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