[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’}Îx, 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’}; xÎ{x’}, Up’.

 

This that x isn’t its properties, introduces the issue of holism/meridioism:

 

x={x’}±q.

 

Where q defines the holistic/meridioistic additional/vanishing properties, to/vanishing from theoriginalcluster 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, that’s 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,å,..:

 

xÎ{x} ® y.

 

Ex ante: y ® {z}.

 

Ex post: y ® zÎ{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 Ù y)’, witch in spirit underlies the assumption of Na) the Fundallogik generally says z or z’ or z’’ or z’’’, etcetera.