rage at that frat party bro... rage.

recent metaphysics fodder...

'When studying the philosophy of mathematics/metaphysics the question “what is a number?” or more generally “what is an abstract entity?” is unavoidable. The answers to those questions are not simple. A number seems to be a particular kind of thing that has some role in existence, but a number is not the kind of entity that one can hope to observe as a physical object. Surely you can go to any kindergarten classroom and observe the symbol 9 tacked to a bulletin board but that would not be an instance of observing nine individual objects grouped together to form the concept that we know as nine, but even that grouping is not an instance of nine itself, it is just an instance of the specific quantity within a relation that nine represents. So we can observe the groups of things that come together to be instances of the concept nine. But then where is the number nine? I am going to assume in this paper that numbers are tools, and that abstract entities along the lines of numbers and propositions are synthetic abstractions. A synthetic abstraction is an abstraction that occurs after the recognition of a series of relations, that series of relations is then harnessed into a concept through synthetic abstraction. The difference between the word “abstraction” as it is commonly used and the phrase synthetic abstraction is that abstraction takes place after confronting a concept or a thing that impinges upon experience directly and synthetic abstraction requires the conglomeration of a group of relations between entities to get to the point of conception. To clarify that distinction I will give an example. Common abstraction takes place when a person sees a green leaf. A leaf has many characteristics; physical construction, smell, position in relation to the rest of the world, color, and so on. When we observe a green leaf and take note of its color we abstract the notion of green out of the observation of all of that leaf’s characteristics. Green comes into our perceptual apparatus because a certain wavelength of light impinges upon our experience. When we receive that wavelength and have the associated perceptual sensation we have recognized the color green, the word becomes attached to the sensation that we had and we then have the concept of green. The combination of the visible light spectrum and the particular wavelength that we experience as green is what makes it possible for the tools within our perceptual apparatus to abstract the color green. Synthetic abstraction requires a little more effort on the part of the perceiver. In the process of synthetic abstraction there is no clear designated entity or individual element within existence that is being perceived and designated. I will use numbers as an example of synthetic abstraction. Unlike the color green there is no direct connection between the portion of physical existence that we are labeling and the concept that we are using when we use numbers. It seems that the concept of number had to have come about through the recognition of relations. These relations are formed in more complicated ways than direct perception. When we perceive things the lattice of perceptual experience may be broken down into individual entities through the recognition of different characteristics, behaviors, and so on. Sometimes individual entities are similar to each other in enough ways, based on the characteristics we observe with our perceptual apparatus, that those entities get grouped together as a kind of entity. The groups of kinds do not have to be formal. A child may group a balloon and bicycle together because they are both red or because they are afraid of clowns and clowns often wield and manipulate both entities, but these groups come together through a form of trait-recognition relations. Our perceptual apparatus in concert with our organizational capabilities lead to groupings of the entities that are seen to be similar through the recognition of the common traits. Through such a process of trait recognition and relation we end up with aggregates. The quantities, of things being grouped during trait-recognition relations, are what we are describing when we use numbers. When one individual is similar to another individual they are two of a kind. And the system continues sequentially as more individuals enter the mix. I call that synthetic abstraction because it requires more than perception and designation. It requires a more complicated process, a process that involves critical thinking.'