On 6/26/2018 7:14 AM, Jason Resch wrote:
On Mon, Jun 25, 2018 at 10:57 PM, Brent Meeker <[email protected]
<mailto:[email protected]>> wrote:
Logic, laws, and principles are adopted after the fact to clean up
problems perceived in intuitive inferences; and their solutions
are not always consistent (c.f. Russell's definite descriptions vs
free logics, or Graham Priest defense of para-consistent logics).
But logically impossible things don't happen, and logically necessary
things do happen.
The only logically impossible event is "X both happened and didn't
happen." The only logically necessary event is "X either happened or
didn't happen." Logic tells you nothing except what is already in the
premises.
In this sense, can we not view it as logic being responsible for those
outcomes (in either preventing or necessitating something else)?
(Perhaps you would call this /Logos/) that is inherent to the
structure of reality. If logic governs the necessity of reality,
and can give rise to it, how do you see logic as isolated from
true statements about arithmetic?
I don't see formal logic as isolated from arithmetic. Informal
logic is more like a theory of physics. It attempts to capture
and clean up specific areas of discourse but it doesn't
necessarily try to encompass everything. Just as physics leave
geography alone. Logic doesn't /*govern*/ anything. It describes
usage of language (generally restricted to declarative sentences)
that preserves "truth" (which formally just a marker). It has no
more to do with reality than any other application of declarative
sentences.
(I would ask the same question given above)
At the very least, we could use the existence of logical law as part
of ur explanation, in the same way physicists cite physical laws as
part of an explanation for why apples fall from trees.
Sure. We state some premises about mass-energy and metrics and
force-free geodesics and we can predict where the apple will land. But
logic and mathematics just bring out what is implicit in those premises.
1. Hawking: "*What is it that breathes fire into the
equations* and makes a universe for them to
describe? The usual approach of science of
constructing a mathematical model cannot answer the
questions of why there should be a universe for the
model to describe. Why does the universe go to all
the bother of existing?"
"What is there? Everything! So what isn't there? Nothing!"
--- Norm Levitt, after Quine
Everything theories can explain away the arbitrariness of
the equations.
On the contrary, they make everything arbitrary.
This is only a problem for those theoretical physicists who still
dream of one day deriving a single unique set of physical laws
(matching our laws) directly from logic/mathematics.
It is a problem for everyday physicists who are interested in why
this rather than that
Ahh. The Wheeler Question.
and don't consider it satisfactory to say it's because this
happened here while that happened in another world where you
couldn't see...just like we predicted.
We may not always get what we want. Reality may again surprise us
with its size.
"Only two things are infinite. The universe and human stupidity. And
I'm not so sure about the universe."
--- Albert Einstein
1. Feynman: "It always bothers me that, according to
the laws as we understand them today, it takes a
computing machine an infinite number of logical
operations to figure out what goes on in no matter
how tiny a region of space, and no matter how tiny
a region of time. How can all that be going on in
that tiny space? *Why should it take an infinite
amount of logic to figure out what one tiny piece
of space/time is going to do?*"
"Because the world is made of physics, not logic."
- Brent Meeker
That's circular. You're defining physics as something that
inherently should have the appearance of infinities, without
a justification. I think it is is a mystery in want of an
explanation.
Oh, and mathematics makes it exist is not a mystery?
In terms of providing an explanation from simpler assumptions, it
reduces the mystery, at least on that question.
I'm not defining anything. I'm just noting that Feynman's
observation, if true, is evidence against computationalism.
Evidence against digital physics, but not against computationalism.
Oh, yes I forgot. Nothing can count as evidence against
computationalism, it predicts everything and infinitely often.
Many things would count as evidence against computationalism. But if
we already had observations that ruled it out, we wouldn't be talking
about it as we would abandon it as refuted.
1. Wheeler: "*Why these equations, and not others?*"
"These are the ones we invented to describe what we've
seen."
- Vic Stenger
That's not what Wheeler is asking. Of course if physics
were different, our equations would be too. Wheeler is
asking why is physics this way?
And Stenger is answering, "Because these equations work and
others don't."
Work for what? What makes this set of physical laws one that
works (vs. some other possible arrangement, which you think does
not work)?
They work because they predict what happens happens and what
doesn't happen doesn't happen. I think that's how Socrates
explained "true". You keep looking at the wrong end of the
process. Nothing makes the "physical laws work". We make the
physical laws so that they work.
I think Wheeler understood this, but this isn't his question. You
alluded to the mystery Wheeler was questioning up above, when talking
about a search for a final (meta) theory.
If we're to answer these questions, we may need some
kind of /metaphysical/ theory. Preferably one that is
simple, and can explain/predict our observations.
The existence of all possible computations may be one
possible avenue for this.
How would that be any better or worse than "all possible
set theory"
Set's by themselves don't compute anything,
So what. They include things. So they could include all
observations.
Under the computational theory of mind, the sets would have to
include computations, otherwise there could be no observations.
If the set includes computations, then the set of all things
would include all computations, and in terms of being an
explanatory theory of our observations would be identical to the UD.
I like the set of all phenomenon which exist.
What can you tell us about this set?
We see a sample of it.
What does it predict?
Sets don't predict things. We do.
How can it be ruled out?
It can't. It's like the integers, it "exists" by definition.
and so are insufficient to explain observations under a
computational theory of mind.
or "all possible phsyics"
That could work, if you define what is meant by a possible
physics. With computations at least, we have a clearly
defined notion of all possible computations.
No, you don't. It's supposedly uncountably infinite. Do you
have a clear notion of that?
Programs are finite length integers.
There is only one program per integer.
So there is a countably infinite number of programs/computations.
So what? Do you have a clear notion of countably infinite?
About a clear a notion as I have for the number 5. I don't know
everything there is to know about it, but I know a few things about each.
It there a supremum of the digits of pi which will ever be known?
or "all possible novels"?
Novels by themselves don't compute anything, and so are
insufficient to explain observations under a computational
theory of mind.
You keep saying "don't compute anything" as though it were a
given that computationalism is right. If you allow me to
assume physicalism is right I can prove computationalism is
wrong.
I think you need to have some theory of consciousness to reason
about or have a TOEs (which necessarily must include as an
explanation of consciousness).
So you could base a theory of consciousness on novels. In many
novels you are told what the characters are thinking.
Perhaps that would work. Though language is quite ambiguous and I
think there would be a lot of difficult in that path.
So far, it is not ruled out, and might even be
considered to be partially confirmed. It has the power
to answer questions 2, 3 and 4. And for anyone who
accepts arithmetical realism/no-cause needed for
arithmetical truth, then it can answer 1 as well.
All your questions are number 1.
(It looks like your e-mail client changed them when you
separated them)
However, I would point out that Feynman's question
implies that computationalism must be false.
No, this would be a consequence of computationalism as
predicted
Retrodicted. I'm still waiting for predicted.
As far as theories go, the difference between prediction and
retrodiction is only an accident of history.
Except one is infinitely easier than the other.
I agree. But here Bruno didn't propose either theory, and
computational theory of mind wasn't proposed as a theory of QM. Both
theories were independently proposed by different people for different
reasons. Bruno then showed one could follow from the other.
Not really. He has only shown that, if his theory of consciousness is
true, then there will perceptions of superpositions. But then he says
we won't perceive them because computation is classical...even though
computation generated the superpositions.
by Bruno in his UDA. It is a confirmatiom, rather than a
refutation, of computationalism.
His UD produces an uncountable infinity of computations, but
there's no evidence it computes what goes on in a tiny piece
of spacetime.
Under computationalism, it necessarily computes every possible
experience, infinitely often, in infinitely many ways. This
explains the appearance of infinites lurking under the floor when
we peek too closely at what underlies us.
That's another of those sentences that start, "Assuming my theory
is right...all things must be explained by it".
That's a necessary feature of any candidate TOE.
But assuming it's right isn't.
What about objective facts? Do objective facts always concern
real objects?
No, there is intersubjective agreement about theorems of
mathematics. That's why people are tempted to see it as existing
in the same way as perceived objects exist.
I don't follow. Why do intersubjective facts about physical objects
make them real, while intersubjective facts about mathematical objects
does not make them real?
I wrote intersubjective agreement. And intersubjective agreement about
experiences make them factual, i.e. that's how you tell you're not
halucinating, you ask your friend, "Do you see what I see?" Nobody
experiences mathematical objects, only descriptions and definitions and
proofs.
It tells us no matter how much we might build and
develop our theories (axioms) about the integers over
time, we know that we will never finish the job.
So is being infinite a known attribute of reality? Space
appears to be infinite too.
An infinite thing cannot be created by finite creatures in
finite time.
Can it be discovered?
We can discover a finite number of things about it.
Is "being infinite" one thing.
If we take our current theories about them, yes, that is a
consequence. We might find an error in our current theories and
refine them, but I doubt that will happen.
That's right, except Einstein didn't "believe in" the
equations, he believed the equations were describing
something real, but not completely. Otherwise he would not
have spent years looking for a unified field theory that
included spacetime, EM, and matter fields.
I see that as the same motivation and goal of mathematicians.
Except a mathematician wouldn't have cared that a theory didn't
produce the observed matter fields. If a mathematician had
invented SUSY he'd still be happy today; physicist are tearing
their hair out because the LHC results are ruling SUSY out.
They should be extra happy and excited.
In any case, mathematicians faced a similar "hair pulling" event when
Godel showed that Hilbert's effort to axiomatize all of math was a
doomed venture.
Because they thought that proving everything from a few axioms,
hopefully just from logic, would show it was a unity like the physical
world and so there could be a Platonia. Now Platonia has divided into
many worlds and Max Tegmark wants to do the same to physics.
Integers exist independently of the axioms too. The axioms
our just the mathematical analogue of our physical
theories. They are our attempt to "compress" our knowledge
of phenomenon down to the most compact possible form. In
that compressed form, it helps us to then reason, explain
and predict new phenomena.
So they are an abstraction of our knowledge. Doesn't sound
independent to me.
The axioms are no more responsible for creating the integers than
our physical laws are for creating the universe.
I'm glad you appreciate that physical laws don't create the
universe, even if they are about it. So why then don't you
appreciate that the axioms are just a theory of the integers and
that the integers are infinite is just a part of that theory, not
necessarily a fact about the integers (that exist independent of
the axioms). This is the way physicists think about the universe
being infinite: We have a theory in which it could be infinite and
that theory says it will look locally flat and we see that it's
locally flat. So it might be infinite...but we know that's just a
possibility, not something we would rely on in a proof.
Because I take the consequences of our current theoreis seriously.
Don't you?
To quote Trump, "Seriously but not literally."
Do you take it as irrelevant or inconsequential or probably wrong,
when our physical theories tell us our universe is probably spatially
infinite? Or does that lead you to consider the consequences of living
in a spatially infinite universe seriously, and a
(potentially/probably) real possibility?
I consider what it might mean for observations.
>
/ Would you say that mathematics imposes "meta
laws" which must be true across all
possible/imaginable universes?/
Yes I think so, but the meta laws would be physical
not mathematical.
So perhaps the better question to you is: "Might what
we consider now as physical laws ultimately be (or be
derived from) mathematical laws"?
If we're very lucky we might be able to describe
those meta laws mathematically (although almost
certainly not with the mathematics we have now)
Why not? For example, If conscious experience is
ultimately computational in nature, then Turing
machines are sufficient to explain all possible
experiences.
We can already describe Turing machines with our
existing mathematics.
First, that's confusing. A Turing machine is an
abstract bit of mathematics. It isn't "described" as a
real machine might be; it is mathematics.
We use math to describe mathematical objects. What is the
problem?
Second, it's like saying English is sufficient to
explain all possible experiences. The trouble of course
is that good explanation explains the difference between
the actual and the possible.
The trouble with that is you can't use the limited set of
experiences you have access to as evidence of a parsimony of
actualized possibility.
Well that certainly comes as a surprise to me. I thought my
failure to experience a mastadon in my back yard meant that
possibility was not actualized. I'll ask my wife to go look
again.
"I" is indexical to a single instance of conscious experience, it
does not capture all of reality.
True enough. But I've looked three times, so I'm going to
generalize to a theory that there's no mastadon in my backyard.
Maybe you need to start digging. :-)
My dogs already did that.
but I don't think there is any chance of a pure
mathematician ever finding them, we're going to
need physical experiments to give us some hints and
I just hope that doesn't require a particle
accelerator the size of the galaxy.
It will take more work, no doubt.
>//
/ It is physically impossible to arrange 7
stones into a rectangle/
If there were not 7 stones or 7 of anything in the
entire physical universe the entire concept of "7"
would be meaningless.
If there were 0 physical universes, then wouldn't 0
have meaning? Can zero have meaning without the
contrast of 1? Once you have "0 and 1" now you have two
unique concepts, so you get 2. Now you have 3 things,
(and so on).
It's that "and so on" that is problematic.
What is the problem?
It introduces infinities which leads to diagonalization
proofs that some things are "true" but unprovable which leads
to mysticism about where these "true" things reside.
What is the source of the infinite complexity (out of the
ultimate simplicity of "0 and its successors")?
Why do mathematicians struggle for hundreds of years to prove
simple statements, or to discover new reasonable axioms?
Because it's fun. I also belong to an email called...wait for
it...math-fun.
Here is one for you (and that list):
Tomorrow you and another prisoner are to be executed. But you will
both be spared if you can succeed in the following game. You and the
other prisoner have tonight to decide on a strategy for playing this
game: Tomorrow you and your fellow prisoner will be put in different
rooms, and both of you will observe two completely independent and
separate sequences of 100 coin tosses. The goal is for each of you to
choose a position in the other person’s sequence of coin tosses such
that the results of the coin tosses in those two selected positions
match. (i.e., both heads or both tails). What is your strategy?
Example:
Sequence: 1 2 3 4 5 6 7 8 9 ... 100
You see: T H H T *T* H H H T ... T and choose position 3 in your
partner's sequence
They see: H H *T* T H T T H T ... T and choose position 5 in your sequence
You are both spared as you both chose matching results: both Tails.
So we each get to see all 100 results before we have to choose an index?
Brent
Jason
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