1Z wrote:
>
>
>
>Jesse Mazer wrote:
> > IZ wrote:
> >
> > >
> > >
> > >
> > >Jesse Mazer wrote:
> > > > IZ wrote:
> > > >
> > >
> > > > >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.
> > >
> > >
> > >Wanting to find a measure theory doesn't mean you have
> > >found one, and if you havent found one, it isn't a straw man
> > >to say so.
> > >
> >
> > But it is a straw man to say "everything-theories makes the prediction
>that
> > Harry Potter universes should be just as likely as lawlike ones",
>because in
> > fact they do *not* make that definite prediction. If you had just said
> > something like, "everything theories do not yet have any rigourous proof
> > that Harry Potter universes should be less likely than lawlike ones" I
> > wouldn't object.
>
>If they do not yet have any rigourous proof
>that Harry Potter universes should be less likely than lawlike ones
>then they do IN FACT make the prediction that
>Harry Potter universes should be just as likely as lawlike ones
If a theory can't predict the relative probabilities of X vs. Y, that is not
in any way equivalent to the statement that it predicts X and Y are equally
likely. One is an absence of any prediction, the other is a specific and
definite prediction.
>
>Classical physicists din't WANT to make the
>implications that atoms are unstable and will
>implode; nonetheless, classical phsyics makes that
>assumption.
Yes, that is a definite prediction of classical mechanics, and therefore has
nothing to do with examples of theories that cannot make definite
predictions about certain questions in the first place. A more analogous
case would be the fact that string theory cannot at present predict the
value of the cosmological constant; would you therefore conclude that
"string theory predicts all values of the cosmological constant are equally
likely"?
>
>
> > > > > > >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?
> > >
> > >
> > >By having sense but no reference, for instance.
> > >
> > >http://en.wikipedia.org/wiki/Sense_and_reference
> >
> > The sense/reference distinction is about the possibility of our having
> > multiple mentally distinct terms which map to the same real-world
> > object...but what would "sense but no reference" mean?
>
>We can make "sense" of "unicorns have horns", despite
>the lack of reference.
In this case I would say the reference would be to a certain concept which
humans have collectively defined; there is no way you could have a
mind-independent truth about whether unicorns have horns that's separate
from what people collectively believe about unicorns.
>Senses are logically
>interelated in a way that allows us to confirm
>the truth-values of *some* sentences
>without seaking theri references. Those
>kind of sentences are called apriopri, and it
>is almost universally held that mathematical sentences
>are apriori.
Holding that they are a priori is not the same as holding that they lack
references; platonists would presumably agree they're a priori.
>
> > I don't see how there can be an
> > objective, mind-independent truth about a term that doesn't refer to any
> > coherent object or possibility.
>
>I am not asking you to. There are coherent possibilities that
>are not instantiated (or perphaps
>I should say, pace many-worlders, not obviously instantiated).
>
>Nonetheless, we can address many issues about these possibilites
>without peaking into the universe next door. Many-world
>metaphysics is not needed to explain how abstrract reasoning
>is possible.
I agree, and even a "modal realist" philosopher like David Lewis (see
http://en.wikipedia.org/wiki/David_Lewis_(philosopher) ), who thinks that
propositions about possibilities can only be objectively true or false if we
assume all possible worlds actually exist, would not say that there is any
kind of causal interaction between worlds needed to explain our ability to
reason about them.
>
> > Can you think of any statements outside of
> > math or logic that you would say have "sense but no reference" but also
>have
> > a mind-independent truth value?
>
>What difference does it make ? The topic is maths.
The question was to try to help me grasp what you meant by "sense without
reference" and "mind-independent". If it's impossible to come up with any
examples outside of math, that should make you suspicious whether
mathematics really has the strange and marvellous property of there being
objective mind-independent truths about mathematical terms even though they
lack any reference. If you really believe this, you should at least be able
to give an argument about *why* math is different from every other domain in
this respect.
>
>
> > >The case for mathematical Platonism needs to be made in the first
> > >place; if numbers do not exist at all, the universe, as an existing
> > >thing, cannot be a mathematical structure.
> >
> > Again, what does "exist" mean for you?
>
>Capable of interacting casually with me,
Well, I don't think the world obeys mathematical laws because it is causally
interacting with platonic forms, any more than I think the world obeys the
law of noncontradiction because it is causally interacting with platonic
laws of logic. I would say ontology is about the most exhaustive possible
list of objective truths, and any entity referred to in this exhaustive list
of objectively true statements "exists" by definition. With something like a
unicorn, once you have all true statements about peoples' *concepts* of
unicorns, you won't have any additional statements about what unicorns are
"really" like; but with mathematics I think there can be statements that
would be true even if no human had thought about them, or if they had
thought about them but concluded they were false due to some mental error.
Incidentally, does your definition of "exists" mean that you don't think
anything exists beyond the boundaries of the observable universe?
>
>
> > >However, the basic case for the
> > >objectivity of mathematics is the tendency of mathematicians to agree
> > >about the answers to mathematical problems; this can be explained by
> > >noting that mathematical logic is based on axioms and rules of
> > >inference, and different mathematicians following the same rules will
> > >tend to get the same answers , like different computers running the
> > >same problem.
> >
> > "Tend to", although occasionally they can make mistakes. For the answer
>to
> > be really objective, you need to refer to some sort of ideal
>mathematician
> > or computer following certain rules, but that is just another form of
> > Platonism.
>
>
>Not really. You can understand how an ideal system
>would behave by projecting from non-ideal ones. You
>don't need an actual example of one.
Do you think there is any sense in which your projection could be
objectively wrong, even if you believe it is correct?
>
> > > > >
> > > > >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.
> > >
> > >It certainly *could* be, at least. Platonism is *not* the only
> > >philosophy of mathematics!
> >
> > I think it's the only philosophy of mathematics that says that
>mathematical
> > statements have a *mind-independent* truth-value, though.
>
>
>Nope.
OK, can you describe another?
>
> > > > 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.
> > >
> > >So you are claiming that mathematical Platonism is not merely
> > >true but *necessarily* true ? That is quite a claim!
> >
> > No, you misunderstood. I'm saying that *if* you believe that
>mathematical
> > statements have a mind-independent truth-value, that is necessarily is
> > equivalent to what I understand "mathematical Platonism" to mean.
>
>Then you are wrong. MP is an ontological thesis.
You are still misunderstanding, of course MP is an ontological thesis, where
do you think I was arguing otherwise? What I'm saying is that any statement
of the form "there is a mind-independent truth about X" is an ontological
statement, by necessity. It is not a "necessity" to believe that statements
about math are ontological ones, though, because you are free to deny that
there is any mind-independent truth about them (in which case you are
obviously not a mathematical platonist). But your claim that "the truth
value of '17 is prime' is mind-independent" is a "purely epistemological"
claim is what I'm disagreeing with, because again, any statement about
mind-independent truths is an ontological statement as I understand
ontology.
>
> > Of course,
> > you may not in fact believe that mathematical statements have any such
> > mind-independent truth-value.
>
>As I ahve stated, everybody believes that. You are talking
>as though it were an obvious fact that ontolical realsim
>is the only explanation for epistemological objectivity.
Yes, but that's because my notion of "existence" is simply a shorthand for
an element of reality about which there exist objective truths. Perhaps this
debate is just a disagreement about word-definitions, but I suspect that any
other notion of existence would either be too poorly defined to be
meaningful, or would lead to bizarre conclusions like the notion that
nothing exists beyond the boundaries of the observable universe (or beyond
your own past light cone).
>
>
> > >I ma saying that not only does mathematical Platonism "not necessarily"
> > >imply consious observers within Platonia , it just doesn't imply
> > >it *at all*. (For heavens' sake, it doesn't even imply
> > >computational *processes*, since Platonia is timeless!)
> >
> > Most physicists today take a "spacetime" view of the universe in which
>the
> > notion of a global objective past, present and future is meaningless
>(for
> > any given event, it is of course true that everything in its future
>light
> > cone objectively lies in its future and everything in its past light
>cone
> > objectively lies in its past, but there is no objective truth about
>whether
> > events not in either light cone lie in the first event's past, future,
>or
> > present).
>
>So time is local.
But that would make "existence" local too, rather than objective. My light
cones are different from yours, so if you want to say that the past is
"real" in a sense that the future is not, that would make the reality of
events different for each observer.
>
> > Philosophically, I don't think the notion of time "really moving"
> > is even coherent--how could the present "move" without introducing a
>second
> > time dimension, for example? Are you familiar with McTaggart's
>distinction
> > between the A-series and the B-series view of time? Are you arguing for
>the
> > A-series here? If so I think few physicists would agree--see for example
> > http://tinyurl.com/nesh7
>
>http://www.geocities.com/peterdjones/met_time2.html
His argument simply assumes that a moment can "become existent", without
addressing this question of whether we need a second time dimension to make
sense of this. And as he admits, he is "assuming that such a thing as
becoming is possible without describing or explaining it".
>
> > >That is its observatioanl consequence.
> >
> > It's not an observational consequence if you don't happen to be in one
>of
> > the Harry Potter worlds!
>
>Mathematical Platonism also doesn't (obviously) have the resources
>to keep "worlds" separate.
Sure it does. Different Turing machine programs are mathematical objects,
no? If you run a particular Turing machine program which contains
intelligent beings, will they somehow have psychic knowledge of what's
happening in other distinct programs? Obviously not, we could run the
program on a real computer and see that the beings have no such mysterious
knowledge, and barring errors the ideal "Platonic" program should have the
same output as the 'physical' instantiation ('physical' from the perspective
of the most fundamental laws of our universe, which could itself be a
program running in a bigger universe or in 'Platonia').
> > No multiverse theory predicts that observers should
> > have an omniscient view of all universes, they only see the one they are
> > living in.
>
>All mathematical multiverse theories have the implication that
>I have many identical counterparts.
"Identical" only to the extent they are experiencing the exact same things
you are. There's no reason to think that counterparts basically similar to
you but having different experiences (say, of a hippogriff flying through
the window) would have some sort of psychic knowledge of each other.
>
> > I have my doubts that philosophers of
> > mathematics would see the categories described here as mutually
>exclusive.
> > For example, a formalist, to the extent he believes there is an
>objective
> > truth about whether certain statements are derivable from a set of
>axioms
> > and rules of inference, is just a species of platonist as I would define
>it;
>
>which is not how eeverybody else defines it.
If not, then perhaps that's just because they don't in fact think that
"formalism" means believing there's an objective truth about whether a given
statement is derivable from a given set of axioms. If you are claiming that
"everybody" does think that formalists believe this, yet they are still not
considered "Platonists" in any way, I'd like to see some evidence for this
claim.
>
> > the objective truth necessarily involves an "ideal" case of following
>the
> > rules without any possibility of error, not any specific mathematician
>or
> > computer which may slip up in deriving new propositions from the axioms.
>In
> > this case the ideal axiomatic system is the "abstract object" which
>there
> > are objective truths about, since the truths cannot refer to any
>specific
> > attempt to implement the system in the real world.
>
>But if any non-Platonic hteory is correct, truths do not
>need to refer.
Can you provide a quote or citation for the idea that any philosophers of
math subscribe to a view where there are objective truths about mathematical
objects yet the statements do not refer?
>
> > Some formalists may not
> > think in this way, but in this case they do not really believe there are
> > objective mind-independent truths about axiomatic systems.
>
>The idea that mathematical truths cannot have been different
>can be supporte without any appeal to ontology.
Again, not if you define existence and ontology in the way I am doing, and I
have serious doubts that there is another way to define these terms in a way
that is coherent and which does not lead to a kind of ontological relativism
where what is "objectively true" can differ for different observers.
Jesse
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Received on Tue Jul 11 2006 - 21:54:58 PDT