The truth of the matter.

I moved back to school this past Wednesday and have been relaxing before courses start for the fall semester.

In the mean time I am continuing to work through Gödel's work on the incompleteness theorem, along with the ZF axiom system.

Truth is the main premise to this thesis, and how this truth can be interpreted through a machine; as for you and almost any being (perhaps there are some that do not perceive the world as I do) realize our surrounding as what we perceive it to be. Where if it is not the case and we rather perceive some false premise, this is also fine, as you have first have perceived those fallacies as truths, but have then (from more sensory input, or cognitive consideration) realized the inconsistency of the situation and have adapted your reality accordingly.

Given a statement of logic, we would like to see what variable combinations give truth to this statement. This is first done by accepting all variables and possible negations as truths, contrary to the Boolean algebraic approach of neg(1)=0, and assigning a specific mapping to these variables (to integers, letters, symbols, etc...) such that each variable along with any necessary negations of variables of the same class to be defined independently. It is now that we can define the statement of logic in a variable independent sense, allowing us to understand completly under the basis of truth.

Next, on to bounded combinatorical spaces and the existential prediacte axioms!