1Z wrote:
>
>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.
No, that is not a fair paraphrase of what I said. I meant exactly what I
said I meant--if a hypothesis is not well-defined enough to tell you the
relative probability of different possibilities, that does not justify the
claim that the hypothesis predicts each possibility is equally likely. Do
you agree with this principle or not?
>
> > >
> > >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.
That difference is irrelevant to my point about probabilities. Again, it is
*always* unjustified to say that because a theory doesn't predict the
relative probabilities of different outcomes, that means it predicts they
are equally likely; it doesn't matter whether or not we are talking about
the probability in the context of a large ensemble of events (say, the
probability a certain type of atom will decay in a 1-minute time period,
where we are repeating the test with a large number of atoms) or in the
context of a single event.
Anyway, it is quite possible that even if string theory could make
predictions about the value of the cosmological constant, it would only be a
probabilistic prediction rather than predicting a single unique value, which
means that if you are prepared to entertain either the MWI of quantum
mechanics or "chaotic inflation" where new universes bubble from prior ones
via inflation, then there might in fact be different "universes" with
different values of the cosmological constant.
>
>
>
> > > > > > >"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.
OK, I see. So what if we are talking about a concept in itself, as in "most
people's concept of a unicorn is that of a horse-like creature with a single
horn"; would the "concept" itself be a reference?
>
> > > > 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.
But I have already made clear that I *don't* think that we need to refer to
platonic forms which somehow causally interact with people's brains in our
explanation of how people reason about math, just like David K Lewis doesn't
think we need a causal interaction between different possible worlds to
explain how people reason about possibilities.
> > > > 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.
That's pretty vague--unique in what respects? Does uniqueness in these other
respects somehow justify the belief that it is unique in the respect of
involving both sense-without-reference and mind-independence?
>
> > 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.
That doesn't remotely resemble an argument--can you define precisely what
"deeper level of abstraction" means, and why "deepness of abstraction"
should be in any way related to statements that lack sense but are
objectively true?
>
> > > > >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,
No I'm not. In terms of the notion that "existence" just means the entities
you'd need to refer to in an exhaustive list of all objective truths, the
idea that "we are already inside Plato's heaven" could be understood to mean
that as long as you include all the true statements that deal with the
mathematical question of how a theoretical universe with our laws of nature
and initial conditions would behave, then your exhaustive list of truths
doesn't need to include any additional non-mathematical truths which tell
you this particular mathematical description is actually "physically
instantiated" or something like that.
Of course, I'm not sure I believe myself that the exhaustive list of true
statements would include *nothing* but mathematical statements--I think it
might also have to include some truths about consciousness and qualia. In
this sense, it is conceivable that the exhaustive list of truths would tell
you that only some mathematically-describable worlds containing intelligent
life would actually lead to conscious experiences, while others wouldn't--in
this sense only some (or one) possible world would be "real". I think it's a
lot simpler to just assume all mathematically-possible observers are equally
real with respect to consciousness, but I can't prove it obviously. Still, I
have no idea what it would mean to say that some mathematically possible
worlds are *physically* real if "physical" was meant as anything other than
a shorthand way for talking about consciousness.
>
>
> > 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".
Well, put it this way--as long as the expansion of the universe is not
slowing to zero in the limit as time goes to infinity (and observational
evidence suggests the rate of expansion is actually accelerating), then any
event beyond the boundaries of the observable universe at this moment of
cosmological time will never, ever be able to have any causal influence on
us, because the space between us and the point where the event occurred will
always be expanding faster than light from the event can close the gap
between it and us. So unless relativity is wrong and it's possible to travel
faster than light, you would not in principle be "able" to observe anything
happening beyond the observable universe, at any point in the future. So do
you think that anything "exists" beyond the observable universe? And what if
you and I are in different galaxies, so that the boundaries of the
"observable universe" are slightly different for each of us? Do you think
that existence is relative to the observer, rather than being objective and
universal?
>
>
>
> > > > "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.
But again, to have a notion of objectivity you must have at least an ideal
of an error-free theorem-producer (though again, I'm not claiming that such
an ideal is causally interacting with us from its place in platonic heaven,
as you say our thought-processes about such ideal systems are based on
projecting from real ones).
>
>
> > > > >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.
Are you sure? Does empiricism say there are objective mathematical truths
separate from whatever empirical "observations" we happen to make, for
example?
>
> > > > > > 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.
But as I pointed out, it is common among philosophers to define "being" in
terms the set of all possible objective truths. I certainly don't think many
philosophers would define "being" the way you do in terms of ability to
causally interact with us.
>
> > 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
Then I think you are defining "ontological" in a different way from most
philosophers, or at least most analytic philosophers of the 20th century
(the 'continental' philosophers have their own way of thinking about
ontology, but then continental philosophers hardly ever deal with philosophy
of math).
>
> > 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...
I acknowledge that with *your* definition of existence, mathematical objects
do not exist. But I think you're using a pretty idiosyncratic definition
that would be miles away from how most analytic philosophers would define
existence, in particular those who work with philosophy of math.
>
> > > > 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.
You're acting as though we have some mutually agreed-upon prior definition
of "existence" which is separate from objective truth, and that I am trying
to make an *argument* that objective truth implies existence in this sense.
But that's not what I'm doing at all--I am *defining* the word "existence"
in terms of objective truth, not making an argument. I agree that if
existence is defined in your way instead of my way, then objective truth
doesn't imply existence, but then I think you're using a very weird
definition which is different from how virtually any analytic philosopher
would define it, and which leads to internal problems like the issue of
whether anything "exists" beyond the boundaries of the observable universe.
>
> > 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.
Yes, that's becoming more clear as we go on.
>
>
>
>
> > 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.
Yes, but as I pointed out above, events happening at the current
cosmological time outside the current observable universe cannot ever have
an effect on anything in your future light cone, nor can they have been
affected by any event in your past light cone, assuming the expansion of
space is not slowing to zero.
>
> > >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.
I don't understand how this response addresses the issue of needing a second
time dimension. Our notion of spatial movement depends on the idea of a time
dimension for something to have moved from one location in space at an
earlier time to another location at a later time; if you believe the present
is "moving forward" along our universe's time dimension, that requires some
sort of meta-time for it to make sense in the same way (as in, 'at an
earlier point in meta-time, the present moment was 1985; but later in
meta-time, the present moment had moved forward to 2006'). And then you have
the same issue with whether you take an A-series view or a B-series view of
meta-time, and if you want to adopt an A-series view you'd have to introduce
meta-meta-time to make sense of that, and so forth.
>
> > . 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.
It's "philosophically respectable" because it has such a long history, but I
can think of a number of similar ideas with a long history that don't seem
in any way coherent to me, like the notion of "free will" as distinct from
determinism or randomness or any combination of the two.
>
> > >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 ?
Sure, but you still aren't explaining how this suggests beings in one
program would have knowledge of programs different from their own. Obviously
if you had two simulations which behaved identically in some region of
simulated space and time, then simulated observers within these regions
would have identical experiences, but they are still both experiencing
things which happen in their own simulation, they have no knowedge of events
which don't correspond to anything in their simulation, which is what you
seemed to be suggesting earlier when you claimed that if the "everything"
idea was right we should be able to observe events in alternate worlds which
didn't happen in our own world.
>
>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.
But we're not talking about keeping identical things separate, we're talking
about keeping *different* things separate, namely different worlds within
the "everything" (like a lawlike universe vs. a universe that obeys one set
of laws up to a given moment but then switches over to totally different
'Harry Potter' laws after that moment).
>
> > 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.
But the programs themselves are distinct, just like the integers 8 and 9 are
distinct. Are you saying that we can have no concept of 8 and 9 being
different numbers without referring to specific collections of 8 objects and
9 objects at different spatio-temporal locations? If you're not saying this,
what makes programs any different from integers? After all, you can make a
one-to-one mapping between the set of all integers and the set of all turing
machine programs.
>
> > 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.
Unless you are an extreme mind/body dualist, the feelings and thoughts of a
being in a computer program should correspond to the type of
information-processing going on in his simulated brain, and should generally
correspond to what the simulated being claims to be experiencing within the
simulation. If he doesn't say he's experiencing an infinite number of
universes at once when you examine the program's output, then you can
probably assume he isn't. Of course there is still the issue of whether he's
actually "experiencing" anything at all, or whether he's a philosophical
zombie with no qualia at all (see
http://en.wikipedia.org/wiki/Philosophical_zombie ).
>
> > ('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.
I don't understand this comment. What would it mean for the program to be in
the laws of physics? And what relation does this have to the context of my
claim that 'barring errors the ideal "Platonic" program should have the same
output as the 'physical' instantiation'?
>
> > > > 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.
OK, but the point is that the version of you in the universe where the laws
of nature *didn't* change after time T is no longer identical to the version
of you in the universe where they did, and there's no reason that you in the
non-Harry-Potter universe would have any awareness of what he's experiencing
at this moment.
>
> > 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.
Yes, I agree. But again, the version of you in the universe with no HP
events would not have any awareness of them.
>
>
> > > > 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.
Only in the sense that they must be included in an exhaustive list of
objective truths about reality. Again, my understanding is that this
basically is how most analytic philosophers would *define* existence,
including philosophers studying philosophy-of-math.
>
> > 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
I didn't just ask for evidence that formalists and Platonists are different,
I asked for evidence that there is anyone who considers them completely
different but who *also* understands "formalists" to be acknowledging that
there are objective mind-independent truths about whether a given formal
system produces a given theorem (as opposed to just understanding
'formalists' to be saying that mathematics is a game we humans play with
deriving theorems from axiomatic systems, without making any claims that
there is an objective truth about whether our derivations are 'correct' or
not).
>
> > >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
OK, but are you assuming that purely logical statements don't refer?
>
> > >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.
As I said earlier, this criticism would only make sense if we had some prior
notion of "existence", and I was trying to make the argument that objective
truth necessarily implies this prior notion. But I'm not, I'm just defining
the word "existence" in terms of objective truths, because I can't think of
any way to define the word that seems coherent and which doesn't lead to
bizarre conclusions like "nothing exists beyond the boundaries of the
observable universe" (except possibly for the notion of equating existence
with consciousness, which might make sense and would potentially allow for
mathematical structures containing intelligent observers which nevertheless
don't 'exist'). I agree that if we define "existence" in your way,
mathematical objects do not exist. I just don't think your way of defining
it is how most philosophers would define it, particularly the analytic
philosophers who study philosophy of mathematics; most of them would define
it in a way more similar to mine, I think. This is a sociological question
rather than a philosophical one, I suppose we'd have to do a poll or
something to be sure.
Jesse
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Received on Thu Jul 13 2006 - 00:56:23 PDT