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Topic: Mathematics and the Roots of Postmodern Thought
Replies: 101   Last Post: Apr 7, 2013 10:38 PM

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dan.ms.chaos@gmail.com

Posts: 409
Registered: 3/1/08
Re: Mathematics and the Roots of Postmodern Thought
Posted: Mar 26, 2013 7:05 AM
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Argued ... like a true scientist . We can do mathematics without any
appeal to science . However, science cannot function without a
mathematical framework. (all 'scientific models' are mathematical
models)

> We are born scientists. Children seek to understand the world around them; they do science. It's only later in life that they learn about the power of mathematics to help them reason about the world around them.

Some of us may be born scientists .Certainly not the majority (the
same being true for mathematicians , or philosophers ) . How else
would you explain religious inclination? I'm sensing you're using a
far too narrow definition of the human condition . I for one, as a
child , was never to much interested in exploring nature . I was far
more focused on internal experience and phenomena . I would stare at a
toy for hours (the toy in and of its self may have been boring, I
imagine ) , and imagine and construct fantastical scenarios .
And I was fascinated and preoccupied with numbers .A vivid memory is
that at about the age of five, I arranged the numbers from 1 to 25 in
a 5*5 square , according to some random rule . Then , with ave and
wonder , as I calculated the sums, I saw that it was what I would
later learn to call a 'magic square' . Does that exclude me from your
model ?

>"You "assume" that you are part of the world, and you "assume" that you are capable of reasoning about the world."

Not exactly . The ideal observer , for science , has always been
'external observer' the one that would 'see' reality without in any
way being part of it or influencing it . Like science, he would have
no 'need' for self-reflection . So you don't assume you're part of the
world . That's why even so many scientists struggle with quantum
mechanics .
Anyway , event taking into account these additional assumptions, how
does that have any bearing on my argument ?
All apples will turn violet tomorrow .

>"Science: first you observe the world, then you build up a conceptual model of the world, then you consider the implications of that model, then you experimentally test those implications."


I tell a scientist my mathematical theorem that no natural number's
cube can be written as the sum of two non-zero cubes . How would he
go about to test (prove or disprove ) that theorem ? According to 'the
scientific method' numbers are just distinct individuals that have no
necessary harmony as a whole . So the scientist would , in attempting
to disprove the mathematician , build a machine that tests for every
number, one at a time, if it can be written as the sum of two cubes .
If he finds one , too bad for the mathematician . A likely story. But
my money's on the one who has correct proper knowledge of the
situation , namely the mathematician . Having an infinite amount of
numbers to test , the scientist will never be able to finally prove
the mathematician . He would have to be on the negative side, not
because of any bearing of reality , but because only a negative answer
would finally put an end to the scientist's
sisyphean struggle of testing numbers .

Try arguing that induction is impossible with a mathematician .

If the world is, in truth , mathematical, then for a sufficiently
powerful and intuitive mind , the whole model-building process would
become a futile exercise . Have you ever seen 'The Matrix' ? Compare
Neo's vision of The Matrix http://josefflorian.files.wordpress.com/2012/10/large-matrix-blu-ray7.jpg
to the scientist, working within the Matrix, building his models and
obeying his 'falsifiability principle' . Which one is closer to
apprehending the reality of the Matrix ?

>Religion already does that.
Religion has made a lot of falsifiable claims , (fixed stars ,
geocentricism) , and they have indeed been falsified . It also made
claims that were essentially meaningless , neither provable nor
disprovable . Compare to mathematics/reason, the domain of certainty ,
who's claims (the infinitude of primes for example ) are as valid now
as they were 3000 years ago .

With a few notable exceptions , religion has been the domain of
fantasy , not reality . Then again ,religion and mathematics have
been, for the most part , disjoint ever since the end of antiquity
("Let no one enter here who is ignorant of mathematics" ,inscription
on the platonic academy. )

Even if religion makes non-falsifiable claims, your argument is based
on a fallacy : http://en.wikipedia.org/wiki/Association_fallacy

>It's an argument for its silliness.
I find this http://en.wikipedia.org/wiki/Gabriel%27s_Horn silly .
Also the existence of a continuous space filling curve :
http://en.wikipedia.org/wiki/Hilbert_curve .
I also find the experimental violation of Bell's inequality
hilarious .
Since when has silliness ever been an argument for or against the
truth of a statement ? Only a post-modernist would seriously consider
it as such. The truth doesn't give a damn about whether or not you
find it silly . All modern scientific theories are incomplete and
subject to revision .Gödel's theorem is here to stay .

Science is about the journey . A complete theory of everything would
leave scientists depressed and without occupation .They would still
conduct experiments to try and falsify it, no matter what
rationalistic proofs it rests on .It is within their interest to
produce as many theories as possible to later falsify. Mathematics is
about the destination .

More on Gödel: http://www.youtube.com/watch?v=cG7MyZtGSB0
More on the empiricism/rationalism conflict: http://www.youtube.com/watch?v=-W8fA0Z2cRE





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3/25/13
Read Mathematics and the Roots of Postmodern Thought
David Petry
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dan.ms.chaos@gmail.com
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