Date: Mar 25, 2013 10:32 PM
Author: David Petry
Subject: Re: Mathematics and the Roots of Postmodern Thought

On Monday, March 25, 2013 2:19:09 PM UTC-7, Dan wrote:
> On Mar 25, 7:14 pm, david petry <>
> wrote:

> > 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.

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

I doubt there's any truth to that at all.

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.

> To attempt to apply the ridiculous constraints of science to mathematics
> seems to me , frankly, ludicrous

If we agree that the purpose of mathematics is to help us reason about real world phenomena, then it most certainly is not 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 .

That's not really true. You "assume" that you are part of the world, and you "assume" that you are capable of reasoning about the world. Those are not trivial assumptions.

> 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.

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.

> 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 .

Religion already does that.

> Godel's theorem is incompatible with falsifiability , but that is not
> an argument for its falseness ,

It's an argument for its silliness.