On 3/25/2013 4:19 PM, Dan wrote: > 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. >
I liked your explanation of the necessity attached to universals. Very astute.