I was compelled to pick up Leibniz’s Monadology after a comment from John Barrow in Smolin Lee’s “The Life of the Cosmos” that anyone who is interested in Cosmology should read him. I have found Cosmology interesting for two reasons: physically it tells us some very interesting things about the nature of the Universe, and philosophically  it is unlike any other scientific (or non-scientific) theory because science (or any other mode of thought) makes theories as a way to describe a class of phenomena, objects, or ideas and therefore one can’t have a theory about only one phenomenon, object, or idea. This is exactly what Cosmology is: a theory of the history of one thing, the Universe which is by its very definition is all that is, was, and will be. Such a theory must be different from all other theories, in its very construction. Perhaps the one other form of study to come close to Cosmology is monotheistic Theology, as its subject is the one God; the main difference being one usually can’t do experiments on God.

One question that a Cosmology must answer is that of initial conditions: What is the origin of the structure (or properties) of the basic elements in the Universe, if they have any properties? In its modern form, this reduces to asking why do elementary particles (electrons, photons, and so on) have the masses, charges, and initial distributions in phase space (positions and momenta) that they have? The current standard theory of Cosmology has no answer. If we can envision a more advanced more unified physics based on one elementary particle, we still have the same problem, unless this one elementary particle will have no properties at all! I am not sure if this theory would still be physics and not metaphysics. Leibniz has avoided this initial conditions problem altogether in his Metaphysics by simply making the basic elements non-physical eternal entities completely devoid of structure which he called monads. I must say that Leibniz arrived that the concept not to avoid this problem of initial conditions but rather metaphysically, as he considered “unity” and “simplicity” to be one and the same and both to be the condition for being. So he concluded that the basic units of the Universe should be simple, i.e. structureless, substances, otherwise they wouldn’t be units at all. He also concluded that they are the only elements of the Universe since they are the only ones satisfying the condition for being. I will have more to say about these two basic metaphysical truths that Leibniz arrived at. but let me first tell what follows from them.

My first reading of Leibniz’s Monadology was surprising. It seemed that some of the first 18 sections were describing the wavefunctions of quantum mechanics: a concept which physics has arrived at to describe nature at the sub-atomic level, and its use has been extended to describe almost all phenomena at all distance and energy scales with exception of gravity especially in its maximum strength near very compact objects like black holes. Here are some of the properties of monads that Leibniz writes down which fits QM wavefunctions. From section 2:  “no extension, or figure, or divisibility is possible.” From section 8: “However, monads must have qualities, otherwise they would not even be beings.” From sections 11, 12 ,13: “the natural changes of the monads proceed from an internal principle” and “there must also be an internal complexity of that which changes” and “this internal complexity must enfold a multiplicity in unity or in the simple.” Section 15: “The action of the internal principle which brings about the change or the passage from one perception to another may be appetition. It is true that appetite cannot always attain altogether the whole perception to which it tends, but it always obtains some part of it, and so attains new perceptions. From section 17: “perceptions and what depends upon it is inexplicable on mechanical principles, that is, by figures and motions.” People didn’t like the properties of wavefunctions at their first conception; this is referred to as “the weirdness of the quantum world.” It would be too much to say that Leibniz had the faintest idea of quantum mechanics, but it wouldn’t be too much to say that Leibniz knew for sure that the concept of particles at his day was not to last long, and that he did look for an alternative. 

After a very condense introduction to the monads and their properties scarcely sampled above, Leibniz goes on to state his basic two laws on which the Universe is to be built out of these monads. First, the Principal of Non-Contradiction, which basically says that a truth is possible if (but not only if) it is non-contradictory to other truths. Second is the Principal of Sufficient Reason, which in short makes the further demand that a truth is “chosen” to be actual only if there is sufficient reason to choose over all the other possible truths. Combined with Leibniz’s belief in an all-good, all-powerful God, this results in the ultra optimistic conclusion that the Universe we live in is the best of all possible Universes. I think this is the most holy marriage of Christian Theology to postmodern hippie metaphysics in a time way before their legal marrying age, but it really depends on who you think is legitimate enough to bless this wedding.        

My second reading of the Monadology was better. I saw that Leibniz’s monads were not just the basic elements of physical reality but of the whole of reality. I was blinded by physics to not see his metaphysics. Getting back to his ideas of being, especially that of simplicity and unity being identically one and that they both predicate Being. Is it true that a Cosmology must say something about Ontology? Something substantial? I will post more soon.