Roger Clough, [email protected]
10/31/2012
"Forever is a long time, especially near the end." -Woody Allen
----- Receiving the following content -----
From: Bruno Marchal
Receiver: everything-list
Time: 2012-10-30, 12:38:34
Subject: Re: Numbers in the Platonic Realm
On 30 Oct 2012, at 14:23, Stephen P. King wrote:
On 10/30/2012 7:30 AM, Bruno Marchal wrote:
On 29 Oct 2012, at 22:38, Stephen P. King wrote:
On 10/29/2012 1:08 PM, Bruno Marchal wrote:
On 29 Oct 2012, at 14:36, Stephen P. King wrote:
[Bruno Marchal wrote:] So numbers are universal and can be treated
mathematically as always.
I agree, but the concept of numbers has no meaning prior to the
existence of objects that can be counted. To think otherwise is
equivalent to claiming that unspecified statements are true or false
even in the absence of the possibility of discovering the fact.
Dear Bruno
I think you confuse numbers, and the concept of numbers.
No, I do not. My claim is that Numbers are objects in the mind of
conscious beings.
This contradicts what you said before. It contradicts comp
immediately, as comp needs the understanding of what a computer can
do, even in absence of any conscious observer.
Dear Bruno,
It contradicts your version of comp, yes, but not mine, as I see
minds and numbers as co-existing simultaneously, there is no
ontological priority between them in my version.
Comp is only the assumption that the brain is a machine, to be
short. Then it is proved that the TOE is arithmetic (or recursively
equivalent). Matter and mind arise from the numbers (and + and *).
If you reintroduce a mind assumption, mind will be epiphenomenal. It
you reintroduce matter, it will be epinomenal.
If there does not exist worlds where entities to whom numbers are
concepts then there is no such thing as a concept of numbers in such
worlds.
But with comp, a conscious observer is explained by number
relations. We explain the concept of numbers, and of human
understanding of numbers, by number relations (computations).
Sure, but we should be able to 'go the other way' as well! You
seem to insist on a well founded relation where as I do not!
I derive proposition. I suggest nothing, nor do I insist on nothing,
except on reasoning validly. I am not a philosopher. you must
understand the technical result before philosophising on it. It is
subtle as comp makes a part of philosophy of mind into a branch of
science (indeed, arithmetic/computer science).
My argument is that concepts of truth and provability of theorems
apply only to the concepts of numbers and their constructions, not
to numbers themselves.
Truth applies to proposition, or sentences representing them for
some machine/numbers. If not, comp does not even makes sense.
Your version, yes.
Not my version. "My" version is just a technically more precise that
the version used in some literature. Comp is the same for everybody.
"My" Version implies all other one, as it is a very weaker version
(because it does not depend on which level of substitution we use).
And then your argument is not valid, as with numbers, the miracle is
that we can specify the concept of numbers, as this result in
defining some arithmetical sigma_1 complete theory in terms of 0,
s(0), ... and the laws of addition and multiplication, that
everybody understands (unless philosophers?).
I am a philosopher! My argument rests only on the fact that the
'miracle' is exactly as you state it here: we exist and have a
concept of numbers and can ascertain the truth of arithmetic
statements. My claim is that truth valuations supervene on the
ability of consciousness to form concepts of numbers.
That is idealism, if not solipsism. In comp plotinus term, you
confuse the outer God (the objective ultimate truth) and the inner
God, or the sould of the individual inquirer.
No, Idealism is that only the mind exists, i.e. idealism takes
the mind as ontologically primitive. Solipsism is the condition of a
mind such that it can only interact with some version of itself.
Given that matter comes from the numbers, if the number comes from
the human mind, everything comes from the human mind. This is a
version of (collective) solipsism.
I question the entire idea of numbers existing as separate Platonic
entities. In the absence of consciousness, there is no such thing as
a concept!
Again, we need only the relation between the numbers, not the
concept of numbers, which with comp will be explained by computation
occurring in the brain of some machine/number.
Let me ask you: Do numbers have "concepts" of each other" YES!
Godel numbers are a way for one number to have a concept of another.
You can't be serious. A Godel number is a coding of something, which
can indeed be a number. For a concept you need a thinking universal
number; not just a faithful coding. Some numbers can be said having
concept of other number, but just because some numbers implement
sophisticated person relatively to their most probable computations.
No? If they do not have something equivalent to concepts, how can
they dream?
Yes, the universal numbers can have concept.
This is just to show that your idea implicitly considers that
concepts are 'mental' and that if numbers can be coherently said to
have minds then their concepts supervene on their minds. But what
are numbers as themselves - as objects?
We don't ever know that. But we don't need to know that, as we agree
on the axioms, and reason from that. It is not philosophy.
What can know the 'in-it-self-ness' of a number such that that
'in-it-self-ness' is not a concept?
?
PS BTW, from a computer scientist perspective, your use of NP never
succeed to make sense. I don't dare to ask you to elaborate, as I am
afraid you might aggravate your case. The NP question is fundamental
and has many interesting feature, but it concerns a local
tractability issue, and is a priori, unless justification, not
relevant for the arithmetical body issue, nor number's theology
(including physics) issue, etc.
It is the argument is sound and is the same kind of argument as
what Kripke used to discuss the idea of possible worlds. In http://en.wikipedia.org/wiki/Possible_world
we read:
"There is a close relation between propositions and possible
worlds. We note that every proposition is either true or false at
any given possible world; then the modal status of a proposition is
understood in terms of the worlds in which it is true and worlds in
which it is false."
All this presuppose numbers at the outset. World in Kripke are only
elements of any set having a binary relation. You must study the
math, not use the naive interpretation based on the use of common
terms.
Please, you are not addressing my critique, but some straw man.
You are smarter than to do that!
Rephrase your critics. You lost me, as I don't even see the critics.
Solutions to equations or computations are not available until
after they are actually solved.
That is constructive thinking, again incompatible with comp,
although retrieved and explain for the subject. This is akin to your
solipsism above.
Where am I claiming that only my thoughts exist? Could you define
what solipsism is and how I am being such above?
Because you seem to think that a solution of an equation exists only
if we have found the solution. I think that arithmetic is boolean,
and so a solution exist or does not exist independently of me and you.
Of course it is hard to guess what you think as long as you don't
propose a theory.
Oh, so its OK that you do not think that you propose a theory,
but it is a crime is someone else does that. You are being a
hypocrite with that claim! How childish! Stop trying to evade my
critique.
I am trying hard to get it, and don't succeed, and point that this
fact might come by my unability to see what are your assumption.
My solution to this is to not go so far as you do in Step 8.
You can't make the conclusion of a reasoning false by stopping the
reasoning. This will only make you ignorant of a conclusion.
blah blah blah...
?
Let me try to be more explicit:
From your paper http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHAL.pdf
:
"Instead of linking [the pain I feel] at space-time (x,t) to [a
machine state] at space-time
(x,t), we are obliged to associate [the pain I feel at space-
time (x,t)] to a type or a sheaf of
computations (existing forever in the arithmetical Platonia
which is accepted as existing
independently of our selves with arithmetical realism). "
Yes. That is already true in a concrete robust physical universe
(robust = own a non stopping UD).
OK, so how does it remain true when there is no physical
universe? How can actions be defined on entities that are, by
definition, static and eternally fixed? You result is self-
stultifying here - not self-contradictory. If we take step 8 to be
correct then there is no possibility of a means to communicate the
meaningfulness of comp to anything other than the mind of Bruno
Marchal, since his chalkboard can be, do be consistent not a
"physical object" and thus is at best a "dream".
? The chalk seems to be obviously a physical object. But comp
explains where it comes from.
Whose dream? Dreams of Numbers. What makes how are the dreams of
numbers more "special' than the dreams of Pink Unicorns or Purple
Ponys?
If you have a theory of Pink Unicorns precise enough to be proved
Turing universal, it is OK.
The laws of both mind and matter are totally independent of the
initial objects you assume, be them numbers or combinators, or Pink
Unicorn. Just give me the axioms you assume on Pink Unicorns.
We have discussed how concepts and objects are not the same
thing, so what is the object aspect of a number?
We don't need to know that. We need only to agree on the axioms:
x + 0 = x
x + s(y) = s(x + y)
x *0 = 0
x*s(y) = x*y + x
together with some axioms on equality.
How does a number demonstrate its nature other than through
concepts? It cannot!
It can. Read any textbook in mathematical logic, or theoretical
computer science. Or G?el original papers. It is coneptually not so
difficult, just long and tedious, as it it an implementation of high
level notion (concept of number) in low level notion numbers,
addition and multiplication.
I am pointing out that the idea of computations "existing
independently of our selves" is wrong in that it conflates the
meaning and truth valuation of numbers with the existence of numbers
as Platonic objects.
You seem to ignore that this conflation is not us, but the doing of
the (universal) numbers themselves, and this independently of me,
you, or universes.
OK, then this very independents prevents any meaning from being
associated with its existence and thus the ability for "this
sentence is true" to refer to itself vanishes (as it would for any
Godel Numbering that does exactly the same thing or any derivative
thing).
Why would meaning disappear? I guess you are again violating comp.
The meaning and consciousness is preserved in the digital
(arithmetical) emulation.
Independence isolates and cuts off connections, so do not claim that
the results of those connections remain once independence is claimed.
Then you say no to the doctor.
There is no such thing as "running" or "implementing" or "meaning"
or anything that is anything derivative of an action if step 8 is
correct as you state it therefore AUDA is steaming rubbish if you
insist on it. Why? Because AUDA (and all the argument about G and G*
and Z and Z*, etc) is "independent' of physical implementation and
that independence goes both ways - it independence is applied
coherently.
? All statements referred to in AUDA are theorems in PA. (the theory
above + the induction axioms). And the theory above proves that
already, as it emulates (but is different from) PA.
If A and B are independent then they have nothing to do with each
other at all, unless their is some C that is prior to A and B. If A
and B are independent of the physical and timeless, there is nothing
prior to them therefore no relation or prior to them can be used to
infer any relation what so ever between them.
You might be correct here, and that is why it is a good thing that
the *primitive* physical universe does not exist, as it would be
indeed totally independent of any mind, and would be an epinomenon.
Even the common naming conversion, A and B, is treachery as it
tacitly assumes that there are two objects that can be
simultaneously known and distinguished both between each other and
some common background vanishes is they are independent and
timeless. Your concept of Platonism is deeply flawed.
But here you lost me again.
You should spend some time studying philosophy if you are
going to pretend to make philosophical arguments.
I do not. That's the point.
It is absurd to refer to the claim that the truth of "17 is prime"
depends on any one person or entity, but the claim that the truth of
"17 is prime" is knowable by any person is not absurd.
It is absurd with comp, as knowing, despite NON arithmetical in the
logical sense, is still defined in purely arithmetical terms. If
not, you will not surive with an artificial brain, even concrete.
No, it is not absurd, except for you that allows concepts of
actions, such as "implements" and "runs", to exist when they cannot
be coherently defined.
But they can. I already define them once (or twice). read any
textbook in theoretical computer science. running, implementation,
etc. are purely mathematical notion. It just happens that we can
approximate them through a physical reality, and that is what make
comp possible. But the the physical reality appears to be
necessarily emerging from the numbers and their mind (or the mind
associated to person associated to the arithmetical relations, to be
more precise).
If we stipulate that the content of knowledge exists somehow prior
to that which knowledge supervenes upon, we are being absurd.
This is just realism. The semantical content of knowledge as to
exist independently of you if you don't want to fall into solipsism.
How is it related to the word "real" at all? You are only showing
us the mathematical theory of a consistent solipsist
Not at all. On the contrary I ascribe mind to numbers (in relation
with opther numbers). It is the contrary of solipsism.
and, as a consistent solipsist you are unable to conceptualize that
you are wrong, after all "it is absurd that anything contradict the
solipsist as only it exists and its existence is only possible if it
is consistent".
Some thing is "real" only is that reality is common for many,
thus solipsism and realism are mutually exclusive.
Of course.
The content of knowledge and the ability of knowledge occur
simultaneously or not at all.
With comp they "occur" as consequence of + and * laws.
No. There is no "occurance" in your comp.
The machine 678 on argument 456 stop after less than 456789 steps.
That is a statement which if true can be proved in arithmetic, and
you can defined many notion of occurrence from it.
Nothing can possibly "occur".
An infinity of emulation of the collision of the Milky way and
Andromeda occurs in arithmetic.
In your result these is only "is".
In GR too. In physics you can always replace a dynamical phenomenon
by a higher dimensional statical structure. With comp we get the
higher structure at the start. Dynamics arise in the internal inside
views.
X is Y, not any X occurs iff Y. There are no coherent concept of
actions in your comp.
There are many.
You really seems to lack even just the computer science intuition.
Please study the book by Mendelson, or ask precise question, but
most of it have already been explained.
Absent the "concept" of numbers there is no such thing as
valuations of numbers
Then 17 is prime only since humans exist on the planet? or since
insects use this to regulate mating?
This is solipsism/idealism.
You fail to read temporarily or is it OK to attack straw men?
Read further of my post.
The fact is that your current posts makes me doubt about your
position on "17 is prime independently of us".
because the notion of Platonic objects considers objects as existing
independently as some singular "perfect" version that is then
plurally projected somehow into the physical realm, as we see in the
Allegory of the Cave. This is a one-to-many mapping, not a one-to-
one mapping.
? (so you postulate conscious observer *and* physical universes?).
Your theory looks more and more like Craig's non comp theory.
They are very similar, I admit that. You have no idea what
Craig's idea is as demonstrated by your inability to describe it
accurately as anything other than rubbish or noise.
I have great respect for Craig's attempt to defend a non comp
theory. But you seem to want both comp and a Craig-like theory, and
then that is what I have shown inconsistent. Craig's theory is
consistent, as it assumes non-comp. But your "theory", as far as I
understand it, is not. Now Craig is not consistent in most of his
argument against comp, as his conversation with Stathis illustrates,
but that is another point.
How exactly is a "type" or "sheaf" a singular and "perfect"
version of each and every computation and yet be something that has
individuated valuations? Individual valuations of computations are
only those that occur as physical instantiations of computations
"physical instantiation of computations" is something in needed to
be explaiend, not assumed, if we want to understand something (not
just comp). Computation evaluation is a too fuzzy terming for me.
A physical instance of a computation is the existence of a
physical system that can "run" a universal turing machine.
Trivially true. The whole point is that such a physical existence
will no more be primary.
It can do so, among other things, because it uses resources of time
and/or memory to transform through some set of states such that it
reproduces the functions of the UTM.
Agains that is true for the physical universal machine. But not for
all universal machine, and the physical emerges from the work of all
universal machines.
Straight forward idea that we see in texts on computers. Nothing new
or magical...
because computers are thought as physical, since we build them. but
the mathematical notion preceded it, and does not rely on physical
notion of resource, but on mathematical notion of "enough memory".
and thus they do not "exist" in Platonia.
Then Church thesis has no more meaning.
To you, perhaps. What a pity!
To everyone. If arithmetical realism is excluded, you can no more
explain the consistency of Church thesis by the diagonalization. You
need to believe that for all i and j, either phi_i(j) stops or
phi_i(j) does not stop, independently of you.
The Many exist in the physical worlds, no?
Primitive one?
No. Not primitive, derivative. No different from how numbers are
derivative in my thinking and that of most natural philosophers.
?
Your mistake is in assuming strict ontological well foundedness;
? Comp makes this possible.
the idea that there has to be a irreducible ontological primitive
that has innate properties. If you would read Bertrand Russell's
discussions of neutral monism then you might see his explanation of
what I am proposing and not have the straw man of my terrible
writing to use as a shield of your unwillingness to try to
understand what I am trying to communicate to you.
You are quite unfair as I try hard.
Irreducible objects, in the ontological sense, cannot have a
particular set of properties as such is to exclude all other
possible properties without justification. To claim that numbers can
be ontologically primitive and yet have valuations and abilities is
to deny their irreducibility, as values and abilities are
derivative, not fundamental or innate.
Give me the entire quote of Russell. keep in mind that Russell
philosophy has been refuted by G?el, also. But the very existence of
principia mathematica makes me doubt that Russell ever defended an
ontology with object who irreducibility prevents them to have
properties; such an ontology would be by construction not amenable
to scientific analysis.
I propose a rephrasing of your statement above: We identify the
1p qualia to a sheaf of computations (as bisimilar Boolean Algebras)
that is dual to physical machine states at diffeomorphically
equivalent space-time coordinates (x, y, z, t). This is a
restatement of the Stone duality into COMP-like terms. ;-)
That does not make sense to me. Sorry.
Read some more books on philosophy, such as The Problems of
Philosophy
I read it, and it does not say one word related to the paragraph
above.
it might make sense in some non comp analogical theory of mind, with
mind and matter explicitly defined in term of non computable
diffeomorphism. But this looks to me like making the mind-body
problem more complex just for fun.
No, I am trying to show you how to solve the 'arithmetic body'
problem.
You have just to see if the arithemtical quantization defines the
measure, as it seems to promise up to now. If not, then comp +
(theatetus definition) is refuted.
All what I have done is a translation of the arithmetic body problem
in arithpmetic. The solution can only be technical, although some
variability exists due to the use of the classical theory of
knowledge. It is already a mircale that the Theaetus definition of
knowledge gives rise to the classical theory of knowledge. Without G?
el and L?, that would be impossible.
(The idea of diffeomorphic equivalence is discussed in detail here: http://plato.stanford.edu/entries/spacetime-holearg/Leibniz_Equivalence.html
)
When you say:
<<
Yes, this is the Pre-Established Harmony, but as I have argued
before this concept is deeply flawed because it tries to claim that
the solution to NP-Hard problem (of choosing the best possible
world) is somehow accessible (for the creation of the monads by God)
prior to the availability of resources with which to actually
perform the computation of the solution. One cannot know the content
of a solution before one computes it, even if one is omniscient!
I don't find any sense.
How is this so difficult for you to comprehend? The Platonic
Realm is defined as timeless, everything in it just 'exists', no?
Only in the sense that if some proposition P(n) is true
independently of me, then ExP(x) is true independently of me.
But you are not the only entity involved in the truth of P(n)!
?
I am not involved at all.
You pretend that it is possible for something to be so absurd! P(n)
is true only because it is possible to implement some version of
P(n) and verify that indeed P(n) is true.
Then arithmetic is no more boolean, and both "yes doctor" and
"church's thesis" have no more meaning.
The mere Platonic existence of P(n)
P(n) does not exist.
n exist, and P is true or false about it.
is insufficient for truth as truth is a derivative evaluation.
Not at all. truth is a matter of fact.
It cannot be ontologically irreducible.
Truth is is the easiest notion to conceive as irreducible, for a
platonist.
Therefore any argument that shows that "if A does not exist then
neither does B if B requires A to exist" is true in Platonia as
well, (we stipulate the existence of Platonia as defined for the
sake of this statement). If a solution to a computation cannot exist
until the computation is run then if the resources required to run
the computation do not exist then there does not exist a solution to
the computation!
So you cannot compute 10^1000 + 10^1000, and your theory is
ultrafinitist (and so non-comp).
False. Straw man argument.
Then why do you say that a computation has to be run to assert the
existence of its solution. And run by who, and where?
I propose that we can easily resolve this conundrum by stating
Computational universality as: "A computation is universal if and
only if it is independent of any particular physical implementation."
Universal applies to finite entity (numbers, humans, machines,
language). Not to computations, although the running of a universal
dovetailer can be said universal in some context, but only by abuse
of language.
So? How does that contradict my definition of universality?
The computation of 2+2 will not depend on any particular
implementation, yet it is not universal.
This allows for the existence of physical implementations,
Comp allows this too; without the need of assuming physical realities.
Rubbish. You must assume the a priori possibility of physical
reality to even have a coherent notion of comp or else it is, at
least, not communicable.
I have already explain why this is a confusion of level.
even those that are themselves defined by correlations between
sheaves for computations. This sets up a relation between
computations - as abstract or immaterial objects - and physical
systems that seems consistent with "COMP minus Step 8". We can
recover the picture of step 8,
Step 8 is a consequence of comp, like all steps in the UDA. 'Comp
minus step 8' implies that 0 = 1.
LOL, no. It only means "'Comp minus step 8' implies that 0 =
1." for a consistent solipsist.
Then you have to find a flaw.
in a way that is truly neutral ontologically, by changing its single
directed arrow to a pair of oppositely directed arrows, but this one
that occurs only in the ultimate sense of the elaboration of all
possible physical worlds consistent with Pratt's idea.
1004.
Straw Man.
Then you have to elaborate.
This idea, BTW, is consistent with the concept of Indra's Net, as
an inversion of the idea that every Jewel reflects all others: Every
jewel is a physical world that is defined by all computations of it.
Note also that this naturally includes self-computation as jewels
also reflect themselves. ;-)
I have no more any understanding by what you mean by "physical
world". It seems like a God-of-the-Gap.
I define a physical world as the set of mutually non-
contradictory 1p for some set of non-solipsistic entities that have
certain properties that at least allow for some coherent notion of
communication between those entities.
Then the physical reality emerges from the 1p. Like in comp. why do
you take so much time to criticize comp for not assuming a physical
reality. And how do you define 1p, without using physics or notions
of resources.
I hope you don't mind my frankness. I wouldn't say this if I did not
respect some intuition of yours. But math and formalism can't be a
pretext for not doing the elementary reasoning in the philosophy of
mind. If you use math, you have to be clearer on the link with
philosophy or theology. To be understandable by others.
I am trying to be clear. I will correct and rephrase my verbiage
until you understand it.
It would help to tell us what you assume at the start. from what I
understand it is just contradictory. Pratt assumes more than
arithmetic. All paper you refer too assumes more than arithmetic.
Your notion of consciousness and of physical universe seems to be
very fuzzy and clearly not comp-compatible.
My point is that you are not "just assuming" arithmetic. You
assume, additionally, at least that there is qualia.
In UDA. No more in AUDA. They are defined and explain in arithmetic,
as UDA eventually forces us to do.
I reject the idea of an entity, 'God', whose total purpose is to
"observe" the Reality of the Universe!
Comp too. Comp rejects also the primitive reality of a physical
universe.
So do I. I reject as ontologically primitive anything that is not
property neutral.
This makes no sense. It must be nuetral with respect to mind and
body. Not neutral to any properties, as your theory will be unable
to derive anything.
If we accept the idea that numbers exist in our complete absence,
then it follows that an entity like us cannot exist just to observe
the existence of numbers (or anything else).
? ? ?
Why postulate the existence of a special entity that does what we
collectively are already doing?
Why postulate physical computations, and comp, when comp explains
how physical computations emerges in our mind through the existence
of the computations in arithmetic?
No, it does not do so alone. Comp requires the implementation of
a physical symbolic representation of the idea for it to be even
evaluated and thus implicitly requires something physical even if
that "physicality" is derivative and not ontologically primitive.
Then I don't see why you critics the consequence of comp, as it
shows exactly this.
Read Russell's book ad stop using straw amn arguments about my
pitiful attempt to help you solve a problem that you ackowledge
exists in comp.
The existence of that problem is the main result (UDA)
Then I transform it into a problem in arithmetic (AUDA).
It is our collective consciousness that Constitutes the Platonic
Realm, IMHO. A theory that there is some independently existing
realm is a gross violation of Occam.
But you do it for the physical computations, like in this post,
despite you often pretend the contrary in other posts.
Bruno
http://iridia.ulb.ac.be/~marchal/
Stop using logical fallacious statements.
Which one. How is it fallacious? I might have been wrong, but you
have to elaborate on the clarity of your statements.
Bruno
http://iridia.ulb.ac.be/~marchal/
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