Truth

We know that Ontological Logic describes the Faculties of Reason and Logic, what can henceforth be called the Intelligible Realm or the Realm of Knowledge. Ontological Logic is rested upon Ontological Circles, which allow for any statement to acquire ontological value, this is to say that any statement of concepts (words) pertains to the actual existent entities themselves. But if logic is to be treated as the life blood of the Intelligible Realm, then Ontological Logic provides a platform to merely explore the waters of the ocean, but its totality as a singularity has not been addressed. I have also spoken of Ontological Logic as formulating logical concepts through pure nameless intuition and understanding but not precisely elucidated into what this pure understanding is. In this article I aim to unify my discussion on the Intelligible Realm through the introduction of truth into my philosophy.

First and foremost we should address the issue of truth relative to the context of a logical system, the system of which would be a form of Ontological Logic as we shall see. We can say a statement is true if it agrees with the pure understanding of the mind through the singularity structure, but since concepts themselves must necessarily be about the singularity structure itself, it follows that a statement is true if it is meaningful. To say that 'a singularity is the totality of form' is true, but the truth does not lie in the statement itself but in the pure ontological category of being, that there is the part and the whole, and our definitions of a 'singularity' and 'form' coincide with this. To say that 'a form is the totality of singularity' is false by our current definition of singularity and form, this statement of concepts is not meaningful with these definitions because it doesn't actually describe anything at all. There is no part which is the totality of its whole, I use italics here to denote the 'nameless structure' and not the concept. Of course in switching our definitions of 'singularity' and 'form' the statement becomes meaningful. Truth in Ontological Logic is thus not a category of the system itself, it cannot be formulated in words. We see this in mathematical logic where truth is treated as an inductive property defined within a logical system,  but a universal absolute formulation of truth simply does not exist. Truth is established in comparing the written form of logic to its pure understanding.  

This is the formulation of truth in Ontological Logic, I shall now address the idea of truth in a Logical System. Ontological Logic is the foundation of all logic in pure nameless understanding, but traditional and mathematical systems of logic are concerned with named statements themselves as displayed below:

A Singularity

↕  Ontological Logic relates

Concept: Of the Singularity

↕ Systems of Logic relates

Concept: Statement of Concepts concerning the Singularity

Of course this hierarchy can be formulated in Ontological Logic itself, and it is clear that the relation between the concepts is a reflection of the relation between the singularity and its respective concept. Since this applies for every statement and formulation of each logic it necessarily follows that a system of logic is a reflection of Ontological Logic. This is the justification behind calling Ontological Logic the singularity of all logical systems. Truth in itself is also reflected into the logical system, a statement of concepts in the system is true if it agrees with the axioms, rules and definitions of the system itself, i.e. the logical formulation of the abstract singularity in concepts, and by the hierarchy this 'logical truth' is true if it agrees with its 'ontological truth'. Note carefully that by truth here I am referring to a universal definition rather than the mathematical one, in terms of mathematics this definition would coincide more with provability, a general statement in the system is true if it can be proven from it.

Mathematical logic from an ontological perspective is awkward, but by its own acknowledgement the common systems of logic are not meant for existential categorisation but rather to provide a constructed platform to ensure consistency. Mathematical logic necessitates the use of naive set theory in its construction, it is this pure naive mathematics which must be taken to be the logical system in the above example. In an actual logical system such as the propositional or predicate calculus the entities of existence are contained within a domain and hence trivialised. It is not these elements of existence that are of concern to the logical system, but it is the rules of their manipulation that mathematical logic studies, for it is here that the notion of consistency and provability arise. Now after addressing this problem we must add an addendum to the argument:

Concept: Statement of Concepts

↕ Interpretation

Concept: Model 

Now this fits the notion of truth of mathematical logic, the statement of concepts is inductively defined to be 'true' mathematically if its interpretation within the model or structure fits what 'it ought to look like'. The hierarchy detailed above thus provides a sense of reflection of truth from the logical statement to the model. I hesitate to amalgamate the two hierarchies together due to complications that emerge by the formulation of mathematical logic which I detailed in the above paragraph. This is not to say that my notion of truth breaks down, but rather it could be said that mathematical logic is not really what we want a logic to look like, with its focus on relation rather than elements. This is perfectly acceptable of course in treating the relations themselves as the singularities, but then I would be interpreting mathematical logic in a way it is not intended to be, as a mathematician I would not be comfortable with this situation. Mathematical logic in some sense provides a closed system of study, but from the meta-view it is clear that the closed system must rest on some prior ontological condition, and this placement into my view of the hierarchy of being allows for us to analyse the situation of mathematical logic. For fear of writing excessively (if I have not already done so) and due to the vast sophistications and subtleties of the interaction of mathematics with philosophy I will end the discourse on this interaction here.

For my last perspective on logical truth I will explain the variation of truth with Worlds of Being. The statement 'the Earth is a planet' is a true statement in this world of being but a false statement in another. To say that 'the Earth is a sun' is true in another universe of the imagination. but false in this one. We have a statement of concepts about a World of Being, and the World of Being itself is a form of the Cosmic Imagination. The statement is true if the World of Being it pertains to is true, but since all Worlds of Being are 'true' in that they exist within the Cosmic Imagination it follows that universally speaking every statement is true in that it is meaningful since it refers to something. The universal definition of truth should therefore not be applied to statement within the World of Being, we must treat the World of Being as a logical system but more powerfully than this we are to treat it as the only logical system. In this case there is only this universe, only what we perceive and conceive inside it, as such existence is reformulated to a constricted understanding as presence within this World of Being. The 'Earth is a planet' is true and the 'Earth is a sun' is false. Of course, this does come down to our perception of this World of Being, perhaps the Earth is a sun in some sort of parallel universe which is apparently contained in this World of Being. The difficulty in ascertaining perception and conceiving the world of being as it really is explains the widespread prevalence of falsehood and lies in our world.

What I speak of next is the Ideal of Truth. If we are to assume all thoughts to be meaningful then all thoughts are true. What their truth is cannot be a thought, it must have a higher ontological state of existence. The beauty here is that this state of existence refers to the 'nameless pure understanding' that Ontological Logic forms the bridge to. This nameless pure understanding is the singularity of all thought, what I call the Ideal of Truth. All thought is a form of truth, and by volition of the will all thought is a striving towards truth. This Ideal is the seed and singularity of the Intelligible Realm, of the Known, Truth, as I shall explain in my next article is an aesthetic form of a more powerful and greater ideal, truth is understanding, and understanding is a feeling, or becoming.