Monads within monads within monads-- matter, strings and atomic structure     

First I'm going to have to take you, searchlight in hand, through    
the darkest, most difficult topic in Leibniz's philosophy, which     
is difficult for beginners, especially if they're materialists.   
The dark passageway is what Leibniz means by "substance"    
and "monad". Leibniz sometimes refers  to substance as if it    
were  a description of a physical object, but these both only    
apply to mental entities.    

Leibniz  developed his idealistic theory of monads before anything was known    
about atomic physics, so, although being aware of the possibility from the    
ancient Greeks, he did not include atoms specifically in his theory.   
Instead, he used Aristotle's concept of substance, but allowed it to   
be continually changing. In place of physical atoms, he based his philosophy 
on the corresponding mental quantity, the monad. 
Without going into great detail, Leibniz used an atom of mind, 
the monad,  

Leibniz began by asking, in the tradition of Descartes, if there might be any 
fundamental quantity, anything certain, on which he could base his philosophy.  
He found that everything in spacetime could be divided  an infinite number of 
times, so that the fundamental quantity must not be physical. Today we know that
there may be a size limit, the atom or fundamental particles, but one cannot
isolate these, due to the Heisenberg Uncertainty principle.  Here I use
isolatability instead of infinite divisibility to dismiss anything physical
(anything in spacetime) as being fundamental. That includes space and
time, which are infinitely divisible. Also, there are arguments
by others such as Paul Davis that matter is not fundamental.

Next then we ask whether mind has fundamental units
on which to build a philosophy. If you recall the double aspect
theory of mind, you can see that parts of the brain, while
not being fundamental, possess fundamental functions,
such as units of memory, or visual or sensory motor functions.
So it appears that mind, a mental substance, can be divided up 
into fundamental or logical wholes or concepts. 
Leibniz then used these units of mind or monads as the
fundamental "mental atoms" of existence. 

A monad then is a complete concept, a whole. a simple substance
of one part. A monad may and probably does have variations within,    
but it is a whole, constantly changing entity which, being so, does not have a  
boundary within, as long as we assess the whole as a single function.
Thus man as a monad contains a brain as a monad which contains
neurons as monads. Note that, although each of these monads
is physically within the others, the monads are to be classed
as functions within functions, and may not be directly related to
the physical monads.

A piece of matter would mentally consist of a monad for the whole,
inside of which (here both mentally and physically) are a huge 
number of monads for the atoms. Then if we look further, we 
might have within the atom monad, monads for its subparticles 
such as electrons, protons and neutrons. Similary each
atom is made up of strings. I would suspect that the various modes
of vibration would be further monads inside the basic atom
monad. Higher frequency strings inside lower frequency strings.

If we look at this abstractly, as on a spreadsheet,  we see that
the universe can be characterized topically, as monads within
monads, depending on how finely we focus our vision.


Dr. Roger Clough NIST (ret.) 5/7/2013     
See my Leibniz site at

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