Bruno Marchal wrote:
> On 17 Aug 2009, at 19:28, Flammarion wrote:
>> On 17 Aug, 11:17, Bruno Marchal <marc...@ulb.ac.be> 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
>>> Are you saying that without platonism, the square root of 2 does not
>> 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
>> 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
> 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
> 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
>> 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
>>>> 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
>>>>> mathematical (immaterial) objects. Which of course are "no
>>>>> 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
>>> unless it opt for eliminativism of persons and/or non
>> 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 6 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
>>>>> (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
>>> 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
>>> 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
>>> Would you say that the 1000^1000th base ten decimal of PI is a
>> 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
>>>>> 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,
>>>>> 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
>>> 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,
>>> is part of comp.
>> if AR is as claim abotu the immateial existence of numbers it does
>> 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.
The above of course is a set of tokens symbolizing a set of cardinality eight.
that it symbolizes something depends on humans interpreting it. This seems
similar to the
MGA and the idea that a rock computes every function. They depend on being
some context or environment. I'm happy to abstract them from their environment
to get a
manageable model. I'm not so comfortable to say that that abstraction doesn't
environment and is what is really real.
> If you really believe that the number 7 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.
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