Leibniz on Necessary Being
   
What, asks Leibniz, sufficiently explains a contingent being? “Contingent” here simply means something that could have been other than it is. The entire composition of the universe, the total aggregate of substances throughout space and time, are all contingent. There are other possible things, he reasons, but there are also other possible universes that could have existed but did not. All the many contingent things in the universe, he concludes, do not sufficiently explain themselves. There must be, Leibniz insists, something beyond all the contingent things which explains them, something which is itself necessary and therefore requires no explanation other than itself.
God, Leibniz concludes, is the necessary being which provides the sufficient explanation of all contingent things–why the universe is the way it is rather than otherwise. To this point in Leibniz’ reasoning, God’s necessity is the only aspect proffered (there is little religious or theological signification in this initially unembellished metaphysical concept). God as a being may be necessary, but if the contingent universe were a mere random or arbitrary act of God, then God would not comprise the required explanation of all things.  
God must not only be necessary but also the fount of the intelligibility of all things. It must be possible, therefore, to inquire into the reasons God had for creating this universe that actually exists rather than some other. And if we are to explain the lucidity of the universe by God, then God must have such comprehension that God could be said to know what it is that is being allowed to exist–that is, God must be able to grasp whole concepts and to see at once the total demonstration of things. God so far is therefore (1) a necessary being, (2) the explanation of the universe, and (3) the infinite intelligence.
[paraphrased from www.iep.utm.edu/leib-met/#H5]

              Leibniz on Necessary Being

 

What, asks Leibniz, sufficiently explains a contingent being? “Contingent” here simply means something that could have been other than it is. The entire composition of the universe, the total aggregate of substances throughout space and time, are all contingent. There are other possible things, he reasons, but there are also other possible universes that could have existed but did not. All the many contingent things in the universe, he concludes, do not sufficiently explain themselves. There must be, Leibniz insists, something beyond all the contingent things which explains them, something which is itself necessary and therefore requires no explanation other than itself.

God, Leibniz concludes, is the necessary being which provides the sufficient explanation of all contingent things–why the universe is the way it is rather than otherwise. To this point in Leibniz’ reasoning, God’s necessity is the only aspect proffered (there is little religious or theological signification in this initially unembellished metaphysical concept). God as a being may be necessary, but if the contingent universe were a mere random or arbitrary act of God, then God would not comprise the required explanation of all things.  

God must not only be necessary but also the fount of the intelligibility of all things. It must be possible, therefore, to inquire into the reasons God had for creating this universe that actually exists rather than some other. And if we are to explain the lucidity of the universe by God, then God must have such comprehension that God could be said to know what it is that is being allowed to exist–that is, God must be able to grasp whole concepts and to see at once the total demonstration of things. God so far is therefore (1) a necessary being, (2) the explanation of the universe, and (3) the infinite intelligence.

[paraphrased from www.iep.utm.edu/leib-met/#H5]

Six-Dimensional Boolean Lattice of Hexagrams
 
It is my intention in this blog to demonstrate that inevitability in the structure of the universe such as described by Brian Greene in the preceding post is factual, that it is based on the essential necessary geometry of space, time, matter, and energy, and that it can be effectively described by a simple algebraic geometry with relatively few elementary rules of symbol manipulation using a very old form of notation in a new way.
The image above [click image to enlarge] demonstrates the 6-dimensional combinatorial analysis of the 64 I Ching hexagrams in terms of Boolean algebra. Our goal here will be to demonstrate these same relationships in simple geometric form and show how doing so results in a mapping of the elementary particles (or strings) and the four forces of nature (strong, weak, electro-magnetism, and gravity.) The structure arrived at is internally self-consistent and unique (in the sense that no alteration is possible without destroying its efficacy.) Additionally, this mapping could result in a revolutionary new model of the atom, one consistent with the current findings of particle physics and superstring theory but in some ways going beyond both.
Note - A two dimensional projection of the Boolean lattice is shown here. However, the structure itself should be understood as a 6 dimensional hypercube.
Click image above to enlarge.
Image credit:  Dr Andreas Schöter         [http://www.yijing.co.uk/downloads/LoA.pdf]
© 2012 Martin Hauser

Six-Dimensional Boolean Lattice of Hexagrams

 

It is my intention in this blog to demonstrate that inevitability in the structure of the universe such as described by Brian Greene in the preceding post is factual, that it is based on the essential necessary geometry of space, time, matter, and energy, and that it can be effectively described by a simple algebraic geometry with relatively few elementary rules of symbol manipulation using a very old form of notation in a new way.

The image above [click image to enlarge] demonstrates the 6-dimensional combinatorial analysis of the 64 I Ching hexagrams in terms of Boolean algebra. Our goal here will be to demonstrate these same relationships in simple geometric form and show how doing so results in a mapping of the elementary particles (or strings) and the four forces of nature (strong, weak, electro-magnetism, and gravity.) The structure arrived at is internally self-consistent and unique (in the sense that no alteration is possible without destroying its efficacy.) Additionally, this mapping could result in a revolutionary new model of the atom, one consistent with the current findings of particle physics and superstring theory but in some ways going beyond both.

NoteA two dimensional projection of the Boolean lattice is shown here. However, the structure itself should be understood as a 6 dimensional hypercube.

Click image above to enlarge.

Image credit:  Dr Andreas Schöter         [http://www.yijing.co.uk/downloads/LoA.pdf]

© 2012 Martin Hauser