On 17 Aug 2009, at 19:28, Flammarion wrote:
>
>
>
> On 17 Aug, 11:17, Bruno Marchal <marc....domain.name.hidden> wrote:
>> On 17 Aug 2009, at 11:11, 1Z wrote:
>>
>>> Without Platonism, there is no UD since it is not observable within
>>> physical space. So the UDA is based on Plat., not the other way
>>> round.
>>
>> Are you saying that without platonism, the square root of 02 does not
>> exist?
>
> Yes, the square root of two has no ontological existence.
All what matters with comp is that things like the square root of 2
has a notion of existence independent of "me".
>
>> Prime number does not exist?
>
> Yes, prime numbers have no ontological existence
I guess you make a "material" ontological commitment. One of my goal
is to explain, notably with the comp hyp, that a term like matter has
no referent. This would explain why physicist never use such
ontological commitment explicitly.
To say that matter exists simply is a non rational act of the type
"don't ask". UDA makes just this precise by reudcing the mind body
problem to a body problem.
>
>> That mathematical existence is a
>> meaningless notion?
>
> Sense but no refence. Mathematical statements have
> truth values but do not refere to anything outside the
> formal system.
Then they have no truth value. What you say is formalism, and this has
been explicitly refuted by mathematical logicians.
We know, mainly by the work of Gödel that the truth about numbers
extends what can be justified in ANY effective formal systems (and non
effective one are not really "formal").
But I know that there are still some formalists in the neighborhood,
and that is why I make explicit the assumption of arithmetical
realism. It is the assumption that the structure (N, +, x) is well
defined, despite we can't define it effectively.
>
>> Mathematics would be a physical illusion?
>
> A referentless formal game, distinguished from fiction
> only by its rigour and generality
You evacuate the whole approach of semantics by Tarski and Quine. I
will not insist on this because I will explain with some detail why
Church thesis necessitate arithmetical realism, and why this leads
directly to the incompleteness and the discovery that arithmetical
truth cannot be captured by any effective formal system. The formalist
position in math is no more tenable.
>
>> But physics use mathematics, would that not make physics illusory or
>> circular?
>
> No, because it uses mathematics empirically. The same
> language that can be used to write fiction can be used to
> write history. The difference is in how it used. not in the langauge
> itself
I don't see any difference in the use of analytical tools in physics
and in number theory. The distribution of the prime numbers is
objective, and this is the only type of independent objectivity needed
in the reasoning. Nothing more.
>
>>> It's a perfectly consistent assumption. THere is no
>>> disproof of materialism that doesn't beg the quesiton by
>>> assuming immaterialism
>>
>> Well, I do believe in the natural numbers, and I do believe in their
>> immateriality (the number seven is not made of quantum field, or
>> waves, or particle).
>
> Then you are a Platonist, and you argument is based
> on Platonism.
I believe that the truth of arithmetical statement having the shape
"ExP(x)" is independent of me, and you and the physical universe (if
that exists).
You can call that Platonism, if you want, but this is not obviously
"anti-physicalist". Non-physicalism is the conclusion of a reasoning
(UDA).
Given that Plato's conception of reality is closer to the conclusion,
I prefer to use the expression "Arithmetical realism" for this (banal)
assumption, and Platonism or non-physicalism for the conclusion. But
that is only a vocabulary problem.
>
>> So either you tell me that you don't believe in the number seven, or
>> that you have a theory in which the number seven is explained in
>> materialist term, without assuming numbers in that theory.
>
> The latter.
Show it. I know an attempt toward "science without number" by Hartree
Field (wrong spelling?), but I found it poorly convincing. Most
physicists accept the objectivity of numbers. Even more so with the
attempt to marry GR and QM.
>
>>>> This leads to major difficulties, even before approaching the
>>>> consciousness problem.
>>
>>> Such as?
>>
>> Explaining number with physical notions,
>> and explaining, even partially, physical notions with the use
>> numbers.
>
> That is just a repetition of the claim that there
> are problems. You have not in the least explained what
> the problems are.
UDA is such an explanation. AUDA gives a constructive path toward a
solution.
>
>>> You arguments here are based on the idea
>>> that primary matter needs to be given a
>>> purely mathematical expression. That in turn
>>> is based on an assumption of Platonism. If
>>> Platonism is false and materialism true,
>>> one would *expect* mathematical explanation
>>> to run out at some point. Your "difficulty" is a
>>> *prediction* of materialism , and therefore a
>>> successfor materailism
>>
>> Not at all. Cf the "even partially" in my sentence just above.
>
> That sentence does not demonstate anything
> about anything.
>
>>>> and some physicists are already open,
>>>> independently of comp, to the idea that physical objects are
>>>> relative
>>>> mathematical (immaterial) objects. Which of course are "no
>>>> material".
>>>> Wheeler, Tegmark, for example.
>>
>>> They have a consisent set of assumptions. So do
>>> their materialist oponents. You can't get an "is true"
>>> out of a "might be true"
>>
>> Well the movie graph conclusion is that materialism is not
>> consistent,
>> unless it opt for eliminativism of persons and/or non
>> computationalism.
>
> Materialism=true and computationalism=false is a consistent
> set of assumptions.
I am not even sure of that, but given the fuzziness of the notion of
"primitive matter", why not. May be God created it in 06 days, or the
big bang in zero seconds.
I always felt that taking notion of matter, or consciousness, for
granted, is a creationist-like move on the type "don't ask". UDA shows
that we have to ask more precisely when we assume that personal
consciousness can be invariant for the change of implementations done
below the substitution level.
> Moreover, the movie graph doesn;t prove
> what you say it does since it involves an illegitimate move from
> "minimal physical basis" to "no physical basis".
It goes explicitly to "no physical activity" in the MGA3 thread. But
MGA2 is enough, due to the "qua computatio" condition in the "yes
doctor" hypothesis. I guessed that your problem is in the
understanding of UDA step-8.
>
>>>> I tend to believe in many immaterial things. Some are absolutely
>>>> real
>>>> (I think) like the natural numbers.
>>
>>> There's your Platonism again. Believe what you like, but don'
>>> call it proof.
>>
>> Given that the theorem is "comp => platonism", and given that I am
>> open to the idea that comp could be correct, I am of course open to
>> the idea that Platonism may be correct.
>
> The theorem is platonism=>UD, UD=comp=>immaterialism
I am glad you see this. All what I have to do is convince you that
formalism does not work for arithmetic and mathematical computer
science.
>
>> But again, I don't need platonism (non-physicalism) to be an
>> arithmetical realist, like all classical mathematicians.
>
> Yes you do. The UD doesn't exist physically. If it doesn't
> exist non-physically either, it doesn't exist, and I am not
> a programme running on it.
Because you don't believe in anything non physical. But this comes
from your "formalist" position which does no more make sense after
Gödel. Each formal system, and machine, miss almost all arithmetical
truth.
>
>> This is
>> explicit in the assumption. The non physicalism and general
>> immaterialism is a consequence of the movie graph argument. What is
>> wrong with it?
>
>
> The movie graph doesn;t prove
> what you say it does since it involves an illegitimate move from
> "minimal physical basis" to "no physical basis".
See MGA3. Actually the contradiction appears, in the movie graph, even
when the whole physical activity is still there, but is no more
corresponding to any computation. This is a subtle point, no doubt,
and it asks for an understanding of the computational supervenience
thesis, which I am explaining in the "seven step series" thread.
>
>>> It changes everything. If the UD is a useful ficiton, I cannot be a
>>> programme running on it, any more than I can book a flight to
>>> Narnia.
>>
>> Would you say that the 1000^1000th base ten decimal of PI is a
>> fiction?
>
> Yes. I don't beleive in *any* pixies, not a single one.
All what I need is that the statement "the 1000^1000th base ten
decimal of PI is even" is true or false independently of the
existence of me, the planet earth or the physical universe (if that
exists).
>
>>>> There is a sense to say those universal machines do not exist,
>>>> but it
>>>> happens that they don't have the cognitive abilities to know that,
>>>> and
>>>> for them, in-existence does not make sense.
>>
>>> If they don't exist, they don't exist. You don't have the
>>> rigourous mathematical argument you think
>>> you have, you have some baroque Chuang-Tzu metaphysics.
>>
>> I do like Chuang-tzu, and I can see the relation between comp and
>> Chuang-tzu, although it is more clear with Lao-Tzu, as you may see in
>> "Conscience et Mécanisme", where an explicit correspondence is
>> suggested.
>
>> So, what you tell me is that you don't believe in *any* form of
>> mathematical existence.
>
> Not in any, and not in any pixies either.
>
>> So you reject arithmetical realism, and thus you reject comp.
>
> The computaitonal Theory of Mind has no implications about Platonism.
Comp is based on the notion of digitalness, which needs Church thesis.
I will explain in detail why Church thesis needs arithmetical realism.
I think that you are confusing everyone by switching "arithmetical
realism" with "Platonism". If you call "Platonism" what I call
"Arithmetical realism", I will put the result in the following way:
comp => non physicalism. It leads to a reduction of the mind-body
problem to the search of an explanation of stable beliefs in matter,
without matter. AUDA provides the explanation, yet not the physical
theory (but still the logic of physical propositions). It explains the
appearance of "many worlds" below the substitution level.
>
> You may of course mean something else by "comp".....
>
>> Arithmetical realism is needed to give a sense to Church thesis,
>> which
>> is part of comp.
>
> if AR is as claim abotu the immateial existence of numbers it does
> not.
> Not even remotely.
AR is a claim that number exists independently of my body and soul.
Number are immaterial, by definition. You don't need a theory of
matter to explain what numbers are. On the contrary, all book which
talk on matter assumes them more or less explicitly.
>
>> Some posts ago, you seem to accept arithmetical realism, so I am no
>> more sure of your position.
>
> I may have assented to the *truth* of some propositions...
> but truth is not existence. At least, the claim that
> truth=existence is extraordinary and metaphysical...
Mathematical existence = truth of existential mathematical statement.
The number seven exists independently of me, is equivalent with the
statement that the truth of the mathematical statement Ex(x =
s(s(s(s(s(s(s(0)))))))) is true independently of me.
If you really believe that the number 07 has no existence at all, then
the UDA reasoning does not go through, but then you are abandoning
comp because you can no more give sense to digitalness. You can still
say "yes" to a doctor, but you have to refer to some analog material
object, and not accept that you survive "qua computatio". This plays a
role in step-8.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Received on Tue Aug 18 2009 - 10:12:12 PDT