On 9/3/2012 9:36 AM, Roger Clough wrote:
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/—which 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 different perspective.
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…And he considers all the faces of the world in all
possible ways…the result of each view of the universe, as looked
at from a certain position, is…a substance which expresses the
universe in conformity with that view. (1998: 66)
I must point out that this quote precisely describes an infinite
NP-Complete problem! Consider the simple example of the Traveling
Salesman that must consider all possible routes to the cities she must
visit to find the path that is the shortest that covers all the stops
she must made. Finding the solution requires a computation that consumes
resources that increase exponentially with the number of differing
possibilities. This it would require aleph_1 resourses to compute such a
problem what had only aleph_0 different possibilities.
Even God itself cannot contradict mathematical facts. Thus there is
no Pre-established (or ordained) Harmony, as such is a
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.
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