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So, "I am thinking", not: "I know what I am thinking", due to the fact that thinking is thinking--not an observed thought occurring somewhere else. It is construable to "know" thoughts in others, but thinking and knowing describe quite different things. Cardinality and ordinality of number are like this. Critically analyzing cardinality and ordinality would apply the wisdom of Wittgenstein's contrast of thinking to knowledge to the reality of numbers. From an original point of view and according to an original point of view, knowledge of other exists--but knowledge is: functional renderings of original-self-hood, to name otherness-than-self and logically declare another self, and yet something not itself, on principle. Say, for example, that some thing is compared to another thing. The initial thing is x. Another thing is y. x is x; y is 'know-able' by x if y is meaningful according to x. To 'know' y from given x would be either, to totally identify, because the difference would be apparently nothing; or else to partially identify according to x stuff or some of x stuff as apparently within y. The deep sense to the procedure is: conversation and vocabulary are engendered according to 'x that is' and stays purposely relevant and sensible even while examining something other than x. But can difference within otherness be explained by 'what is'? Recognition of kinship between objects of a "self" and Self itselfIn numbers, simply assume "what is", fundamentally, is one something: x is x. Notice that order for or within this number doesn't matter. To be a thing, a number is, cardinally and existentially some set thing.
Ones exist fundamentally within number whether or not ones fully coordinate between a first and second number. If two numbers are compared and the one of "number 1" coordinates its self to 1 one of another number, then x = y (or 1 = 1). Notice that non-existence of difference might have an identity/name like "reflection". If two numbers are compared but the one of "1" remains un-coordinated to any one of the "other number", we must construe the other number should be cardinally named for a lesser, in this case, empty set-of-ones and called "0". (x = 1 and is not equal to y = 0). Notice that existence of 0 might have an identity/name resembling "comparatively not" or "other that is not self in any coordinate-able way". (Since there evidently is not "nothing" generally speaking, I would call 0: "that which we [do] not-know". Notice that to not-know is something that has to be done--for example, by a lack of coordination of self to other.) So a single one is singly one "number 1" and an empty set is singly another "number 0". Already, if there is "1", there is guaranteed to be more than one named number. So far we have two numbers. It follows that: numbers name themselves by counting themselves, as they must logically exist. 1 and 0 and "2" that counts them up is three numbers . . . etc. Interestingly, 2 is a number that counts two existences so is made up of two ones. But to be x is simply: being x ones. A cardinal number x is a single thing that is the name of x ones. For given number x, the number would be cardinal. Then, for y as an other-number, x order-irrelevant ones will completely resemble y order-irrelevant ones when x and y are the same cardinal number (which looks like x = y). Imagine drawing one to one lines from a first set of ones to a second set of ones. The act of seeing resemblance between two sets makes an argument of otherness-of-y: ordinal-- because a one-to-one comparison occurs once each one per set, uniquely. In other words, one-to-one happens one at a time, in analytical terms. Notice that comparison absolutely confers an (often moot) order. If something is construed to be y, then y is declared: cardinally y ones--as long as its existence is recognized. The concept that number is declared cardinal but known ordinal-ly by comparison to an original number one gives y sense according to x. By "1", all numbers are named assuming numbers exist comparatively. Given 1; p, q, r, s . . . are count-able and deemed existent. p, q, r, s . . . can be any numbers, 0, 1, 2, 3 . . . Recognition of greater objects in another self and subsequent assessment by the SelfWhen, y > x, an interesting situation occurs. By what terms can x "know" y if y is other than x in a larger way? If numbers exist other than x--unless no number is larger than x [[which in a certain way is arguable]]--in terms of counted ones that name number, y may possess ones technically uncoordinated to and beyond x and yet analytically reasonable to x by the fact of existence of ones in x. Imagine you are nothing in particular. You know number because an idea of other-than-self leads you to compare one-self to less (which, incidentally, is another "nothing in particular"). Now you can increasingly imagine all numbers of things increasingly relative to your increasing knowledge. One being of nothing-in-particular founds everything, theoretically. Since others must exist, being is sensibly destined to recognize otherness--including otherness greater than self due to (creative) extension of oneself to otherness. Recognizing another that is defined within known terms requires seeing a parallel, ordinal relationship of self to other. Recognizing greater-than-self requires an assumption (faith) of existence of self and other as countable existences, which is effectively imaginable due to existence (in spite of otherness not already being "known"). Finally, it makes sense to be nothing in particular. After all, it is not required that anything in particular be known--if you exist. Can existence that extends itself be nothing in particular? Not by the knowledge and identities created when extending self-faiths to others, especially greater-others. No conscious being stays nothing-in-particular very long. |
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