Re: Why does everyone do it?
- From: david petry <david_lawrence_petry@xxxxxxxxx>
- Date: Mon, 1 Sep 2008 20:03:26 -0700 (PDT)
On Sep 1, 6:48 am, "G. Rodrigues" <sorlak...@xxxxxxxxxxx> wrote:
On Aug 31, 10:04 am, "G. Rodrigues"
<sorlak...@xxxxxxxxxxx> wrote:
So, you do admit that Set theory is "essential forunderstanding current theories about how the world
works".
Set theory has become part of the language of modern
mathematics, and
the mathematical physicists often borrow that
language. So one would
have trouble understanding what the mathematical
physicists are
talking about without knowing at least a little about
set theory.
Let's keep this discussion as simple as possible.
At the end of the day, the physicist wants to
compute. That is, he
wants a computer program such that he can plug in the
parameters
characterizing some experimental setup, and then the
computer will
spit out numbers that can be interpreted as making
predictions about
the outcome of that experiment. That's the holy
grail of physics.
Emphatically, the physicist is searching for an
object (a computer
program) that lives within the world of computation.
Set theory
implies the existence of a world of the actual
infinite lying beyond
the world of computation, and in fact, it adds
nothing to mathematics
except for that fantasy world. It is my claim that it
is rather
ludicrous to search in the world lying beyond the
world of computation
when what you are looking for lies within the world
of computation.
I believe that's a simple and valid argument proving
that set theory
cannot be essential for understanding how the world
works
1. My reply was mostly prompted by your statement that Set theory
is not *useful* in modelling the world. Although not in so many words,
you seem to recognize that you were wrong.
"Useful" is a somewhat subjective notion, and so I admit I was sloppy
when I said that set theory is not useful for modelling the real
world.
2. I never claimed that Set theory was *essential*, in the sense that
apart from it we have no way of understanding the world. I do not recall
ever reading anyone claiming that. It is a strawman of your own doing.
I think you are not being honest here. I clearly stated that set
theory is not essential to our understanding of the world, and you
argued very loudly against what I was saying, and hence I was
reasonable in concluding that you think it is essential.
3. Apart from your claims that it can be done, do you actually have some
evidence that the mathematical edifice, say of QM, can actually be done
outside Set theory?
If I recall correctly, it was no less a figure than Richard Feynman
who said that if all the fancy schmancy mathematics were never
invented, physics would have been set back by less than a week.
4. Even if such a reconstruction is done, can be done, will be done, what makes you say that physicists will suddenly start to learn and employ your shiny new tools? This is a purely mathematical foundational problem, why should they *care*?
Some people care about the notion of truth.
.
- References:
- Re: Why does everyone do it?
- From: G. Rodrigues
- Re: Why does everyone do it?
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