Benefit and belief

[rusi]

On Oct 17, 7:34 pm, Steven D'Aprano <steve
+comp.lang.pyt... at pearwood.info> wrote:
> That is no more deep and meaningful than the fact that while some people
> say "one plus one equals two", others say "eins und eins gleich zwei",
> some say "un et un fait deux" and some say "один и один дает два".
> Regardless of whether you write two, zwei, два, δυο, 2 (in decimal), 10
> (in binary), II (in Roman numerals) or even {0,1} using set theory
> notation, the number remains the same, only the symbol we use to label it
> is different.

And Ben said:
> A belief that doesn't match reality is a delusion. That doesn't change
> when someone thinks it's an epiphany: it's still a delusion.

> If a claim about reality doesn't actually match reality, it's untrue.
> That doesn't change when someone believes it: it's still untrue, or
> claims it's “part of a bigger picture”.

These are classical platonist claims:  In short objective reality
exists aside from the subjective perception of it.
Here is an extract from Gurevich's
http://research.microsoft.com/en-us/um/people/gurevich/opera/123.pdf
------------------------------------------
Q: Still, most mathematicians are Platonists, is that right?
A: I think so.
Q: Somehow we independently grow to become Platonists.
A: I do not think it is always independent. To an extent, we learn the
attitude.
I remember, in a geometry class, my teacher wanted to prove the
congruence of
two triangles. Let’s take a third triangle, she said, and I asked
where do triangles
come from. I worried that there may be no more triangles there. Those
were hard
times in Russia, and we were accustomed to shortages.
Q: What did she say?
A: She looked at me for a while and then said: “Shut up”. But
eventually I got
the idea that you don’t have to build a triangle when you need one;
all possible
triangles exist ahead of time.
--------------------------
Quantum physics would not exist if all physicists were as cock-sure of
objective reality.

Nor would computer science.

Heres a capsule history:
Kronecker and Cantor disagree on whether sets exist. K: Only numbers
exist. C: All manner of infinite sets exist
A generation later and continuing Hilbert and Brouwer disagree on what
constitutes a proof
A generation later Godel sets out to demolish Hilbert's formalist
agenda.
Turing tries to demolish Godel. He does not succeed (Simple questions
turn out to be undecidable/non-computable.
However a side-effect of his attempts is... the computer

Python version:
The integers that exist in builtin type int exist somehow differently
from the integers in function nats
def nats():
...   n = -1
...   while True:
...     n +=1
...     yield n

which once again exist differently from the integers in range(10).

In short: To be a computer scientist (as against classical scientist)
is to know that "to exist" "to be true" "to be valid" are more real
valued than boolean predicates