# Re: A Dialog comparing Comp with Leibniz's metaphysics

```Hi Roger,
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On 01 Sep 2012, at 15:59, Roger Clough wrote:

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A Dialog comparing Comp with Leibniz's metaphysics

Abstract

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The principal conclusion of this discussion is that there is a striking
```similarity between comp and the metaphysics of Leibniz,
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I agree. that is why two years ago I have followed different courses on Leibniz. But it is quite a work to make the relationship precise. It is far more simple with Plato, neoplatonists, and mystics.
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```for example that the natural numbers of comp are indeed monads,
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I am glad you dare to say so, but that could be confusing. You might define monad, and define precisley the relationship.
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```but a critical difference is that not all monads are natural numbers.
And not all substances are monads. For students of comp,
this should be of no practical importance as long as the
computational field is confined to natural numbers.
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It is, by definition.

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```Which is the basic method of comp. However, if one goes
outside of that field, a reassessment of the
additional mathematical forms in terms of substances

ROGER (a Leibnizian): Hi Bruno Marchal

Perhaps I am misguided, but I thought that comp was moreorless
a mechanical model of brain and man activity.

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I am not a comp advocate. I use comp because it gives the opportunity to apply the scientific method to biology, philosophy and theology. I search the key under the lamp, as I know I will not find it in the dark, even if the key is in the dark.
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I am just a technician in applied logic. I inform people that IF comp is correct, then physics arise from elementary arithmetic, which includes a theology of number. The fundamental science, with comp, is the thology of numbers (that is: the study about the truth on numbers: this includes many form of truth: provable, feelable, observable, knowable, etc. With the usual classical definition. It masp closely with the theology of the neoplantonists and of the mystics, and certainly some aspect of Leibniz.
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... Not really. Comp is the hypothesis that there is a level of description of my brain or body such that I can be emulated by a computer simulating my brain (or body) at that level of description.
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ROGER: Very good. "At that level of description" is exactly the point of view I have adopted regarding Leibniz's metaphysics,
```discussed below.
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OK.

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This is wholly my own version, since a possible problem arises in understanding what a Leibnizian substance is. The reason is that Leibniz describes a substance as potentially any "whole" entity, that being either extended body or inextended mind. But because extended bodies (despite L's familiarty with atomism)* can always be divided into smaller inextended bodies, extended bodies cannot be substances in L's metaphysics. Hence L substances are
```the inextended representations of extended bodies.
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OK. (Of course here 'substances' are not the Aristotelian primary matter).
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*[In my view, the issue that fundamental particles cannot be subdivided, can be replaced by the the Heisenberg Uncertainty principle, which in effect allows one to consider corporeal bodies as inifinitely divisible in the sense that one cannot arrive at final separate pieces without uncertainty. So one cannot come to a final state, holding up L's argument that corporeal bodies
```cannot be sustances. There's nothing left that one can point to. ]
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I can agree, but Heisenberg uncertainties are an open problem in the comp theory, as the existence of particles, space, physical time, etc.
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Natural numbers qualify as Leibnizian substances, since they are inextended
```and not divisible.
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Well, 24 is divisible by 1, 2, 3, 4, 6, 8, 12 and 24.

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OK, you can take it as a joke. But I fear you put too much importance in the particular notion of numbers, ad we can use LISP programs instead of numbers. This plays some role in the derivation of physics from the comp first person indeterminacy.
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I do see your point that numbers "are not divisible", though. But Fortran program, machines, neither, in such a similar sense.
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They also do not have parts, so in L's terms, they are simple substances, which is another name for monads. Natural numbers are thus (Platonic) monads, although not all monads are natural numbers. A man-- me, for example-- is not a natural number even in the Platonic realm, but yet is a monad, separates comp from L's metaphysics.
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I'm afarid that your notion of monad becomes to general, as with comp, a term like a man is ambiguous. Either we refer to his body, and that is a (relative) number, or to its soul, in which case, comp prevents us to take it as a number. It is nothing third person describable. Todays machines already know that, if you listen carefully (which asks for work à-la Gödel-Löb, but terrribly simplified by the use of Solovay theorem on G and G*.
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In addition, not all substances are monads. Those with more than one part, for example. This critical difference also separates comp from L metaphysics.
```At the same time, I am only looking at the difference

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Since time and space are in extended form, they are similarly infinitely divisible and hence are not substance and cannot be monads. The monadic world must then be entirely Platonic.
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In comp, space and time are, like in Kant, in the understanding of a machine. It is not ontologically real.
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We now turn to the "at that level of description" issue, since although corporeal
```bodies are not substances, they can have physical parts.
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But a simple substance or monad is a mental substance without parts, so
```that we can only speak of a man as a whole thus as a monad.
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And that is precisely how Leibniz treats a man-- as a monad which is also a homunculus. With the traditional tripartite division into intellect, feeling, and body.
```With no barriers between, since they are all mental representations.
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? There can be barrier in mental representations, no?

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```Thus
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there is no logical problem with having body act on intellect and feeling,
```vice versa, or in any combination.
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Leibniz goes further to treat all monads as homunculi-- but with levels
```of intellect, feeling and body both appropriate to the substance
and individual. Thus men have all three divisions, some with greater
intellect than others, and so forth.
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Animals do not have (any significant) intellect, only feeling and body.
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I don't think so. But it is out of topic. They do have feeling, body, and intuition. Right, they have more limited intellect, but that might be an advantage.
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```Rocks only have body as a suignificant component.
He does not rank vegetables but I personally would assign them
to the animal category.
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Me too.

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BRUNO:-- either the idealistic or mental or inextended form of an extended corporeal body as a whole -- or the extended body itself (which may at the same time have some variations in composition and many types of substance).
```ROGER: No problem.
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I have no written the sentence above. Extended bodies are mental images.

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BRUNO: Comp is neutral on this level [of the properties of an extended body].
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I said only that the reversal between physics and machine's psychology follows whatever the level is proposed. The consequences follows only from the existence of the level, and it is nice as the substitution level cannot be know for sure.
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It might be a very low level like if we needed to simulate the entire solar system at the level of string theory, or very high, like if we were the result of the information processing done by the neurons in our skull. Comp entails that NO machine can ever be sure about its substitution level (the level where we survive through the digital emulation), and so comp cannot be used normatively: if we are machine, we cannot know which machine we are, and thus "saying yes" to the digitalist doctor for an artificial brain demands some act of faith. It is a theological sort of belief in reincarnation, even if technological. It is theotechnology, if you want.
```No one can imposes this to some other.

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Then I show that comp leads to Plato, and refute Aristotle metaphysics.
```There are no ontological physical universe.

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the physical universe emerges from a gluing property of machines or number's dream. The physical universe appears to be a tiny facet of reality. The proof is constructive and show how to derive physics from machine's dream theory (itself belonging to arithmetic); but of course this leads to open problems in arithmetic. What has been solved so far explains already most of the quantum aspect of reality, qualitatively and quantitatively. The approach explains also why from the number's points of view, quanta and qualia differentiate. The work is mainly a complete translation of a part of the 'mind- body problem' into a 'belief in matter problem' in pure arithmetic.
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ROGER: I will pass on most of this for now as for one thing I do not understand what normalization is.
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I don't use the term "normalization". I use "normatively" above, and it is used to describes theories which can be used to prescribe behavior. But comp protect the souls against all such prescription. Universal numbers are universal dissident, they reject all theories prescribing behavior. They don't reject practical laws, but they reject general judgement on behaviors, or recipe in everyday life.
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The only issue that sticks out is Aristotle. My point of view
is that when in Leibnizland one whould think and do as Leibniz did.

And when in Aristotleland  one should do as Aristotle said and did.
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?

Well, if comp is correct, Aristotleland does not exist.

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ROGER: I obviously need to peruse your main idea .
Do you have a link ?
BRUNO: The more simple to read in english is probably the sane04:

http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
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Abstract: I will first present a non constructive argument showing that the mechanist hypothesis in cognitive science gives enough constraints to decide what a "physical reality" can possibly consist in. Then I will explain how computer science, together with logic, makes it possible to extract a constructive version of the argument by interviewing a Modest or L?ian Universal Machine.
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Reversing von Neumann probabilistic interpretation of quantum logic on those provided by the L?ian Machine gives a testable explanation of how both communicable physical laws and incommunicable physical knowledge, i.e. sensations, arise from number theoretical relations.
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Oh, I see there is a sequel. I comment a sentence here:

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```In either case, the entire universe might be envisioned as a gigantic
digital golem,
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There is something that some people can take some time to get it right: if comp is correct (meaning that my brain is Turing emulable), then there is no universe per se, but there is an appearance of a universe, and that appearance is not definable in terms of a digital structure. Nor is consciousness, truth, feeling, intuition. Except for my brain description, comp confronts the machine with a ladder of non computational realities, climbing beyond the constructive ordinals. Arithmetic seen from inside is far bigger than even the already quite non computational arithmetic truth.
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Bruno

http://iridia.ulb.ac.be/~marchal/

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