Hi Bruno Marchal
Natural numbers are monads because
1) the are inextended substances, which is redundant to say.
2) they have no parts.
That's a definition of a monad. Except to add that monads are alive,
except that numbers are not very alive. I imagine one could write
an entire scholarly paper on this issue.
OK-- thanks-- there is a level of description that is comp
Yes, there are a number of differences between Aristotle's substances
and Leibniz's. I would go so far as tpo say that they have
little in common:
"Leibniz's substances, however, are the bearers of change (criterion (iv)) in a
very different way from Aristotle's individual substances. An Aristotelian
individual possesses some properties essentially and some accidentally. The
accidental properties of an object are ones that can be gained and lost over
time, and which it might never have possessed at all: its essential properties
are the only ones it had to possess and which it possesses throughout its
existence. The situation is different for Leibniz's monads梬hich is the name he
gives to individual substances, created or uncreated (so God is a monad).
Whereas, for Aristotle, the properties that an object has to possess and those
that it possesses throughout its existence coincide, they do not do so for
Leibniz. That is, for Leibniz, even the properties that an object possesses
only for a part of its existence are essential to it. Every monad bears each of
its properties as part of its nature, so if it were to have been different in
any respect, it would have been a different entity.
Furthermore, there is a sense in which all monads are exactly similar to each
other, for they all reflect the whole world. They each do so, however, from a
For God, so to speak, turns on all sides and considers in all ways the general
system of phenomena which he has found it good to produce匒nd he considers all
the faces of the world in all possible ways卼he result of each view of the
universe, as looked at from a certain position, is卆 substance which expresses
the universe in conformity with that view. (1998: 66)
So each monad reflects the whole system, but with its own perspective
emphasised. If a monad is at place p at time t, it will contain all the
features of the universe at all times, but with those relating to its own time
and place most vividly, and others fading out roughly in accordance with
temporal and spatial distance. Because there is a continuum of perspectives on
reality, there is an infinite number of these substances. Nevertheless, there
is internal change in the monads, because the respect in which its content is
vivid varies with time and with action. Indeed, the passage of time just is the
change in which of the monad's contents are most vivid.
It is not possible to investigate here Leibniz's reasons for these apparently
very strange views. Our present concern is with whether, and in what sense,
Leibniz's substances are subjects of change. One can say that, in so far as, at
all times, they reflect the whole of reality, then they do not change. But in
so far as they reflect some parts of that reality more vividly than others,
depending on their position in space and time, they can be said to change. "
There are whole talks on monadic change on Youtube.
Roger Clough, rclo...@verizon.net
Leibniz would say, "If there's no God, we'd have to invent him
so that everything could function."
----- Receiving the following content -----
From: Bruno Marchal
Time: 2012-09-02, 08:37:43
Subject: Re: A Dialog comparing Comp with Leibniz's metaphysics
On 01 Sep 2012, at 15:59, Roger Clough wrote:
A Dialog comparing Comp with Leibniz's metaphysics
The principal conclusion of this discussion is that there is a striking
similarity between comp and the metaphysics of Leibniz,
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.
for example that the natural numbers of comp are indeed monads,
I am glad you dare to say so, but that could be confusing. You might define
monad, and define precisley the relationship.
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.
It is, by definition.
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
would have to be made.
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.
BRUNO (a comp advocate):...
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.
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.
.. 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
ROGER: Very good. "At that level of description" is exactly the point of view I
have adopted regarding Leibniz's metaphysics,
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.
OK. (Of course here 'substances' are not the Aristotelian primary matter).
*[In my view, the issue that fundamental particles cannot be subdivided, can be
by the the Heisenberg Uncertainty principle, which in effect allows one to
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
cannot be sustances. There's nothing left that one can point to. ]
I can agree, but Heisenberg uncertainties are an open problem in the comp
theory, as the existence of particles, space, physical time, etc.
Natural numbers qualify as Leibnizian substances, since they are inextended
and not divisible.
Well, 24 is divisible by 1, 2, 3, 4, 6, 8, 12 and 24.
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
I do see your point that numbers "are not divisible", though. But Fortran
program, machines, neither, in such a similar sense.
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,
not all monads are natural numbers. A man-- me, for example-- is not a natural
even in the Platonic realm, but yet is a monad, separates comp from L's
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 ?-la G?el-L?, but terrribly
simplified by the use of Solovay theorem on G and G*.
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
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
In comp, space and time are, like in Kant, in the understanding of a machine.
It is not ontologically real.
We now turn to the "at that level of description" issue, since although
bodies are not substances, they can have physical parts.
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.
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,
With no barriers between, since they are all mental representations.
? There can be barrier in mental representations, no?
there is no logical problem with having body act on intellect and feeling,
vice versa, or in any combination.
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.
Animals do not have (any significant) intellect, only feeling and body.
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
Rocks only have body as a suignificant component.
He does not rank vegetables but I personally would assign them
to the animal category.
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.
I have no written the sentence above. Extended bodies are mental images.
BRUNO: Comp is neutral on this level [of the properties of an extended body].
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
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.
Then I show that comp leads to Plato, and refute Aristotle metaphysics.
There are no ontological physical universe.
the physical universe emerges from a gluing property of machines or number's
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.
ROGER: I will pass on most of this for now as for one thing I do not understand
what normalization is.
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
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.
Well, if comp is correct, Aristotleland does not exist.
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:
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.
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.
Oh, I see there is a sequel. I comment a sentence here:
In either case, the entire universe might be envisioned as a gigantic
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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