A type of thing is a consistent invocation of sensations that a person identifies. A type of thing will be referred to formally as a quality set, in that it is a set of distinctive qualities one identifies as being fulfilled. For example, a cat is quality set regarding the slenderness of the nose, the shape of the back, and its distinctive femur. A quality set often itself requires the sensation of quantity, as multiple qualities are required. For this reason, it is best we use a more rigorous quality such as blueness, being the invocation of the sensation of blue. The invocation of such a sensation cannot be reduced to anything fundamental, and thus is a pure, single quality. This will allow us to concentrate solely on the faculty of quantity instead of simultaneously wresting them both.
A quality is some invocation of raw, conscious sensation. For example, the sensation of blueness is a quality and its often invoked when we look at the sky. A quality in its purest sense is the most fundamental property conceivable. The physical phenomena that arouses blueness in the retina may be broken down into a photon wavelength. However, the experience of blueness cannot be an emergence of any rational, underlying phenomena. All qualities are logically inexplicable. We can only take their existence for granted, and any attempt to rationalise them in futile. Blueness as a faculty is beyond causation, at least in the mechanical sense we are accustomed to in this universe. We cannot know the nature or mechanics of quality as knowledge itself is an emergence of the mechanics itself. Our experience as conscious beings is filled with pure quality. All sensations, thoughts, and relationships with phenomena that appear to exist outside our experiences are composed of simultaneous qualities. Visual phenomena relies heavily on the sensation of spacial dimension, that distance exists. Our hands, the dirt, and the wind are composite qualities, which can be broken down into the fundamental qualities. For example, the concept of a leaf can be reduced to the qualities of its spacial dimensions, the rustling sounds, the rough textures, and the brown hues. It could be said that all that is known to exist, in and of itself, is pure quality. The universe exists as a source of invocation of the senses, therefore we can suppose the universe exists.
Quantity refers to the sensation of multiple instances of a type of thing. Quantity is taken for granted, but the entire phenomena of multiplicity is merely an illusion to a conscious subject who in the privileged position of interacting and computing existences as if they were simultaneously occurring. Suppose 2 separate retina cells are excited by 2 isolated blue photons. From the perspective of the cells, only the event of which they interact with exists. It is only by the computation of the interaction in a simultaneous fashion that the events are occurring as if they were at the same time. Only by apparent simultaneity does the subject interpret multiplicity, that 2 blue events can even occur.
The sensation of quantity can also be invoked even when the events are not physically simultaneous, provided at least that the event occurring is memorised and therefore simultaneity can be simulated mentally.
We can easily deduce that quantity is in fact a product of computation regarding simultaneous input. This is illusion of multiplicity and therefore quantity. It is from this faculty that we can mentally build the idea of higher level categorisation of things having multiple qualities. In fact, it is from this human perspective that mathematics itself is built from. Therefore, we can reduce that mathematics is not in and of itself but a consciousness rendering of simultaneous sensations, and further, simultaneous fulfilment of sensations.