:)

[Reciprocality]

It is literally impossible that I'm not 100% correct, put it all together and you have the method by which paradoxes are solved.

[Reciprocality]

Few days ago: "Axioms precede definitions, they are subject and predicate in unity, this is the meaning of self-subsistence. This is the inverse of substance, that is, self-subsistence is something without predicates."

Today: "If you believe these axioms have anything in themselves to do with predicates and properties then I don't know what more I can do, you are just inconsistent on purpose at that point."

Semantically these two statements ^ are inconsistent, but since I would never dare to assert anything without logical reason we must resolve it by creating distinctions.

 

The axiomatic subjects I spoke of earlier, each of which are conceptual dualities and of a reality beyond your personal power, yet given to thought only through that personal power, are conceptual-substance, subsistence and immanent truth, when they are applied as predicates it is never they that are true or false, but instead the subjects on/of which they are applied that are either owed or not owed such predication.

A state of something is a process, and NOT that something. Accidence vs Substance

Truth vs Falsity.

[Reciprocality]

Truth and falsity is precisely such a duality which can not be immanent, that is, that something had the possibility to be false means that you put up standards that it may fail to meet, these standards are taken from the pool of axiomatic subjects but lose their nature as substance immediately upon predication of new subjects. That is, there is in the application of standards a delaying of what is otherwise effortless, a resignation of what is immediately given to that which is mediately given, a procrastination of sorts, an expectation of future events, a becoming and when taken to extremes: never to have been.

This does not mean that there aren't immanent truths, only that there are no things opposite of such immanence, in fact, not even the concept of negation, which is the only possible kind of "nothing" and is therefore the evidence of the impossibility of an actual state of complete absence, is beyond immanence.

[Reciprocality]

There is a reality beyond the immediately given, but it is not a thing in itself, instead it is composed of axiomatic subjects, this is the composition of creatures in whose mind there can exist an interpretation, essence or story of what "you" are to them, through mutually exclusive interpretations will people in social groups approach the essence of their subject, which in this example were you.

The independent "reality" of you do not exist in the world, instead a contingent reality of you becomes through the intelligence of social dynamics.

In addition, you change by the feedback of that becoming.

 

^ All of this is actually self evident, it goes without saying, i feel silly for having said it for this reason, yet it has to be said and is true of every conceivable thing.

[Reciprocality]

1. Spontaneity of composites (ideas), 2. Immanence of indivisibles (senses) and 3. concepts from non-contradiction form the three kinds of elements in the set of the axiom of foundation.

The two first in conjunction form the geometric indivisibles under the necessary conditions of time, space and memory (effortless judgement of spatial awareness (non-opposition(intention) / impenetrability(extension))), while geometry in the abstract is formed first under formalisation whereby the indivisible of composite ideas is cut out of their reference frame, constituting dimensionality. (inside/outside, here/there, over/under)  And when represented in time as opposed to space units vs metrics through practice of counting. 

 

 

The two former (1, 2) are substances onto their own, while only the former can change form and be applied as predicate/condition, and only the latter can fail as condition for true statements (the former can not even attempt such a task).

That the idea can never fail as a condition is not a curious proposition, for when it comes to judgements it is never the condition which is under doubt, for all the rest rests instead on it, such that something out there may or may not be a lamp under the condition of our idea of lamps. While a concept on the other hand, can fail at being the condition for a positive conclusion, since positive conclusions could never have been reached without concepts, such that the concept of a `pattern` could fail as condition for the conclusion of an entropic state or the concept of `inductive` could fail as condition for the conclusion in an arithmetic operation.

Logic in other words must allow the major premise itself to fail the minor one, as much as the other way around, while judgements themselves could never fail, and renders invariably the minor under them, and when the judgement is said to be false it is actually the judged instead which is false. Or simply: there are no true narratives, only narrated things.

 

When concepts of reason are made we use ideas (spontaneously derived from personal or social experiences, IDEAS, or forcibly abstracted coincident IMAGES) not as predicates but as subjects, and render them under conditions of one another, just like concepts themselves, though the concepts made from ideas are impossibly positive conclusions, and only ever negative ones.

It would be impossible for a concept made from ideas to be positive, since no concept of reason could ever affirm or point to anything in the world, instead concepts of reason are made from the contradictions which arises when nothing but ideas are put to use, and affirm instead the world negatively through those ideas.

If sails as mere ideas were put to use for the thinking of the relative motion of boats then surely some may find themselves happily ignorant of sea travel, while they who find insufficiencies on part of such imagery under the need for the food only the sea could provide them would put the sail itself under scrutiny and condition it under the idea of winds and find therefrom that the area of the canvas is proportional to the speed of the vessel.

That the universal cognition of non-contradiction takes the form of insufficiencies more so than denials/negations when put to use between ideas shows us only that our mind are so well trained to subtleties of social language that it has imagined blindly away the universal contained in the particular.

[Reciprocality]

The spontaneity of the composite of ideas is as much an affinity for ideas through composites, their universal form is variability, and their mutual relation is retrospectively disjunctive, while their posterior relation is non-disjunctive and opens up for new ideas.

 

Or in the concrete, light bronze and dark gold are ideas in an array of a finite sum of judgements under large quantities of possible variations, outside this finitude nothing is possible except for in relation to new experiences.

[Reciprocality]

Set theory is the most ridiculous system I have come across, it attempts to reduce mathematical statements into its syntax by saying that if a mathematical conclusion can not be formed under the notion of containment then the conclusion has no foundation. Every "axiom" clashed onto its theory comes out of the logical inconsistencies of their absence, there is no end to how many axioms we may discover by reversing the order of everything like these theorists has done.

So it reduces therewith logic to syntax as well, it has fooled itself into thinking that the uniformity of openness could be a foundation for discursion of closedness. Its silliness is identical with the liars paradox.

It fails on every account, for nothing is logical without substance, and there are no substance in the methods themselves of its portrayal, you see the recursion of the inverse?

 

Mathematical conclusions are literally founded on the very nature of their axioms employed as premises/conditions, all of which are dualities, through deducing those conclusions. There is no second layer of foundation, the only reason set theory seems like a good idea is because complete openness of syntax accepts every arrangement, and that nothing what so ever is possible without complete openness, but possibility is a different concept than foundation.

A possibility is opposite of necessity, while a foundation has no opposite. (neither of the quasi opposites of 1. its negation (non-foundation) or 2. its instantiations are dual to it)

The former is a conceptual distinction (logic), the latter is an ideal distinction (judgement), the former can not be pointed to literally, the latter can always be pointed to literally.      A foundation, since its instantiations can be either possible or necessary can not be only one of them, which it would need to be for it to be identical with either, as set-theory implies.

 

Anything (whatever it is) is either possible or necessary, while it may not be a foundation for anything logically, and since concepts has for their nature that all things without exceptions must be expressed by means of them, such that nothing in particular could ever be expressed only by one of them, so therefore are foundations, since particular things are expressed by this whole domain and nothing opposite of this domain could ever express another particular, ideas of judgement.

Foundations on their own are impossible, each of them are concepts (and only the mathematical ones can be on their own) while the whole of them are an idea, the whole of foundations is the mere wish to think concepts without logic, or telling stories without performing a deduction.

The whole of foundations is truly a remarkable thought entity, for it can only be a concept when it is not an idea and only an idea when it is not a concept, (it is like trying pointing to variability itself with regard to concepts yet you can not even point to any one of them), the completeness of foundations would be even more of an insane task, for it would ask of the variability that it manifested in each conceivable and unconceivable way.

[Reciprocality]

So simply:

Containment of set theory is syntax (knowably)

Syntax is dimensional mathematics (knowably)

 

And set theory tries to reduce non-dimensional mathematics not only to dimensionality but to a subset of dimensionality and it tries to do so unknowingly/unwaveringly and it does so blatantly, by saying of mathematical statements that their possible proofs would be negated if they weren't expressible syntactically.

I absolutely love it, since its intuition is that because syntax should be open for everything then therefore whatever it is closed to must be the faulty part, but nowhere is it therefore implied that the syntax is itself its foundation, only the method of its foundation.

The actual foundation are the axioms themselves, and they are true independently of the convenient addition that syntax always lends itself to their aid. If on the other hand syntax would ever be discovered to fail our axioms this would in no way express the falsity of the axioms themselves, nor would it even constitute the inconsistency of their conjunction, instead this would imply the insufficiency not of syntax as a whole but of the subsection of syntax employed: containment.

To my awareness there is no fault with containment, but if there were problems with the logics of the conjunction of axioms expressed in containment, we can be certain it would be the fault of containment.

[Reciprocality]

I am so fucking glad I never went to university, and holy grail I would have a field day with them if I went there today. 

 

I have discovered that negative numbers are a hoax, not in relation to the positive numbers, but in opposition to them "beneath" them.

That is, there is no such thing as a progressing line from -3 to +3, this is an inconsistent idea already on the face of it, since you would have to first ascend from 1 to 2 before you had the chance to conceive a -3, and this is literally universally the case for every possible human, because it is true by the definition of numbers as such.

If I also introduce how infinity is reducible to proportionality of geometry, and could never hope to be even attempted in relation to progressing lines non-geometrically as is supposed meaningful by those who speaks of infinite natural numbers (1, 2, 3...n) 

The whole concept of an infinity of natural numbers is negated by the concept of exponentiation unless you presuppose in the definition of "numbers" things that are infinite, which would be cute. Instead there is no such thing as an uncounted number, while on the other hand there are uncounted infinities, that is, circles, triangles and distances under condition of one another. (the shapes and silhouettes must be counted, but only the logical operation in addition to that counting will make us reach infinites)

The reason exponentiation negate natural number-infinity is that however much you count you can count twice that. (exponentiation is counting of counting, so the same applies for exponentiation, if you then wish to count the counting of counting then again there will always be a new dimension of counting, and I know you smirk now since you imagine that I must have negated myself by saying that there will always be a new dimension of counting, but it is I who laugh since the "always" is literally conditioned on the counting itself, and becomes a "not really" when you don't, the "always" and the "infinity" are literal subsets of the counting themselves, since though they are conditioned on them they only appear as possibilities under some of the times you do count.

 

If you have any idea about the theories of Georg Cantor and understood them it should also be obvious that what I say do not negate his theories, nor the other way around, instead all I have done is redefine the concept of number such that IT actually becomes consistent. Numbers are non-geometrical finites of time (this is without any possible doubt correct) and geometric shapes are non-numerical proportions of space, when things appear infinite in the former domain they actually have their proper basis in the latter domain. 

When you define the natural numbers as infinite, they are no longer numbers, this is not opinion, all you need are some minor thinking skills, what is most curious is that all I just said has a red lining to how I solve every possible paradox, by conceiving the simplest distinction possible, going all the way back to Aristotle: idea (the number 1, the counted, containment, whole, man) and concept (conditioned conclusion, derivative, proportion, duality).

 

Thinking about negative numbers is like thinking about negative animals, instead of just negating them. It would be like stopping at the zoo a Monday morning and then imagining negative elephants by the off chance you saw an empty cage. What is also funny is that if you really insist on thinking negative numbers (under the condition that numberlines should be infinite both ways) they actually exist on the scale of 0 to 1, since an actual "1" only exist as a 1 of 2 and thus on the "scale" of 1 to 2. That is, 1 is the actual zero-point, for division and multiplication is the only actual logic of numbers and everything logical is 1 until it becomes 2, while on the other hand everything empirical is 0 until it becomes 1.

In final conclusion, it is the insistence that we should treat logic as empirical and empiry as logical that has our models confused, everything bounces of the number 1 such that the duality of multiplication and division is deconstructed, it is all just proportionality/ratio, for there is no such thing as a possible mathematical theory that is not expressible in the complete absence of anything explicitly "negative", instead it has been invented as a useful tool, but as is the case everywhere where tools of syntax is invented: it becomes real for us.

 

Wait til I get to algebra, the literal formalised insistence on involving unfinished answers in our questions.