Discourse on the Empty Set

In the article 'Ontological Logic' I addressed the issue of totality being analogous to the empty set. If one doubts totality and oneness as actually existing, then it would follow that the concepts of 'singularity' and 'conception' themselves would fail to acquire meaning. If one may recall the article 'Metaphysics of Awareness', I addressed the issue of nothingness; I said that if the human mind is to be aware of ‘nothingness’ then it is to be treated as a category of existence. This of course contradicts our conventional understanding of nothingness, so perhaps it is that our conventional understanding should be re-examined? From a similar perspective conventional understanding of emptiness would again fail us in this case, as I shall expound below.

The heart of the matter and what may seem contradictory at first glance is that emptiness is a totality. The concept of a singularity pertains to an abstracted totality; to isolate an instance of this totality we would use an abstracted form, what we call an aspect of generalisation. One particular aspect of generalisation may be emptiness; the argument is that conception of emptiness produces emptiness itself, which would not result in a higher ontological state. In a similar fashion it could be said that a totality of totality does not produce a higher ontological state, but the process is used in establishing an ontological circle. The isomorphic nature of these two arguments is no coincidence; emptiness can be used to establish an ontological circle in itself which should then imply that emptiness is an ontology in itself, which I shall now show.

The reason I justify using the empty set as direct analogy is that an idea of 'emptiness' in itself is not truly 'empty', in its becoming an idea. This is analogous to the argument on the nature of nothingness. From a mathematical perspective it is possible to isolate that which 'is really empty' by adding a basic structure to it. It is in this basic structure that the totality arises, for we can now meaningfully speak of the emptiness to ascertain its mode of existence. 'Emptiness' can now be treated as a category of existence, a property which can be assigned to every element of being. The empty set must be compared to every possible element to ensure that it really is 'empty'; the empty set is consequently the absolute totality of the emptiness of every element. It is by virtue of this ontological totality that the ordinal hierarchy may be constructed, in taking the set of the empty set, which I would call 'conceiving' it, a greater structure is produced. What the empty set really represents then is a basic set structure, moreover its singularity, and the abstract intuitive 'emptiness' becomes a complete totality in itself.

The argument is an illustration of ontology as being the foundation of being, to criticise ontology would occur upon its very grounds of being, the criticism itself would contain an ontology which would establish its self-contradictory nature.

I will also address the idea of conception of being an 'identity' operator, that which gives us the element of conception being conceived upon back untouched. In its operator status there is a structure holding the category of the 'identity characteristic', as such a category of existence is formulated. Each operator must be compared to this category to ensure the identity operator leaves the operand unchanged, thus the operator could be said to be a totality of the identity characteristic. Therefore if we are to call conception an identity operator then we must concede that it will nonetheless be a totality in itself, and this totality allows us to assert its meaningful nature via the Fundamental Ontology.