From the philosophical discourse we have embarked upon in metaphysics in particular, it makes sense to speak of the singularity of the mind as the totality of being which we identify ourselves with. But this speaks nothing of the idea of thought and will, of the fundamental ability to perceive and conceive as aspects of cognition rather than spectacles of structure.
What is required is some construction to elaborate on some relationship between various structures, an operation between them. The present discussion is to hopefully illuminate the latter construction which may not seem self evident or even natural perhaps. This may very well be the case, but consistency of reasoning is paramount and sufficient, the overarching idea of my philosophy is not to present the final condition of human thought and the ubiquitous system which fully defines and explains all things. I simply seek a perception of reality, as in this life at least it seems that conception of absolute truth is all but above ourselves. When searching for a definition of our operation we must question whether it should occur between form, singularity, or both. As form represents individual representation of the true ideal it is impossible to construct a singularity from this, or to come to any other understand other than that which is immediately present. Singularity on the other hand does provide a path towards greater understanding, we can utilise its sum totality but is questionable as to what effect this would have on a structure already embodying its own sum totality. As such we conclude that our operation must include singularity and form to provide a meaningful path towards self realisation.
We define a singularity expansion about a form. Intuitively this is a process of constructing a singularity from a given form; we can centre our expansion about a particular form and take a summation indexed by the singularity itself cycling through each form to produce infinite generalisation. An insight gleaned is that any totality could index the expansion, it need not necessarily be the initial singularity - provided that the indexing singularity is of a greater state of existence than the subject singularity*. It is possible to use another singularity to index our expansion, setting this to be the 'mind' we come to our definition of our operator, 'cognition'.
Thought is the acquaintance of the mental spirit with a particular idea. The category of thought is comprised of the voluntary and involuntary; the involuntary consists of an idea stemming from a material stimulus. The involuntary mechanism can be described in some detail by science, a mathematical exposition would be more useful philosophically, and it is here that we can utilise modelling the mind/body complex in this scenario by a logical system. The voluntary mechanism of thought is much more difficult to describe but seems to revolve around an idea of 'will'.
Our conception of the world (external reality) follows by cognition about a particular idea and situation. That is the totality of external awareness is centered around a particular physical frame, awareness is restricted but the singularity expansion remains possible as with each physical frame of awareness an idea is associated. Ideas exist as singularities, the intrinsic nature of infinity allows for complete generalisation onto reality from any given moment. The mathematical detail of this argument is to to simply observe external reality as a 3-dimensional space adding further sets to account for any other perceived variations such as colour, sounds, etc. This system accounts for the involuntary stimulus and primitively associates thought by necessity.
*In my previous post we construct a transfinite sequence of singularities through generalisation. This statement deals with the problematic nature of using something of a lower state to index a higher state, which may seem contradictory to the very nature of generalisation via the mind. The difference is that the mind is innately equipped with a power to 'apparently generalise' any phenomenon (the innate characteristic is what I would characterise as an ontological truth). I.e. a lower cardinality cannot be used to index a set of higher cardinality, but the mind is unrestricted by comprehension - we can construct any cardinality. Of course at some point it may be that we are incorrect in assuming that our generalisations are meaningful, and this is where the proof picks up in the previous article.
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