On 7/1/2012 7:45 PM, Jason Resch wrote:
On Sun, Jul 1, 2012 at 8:36 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 7/1/2012 5:21 PM, Jason Resch wrote:
On Jul 1, 2012, at 6:27 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 7/1/2012 2:46 PM, Jason Resch wrote:
On Jul 1, 2012, at 2:07 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 7/1/2012 11:50 AM, Jason Resch wrote:
On Sun, Jul 1, 2012 at 1:20 PM, meekerdb <[email protected]
<mailto:[email protected]>> wrote:
On 7/1/2012 4:59 AM, Bruno Marchal wrote:
On 01 Jul 2012, at 09:41, meekerdb wrote:
On 7/1/2012 12:17 AM, Bruno Marchal wrote:
On 30 Jun 2012, at 22:31, meekerdb wrote:
On 6/30/2012 12:20 PM, Bruno Marchal wrote:
On 30 Jun 2012, at 18:44, Evgenii Rudnyi wrote:
I think that you have mentioned that mechanism
is
incompatible with materialism. How this follows
then?
Because concerning computation and emulation (exact
simulation) all universal system are equivalent.
Turing machine and Fortran programs are completely
equivalent, you can emulate any Turing machine by a
fortran program, and you can emulate any fortran
program by a Turing machine.
More, you can write a fortran program emulating a
universal Turing machine, and you can find a Turing
machine running a Fortran universal interpreter (or
compiler). This means that not only those system
compute the same functions from N to N, but also
that
they can compute those function in the same manner
of
the other machine.
But the question is whether they 'compute' anything
outside
the context of a physical realization?
Which is addressed in the remaining of the post to Evgenii.
Exactly like you can emulate fortran with Turing, a little
part of arithmetic emulate already all program fortran,
Turing,
etc. (see the post for more).
Except neither fortran nor Turing machines exist apart from
physical realizations.
Of course they do. Turing machine and fortran program are
mathematical,
arithmetical actually, object. They exist in the same sense that the
number 17 exists.
Exactly, as ideas - patterns in brain processes.
Brent,
What is the ontological difference between 17 and the chair you are sitting
in? Both admit objective analysis, so how is either any more real than the
other?
You might argue 17 is less real because we can't access it with our senses,
but
neither can we access the insides of stars with our senses. Yet no one
disputes the reality of the insides of stars.
We access them indirectly via instruments and theories of those instruments.
Are numbers not also inferred from theories of our instruments?
But not perceived. They are part of the theory, i.e. the language.
Other branches of the wave function are not perceived either. They are
part of the
theory though, so can be considered real.
Or not. They are part of a theory that has great predictive power, which
is why we
think the theory is a good one - not necessarily *really real*. Being
'considered
real' is just a sort of provisional assumption for purposes of calculation.
The
wave function that is written down is just a way of summarizing an
experimental
preparation. Whether there is also a *really real* wave function of the
universe
(or even of the laboratory) is moot.
They are real according to the math of QM, which is one of the most solidly established
theories. You can doubt they are real, but it is like doubting the theory of evolution.
In any case, my point was that there are many things in science we cannot perceive that
are given the status of "real" or "extant", so perceptibility cannot be a requirement.
If you need more examples, consider no instrument has ever observed a quark. Nor has
any instrument peered beyond the cosmological horizon. Yet most particle physicists
believe quarks are real, and most cosmologists believe the universe is more vast than
the Hubble volume.
Numbers and Turing machines are part of Bruno's theory. I don't see the
difference. Why can't Turing machines exist?
Sure they can. I can program this computer to be one - except it might run
out of
'tape'.
No one disagrees that we can make physical approximations of Turing machines. The
Turing machines I am referring to are the ones you deny the existence of. From above:
Brent: Except neither fortran nor Turing machines exist apart from physical
realizations.
Bruno: Of course they do. Turing machine and fortran program are mathematical,
arithmetical actually, object. They exist in the same sense that the number 17 exists.
Brent: Exactly, as ideas - patterns in brain processes.
To be specific, those Turing machines that exist in the same sense as the number 17.
Those that are neither physical realizations nor ideas or patterns in brain processes.
We use instruments (physical computers) in the study of computer science. As Edsger
Dijkstra said: "Computer science is no more about computers than astronomy is about
telescopes."
Regarding things that exist yet we cannot see directly, you said: "We access them
indirectly via instruments and theories of those instruments." What is computer science
studying if not these mathematical objects? As Dijkstra said, computer science isn't
about computers. These are merely the instruments of computer scientists, in the same
sense telescopes are instruments for astronomers.
Are computer scientists really spending all their time studying objects that are merely
"patterns in brain processes" or is there something more fundamental being studied?
Something that is brain pattern independent?
For example, computers are instruments that let us observe and study the
properties of various Turing machines, which themselves are mathematical
objects.
You might argue the chair is more real because we can affect it, but then
you
would have to conclude the anything outside our light cone is not real, for
we
cannot affect anything outside our light cone.
You can kick it and it kicks back.
Math kicks back too. If you come up with a proposition, it kicks back with
either true or false.
Only metaphorically.
The whole "it's real if it kicks back" idea is a metaphor. I think the
point of
the metaphor is that to be real something needs to have its own properties
which we
have limited or no control over. It is not malleable to our whims or will,
but
resists attempts to change it.
So clay isn't real? Set theory isn't real?
Do you really not see any difference between tables and chairs and people and numbers,
sets, classes, homomorphisms, adjectives? Whether you want to bestow the honorific
'exists' on these things, only a philosopher can wonder whether they are all the same kind
of thing.
But we can interact with it and potentially change it.
We can't interact with the past, things beyond the cosmological horizon, objects in
other branches of the wave function, things outside our light cone, etc.
Sure we can. Interact isn't necessarily to change, it's also to be changed by.
Clearly, the potential for interaction is not required for something to be considered
real. No where in the definition of exists or real is there any mention of potential
for interaction:
re·al
adjective
1. true; not merely ostensible, nominal, or apparent: the real reason for an
act.
2. existing or occurring as fact; actual rather than imaginary, ideal, or fictitious: a
story taken from real life.
3. being an actual thing; having objective existence; not imaginary: The events you will
see in the film are real and not just made up.
4. being actually such; not merely so-called: a real victory.
5. genuine; not counterfeit, artificial, or imitation; authentic: a real antique; a real
diamond; real silk.
I notice that mathematical objects are non mentioned.
Of course there are many events outside one's lightcones which one infers as
part of a model of reality based on the events within one's lightcones,
e.g. I
suppose that the Sun continues to exist even though the photons I from
which I
infer it's existence are from it's past.
Explain then why one is mistaken in supposing mathematical objects exist,
when
they can be inferred according to some models of reality.
Explain why Sherlock Holmes doesn't exist according to Conan Doyle's model
of reality.
Sherlock holmes does exist, but then what is Sherlock holmes? A character
described in some books.
Conan could have changed anything he wanted about Sherlock holmes, and
therefore he
doesn't "kick back".
You forget how he was forced to revive Holmes by the public after he killed
him off.
Exactly. Anything goes for some textual description of an imaginary setting and
character. This is not true in computer science or math. I can't change which numbers
are prime or not. These are objective properties, like the gravitational constant.
You can define a different axiomatic system, add or subtract axioms to systems.
If you asked two people what properties Sherlock holmes has that were not
answered
in the book there would be no agreement, and no way to study Sherlock
holmes as an
objectively real object. Only the texts can be studied.
That's right. We can discover properties of real things that are not part
of their
defining description - unlike say the number 17.
Not true. There are millions of properties that one could state about 17, which are not
part of 17's definition, which states merely that 17 is the successor of 16.
For example, was it obvious to you from the description of 17 that 17 is the only prime
number that is a Genocchi number ( https://en.wikipedia.org/wiki/Genocchi_number )?
No, but it was implicit in it's definition.
Of course you can say it was possible to have determined that from some axioms, but what
axioms to use are as much discovered and evolved as our laws of physics. We can
discover more powerful axiomatic systems just like Relativity was a more powerful
physical theory than Newtonian physics. Having the complete definition for an apple as
a Newtonian object will not yield us all the actual properties of the apple (such as
time dilation and length contraction when the apple accelerats to a high velocity)
because we are operating in an incomplete system. Likewise, we cannot derive all true
facts about 17 with a fixed set of axioms.
This is not true of mathematical objects. Properties are not enumerated in
some
text. They are not subject to be defined or changed by some authority. Two
mathematicians, whether on earth or on different planets can make the same
discoveries about the same objects.
Further, mathematical realism is a useful scientific theory. It provides
explanations for scientific questions. Why you don't see it as a
legitimate theory
is a mystery to me.
I see arithmetic as a legitimate theory of things you can count, i.e. it
describes
the results of some operations with them, provided you map the theory to
the things
in a valid way. But the same it true of say the theory of elastic bodies.
Arithmetic is much richer than you you give it credit for.
Or maybe the theory of elastic bodies is richer than you give it credit for.
If you don't support the theory, that is fine, but it seems like you
discount it's
possibility altogether because only "real physical things" can be real.
I don't discount the possibility that Bruno's 'everything is arithmetic'
might be a
good model, I just haven't seen any predictive power yet.
Everything theories explain quantum randomness, explain the appearance of fine
tuning,
You miss the difference between predict and explain. Theology was very, very good at
explaining.
and in general, are in line with the trend of science which has gradually been expanding
our concept of reality:
1. Our world and the sky above it are all that exist (since ancient times)
2. Our world is one of many worlds orbiting the Sun (Nicolaus Copernicus in
1543)
3. Our sun is one of many stars in this galaxy (Friedrich Bessel in 1838)
4. Our position in time is just one of all equally real points in time (Einstein in
1905)
5. Our galaxy is one of many galaxies (Edwin Hubble in 1920)
6. Our history is just one of many possible histories (Hugh Everett in 1957)
7. The observable universe is a tiny fraction of the whole (Alan Guth in
1980)
8. Our laws are one of 10^500 possible solutions in string theory (Steven Weinberg
in 1987)
9. String theory is just one among the set of all valid structures (Max
Tegmark in 1996)
Some of those are about things that can be tested, some are just about the relations
within a theory, some are just speculations.
My metaphysical view is that only some things are real. When you start
from
premises like 'everything exists' you've just set yourself the task of
saying why we
have only the experiences we do, the ones for which we invented the word
'real'. If
you can't satisfy that task, then you haven't gotten anywhere.
I agree that solving one problem (ontology) has created a new one (predicting
experiences), but if solutions to old problems didn't bring new questions, science would
have hit a dead end long ago. But just because we are faced with a new problem does not
mean we haven't gotten anywhere.
Also, how do you know the chair is anything more than a pattern in a brain
process?
How do you know you're not a brain in a vat? or a pattern in arithmetic?
This was my point. You say math exists only in our minds. But an
immaterialist
could say the same of the chair.
He could say it, but he would be redefining what 'exists' means.
What is your definition?
Of course we could all be deluded and living the Matrix, but that idea has
no
predictive power. I already gave a definition of exists, that which we can
interact
with;
I don't think "potential for interaction" works, given the examples I listed above for
things thought to exist, but are impossible to interact with.
although it's more than that since we interact with things in our dreams.
Have you
ever read one of those adventure novels written for kids in which at
various points
you make a choice and it says go to page xx, so that the continuation of
the story
depends on your choice? That's the way math textbooks are. You start with
axioms
and you deduce things from them or a while, then you introduce a new axiom
and see
where it leads, then you consider a contrary axiom and consider what it
implies.
Axioms are like theories in physics. Some lead to dead ends, some lead to
deeper truths.
And some contradict others.
Your concept of mathematics is like what Hilbert had hoped for but Godel showed could
not be.
But Godel didn't show that true=exists.
Brent
--
You received this message because you are subscribed to the Google Groups
"Everything List" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/everything-list?hl=en.
