Not, Truth and the Universe

When we create any proposition we are at the same time eliminating other "similar" propositions.

This process of elimination is called "negating". Without negation all propositions would have the same standing.

The negation process occurs under a universal, or a context. This is most clearly seen in set theory where A n A' = U gives the set of all things under discussion. U is not "All things" simply the limit of the discussion.

Given any proposition we have a relationship to the limit of the discussion through the "not" operator.

Truth and Falsehood lie outside the Universal as shown by Godel since statements can be true but cannot be proven within the Universal.

However a proposition which is deemed true gives rise to false propositions through negation.

When we define a proposition then it follows that this is being done under a larger context that allows for the propositions negation.

The negation of the Universal, i.e. the set of things we are not in discourse about, is not defined and creates a limit for "existence" within set theory. Thus existence is assumed for the elements of a universal (may even be the same thing).

The "God paradox" arises then when we use the elements of a set A to build the Universal, because the Universal contains both A and A' and so A cannot construct U.

Take the example of brains. The set of things to do with cognition are limited to "Brain". Then if we make an identity between brain and our experience, and we acknowledge that we know nothing outside our experience, then we know nothing outside our brain, the brain becomes the Universal. But our brain was originally defined as a subset of our knowledge. A creates U and so A' has no existence! We are simply eliminating elements to force U to A rather than explaining U.

U cannot be explained in terms of a subset since U = A & A'

A set such as T = {T} assumes an ontology: T, T', {T}, {T'} and a greater U. work this out...

In Hegelian logic a proposition A, entails its counter proposition A' and the possibility of a new set {A, A'} forces the U to expand to encompass it.

Hermeneutics may b of interest. This would say that we must take all the elements together to explain the whole system. It cannot be done heirachically bottom up, or top down.