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Today I heard that any object is an agregate of many, but finitely many Leibniz monads.

I would like to know if it can be counted how many monads form an electron or proton. What is the difference and connection between a monad and an atom?

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    Monad is a metaphysical concept in Leibniz's philosophy: of course, as every philosophical idea, is highly controverse and debated... – Mauro ALLEGRANZA May 10 '16 at 12:30
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    "The ultimate expression of Leibniz's view comes in his celebrated theory of monads, in which the only beings that will count as genuine substances and hence be considered real are mind-like simple substances endowed with perception and appetite." Thus, monads ar not phisical atoms; we can say that they are "metaphisical" atoms. – Mauro ALLEGRANZA May 10 '16 at 12:33
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    See also the related post on what Leibniz calls a monad. – Mauro ALLEGRANZA May 10 '16 at 12:39
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    @Mauro Allegranza What is a "metaphysical" atom? – Jo Wehler May 10 '16 at 15:21
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    @JoWehler - a monad... – Mauro ALLEGRANZA May 10 '16 at 15:24
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The person who most likely first uttered the statement,

[An] object is an aggregate of many, but finitely many Leibniz monads

is John Dalton who proposed the theory of atom in 1805 (cf., Leibniz: Prophet of New Era Science by J. Lawrenz).

What is the difference and connection between a monad and an atom?

Leibniz (1646-1716) in the history of philosophy is known for the monad theory. The philosophical issue of the 17th century was the mind-body problem (or more broadly, the seeming causal interactions of things in the physical world), originating from the defects in the Cartesian dualist view of substance. To post-Descartes scholars, explaining the nature of substance amounted to solving the problem. In the big scheme of the history of thought, the monad theory can be viewed as an attempt at a solution. Here I explain Leibniz's conceptions of the monad (for detail, refer to the excellent entry, "Gottfried Wilhelm Leibniz" in SEP), and show which conception Dalton borrowed from Leibniz.

Postulation of the logical conception of substance

To explain what substance is, Leibniz takes us to the God's point of view. From the omniscient point of view, the past, the present and the future of a thing is already contained in that thing. Translated linguistically, all the predicates that are true of the subject is already embedded in the subject. To God, the happenings in the physical world are, so-to-speak, analytic truths.

To Leibniz, substance must be something like analytical truth from God's point of view. Since a thing that contains everything in it (e.g., its past, present, future, even the whole universe and soul) is analytical truth for God, substance must be something that contains everything in it. For this reason of unity, substance cannot be divided. Since nothing that is divisible is substance, to Leibniz, the Cartesian matter, which is divisible, is not substance. The Leibnizian way of understanding substance is called the logical conception of substance. To avoid confusion, Leibniz calls his idea of substance (a thing that contains everything within) monad. These are some lemmata of this nature of monad (I list them without proof):

Lemmata

  1. There can be no two monads that share exactly the same properties in all possible ways: if they did, they must be actually one monad referred to by two different names.

  2. Each monad is self-contained and self-sufficient. Monads do not interact with each other and cannot influence the acts of others. Thus, there is no causal interaction among monads. (To explain the seeming causality of the physical world, Leibniz needs another postulate, called the pre-established harmony).

  3. Monad is indivisible and indestructible due to the unity (self-containment) nature.


As you can see, Dalton's atom is borrowed from the lemma 3. By the time Dalton was around, Leibniz's metaphysical conception of monad was far out of favor. But his idea that the world was made of something that cannot be divided any further survived and prospered.

  • Nice answer. It's helpful to contrast Leibniz's monad with Spinoza. Where Spinoza and Leibniz agree that substance is indvisible, Spinoza has a monolithic substance that he conceives as the identity of God and Nature. By contrast, Leibniz conceives of a plenitude of indivisible substances, i.e., monads, each of which is a part of the whole that condenses the whole in itself. Arguably, this difference stems from the remainder of Leibniz's early (though abandoned) commitment to atomism. To escape the materialistic implications of atomism, Leibniz conceives of the monad as a "spiritual atom". – transitionsynthesis Aug 5 at 18:01
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As far as I understand, monads are not physical objects. I can understand that the beginning of the definition is really close to what would be an elementary particle. One of the major property of the monad, is that it is a simple object, without parts.

But it is said to be a spiritual object, not a physical one. Monads have "souls" and are, in a way, unique. They can't be destroyed or created (unlike particles) It might be understood as atoms for animals or organic entities. So you can't count how many monads you have in a particle. It gets tricky as Leibniz use it to talk about god and his conception of the universe. This related post as already been linked in comments but I found it really useful : What is it that Leibniz calls a “Monad”?

By the way the proton is not an elementary particle. It's made of quarks (three valence quarks, two "up" and one "down" : uud) exchanging gluons to interact. In the standard model, quarks and electrons (electrons are the most common lepton) are elementary particle.

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