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
even if they Everything theorists don't WNAT them
to make that prediciton. The implications of a premiss
are what they are, not what we want them to be.

Classical physicists din't WANT to make the
implications that atoms are unstable and will
implode; nonetheless, classical phsyics makes that
assumption.


> > > > > >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. 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.

> A term that is
> completely meaningless, like a round square?

A refernceless term only needs to be contingently
non-existent, like "present King of France". Logical
impossiblity is over-egging it.

> 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.

>  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 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,


> >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.


Many-world
metaphysics is not needed to explain how abstrract reasoning
is possible.

> > > >
> > > >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.

> > >  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.

>  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.

It is almost trivial that it isn't. Alternative explanations are listed
in
standard references.


> >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.

> 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



> >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.

> 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.


> Is Peter D Jones a philosopher?

That depends on what you mean by "philosopher"...

> 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.

> 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.

> 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.

> Jesse


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