Date: Mar 25, 2013 5:26 PM
Author: fom
Subject: Re: Mathematics and the Roots of Postmodern Thought

On 3/25/2013 4:19 PM, Dan wrote:
> On Mar 25, 7:14 pm, david petry <>
> wrote:

>> On Monday, March 25, 2013 7:37:18 AM UTC-7, Dan wrote:
>>> On Mar 25, 7:28 am, david petry <>
>>> 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.

I liked your explanation of the necessity
attached to universals. Very astute.