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.