% is not an operator [was Re: Verbose and flexible args and kwargs syntax]

[Eelco]

On 14 dec, 12:55, Arnaud Delobelle <arno... at gmail.com> wrote:
> On 14 December 2011 07:49, Eelco <hoogendoorn.ee... at gmail.com> wrote:
> > On Dec 14, 4:18 am, Steven D'Aprano <steve
> > +comp.lang.pyt... at pearwood.info> wrote:
> >> > They might not be willing to define it, but as soon as we programmers
> >> > do, well, we did.
>
> >> > Having studied the contemporary philosophy of mathematics, their concern
> >> > is probably that in their minds, mathematics is whatever some dead guy
> >> > said it was, and they dont know of any dead guy ever talking about a
> >> > modulus operation, so therefore it 'does not exist'.
>
> >> You've studied the contemporary philosophy of mathematics huh?
>
> >> How about studying some actual mathematics before making such absurd
> >> pronouncements on the psychology of mathematicians?
>
> > The philosophy was just a sidehobby to the study of actual
> > mathematics; and you are right, studying their works is the best way
> > to get to know them. Speaking from that vantage point, I can say with
> > certainty that the vast majority of mathematicians do not have a
> > coherent philosophy, and they adhere to some loosely defined form of
> > platonism. Indeed that is absurd in a way. Even though you may trust
> > these people to be perfectly functioning deduction machines, you
> > really shouldnt expect them to give sensible answers to the question
> > of which are sensible axioms to adopt. They dont have a reasoned
> > answer to this, they will by and large defer to authority.
>
> Please come down from your vantage point for a few moments and
> consider how insulting your remarks are to people who have devoted
> most of their intellectual energy to the study of mathematics.  So
> you've studied a bit of mathematics and a bit of philosophy?  Good
> start, keep working at it.

Thanks, I intend to.

> You think that every mathematician should be preoccupied with what
> axioms to adopt, and why?

Of course I dont. If you wish to restrict your attention to the
exploration of the consequences of axioms others throw at you, that is
a perfectly fine specialization. Most mathematicians do exactly that,
and thats fine. But that puts them in about as ill a position to
judged what is, or shouldnt be defined, as the average plumber.
Compounding the problem is not just that they do not wish to concern
themselves with the inductive aspect of mathematics, they would like
to pretend it does not exist at all. For instance, if you point out to
them a 19th century mathematician used very different axioms than a
20th century one, (and point out they were both fine mathematicians
that attained results universally celebrated), they will typically
respond emotionally; get angry or at least annoyed. According to their
pseudo-Platonist philosophy, mathematics should not have an inductive
side, axioms are set in stone and not a human affair, and the way they
answer the question as to where knowledge about the 'correct'
mathematical axioms comes from is by an implicit or explicit appeal to
authority. They dont explain how it is that they can see 'beyond the
platonic cave' to find the 'real underlying truth', they quietly
assume somebody else has figured it out in the past, and leave it at
that.

> You say that mathematicians defer to authority, but do you really
> think that thousands of years of evolution and refinement in
> mathematics are to be discarded lightly?  I think not.  It's good to
> have original ideas, to pursue them and to believe in them, but it
> would be foolish to think that they are superior to knowledge which
> has been accumulated over so many generations.

For what its worth; insofar as my views can be pidgeonholed, im with
the classicists (pre-20th century), which indeed has a long history.
Modernists in turn discard large swaths of that. Note that its largely
an academic debate though; everybody agrees that 1+1=2. But there are
some practical consequences; if I were the designated science-Tsar,
all transfinite-analysist would be out on the street together with the
homeopaths, for instance.

> You claim that mathematicians have a poor understanding of philosophy.
>  It may be so for many of them, but how is this a problem?  I doesn't
> prevent them from having a deep understanding of their field of
> mathematics.  Do philosophers have a good understanding of
> mathematics?

As a rule of thumb: absolutely not, no. I dont think I can think of
any philosopher who turned his attention to mathematics that ever
wrote anything interesting. All the interesting writers had their
boots on mathematical ground; Quine, Brouwer, Weyl and the earlier
renaissance men like Gauss and contemporaries.

The fragmentation of disciplines is infact a major problem in my
opinion though. Most physicists take their mathematics from the ivory-
math tower, and the mathematicians shudder at the idea of listning
back to see which of what they cooked up is actually anything but
mental masturbation, in the meanwhile cranking out more gibberish
about alephs. If any well-reasoned philosophy enters into the mix, its
usually in the spare time of one of the physicists, but it is
assuredly not coming out of the philosophy department. There is
something quite wrong with that state of affairs.