Jesse Mazer wrote:
> 1Z wrote:
>
> > > 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.
IOW, if MMW heories worked, MMW theories would work.
> >
> >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"?
That isnot really analogous becasue the CC can only have one
value at a time.
> > > > > >"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;
No, that's the sense. Sense is in-hte-head , reference
is out-of-the-head.
> 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.
The unicorn example is an example of sense without
reference. It is not an example of mind-indepnednet truth.
> >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.
Analycity explains apriority, and sense explains analycity.
> > > 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.
If we can reason about (for instance)
historical what-is without concrete ferefernces is parallel
dimensions, we can reason about maths without taking
a trip to Plato's heaven.
> > > 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.
No it shoudn't. Maths is obviously unique in a number of respects.
That is why there is such a subject as philosophy-of-mathematics.
> 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.
It is on a deeper level of abstraction.
> > > >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.
If you are going to claim we are already inside Plato's
heaven, as many on the list do, you are laready dealing
with a stronger definition of ontology than that,
> 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.
Yes. Mathematics is constrained by rigourous internal logic. Science
is constrained by observation. Fairy-tales aren't constrained by
anything.
They all work in quite different ways.
> Incidentally, does your definition of "exists" mean that you don't think
> anything exists beyond the boundaries of the observable universe
That depends on what the "able" means in "observable".
> > > "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?
It could be wrong. So it doesn't necessarily
deliver objectivity, Hiwever it allows us to understand
what objectivity is.
> > > >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?
Formalism is a bit iffy. Apart from that, they all do.
> > > > > 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 obviously epistemoligcal, It deals with truth, not being.
> 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).
I believe there is mind-independent truth about them AND deny they are
ontological
> 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.
How can it be ontological when it says nothing about being, existence,
etc ?
Bearing in mind that *my* definition of existence entails the
possibility
of causal interaction...
> > > 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.
Oh come on, that's like defining God as a necessarily
existing being. You need to *show* that truth
implies existence, not just assert it.
> 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).
It is very much a disagreement about word-definitions.
> 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.
Not if ptoetnial causal interaction is allowed to run in both
directions. There
is chain of ackward causes linking me to the BB; running forward again,
another chain connects to events outside my light-cone.
> >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
We don't, since nothing changes once it has come into existence.
> . And as he admits, he is "assuming that such a thing as
> becoming is possible without describing or explaining it".
It is philoosphically respectable to regard tiem as fundamental.
something has to be fundamental.
> >Mathematical Platonism also doesn't (obviously) have the resources
> >to keep "worlds" separate.
>
> Sure it does. Different Turing machine programs are mathematical objects,
> no?
Different substrings within TM programmes can be identical, no ?
Bearing in mind that the physical universe provides us with a
mechanism --
spatio-temporal location -- which allows identical things to be kept
separate,
and which doesn't exit in Platonia.
> 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
uh-uh! Real programmes are run at distinct spatio-temporal
locations. They don't exist in Platonia.
> 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
That is beside the point. The question is
waht it woould feel like to be in the programme.
> ('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').
The laws of physics, then, are "in" the programme -- not vice--versa.
> > > 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.
Nope. Also identical in that they share all my memories up
until time T , when things turn Harry Potter.
> 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.
They would share my memories, identify themselves as me,
and so on. There would be counterparts which have my memories
up to time T, then an outpurst of HP, then normal memories from time
T+1 onwards.
> > > 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.
It's because they do think Platonism means numbers exist in some sense.
> 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.
Formalism is alaways cited as a different position to Platonism
http://en.wikipedia.org/wiki/Philosophy_of_mathematics
> >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?
"Logicism is the thesis that mathematics is reducible to logic, and
hence nothing but a part of logic (Carnap 1931/1883, 41). Logicists
hold that mathematics can be known a priori, but suggest that our
knowledge of mathematics is just part of our knowledge of logic in
general, and is thus analytic, not requiring any special faculty of
mathematical intuition"
http://en.wikipedia.org/wiki/Philosophy_of_mathematics
> >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.
You are just building your conckusion into your definitions.
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Received on Wed Jul 12 2006 - 06:57:52 PDT