🚀 go-pugleaf

In article <1992Nov3.214913.25344@dcs.qmw.ac.uk>, arodgers@dcs.qmw.ac.uk (Angus H Rodgers) writes:
|> In <Bx5KKt.HA5@unx.sas.com>
|> sasghm@theseus.unx.sas.com (Gary Merrill) writes:

|> 
|> >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?

The group that you (and others in a quite traditional sense) like to refer to
as *natural* science.  (However, it is unclear what (if any) is the
distinction between *science* and *natural science* -- except that
the former frequently is intended to include the so-called *social*
sciences.  It is still neither common nor traditional usage to
count *mathematics* as a science.  While you are correct that one
can harmlessly use "science" to include mathematics -- particularly
if one is explicit about this use -- I do believe that I have
common and historical usage on my side.)

|> >|> >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.

Well, the meaning of "applied mathematics" is a bit vague as well.
Sometimes it is used to refer to certain *areas* of mathematics
(e.g., finite mathematics?) and other times it is used to refer to
the *application* of (pure) mathematics (to science or engineering).

I also think that there is something distinctive about "computer
science" that distinguishes is from applied mathematics.  For example,
much of its domain is not what most people would regard as truly
*mathematcal* (except when this term is used in a very broad sense --
as I think you prefer to use it).

|> >|> A propos of which, are algorithms mathematical objects?
|> 
|> >Well, they may be thought of as *formal* objects.
|> 
|> What does this mean?

Well, I won't attempt a definition at this point.  It may be easier
to get at it via some common distinctions.  Consider the following
questions:

	1. Is logic mathematics? 
	2. Is set theory mathematics?  Type theory?
        3. Is model theory mathematics?
	4. Is formal linguistics mathematics?

Historically, mathematics seems to have centered around such concepts
as *number* and *measurement*.  Since logic does not (in itself)
address these concepts, many feel it is not mathematics.  Similarly
for set theory, etc.  Typically, many philosophers regard logic
as mathematics and many mathematicians regard it as philosophy.  So
the view is that (for example) first-order logic is *not* mathematics,
but cylindirc and polyadic algebra *is* (despite the obvious close
relations here).  But all are *formal* disciplines:  formal descriptions
of the theories, formal statements of fundamental principles and rules,
formal criteria for "goodness"  (proofs, etc.).  ("Formal" in the
sense of "of or pertaining to form".)

Thus it seems reasonable to say that algorithms are *not* mathematical
objects (any more than, say, grammars are).  And this is particularly
true since algorithms do not form a domain of objects that are subject
to operations that are typically thought of as mathematical.  (Actually,
I have to confess that I don't what operations algorithms really
are subject to.  But normally in mathematics one deals with operations
under which the domain is closed.  So while algorithms *might* be
treated as mathematical objects -- for example, by constructing an
algebra of algorithms -- they usually (never?) *are* treated this way.)


|> >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.)

Yes, it makes perfect sense.  However, earlier you denied my implicit accusation
that you may be confusing "precise and formal" with "science".  Now
you seem willing to confuse it with "mathematics".  This may simply
be a reflection of the broad sense that you wish "mathematics" to have.
Use of the broad sense isn't necessarily bad, but often it is important
and fruitful to draw finer distinctions.

|> >|> [...] 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

Does any type of engineering *have* an ontology?  (Civil -- bridges?
Electrical -- circuits?  Software -- algorithms, data structures?)

|> nor logic provides any convincing (to me) answer to the question
|> of what the *objects* are which software engineers work with.

Why should they?  That ain't their job.  They also don't provide an
answer to what is the ontology of physics or psychology.


|> 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
                                                    ^^^^^^^^^^^
I think we agree on this.

|> is immature as a science, but what else do you expect?

This of course does not follow.  I still object to calling it a
"science" -- immature or otherwise.  Usually, people want to call
what they do "science" because they think this lends importance
or respect to it.  In fact, this seems to me to be the *only*
motivation for calling computer science "science".  But we don't
need that.  Computer science does not need to ride the coattails
of some other discipline for its respectability.

|> 
|> Great news! You've cracked the problem of the foundations of maths!
|> Tell me all about it! :-)

Sure.  First, tell me what the problem is.
-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm