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

[Eelco]

On Dec 15, 4:43 am, rusi <rustompm... at gmail.com> wrote:
> On Dec 14, 10:15 pm, Eelco <hoogendoorn.ee... at gmail.com> wrote:
>
> > 'Kindof' off-topic, but what the hell :).
>
> <deja-vu>
> We keep having these debates -- so I wonder how off-topic it is...
> And so do famous CSists:http://research.microsoft.com/en-us/um/people/gurevich/opera/123.pdf
> </deja-vu>

Well, you are right, there are some deep links here. My view of what
is wrong with mainstream mathematics is its strange interpretation of
the semantics of classical logic. (And I dont think any other schools
get it quite right either; I think finitists may avoid the mistakes of
others, but are rightfully accussed of being needlessly restrictive,
for instance)

This is best illustrated by means of the principle of explosion. It
rests on assuming a contradiction, and then assigning rather peculiar
semantics to them. What is typically left unstated are the semantics
of symbol lookup, but apparently it is implicitly understood one can
pick whatever value upon encountering a contradicting symbol. There is
no well defined rule for the lookup of a twice-defined symbol. Of
course the sane thing to do, to a mind grown up around computer
languages, upon encountering a twice defined symbol, is not to
continue to generate deductions from both branches, but to throw an
exception and interrupt the specific line of reasoning that depends on
this contradicting symbol right then and there.

Conceptually, we can see something is wrong with these undefined
semantics right away. A logical system that allows you to draw
conclusions as to where the pope shits from assertions about natural
numbers could not more obviously be broken.

If you dont have this broken way of dealing with contradictions, one
does not have to do one of many silly and arbitrary things to make
infinity work, such as making a choice between one-to-one
correspondence and subset-relations for determining the cardinality of
a set; one can simply admit the concept of infinity, while useful, is
not consistent, keep the contradiction well handled instead of having
it explode in your face (or explode into the field of transfinite
analysis; a consequece of 'dealing' with these issues by rejecting the
intuitively obviously true relation between subset relations and
cardinality), and continue reasoning with the branches of your
argument that you are interested in.

In other words, what logic needs is a better exception-handling
system, which completes the circle with programming languages quite
nicely. :)