From: Dan Fabulich (dfabulich@warpmail.net)
Date: Thu Sep 05 2002 - 14:24:27 MDT
Lee Corbin wrote:
> Dan wrote
>
> > > > Maybe realism is your favorite language for science (though it's still
> > > > a difficult fit in QM), but non-realism teaches you the most about how
> > > > to look at morality, or at mathematics.
> > >
> > > I don't follow this. Do you have an example for each? I claim that
> > > anything with actual content is best spoken about with realistic
> > > language.
> >
> > In quantum mechanics: the Heisenberg Uncertainty Principle.
> > Subjectivists had been arguing for a world view in which we
> > reify uncertainty as part of our world, in which there are
> > no deeper facts than those about which *we* are certain.
>
> Their's isn't the only view. As gts wrote later, there are
> realistic theories of physics that don't commit the error
> you have in mind here.
My point was that the scientific fruit was born with the subjectivist
view... MWI came later as an attempt to shore up what were perceived to be
philosophical problems with the Copenhagen interpretation.
> In particular, the Many Worlds Interpretation provides an
> entirely satisfactory account for an ever growing number of
> physicists. Years ago followers of MWI were a small minority,
> restricted almost entirely to cosmologists. I think that as
> we continue to free ourselves from the bad thinking of the
> 20th century, the MWI will become more popular. David
> Deutsch, perhaps the greatest exponent of MWI I believe
> attributed to his realistic outlook his discoveries in
> quantum computation.
Perhaps you're right; I think the current scientific field is against it,
and not just for the Occam's Razor problems. (Aside: I actually think the
Razor is a wash in this case. MWI creates more worlds, and therefore more
entities, but Copenhagen creates a special physical category for
observers, and so creates more types of entities. MWI is therefore
favored by Occam's Razor as homogenous, but Copenhagen is favored as
having fewer actual objects. Who wins?)
Lee Smolin raises a good philosophical critique against MWI in his _Life
of the Cosmos_, where he argues that MWI is troublesome because it creates
new *unobservable* entities. He argues, therefore, that it's needlessly
Platonist in the sense that it calls the ideal unobservable world the
"real" world, and calling the world of our observations somehow less than
the real. Only God, he points out, could have a point of view in which it
made sense to say that the worlds split, since we have access only to our
side of the split.
Did you notice a pattern here? Realists and non-realists are never so
simply opposed. Subjectivists are realists about uncertainty, MWI is
non-realist about quantum randomness... you're always a realist about
something and a non-realist about something else.
> > In mathematics, the answer is even easier. Are there *really* numbers
> > apart from the natural numbers? Is 0 real? How about the negative
> > numbers? How about the imaginary numbers?
>
> Yes, they all exist.
Not under all arithmetic axioms. Some of them explicitly rule out their
existence (though it's possible to find analogues, kind of like how Godel
could find numerical analogues to sentences).
> > How about the "supernatural" numbers Hofstadter suggested in GEB?
>
> They are trivial, and cannot be connected up to the rest
> of the discovered numbers, and may even be inconsistent
> with them (I don't recall exactly).
Ah, NO. :) See, the supernatural numbers are like the non-Euclidean
meeting point for parallel lines. They definitely aren't ruled out by the
axioms of arithmetic. I don't have GEB on hand at the moment, but I'll go
home and get it.
The essential point about them was this: Godel's theorem allowed you to
claim that there was a number that had a certain property only if a
certain claim was provable by the standard axioms of arithmetic. He then
went on to try it with the claim "This claim is not provable by the
standard axioms of arithmetic." As the story normally goes, you suppose
that you add that new claim as an axiom of arithmetic, but then you can
find another unprovable claim in the same manner, and so on.
But Hofstadter said: wait a second. Suppose, instead of assuming that
unprovable claim as another axiom, we assume its NEGATION as another
axiom. That means that there are these supernatural numbers with these
supernatural properties [such as the property of translating into a proof
of an unprovable claim], supernatural because you could identify no
particular natural number which had this property (just like how you can't
identify a particular distance at which parallel lines meet in Euclidean
geomtry + a negation of the parallel postulate, or like how you can't find
the natural number that actually *is* the square root of negative one,
even if you let it be the case that there exists one). He went on to
explore these supernatural numbers a little bit (space permitting) and
then discussed something else. Point is that they're definitely not
contradictory, even if they seem like they couldn't possibly exist.
I'll track down the passage with more info. The real point is that
arithmetic is exactly like geometry in this regard: you can have a
consistent and interesting arithmetic which denies the existence of
imaginary numbers, and you can have another consistent and interesting
arithmetic which DOES have imaginary numbers. They're not consistent with
each other, of course, but who cares? You can explore their ("real?")
consequences all the same.
> > In geometry, are we to be realists about Euclid's axioms? What about
> > non-Euclidean geometries? Here, reinterpretations from different
> > systems are obviously fruitful, and obviously non-realist.
>
> I think that geometry isn't really problematical: you have a number of
> axioms, and you have the theorems that flow from those axioms.
But those axioms are contradictory! You give away the farm when you talk
like that. I also think that geometry isn't problematical, but that's
because it's *not realist.*
> Finding out *the* geometry of our universe--- i.e., which one happens to
> characterize (perhaps only to some degree) our universe is kind of an
> empirical question.
Oh, sure, sure. So, we know a few things about this and that, and one of
them is that our universe doesn't have simple flat Euclidean geometry.
So... uh... should we be realists about Euclidean geometry? We know it
doesn't describe our space. Does it describe Euclidean space? Is that
space real?
> Mathematicians are much more worried about set theory. The question is
> "is aleph one equal to the continuum" continues to haunt us realists.
> Godel, Soloway, Penelope Maddy and the rest of us, I think, are put upon
> to explain why a clear answer keeps evading us. (Yes, we already know
> that the problem of the continuum is independent of the Zermelo Frankel
> axioms; the trouble is that Godel among others thought that by now a new
> axiom would have revealed itself to us that would have the right
> characteristics.)
The continuum hypothesis is only one of a huge bag of mathematical
"problems." You can let them bother you, if you're a realist, or not, if
you aren't. :)
Same with the "\exists future" question. If you're a realist, it's a
problem, especially if you're a realist about that formalism. But if
you're not a realist... eh. It doesn't bother me. ;)
> I agree: in some cases it leads to fruitful conclusions, and in some
> cases it doesn't, and we shouldn't be shy about criticizing the efforts
> that we think fail.
We're converging, I see. ;)
> > In case you hadn't noticed, alternate language models have ALREADY taken
> > over the world. ;) We use different language models for different
> > situations all the time; I've already named a few. Studying any of the
> > seminal works here will give you dozens more.
>
> Yes, in specialized areas, jargon is triumphant. But I don't
> think that non-realistic jargon is anywhere worthwhile, do
> you?
Well, you granted me the meaning of life. And say what you will about the
Copenhagen interpretation of QM, I think you could hardly call it
*worthless*. :) And, hey, what *about* those geometries?
> > [snipped metaphysics of whether the future really \exists]
> Good questions. I wish I had something to add. My guess is that
> human languages (like English) are universal in a strong sense,
> and that *anything* can be expressed in them by one intelligence
> so that another intelligence in principle is able to follow. (The
> latter uses his own conjectures, but the description provided by
> the former channels his thinking appropriately.)
Well, I brought up that point for a reason. The point is that there *is*
a difference with regards to which language in which you choose to pose a
problem. Philosophical problems appear in one language that don't exist
in another. This isn't to say that they're "interesting" to one culture
but "boring and unanimously solved" by another. I mean, as in the case of
the metaphysics of the future, that the choice of language actually opens
and closes certain philosophical problems.
I brought up a language in which it would be impossible to avoid using
certainty tenses as an example of a case in which a philosophical problem
of epistemology would be eliminated as ungrammatical. The downside of
realism is that we can't switch to a language in which certainty is part
of the grammar; talk must always be about what it is (without anyone's
subjective certainty), not what we think it probably is.
Should we all switch over to this language? No, probably not. But should
we use it for special cases, like QM? Yes, we should. Furthermore, we
should expect that using it like this will result in real advances in
science, mathematics, engineering (model design, anyone?), as well as
literature, aesthetics and other philosophy.
> > Academic disputes are almost entirely non-violent. I believe
> > that counts for quite a lot!
>
> I think that it's more a reflection on who gets drawn into
> academic disputes. Similarly, theologians *themselves*
> rarely resort to violence (it's their followers). Also,
> don't forget that Fibonacci was chased out of town a few
> times for having bested the *local* Italian mathematician.
I actually didn't know that. :) Was he chased out of town due to a
mathematical dispute? ("The Riemann hypothesis is true!" "False!"
"True, infidel!" "False, scum!") Or was he chased out due to the
mathematician's embarassment? Or is it your point that it doesn't matter?
> Well, then, if you are going to be *that* charitable, why
> not just give me a pass on all my remarks too? :)
Well, I do, sort of...
> You had better be able to call a spade a spade, talk plainly,
> and criticize error when you see it. Anyone who defends
> Latour in the mentioned instance is IMO making a big mistake.
See, I don't think you're making a "mistake" as such. You're arguing for
a different point of view, which I may or may not fully accept as my
primary mode, but which I will at least be able to use in the course of
confronting future problems and questions.
That's the attitude I advocate towards Latour. He's not making a "oops!"
mistake. If he's making a mistake at all, it's something entirely
different from what the school child does when he accidentally claims that
6x9 is 42.
Note that, against this, I DID charge Damien as making a "mistake" when he
argued that he knows that the earth rotates around the sun, but if he had
been a medieval astronomer, he would have known that the sun rotates
around the earth. I argued *from his own point of view* that it couldn't
be correct. In that regard, I could argue with a Euclidean geometer that
some "proof" he had presented couldn't be right, because it would
contradict the parallel postulate, but I couldn't make that argument
against a non-Euclidean geometer.
Or, were you and I were inertial observers moving at relativistic speeds
and disagreed about the length of an object because you had
(coincidentally) made a mistake with your calculator, I could correct you
*from your own frame of reference* as to what an object's length should
be, [on the basis of what I find the length to be, my measurements of your
velocity, and my understanding of special relativity,] but I couldn't
argue that you were simply wrong about your length because you disagreed
with the length I measured.
-Dan
-unless you love someone-
-nothing else makes any sense-
e.e. cummings
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