Ontological Logic

Logic is an area which is one of my greatest joys in studying as a Mathematician, but in presenting my own theory detailing its foundations to the inner cosmos which it projects, is no other than a monumental task which brings me to the limits of my mental capability. The true difficulty of the task lies in the fact that when producing a critique on logic, we must use the rational faculties of the mind to produce it in the first place. To hold this level of introspection and mindfulness and most importantly to bring it from the esoteric darkness into the knowable light is one of the most strenuous yet rewarding tasks a human can undertake.

When I was searching for a theory of logic I used my teleological method of philosophy, what is the 'purpose' of it? To demonstrate the purpose of logic I shall present a brief summary of my philosophy from first conceptions and determine the exact location at which logic arises (though in truth all of my writing rests upon this logic, a detail which I shall address).

We have a 'tree' like structure of the singularity-form hierarchy which we use to perceive reality. The differences between particular forms by the mind are illusory, they are parts of the same whole. This knowledge of reality I have argued is pre-existent in the mind , what we call a priori. The a priori principle is the Will, the seed as the soul from which reality flowers, rested upon the fundamental ontological principle. The names we give to singularities and forms comes a posteriori, from experience. To elucidate upon this matter it is helpful to set the context to forms of the same singularity, let us say different colours. All colours are one in their concept, but as forms we name them; this naming is not innate but comes from our experience in this world. We can then can speak of the singularity of colour itself, a form in its higher singularity which in turn has also been named. Thus all aside from absolute oneness is named and perceived a posteriori.

It is from this naming that we can isolate a conception of logic. A system of logic arises out of the conception of 'concepts'.
A Concept is a name we give to a necessarily abstracted form, by necessarily abstracted I mean that the form is understood within the context of its singularity which has been conceived.

Again there is a hint of ontology in this matter, the concept being conceived is analogous to the form being conceived, the distinction between concept and form is that a 'concept' specifically refers to a human cognitive perception, I do not attempt to hold a concept as anything higher than its name. The purpose of logic can hence be answered, it is to equate the name with the knowable idea which exists as nameless, pure awareness, its singularity intuited in the mind.

I will take an aside here to answer a query the reader will undoubtedly have. Are not the ideas of 'singularities' and 'forms' also names? I shall state here that the 'singularity-form' system arises out of the conception of 'concepts of structure'. They are reflections of the higher seeds of awareness, of the innate being of the Will.

On Ontological Logic

The conception of a form produces singularity, the conception of a concept produces its meaning. I have discussed before that the meaning the mind associates with a particular substance, its teleology, is its existent reality in itself. All reality is awareness. As such, the conception upon concept and of form both indeed lead to their respective singularity.

To answer how it is that a mere name can gravitate an attached existence other than itself, we will equivalently show that the concepts of 'singularity' and 'form' themselves indeed refer to a higher archetypal reality. This is because their archetypal status ensures that all human perception is shaped through their lenses of awareness, all concepts refer to a form of a singularity which can be considered a singularity in itself.

Recall the Fundamental Equivalence:
The conception of a perception of singularity equates to the existence of the higher singularity. 
Singularity is the absolute totality of its form, the abstracted and generalised state of being. For what I said to truly be meaningful, the concept of singularity must itself really be meaningful which would require my faculty of 'conception' to be a real existent thing in the capacity that we have implicitly assumed.
Now recall the Fundamental Ontology:
We can conceive of conception.
We can now see how the two meta-theorems perfectly complement each other to establish the true nature of ontology, being in itself; a phrase I have used many a time, but now I hope that the reader will be beginning to intuit the precise nature of its reality. I wholeheartedly encourage him to independently pursue this cause to arrive at his own perception of truth.
The cautious reader may again believe me to have pulled a fabric over his eyes and performed a deceit before him, surely I am going around in circles speaking of the same thing and not really transcending it? Let us examine the nature of this claim, to say that conception of conception does not produce a higher reality would be to say that one disagrees with the precise reality of conception that I have described. Perhaps, conception is not truly the leading to totality and that the abstract totality I speak of is illusory; perhaps conception is no more than an identity operator which leads the mind back to the initial substance being conceived upon.
I would not disagree.
Conception could be called an identity operator, singularity could be called the empty set. But that is because we have thus far misunderstood the true nature of what these terms mean; what does it truly mean to say that something is empty? I believe that even the mathematicians amongst us have been misleading themselves, I would say unknowingly but instead I must say rather foolishly. For the empty set is actually everything other than empty - a fact which a learned mathematician would himself proclaim to. If we are to compare my work to this emptiness, then I beckon the reader to compare my work to the ordinal hierarchy. As the empty set has led the mind from the mildest shore of the plain finite, to the distant horizon of incomprehensibly large structures, so too will conception lead the mind from ignoble darkness into the light of ontology. I will elucidate upon this matter in my article 'Discourse on the Empty Set'.

When a concept is applied to itself produces itself again, we say that we have completed an Ontological Circle. An example is awareness of awareness, which is no different than awareness itself. We can in fact produce an infinite sequence of awareness, this sequence in its totality can again be conceived. The conception of the sequence as a whole ties it into its higher singularity, and in turn guarantees its existence in a higher reality. The Ontological Circle is really no more than a summary of the unison of the two meta-theorems described above, of the meaningful conception guaranteed by the Fundamental Ontology to the higher existence guaranteed by the Fundamental Equivalence.

I should address the concepts which do not 'complete the circle', such concepts refer to substances whose existence is dependent upon another singularity conceivable by the human mind. Perhaps it is easier to say that the concepts which do 'complete the circle' as it is, are those which constitute the faculties of reason and logic, I shall touch upon this in more detail in my next article.

There are multiple Ontological Circles which can be completed summarised as follows, in order of their construction:
First Circle - Awareness
Second Circle - Singularity
Third Circle - Conception
Fourth Circle - Ontological Logic
We can  therefore speak of any of these concepts meaningfully for by virtue of there being ontologically complete they are what we can call 'self-transcending', by this I specifically mean to say that the concepts in themselves hold more being than mere words can describe. They are beyond perceptive judgements, for they embody the innate judging faculties themselves.

The fourth circle remains to be completed. My system of logic produces an archetype of understanding through concepts of intuition, it then proceeds to critique this very archetype within the system itself. The system is of the system, again we can produce an infinite sequence of systems studying the preceding structure. In completing this circle we arrive to a logic which can be said to be more than a mere system for it can be said to study whatever system itself. This in turn answers a problem mathematical logic, that each such system must be studied by another system to make sense within its logical universe of construction. In truth mathematicians are basing their logic on naive set theory, the purest mathematical embodiment of abstract intuition. In basing my philosophy solely upon this intuition itself through ontology I have sidestepped the issue entirely, and allowed us to glimpse into the heart of the human understanding - the very fabric of its being rather than its appearance or representation perceived.  

It is here that I should address that my system of Ontological Logic pertains only to the conceivable thoughts of the human mind; at its highest level the system rests upon the throne of being, ontology describing the conceiving faculty itself. It is in this highest concept that I would insist that logically speaking we attempt not to move beyond the concept of the conceiving faculty, for our limited thoughts would do injustice to this seat of God's creation. In fact even in my present discourse I would not claim that the mere words on this paper should gravitate some transcendental meaning, what I truly mean is that the reader through his meditations and contemplations may intuit and realise some greater and profound truth that my philosophy should encourage him towards, this is similar to what I spoke of before that one does not simple know truth, he becomes truth.

It is only appropriate now that we end this treatise on logic with a meta-analysis of my philosophy, as being a concept of truth. What we seek fundamentally is a direct perception of truth, for absolute truth in itself (the conception of truth) is of God's being. This perception exists more so than an idea in the mind as we just addressed, which is why I now present my philosophy as being the logical representation of this perception within the thinking faculties.