Written, in part, to amend an earlier erroneous proof. I more precisely define a theorem;
'There exists a greater structure of which we have a perception of but cannot fully conceive.'
If we could fully conceive such a structure, then we would either understand it as singularity or identify ourselves with it. The structure would be contained within the mind. To prove that we can perceive of a superstructure is to prove that we can come to some understanding of the singularity via its forms, and more strongly for the discussion to be meaningful we would also need to prove that one can conceive of this perception.
The beginning of our proof may prove fruitful to the empirical skeptics who find difficulty in ascertaining the true notion of the infinite, whose necessary existence may not be evident when examining the universe from an epistemology of materialistic construction. In a flavour similar to the ordinal hierarchy we can start from some 'empty set' which here need not embody the abstract notion of set theoretic structure requisite to the continuation of said structure throughout the hierarchy. The reason for this shall become more clear later.
Start with some form X1 and continually generalise it in a sequence X1, X2 , ..., Xn, ...
We shall produce a structure greater than this sequence by constructing a singularity of the sequence itself. We must be careful to divide this proof into various cases. It may be that each generalisation is meaningful and a transfinite sequence is produced, thus there must be some initial singularity X which produces each Xn as its substructure. However the case in which we are truly interested is that when the Xn's are not meaningful and are ontologically null extensions of X1. In this case we cannot come to conceive of the singularity of the higher sequence but we can guarantee its existence by conceiving of X1. This is true by necessity since if the conception of X1 produces X1 again then it must be a singularity, and since by premise we supposed it to be known to the mind it has been conceived. The fundamental equivalence does the rest.
The theorem can know be generalised even further;
'For any known structure one can always guarantee the existence of a structure greater.'
The above argument generalises to any subject matter upon which meaning is being ordained. From the unmeaningful we can produce ontological extensions assuming nothing of their validity, (they very may well be null) but the case holds that the extensions themselves are contributing to a perception of meaning. And the conception of this perception originates from our examination of the initial subject matter. It is important to bear in mind that meaning is originating from the singularity and not the form, forms may well be meaningless and I do not doubt or contradict this at all.
To prove the primary theorem we set X to be the singularity of the self. This is the only case in which ontologically null extensions come into effect since no thought greater than the self can be conceived of. But the existence of higher structure is always necessitated by the theorem and so structure greater than oneself is realised.
