Georges Quenot wrote:
> peterdjones wrote:
> > Georges Quenot wrote:
> >> peterdjones wrote:
> >>> Georges Quénot wrote:
> >>>> It is just the idea that there could be no difference between
> >>>> mathematical existence and physical existence.
> >>> Then why do we use two different words (mathematical and physical) ?
> >> For various historical and practical reasons and because
> >> identity is still a conjecture/speculation. Just like we
> >> used to consider "inertial mass" and "gravitational mass".
> >
> > So you meant "there might not be any difference",not "there cannot
> > possibly be any difference".
>
> I meant "the idea is that it is possible that there is no
> difference ...".
>
> >> it would be a
> >> "mathematical monism" in which one and only one particulat
> >> "mathematical object" would exist. This seems logically
> >> difficult and then: why just this one?
> >
> > Why only mathematical objects and not any other kind ?
>
> We were talking of mathematical objects and I asked why only
> one of them would be "given" "physical existence" (as *you*
> suggested).
And my reply is that it is "just so" that only one mathematical object
is instantiated,according to the one theory;
likewise it is "just so" that every mathematical object is
instantiated, and no non-mathematical object is instantiated,
according to the other.
> The question of whether there could be other type of objects
> than mathematical is a different one. I can figure what could
> mathematical objects and that they can exist (though I am
> afraid I cannot easily transmit that feeling). It is harder
> for me to imagine what non mathematical objects could be and
> how/why they happened to come to existence.
My candidates for non-mathematical properties are
1) existence/materiality itself (that is, physical existence in a
partiucalr
place at a partiouclar time)
2) time (causality , laws)
3) consciousness, specifically qualia.
>Did some God pull
> them out of nothingness?
Why would a God be needed to create non-mathematical objects
but not mathematical ones ? Is that a feeling, too ?
> >>> We can go some way to explaining the non-existence
> >>> of HP universes by their requiring a more complex
> >>> set of laws (where "we" are believers in physical
> >>> realism).
> >> Whether HP universes require or not a more complex set
> >> of laws is a very good question but it seems unlikely
> >> that it can be easily answered. For some physicists,
> >> the currently known (or freseeable) set of rules and
> >> equations for our universe *is* compatible with "HP
> >> events".
> >
> > Physical MWI is more constrained than mathematical
> > multiverse theories, so there is not so much Harry-Potterness.
>
> This is just an opinion.
Not at all. The whole point of physics is to find the "right"
mathematical structure to
describe the universe. Such a structure describeds the laws of the
universe and
the laws constrain what is possible in the physical universe.
> It must refer to prejudices about
> what physical MWI and mathematical multiverse theories could
> or could not be.
Phyiscal MWI theories can appeal to a set of constraints that are
"just so" (such as the schrodinger equation) and mathematical
one scan't. This is all extremely obvious, it is prety well given by
the meaning sof
the words "physical" and "mathematical".
http://home.sandiego.edu/~baber/logic/possibility.html
> > Moreover,
> > physical MWIs have measure and can at least predict the HP
> > universes will be rare (or faint, or something).
>
> This question of measure is difficult but I see no reason
> why this should differ between physical MWI and mathematical
> multiverse theories.
Physical theories can appeal to a law of "measure" that is "just so".
> >> Such events might appear in other portions of
> >> our universe. For others, it is just the opposite, it
> >> might well be that there do not exist any set of rules
> >> and equations that would correspond to a "HP universe".
> >
> > There cannot fail to be. The HP game my nephew
> > plays on is a mathematical simulation -- what else
> > could it be?
>
> I am not sure that what your nephew plays with is a rich
> enough mathematical description so that, even if it was
> "turned physical" by some God or magician, it would contain
> conscious beings.
So ? Why should it be impossible for any HP world, however detailed, to
contain
cosncious beings ? A believer in a physical multiverse
theory could argue that wolrds containing conscious beings must
be worlds containing oxygen, for instance. But that is an appeal to
causality, which is an appeal to physical laws that are "just so".
> Furthermore, most of this HP universe is
> in the brain of your nephew. What is in the game would be
> almost nothing without your nephew's imagination to fill
> the (huge) gaps.
[ shrugs ] your mathemtical multiverse contains every possible
structure, however detailed, so it contains a class of structures
resembling
the HP game but with infinitely more detail. You don't seem to be
following your
own hypothesis through.
> >>> However, we are bound to end up with
> >>> physical laws being "just so".
> >> Not really. What is "just so" is that a conscious being
> >> has to live in only one universe at once just as he has
> >> to live in only one place and in only one period of time
> >> at once.
> >
> > That does not follow form the mathematical
> > hypothesis. If I am a set, I am a subset of any
> > number of other sets. If I am a digit-string, I a m a
> > substring of any number of other substrings.
>
> This is where we have a different intuition about what
> mathematical objects can be and what a mathematical object
> containing (description of) conscious beings might be. For
> me this is just like you have to live here and now and not
> in Egypt 3500 years ago.
That is true on the common-sense basis. I don't see any justification
for it mathematically ?
> What "aspect" of a mathematical
> object I could be is not so clear to me but it is unlikely
> to be as trivial as a digit string.
What mathematical object cannot be embedded as an exact duplicate in
another object ? Do you have anything specific in mind ?
actually know ?
> >> It is no more mysterious that I do not live
> >> Harry Potter's life that I do not live Akenaton's life.
> >
> > From the common-sense POV, yes. From the MM POV, no.
>
> Maybe there is more than one MM POV. MM does not really
> have POV. You and I have POV on what MM can or cannot be.
> And they do differ.
it's called "logic".
Hypotheses have whatever implications they have.
> >> And lots of "HP-like" events have also been reported in
> >> *this* world.
> >
> > Nowhere near enough! (compared to what MM predicts).
>
> MM does not predict.
Hypotheses have implications.
> You do and I do from our respective
> interpretations of what MM could or should be (or not).
It's becoming increasin apparent that your mathematical metaphysics is
embedded in a subjective relativism. What is wrong with stating
axioms clearly, and seeing what the consequences are ?
> >>>>>> Do you find that "physical monism" ("mind emerges from
> >>>>> matter activity"),
> >>>>>
> >>>>> All the evidence points to this.
> >>>> OK. So in your view this makes sense and is likeky to be true.
> >>> Those are two different claim: it is likely to be true,
> >>> but seeing *how* it is true, making sense of it is the Hard Problem.
> >>> IMO the hardest part of the hard problem is seeing how mind
> >>> emerges from mathematical description -- from physics in the
> >>> "map" sense, rather than the "territory" sense. Switching to
> >>> a maths-only metaphysics can only make the Hard Problem harder.
> >> As I perceive it, this is the hard problem even starting
> >> with a (classical) physical context. A I perceive it also
> >> placing it in a mathematical context doesn't make it harder
> >> or easier. But this is just from my viewpoint indeed.
> >
> > You didn't say why it doesn't change anything.
>
> I mean that whatever there might be in particles to make
> them real is irrelevant to the question since (this is a
> conjecture) all that is needed to determine the behavior
> of particles is the set of rules and equation they have
> to follow.
If a set of real particles follow one set of equations and not another,
then one set
models real laws and not the other.
> What they are made of (if any) has no influence
> on that.
We were talking about the Hard Problem. If there is no purely
mathematical reason
why one set of equations is followed and another is not, there is
likewise no
purely mathematical reason why one structure is conscious and another
not.
> > I think
> > that having a richer ontology automatically makes it easier
> > to solve metaphysical problems, since you can say that X , Y or Z
> > is intrinsic to the universe and therefore not to be "explained away"
> > as something else. Of course, this manoeuvre should be used sparingly.
> > An intrinsic theory of heat would have been dead wrong.
>
> As long as what is inside particle has no effect on the
> particle behavior I do not see how it can help to understand
> how sets of interacting particles (this is an image) can
> produce consciousness.
If the universe were deterministic, then consicousness would have to
be epiphenomenal. However, the evidence is that the universe is not
deterministic.
> >>> "Epistemic objectivity of maths" means "every competent mathematician
> >>> gets the same answer to a given problem". It doesn't say anything about
> >>> the existence of anything (except possibly mathematicians).
> >> Well, if "every competent mathematician gets the same answer
> >> to a given problem", "competent mathematicians" do not have
> >> much freedom about what they might find as an answer to some
> >> given problems. So there must "exist" "something" that
> >> "constrain" them.
> >
> > Yes: rules, the principle of non-contradiction.
>
> So. These exist for you too? Are they physical objects?
I don't need to hold that they have any existence separate
form mathmaticians or textbooks.
> >> And "this" might even exist in the absence
> >> of "competent mathematician".
> >
> >
> >>> isomorphism is **not** identity!
> >> This is obviously untrue: it might well be that not all
> >> isomorphisms are identity
> >
> > then isomorphism is not identity,
>
> I said "not all". I did not said "none of".
> > since identity is not mere overlap.
>
> Identity is: "f(x) = x".
http://plato.stanford.edu/entries/identity-indiscernible/
> Isomorphism is: "f(a R b) = f(a) R f(b)".
> I am sure you can make it.
http://www.princeton.edu/~jburgess/Kripke2.doc
> >> but, indeed, identity is always
> >> an isomorphism and, hence, at least *some* isomorphisms
> >> *can* be the identity.
> >
> > can be, yes,
>
> Yes. You finally got it. It *can* be.
>
> > but more is needed for MM than Tegmark's hypothesis.
>
> This is a question of viewpoint. I would rather say that more
> than Tegmark's hypothesis is needed for *something else* (or
> something more) than MM.
Tegmark's hypothesis is explcitly a claim of isomorphism.
MM is a claim of identity.
Isomorphims *can* be identity....but to show that one *is*,
something more is required.
> Tegmark's hypothesis is indeed necessary. It might be that is
> is not sufficient but is it necessary to postulate something
> more? What can we explain better with something more? Apart
> from just saying that "it must be richer, we should get more
> out of it"?
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Received on Fri Mar 31 2006 - 09:50:38 PST