Re: OO, C++, and something much better!

[jsa@alexandria (Jon S Anthony)]

In article <vwjybcd2794.fsf@cassin.dcs.aber.ac.uk> pcg@aber.ac.uk (Piercarlo Grandi) writes:

<<Piercarlo says a _lot_ of stuff.  Some of it more or less sensible,
some of it utter rubbish, most of it uninteresting or otherwise empty
of content.>>

> discussed). Mathematicians do invent notation all the time, and do mean
> different things by the same words.

So what?  I already pointed this out several posts ago.

> Well, it has an enormous :-) importance: that your idea that the notion
> of "ordinary maths" has one formal meaning ("THE formal sense", emphasis
> mine) is entirely bogus.

_Your_ "ordinary maths" is ill defined and uninteresting.


> In the present context it matters, because it is you argument that the
> word "operator", in the one and only formal system of mathematics you

Who said anything about only one formal system of mathematics?  Can
you read?  In basically any context, the notion of "operation" is
defined by its semantic and any "syntax" is completely irrelevant.
Different notations are used all over the place but an operation is an
operation because of its semantic - not any glyph that might be used
for it.  Anyone with even a passing familiarity of mathematics knows
this.


> "operator" commonly labels a type of symbols, while it indicates a type
> of functions only if in the context of discussions on operator theory.

Wrong.  Just completely wrong.  Get a clue.  Let's see here.  I have
MacLane's, _Catagories for the Working Mathematician_; Enderton's _A
Mathematical Introduction to Logic_, and Herstein's _Topics in
Algebra_ sitting here handy.  Looking in each of them I see that _all_
of them define an operator as a function f:A^n->A.  Nond of these is
concerned with operator theory.  You are just plain wrong.

Now, what I'd like to know is _why_ in the face of a mountain of
evidence to the contrary, you still _insist_ that _your_ view of what
"operator" means in mathematics is right.  That it is "defined by
syntax or glyphs".  Do you have an inferiority complex or what?


> Some people even believe (quite correctly) that the whole of computing
> is a branch of applied maths (applied intensional logic). Different

Wow.  Here we actually agree.


> Your abysmal ignorance of the simple distinction between a mathematical
> entity (say a function) and a computational one (say a procedure) is
> appalling. There are whole books devoted to such a relationship, which
> is often extremely complex, and in no case one of identity;


Ahem.  You actually seem to know something about PL design based on
some of your past posts.  But, your abysmal ignorance of mathematics
is appalling when it is coupled with your bizarre wanna be ranting.
Nothing you say in all these rambling rants adds up to one iota of
originality; nothing in them is insightful or even remotely
interesting.  They might be reasonable for a student in a first course
in mathematical foundations or logic or maybe philosophy of
language/mathematics.  But when you add to them your laughable
arrogance you just end up looking like a fool here.

Now, I don't claim to know all there is to know about the foundations
of mathematics.  Not by a long shot.  Not even in my wildest fantasies
of intellectual prowess.  But I spent several years working in the
area and it is what I wrote my thesis in.  So, neither am I clueless
here.


/Jon
-- 
Jon Anthony
Organon Motives, Inc.
Belmont, MA 02178
617.484.3383
jsa@organon.com