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 self-contradictory idea.

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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