Date: Mar 25, 2013 5:19 PM Author: dan.ms.chaos@gmail.com Subject: Re: Mathematics and the Roots of Postmodern Thought On Mar 25, 7:14 pm, david petry <david_lawrence_pe...@yahoo.com>

wrote:

> On Monday, March 25, 2013 7:37:18 AM UTC-7, Dan wrote:

> > On Mar 25, 7:28 am, david petry <david_lawrence_pe...@yahoo.com>

> > wrote:

> > > Mathematics and the Roots of Postmodern Thought

> > > Author: Vladimir Tasi?

> > > Oxford University Press, 2001

> > > "[this book] traces the root of postmodern theory to a debate on the foundations of mathematics early in the 20th century" -- from a blurb appearing in Google Books

> > > I've always thought there was a connection:

> > > Theorem: Truth, reality and logic are mere social constructs.

> > > Proof: By Godel's theorem, yada, yada, yada

> > > I actually believe that postmodernism is driving western civilization into a dark ages. And I think that's a good reason for getting mystical metaphysical nonsense out of mathematics. But no one seems to care.

> > Rather ironic that you're attempting to use Godel's theorem to

> > undermine meaning in mathematics .

>

> Actually I'm not. The point I was alluding to is that whenever I see postmodernism discussed on the Internet, Godel's theorem always seems to come up. I think that's silly.

>

> Here's what I actually believe: Falsifiability, which is the cornerstone of scientific reasoning, can be formalized in such a way that it can serve as the cornerstone of mathematical reasoning. And in fact, it's already part of the reasoning used by applied mathematicians; ZFC, which is not compatible with falsifiability, is not a formalization of the mathematical reasoning used in applied mathematics. Also, Godel's proof is not compatible with falsifiability.

>

> It is falsifiability that gives mathematics meaning.

>

> > any well defined program either

> > halts of does not halt , always .

>

> Of course, the constructivists who reject the Law of the Excluded Middle, disagree.

Science originated from mathematics , not the other way around . To

attempt to apply the ridiculous constraints of science to mathematics

seems to me , frankly, ludicrous .

The principle of falsifiability says roughly this : you have this

mysterious entity , the world , like a black box , of which you don't

assume nothing about . Absolutely nothing . A black box that sends out

output that might as well be random . As a result of this , you can

have theories about how the box works, but you can never be sure .

Nothing about the world can be proven true , at most what you think

about the world can be proven false . The box may print out prime

numbers for 1000 years . So , you can assume it only prints prime

numbers . But then you see a composite number . And you're never

allowed to open the box .

Why this asymmetry? Never to prove, only to disprove . That is the

burden of falsifiability . Anything certain is non-falsifiable, by

definition . Certainty gives meaning , falsifiability erodes it. .

What it means is that my theory that 'All apples will turn violet

tomorrow' is not disprovable until tomorrow .

And my theory that 'All apples will at one time turn violet' is newer

disprovable .

In themselves, all models (guesses?) of the world will be

mathematical . Thus , relative only to themselves , being grounded in

the certainty of Mathematics, they will be true . Newtonian Gravity is

and remains a self-consistent theory, and can be simulated to great

extent , it just produces result incompatible with the the empirical

observations of the World . Thus , if we are to assume that the World

works somehow (already a heresy , a complete correct theory should not

be falsifiable ) , then Newtonian Gravity is not how the World

works .

Rather than attempting to extent falsifiability to Mathematics , we

should attempt to extent the adamant principles of Mathematics to the

World, thus freeing it from falsifiability . The pythagoreans knew

things scientists do not , namely , that the World is rational, and

the harmony between man as Microcosm and the world as Macrocosms (as

above ,so below , as within, so without ... know thyself...) .

Numbers are the bedrock of certainty . Here ,falsifiability can and

must stop . There are an infinite 'number' of numbers , (empiricism

and falsifiability are limited by finite observation ) , yet they

are all uniquely determined as individuals and as a whole.

Godel's theorem is incompatible with falsifiability , but that is not

an argument for its falseness , rather, a necessary condition for it

to be true . Indeed , what is mathematics (set theory excluded) is

compatible with falsifiability?

Is the fact that there are five regular polyhedra compatible with

falsifiability? That there are an infinite number of primes ? (Euclid

would be devastated ) That no cubed non-zero integer can be written

as the sum of two other cubed non-zero integers?

I share part of you aversion to set theory , but for entirely

different reasons . Forgive me if my tone seemed attaching, I often

seem outspoken ... Now that I've exposed more of my viewpoint, I

would like to hear more of yours. There's always something new to

learn.