IZ wrote:
>
>
>
>Jesse Mazer wrote:
> > 1Z wrote:
> > >
> > >The clue is our failure ot observe HP universes,
> > >as predicted by Platonic theories.
> > >
> > >It a theory predicts somethig which is not observed,
> > >it is falsified.
> >
> > But this is a bit of a strawman, because most on this list who subscribe
>to
> > the view that every possible world or observer-moment exists (which is
>the
> > idea that the 'everything' in 'everything-list' is supposed to stand
>for)
> > would argue for some sort of probability measure on worlds/OMs which
>would
> > assign much higher probability to worlds with regular laws than to Harry
> > Potter universes.
>
>They *need* that idea, certainly. The success of mathematical MW
>theories
>depends very much on being able to find a natural, intrinsic
>justification for measure.
>
>Physical MW theories are very much on the same side of the fence
>as classical single-universe theories. In both cases, "measure" is
>extraneous
>to what is being measure. In physical MWI, measure is given by
>Schrodinger's
>equation, which is not justified platonically; it is justified
>empirically. In single-world
>theories , measure is 1 or 0 -- the Law of the Excluded Middle holds.
>
> > Quantum theory predicts a nonzero probability of Harry
> > Potter type events too (a bunch of random atoms could tunnel into the
>shape
> > of a living hippogriff, for example), but our failure to observe such
>events
> > in practice is not a falsification of the theory, since the theory
>predicts
> > they'd be ridiculously improbable and we should not expect to observe
>such
> > events on human timescales.
>
>And mathematical MWI *would* be in the same happy position *if*
>it could find a justification for MWI or classical measure.
>
>However, in the absence of a satifactory theory of measure,
>no-once can say that the posit of matter, of material existence
>is useless. To have material existence is to have non-zero measure,
>and vice-versa.
Yes, but the point is that almost all of us on this list want to *find* a
"satisfactory theory of measure" to apply to "everything", so it's a
strawman to say that it's a prediction of "everything" hypotheses that Harry
Potter universes should be just as probable as any other. Some rough
proposals for such a theory of measure have been made in this list in the
past, like the "universal prior" (see
http://parallel.hpc.unsw.edu.au/rks/docs/occam/node2.html or
http://www.idsia.ch/~juergen/everything/node4.html ), or my own speculation
that a theory of consciousness assigning relative and absolute probability
to observer-moments might have only a single self-consistent solution (see
http://tinyurl.com/ekz7u or
http://tinyurl.com/jnaqb for more on this idea).
>
> > >You are not going to get anywhere with the
> > >UDA until you prove mathematical Platonism, and your
> > >argument for that -- AR as you call it --
> > >just repeats the same error: the epistemological
> > >claim that "the truth -alue of '17 is prime is mind-independent"
> > >is confused with the ontological claim "the number of 17 exists
> > >separately
> > >from us in Plato's heaven".
>
> > But that is really all that philosophers mean by mathematical platonism,
> > that mathematical truths are timeless and mind-independent--
>
>nope.
>
>"Platonists about mathematical objects claim that the theorems of our
>mathematical theories - sentences like '3 is prime' (a theorem of
>arithmetic) and 'There are infinitely many transfinite cardinal
>numbers' (a theorem of set theory) - are literally true and that
>the only plausible view of such sentences is that they are ABOUT
>ABSTRACT OBJECTS "
>
>(emphasis added)
What do the words "abstract object" mean to you? To me, if propositions
about numbers have a truth independent of human minds or beliefs, that's
equivalent to saying they are true statements about abstract objects--how
could a statement be objectively true yet not be about anything?
>
>http://plato.stanford.edu/entries/platonism/#4.1
>
> > this is itself
> > an ontological claim, not a purely epistemological one.
>
>Quite. Did you mean that the other way around ?
No, I was responding to your comment:
>You are not going to get anywhere with the
>UDA until you prove mathematical Platonism, and your
>argument for that -- AR as you call it --
>just repeats the same error: the epistemological
>claim that "the truth -alue of '17 is prime is mind-independent"
>is confused with the ontological claim "the number of 17 exists
>separately
>from us in Plato's heaven".
Here you seem to be saying that "the truth value of '17 is prime' is
mind-independent" is a purely "epistemological" claim. What I'm saying is
that it's necessarily ontological, as are any claims about the objective
(mind-independent) truth-value of a given proposition.
>
> > Few would literally
> > imagine some alternate dimension called "Plato's heaven" where platonic
> > forms hang out, and which is somehow able to causally interact with our
> > brains to produce our ideas about math.
>
>Some do. In any case, if numbers don't exist at all -- even
>platonically --
>they they cannot even produce the mere appearance of a physical world,
>as Bruno requires.
But what does "exist" mean in this context? Do you think it makes sense to
say that there is are objective truths about objects which do not "exist" in
any sense? That does not make sense to me. On the other hand, the idea that
mathematical objects "exist" in the sense of there being objective truths
about them need not necessarily imply that possible self-aware observers
within complex mathematically-describable worlds would "exist" in the sense
that they'd be actual conscious beings whose experiences are just as real as
yours or mine (although I think it's a lot more elegant to assume they
would). But I think it's this question of the consciousness of different
possible beings within mathematical structures that's the key one in the
"every universe exists vs. only one universe exists" debate, not whether
mathematical laws are describing the behavior of "stuff" or whether the
mathematical relationships between events alone are all there is (how could
we possibly tell the difference? Believing in 'stuff' as opposed to
bare-bones mathematical relationships is not something that leads to any
distinct measurable consequences, so it has no connection to any empirical
results of science).
Jesse
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Received on Tue Jul 11 2006 - 16:11:57 PDT