Hitoshi Kitada (hitoshi@kitada.com)
Tue, 14 Dec 1999 02:19:13 +0900
Dear Lance and friends,
Thanks for your comments and opinions. Your caution on the "windowless" monads
reminded me of your mail in July 1995, whose part I will quote below.
Lancelot R. Fletcher <lance@interactive.net> wrote:
Subject: [time 1115] RE: [time 1109] Monads (Re: [time 1105])
[HK]
> > I think from these statements that, as a "simple existence"that
> > is a true atom
> > of nature, monad must not be sensible to the outside, and hence must be
> > windowless by definition.
[LRF]
> This is correct, but I think one should add that Leibniz made a particularly
> poor choice of words when he said that monads are "windowless." The reason
> is that we have a pretty good notion of what a windowless enclosure would be
> like. Hitoshi could give us a precise topological definition, but suffice
> it to say that we imagine a closed, continuous membrane with two sides, an
> inside and an outside, but no holes or channels that would allow anything to
> move from the inner surface to the outer, or vice versa. This image is a
> complete falsification of the idea of a monad, because a monad not only has
> no windows, it has no outside! What Leibniz says is that every monad
> includes the entire universe. Its finitude consists, crudely speaking, in
> its including the entire universe from a particular point of view.
[Quotation from your mail in 1995]:
[A part of a long mail of 17,423 bytes on Tue, 11 Jul 1995 19:52:52 -0500
(received on Wed Jul 12 13:46:36 1995 JST) from Lance to Hitoshi]:
Dear Hitoshi,
[snip]
[HK: a part of original time_III.tex]
We should remark here that our notion of ``local systems" is
different from ``monads" of Leibniz. In the sense that local
systems are mutually independent, the notion of our local systems
sounds to resemble Leibniz' notion of monads. However, our local
systems have their own ``windows" as will be imposed as an
assumption in the next section, regarding the observation of the
outside from a local system as an observer. Thus, since any local
system can be an observer of the other local systems, our local
systems are not `closed' monads in the sense of Leibniz.
[LRF]
I have a concern that this citation may produce confusion, and
since you are saying that your local systems are NOT like monads
in certain important respects, the question is whether the
citation is valuable in terms of clarifying your own argument.
The reason I think there may be confusion is that, for many
readers of Leibniz, their "windowless" nature is essential to
what they are, so if you take that away and attribute windows to
them, they are transformed beyond all recognition. This is
connected to what I was saying about "finite" things in Spinoza
in the following way: The reason why the monads are windowless
is not that there is some barrier between one monad and the
others. The monads are windowless because each one of them
includes the entire universe. What distinguishes them is that
each one includes the entire universe "from its own point of
view." But to the extent that each monad includes the entire
universe, it is infinite. Its finitude lies only in the
determinacy of its "viewpoint." [I am not sure that this is a
satisfactory example, but I have always thought of the
monadology as something like a family of integrals, each of
which is infinite along one axis but determinate on another
axis, so the particular integrals (monads) are "infinite in
their own kind" while the whole family of integrals is (for the
purpose of our example) absolutely infinite.] But if each monad
is all-inclusive, there is no possibility of looking at it from
the "outside." If there were any standpoint outside the monad
from which one could observe the mondad, that would be a
limitation -- to that extent the monad would not be infinite,
and hence it would not be a monad.
[snip] ....
[End of quotation]
It seems that I did not respond to this part; I could not find my response in my
hard disk. Now 4 years later I think I am able to make a response:
A monad as a local system has no windows in the sense I wrote in [time 1109].
However, a local system reflects the entire universe by the property that the
universe is stationary (axiom 1 in time_I.tex). Thus any local system includes
the total universe in itself even if it is a finite existence.
On the other hand, any local system can be an observer of other local systems or
an observed. In this sense, a monad as a local system has its windows.
[Rigorously, this is incorrect. Observation is possible only when two local
systems, the observer and the observed, are merged. But in the usual sense of
the word "observation," the two local systems must be regarded as two distinct
local systems, for otherwise the word "observation" does not make sense. In
other words, the word "observation" is itself self-contradictory. It is actually
a merging, not a relation between distinct local systems.]
These two aspects do not contradict: The entireness of each local system
resulting from the stationarity of the entire universe does not cease the
activity of observation of each local system. Because: any local system has its
own time (by time_VI.tex) consistently with the nonexistence of the entire time,
and therefore it can behave as a local part of the universe even if it is the
same as the entire universe, and is able to make observation with the local time
and space of its own being the frame of reference.
In this sense, a monad has no windows as well as has windows in the same
context. [As mentioned, rigorously a monad has no windows consistently with
Leibniz' monads. What makes this contradictory unification between having no
windows and having windows possible comes from the "self-contradictory" nature
of the word "observation."]
[HK]
> > My interpretation is that a monad in the context of Leibniz is a
> > local system
> > without disturbance in my context. Simpleness which Leibniz
> > requires monads does
> > not contradict the plurality of the elements in a local system: A
> > local system
> > becomes a different local system if it is divided, so it is
> > indivisible as local
> > systems and is an elementary unit of existence. "Monads have no
> > windows, by
> > which anything could come in or go out." is true for local
> > systems in the sense
> > that: a local system becomes a different local system if
> > "anything could come in
> > or go out" with respect to the local system, and therefore, as
> > far as a local
> > system remains the same, it has "no windows."
[LRF]
> This may well be a good way to link the idea of monads with that of local
> systems.
>
> On the question about dualism that Hitoshi posed in another message, let me
> offer this suggestion: Consider the possibility that, even in Descartes,
> the idea of mind-body dualism as a dualism of two different substances is
> either a myth or a joke. It is an incomplete formulation of something. It
> is at least possible that the reason Descartes allowed himself to be
> understood as advocating a mind-body dualism was that the alternative, which
> he perceived, was something similar to what Spinoza said out loud, and
> Descartes foresaw the scandal that Spinoza would cause by saying that
> extension is an attribute of God, and therefore, being very cautious,
> decided to disguise his meaning at the expense of making it appear
> inconsistent.
I was not aware of this possibility of interpretation of Descartes' thought as a
disguise. It is an interesting possibility, which might diminish the efforts of
his followers. Descartes in his disguise would have been seeing the later
[Modern] age with smiling :-)
> But Hitoshi asked what was behind the dualism. The key idea that pushes
> Descartes in this direction is the notion of "res extensa." This is
> singular. In other words, what Descartes realized was that his own
> mathematical representation of nature required denying the multiplicity of
> bodies. Nature is a continuum with various properties and relations among
> its parts, but no part or section is fully distinct from any other. Of
> course, if there is only one body, then it seems odd for there to be a real
> plurality of thinking things or minds, and in fact that is also Descartes'
> conclusion, although one less fully appreciated by readers.
So Descartes wanted to explain the contradiction between the singularity of body
and the plurality of mind? And Leibniz tried in his Monadology to give one
solution by the principle of preestablished harmony with admitting the existence
of plural substance: monads as minds?
> You could say that the so-called "mind-body dualism" is really a reification
> of the subject-object distinction. I am not sure whether that is very
> helpful, but, to the extent that the subject-object distinction is a
> characteristic of Western thought that is much less present in Asian
> thought, this may be a way of accounting for the peculiarily Western
> character of the mind-body problem.
This contrast between the west and the east might be correct. During each of my
stays in the US I became eventually irritated with something which I could not
specify. Too strong distinction between subject and object might have been what
I could not specify. While irritated, I had been feeling some comfortableness
on the deep level of mind, which I cannot find in Japan: I cannot find "I" in
Japan, whereas I could find it in the US. Maybe the solution exists between the
two extremities.
> I apologize if the preceding is obscure. I will try to do better after my
> return.
No need for apology, your suggestion was clear enough to remind me of our old
discussion and gave us what is necessary for the present discussion. I
appreciate your appropriate comments and views on the difficult problem between
the west and the east. One tends to avoid making comments on such sensitive
topics, which might cause emotional reactions. When I was searching for the
files that include the quoted part of the old mail, I found other mails of mine
to you in my previous stay in the US in 1997. What I wrote to you resulting from
my irritation was enough to make anyone angry, but you did not take any of them
as personal offensives. It is I who have to apologize.
Best wishes,
Hitoshi
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