 71 975 5241   
Mary & Westfield College,  Mile  | "But what is contact? No two points
End Rd., London E1 4NS, England  | are in contact." -- A.N. Whitehead.