E≠E; Up:

 

I) x=E; Kp.

 

I means that every (possible) possibility is eternal.

 

Given I och T2 per definition defined x≠E(; xE) is finite, simpliciter because E is a smallest infinity. More rigorously, assume not:

 

x≠E; x=[infinite x(E)]:

 

x+E≠E+E; Fp:

 

E≠E; Up:

 

x=[finite x]; Kp.

 

Given this and T1, that nothing can arise from the non-existing Nothing, and an completely calm E, with no waves, mx, smallest x, must be created through (local; T2) contraction initiated by E:

 

E mx:

 

mx=[{mv}mx]; mv=[smallest volume].

 

mxmv as volume, and more compact than mv (or a (uncompressed) volume v>mv). If mx isnt a volume, mx is either a point (p), a cur-ve (k=d(p,p)), or a surface(/plane), for example y=d(k,p); pk. p, k och y are (homogenously) one with E, only something per se, if it is defined so to be, if the mind, so to say, (before its inner eye) draws it in the space:

 

mx are more compact volume (than v(mv); mx owns more density than v).

 

mv are assumed to own exactly the same properties (position excluded), which given I means all properties to define/create all (material) x(E) which can occur in E (more properties than necessary/sufficient for this, is it redundant to define mv to own). And it also, in accor-dance with Up (see below), means that the same {mv} owns the same properties, not different properties, which for example means that the same {mv} cant, in one case define a stable mx, in another case define an unstable mx, which is completed, more rigorously, assume mx to consist of only one mv more than mx:

 

mx=[({mv}+mv)mx]; mx=[{mv}mx]:

 

mx-mv={mv}=0^ (Up disregarded, mv shall be interpreted as being withdrawn (separated) from mx).

 

The same {mv} is thus regarding mx unstable, regarding mx stable, which contradicts that mv, and with that also {mv} (in accordance with Up), owns exactly the same properties:

 

Homogenous atomism prevails, all mx are exactly the same (owns identical properties, position disregarded):

 

Ha) x=(x/mx).

 

A validity of Ha which then rests upon the assumption that (all) mv owns identical properties (position disregarded), which must be rega-rded as a rational assumption.

 

Given this, the (E-)World can quite easily be further defined(/developed), specifically can mx be more rigorously defined, how they be-have as mx per se, and as building x={mx}.

 

Given Ha, Fp can be shown to be valid at Ha-level (x assumed to be the atomistic (logical) constituent(/component) (x in Ha)):

 

[x~y]≠[x~y]:

 

[x(x)~y(x)]≠[x~y(x)]:

 

[x~x]≠[x~x]; Up:

 

Fp) [x~y]=[x~y]; Kp.

 

Assume:

 

x≠{x}:

 

1) x+x≠{x}+x; Fp:

 

x≠x; {x}x, Up:

 

Up) x={x}; Kp.

 

Alternatively, given 1, the following can be defined (the alternative that {x} and x are not related, can directly be excluded):

 

x{x}; x{x}, Up.

 

This that x isnt its properties, introduces the issue of holism/meridioism:

 

x={x}q.

 

Where q defines the holistic/meridioistic additional/vanishing properties, to/vanishing from the original cluster of properties, namely then {x}. q which simpliciter arises from/vanishing in Nothing, given that {x} is unchanged, and of course given that nothing exogen-ously adds to x, of course contrary to T1:

 

Up is the only rational principle; holism/meridioism is irrational.

 

 

Logic

 

The logic defined by primarily Up, defines a world of separate (unique) x, any connection or correlation between x has to be defined, is not there beforehand (ex ante). The E-theory defines eventual connection between x by attraction or by impact(/collision). This in strong contrast to conventional logic which defines (ex ante) connection, coupling between x by an assumption called the Negation:

 

Na) x y(=x=not-x).

 

Na which is valid if any kind of double negation (double, triple, quadruple, etcetera) is assumed valid; Na immediately implies x=x, x y only defines that x=y, no double negation (that y recursively returns to x).

 

Fundamentally, what in the world couples, pairs every x with another x, eternally? Nothing, ex ante, rationally, it is Up which is rational, and further it is up to a definer or an analyst to define eventual coupling between x, for example then by attraction or collision.

 

The Na-logic doesn't particularly see itself as a physic, but it must if it shall (not just by chance) have anything to do with the physical or real/rational reality, thats just a fact.

 

So, Na must logically be ruled out as an irrational assumption, it has nothing to do with the real world. The world that primarily Na defi-nes is simply a saga. Na-logic is not much help in mathematics either, its two variable (x y) world is to limited, cramped. Na-logic can be seen as a bizarrely limited aspect of mathematics (generally including many variables: x,y,z,..).

 

The fundamental rational principals are Up(/Up/Up/Ip/Ip/Kp), Fp and Ha (and Ip). Another principle that can be considered is Dp: (x ~ y)=(x ~ y), but not in general (universally), it must be certain that it is rational in its context before it can be adopted. A principle that definitely not can be considered in general, is of course Na. Which not exclude two variable scenarios, if the definition has reduced itself to a two variable scenario. The E-theory or the Fundamental logic (the Fundallogik) commonly do so, especially so when it defi-nes the two possibilities = or .

 

The difference between Na-logic and the Fundallogik in short:

 

Na-logic) x y; x,y0.

 

Fundallogik) x y; Ir,Ir; x y; x,y0, x=x,z,,..:

 

x{x} y.

 

Ex ante: y {z}.

 

Ex post: y z{z}; Kp.

 

Where Na-logic (categorically) says x or y (The law of excluded middle, in accordance with Na, given the The law of non-contradict-tion: (x y), witch in spirit underlies the assumption of Na) the Fundallogik generally says z or z or z or z, etcetera.