Math-embarrassment results in CS [was: Should non-security 2.7 bugs be fixed?]
rustompmody at gmail.com
Wed Jul 22 15:34:28 CEST 2015
On Tuesday, July 21, 2015 at 4:09:56 PM UTC+5:30, Steven D'Aprano wrote:
> We have no reason to expect that the natural numbers are anything less than
> "absolutely fundamental and irreducible" (as the Wikipedia article above
> puts it). It's remarkable that we can reduce all of mathematics to
> essentially a single axiom: the concept of the set.
These two statements above contradict each other.
With the double-negatives and other lint removed they read:
1. We have reason to expect that the natural numbers are absolutely fundamental and irreducible
2. We can reduce all of mathematics to essentially a single axiom: the concept of the set.
So are you on the number-side -- Poincare, Brouwer, Heyting...
Or the set-side -- Cantor, Russel, Hilbert... ??
> On Tuesday 21 July 2015 19:10, Marko Rauhamaa wrote:
> > Our ancestors defined the fingers (or digits) as "the set of numbers."
> > Modern mathematicians have managed to enhance the definition
> > quantitatively but not qualitatively.
> So what?
> This is not a problem for the use of numbers in science, engineering or
> mathematics (including computer science, which may be considered a branch of
> all three). There may be still a few holdouts who hope that Gödel is wrong
> and Russell's dream of being able to define all of mathematics in terms of
> logic can be resurrected, but everyone else has moved on, and don't consider
> it to be "an embarrassment" any more than it is an embarrassment that all of
> philosophy collapses in a heap when faced with solipsism.
That's a bizarre view.
As a subjective view "I dont feel embarrassed by..." its not arguable other than
to say embarrassment is like thick-skinnedness -- some have elephant-skins
some have gossamer skins
As an objective view its just wrong: Eminent mathematicians have disagreed
so strongly with each other as to what putative math is kosher and what
embarrassing that they've sent each other to mental institutions.
And -- most important of all -- these arguments are at the root of why CS
'happened' : http://blog.languager.org/2015/03/cs-history-0.html
The one reason why this view -- "the embarrassments in math/logic foundations
are no longer relevant as they were in the 1930s" -- is because people think
CS is mostly engineering, hardly math. So (the argument runs) just as general
relativity is irrelevant to bridge-building, so also meta-mathematics is to pragmatic CS.
The answer to this view -- unfortunately widely-held -- is the same as above:
A knowledge of the history will disabuse of the holder of these misunderstandings
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