__________

* If it is valid, it is assumed, defined, that x=y and that y≠x, then x=y only can be in-substituted in Ip (x=x) on the right side: x=x=y, because in-substitution on the left side: x=y=x, of course contradicts that y≠x (if however it is assumed that y=x (then beyond that x=y), then of course x=y also can be in-substituted on the left side). So it is important to keep track of what is defined, what rules one set out for oneself; Conventionally there are examples of free insubstitution in x=x (commonly defined) without symmetry being assumed, which is seen as proof of symmetry (see for example Language Proof and Logic page 50 ), of course completely wrong, it is of course the matter of a tautological proof, proof of something already assumed, namely then symmetry, simpliciter then because it not is possible to freely in-substitute in x=x, without symmetry being assumed.

 

** Given the E-theory in the forthcoming this becomes even clearer, in accordance with especially consciousnesses, for which this with q especially is seen to be possible for (+q) of some, simpliciter are clusters of mx (smallest (material)^ constituents, consciousness={mx}), and nothing else (which of course means that consciousnesses changes when mx moves in {mx}, or mx are added to or subtracted from {mx}).

 

^ mx are material in their specific way, mv (room) are E-theoretically principally also material, although of course not as tangible as mx, se further the E-section.

 

 

Lp

 

The following is assumed, in addition to what is assumed in the preceding section:

 

Lp) [x’~y’]=[x~y], where ~ defines applicable relation sign.

 

Lp (the Equal distribution principle) defines that a relation (between x and y) not change if the arguments/variables change equally (defined by ’). Lp is just only assumed, thus without analysing Lp's validity per se, to see the implications of this assumption, thus of Lp.

 

Assume (for example, even if this particular assumption is highly deliberately made):

 

E≠∞*; E=[the World], ∞*=min[∞]; ∞=infinity:

 

E+E+∞*≠∞*+E+∞*; Lp.

 

To be able to continue it is just only assumed that, thus without deeper analysis (if symmetry (around +: x+y=y+x (symmetrically valid), commutativity) had been valid, that could have been used here, but symmetry is thus not generally valid, so the following is the easiest to assume):

 

Terms can when Up’ is used be unified to places (in which the unifiable is located) in sentences at will:

 

E+∞*≠E+∞*; Up’:

 

E=∞*; Kp.

 

Further assume the intuitive that:

 

d(x’,x)≠d(x’,x]; d(x’,x),d(x’,x]ÎE; (x=[excluding x], [x=[including x]; d(x,x’)=[distance between x and x’]:

 

d(x’,x)+x≠d(x’,x]+x; Lp:

 

d(x’,x]≠d(x’,x]; Up’:

 

t1) x)=x]; Kp.

 

Excluding x is thus identically including x (and vice versa), which at least for volumes is contradictory (or weaker an absurd p-superpositionality, but finds it rationally to call it a contradiction, because it is so patently absurd), for p (points, non-extended positions) maybe not. Anyway, it defines continuity rule in E, that there not exists a distance between p (p]) and a next (to p) closest p (p)).

 

Assume further that only finite distances exists in E:

 

d(x,∞*)ÎE:

 

d(x,∞*]ÎE; t1.

 

E is thus boundless, which means that Nothing not exists beyond E, nor within E, thus given t1 (the continuity), which altogether simpliciter defines that Nothing not exists, which also can be shown more directly ‒ for Nothing it is valid by definition that:

 

xÏNothing; x=[at least one property]:

 

x+xÏNothing+x; Lp:

 

xÏx; Up’; Nothing+x=x or NothingÎx:

 

T1 is valid; Kp (the definition of Nothing leads to a contradiction (xÎx; Ip),* which in accordance with Kp means that Nothing cannot exist).

 

The assumption of Lp thus leads to the conclusion that Nothing not exists, which in no way can be realized before that this result is present, but it can only be trusted in Lp (if Lp is trusted, which Lp not can be, which the further analysis will show), if there is no supporting evidence, such as then T1 (T1 which then is supporting evidence in the previous proof, and also to t1, see further T2 below, even if t1 (obviously) also can be seen as a proof of where Lp leads wrong; In conventional formalism there is an, must be said, idiotic axiom, which defines that true derives true, no, naturally it is the (rational) reason (mind) that decides that, thus what is true (or false)).

 

The preceding just only implicates that E=∞*, that E not is >∞*, it just only follows from Lp, so to more explicitly show that it is valid (in context of Lp), the following is assumed:

 

d(x’,x’’)=d(x’,x)+d(x,x’’)=∞*; d(x’,x),d(x,x’’)<∞*.

 

Given this, there exists an x’’ before which d(x’,x’’) is finite, after which d(x’,x’’) is infinite:

 

d(x’,x’’)<∞*; d(x,x’’)<∞*.

 

d(x’,x’’)=∞*; d(x,x’’]<∞*.

 

Which given t1 defines d(x’,x’’)=d(x’,x’’] to be both finite and infinite in x’’, an absurd/contradictory p-superpositionality, so at least one sub-distance must be infinite, say d(x,x’’), which defines:

 

d(x’,x)+∞*=∞*.

 

It may seem that d(x’,x)+∞*>∞* (or at least ≥), but given the continuous perspective in accordance with t1, two sub-distances must be able to define (exactly) ∞*, this which defines that d(x’,x)=0’, or more commonly that:

 

T2’) ∞*±0’=∞*; 0’=d(x,x’)<∞*.

 

Thus, finite distances are 0’ in relation to infinite distances (≥∞*).

 

Are there distances longer than ∞*? Not finitely added in accordance with T2’, but in that case infinitely added:

 

∞*+d; d≥∞*.

 

Which given the continuous perspective in accordance with t1 (and T1 also, see further the following) defines the existence of distances between ∞* and ∞*+d which not exists, which is absurd:

 

T2) E=∞*:

 

x<∞*; x≠E; xÎE.

 

T2 which also can be stated without the help of Lp (important for the E-section, that it not needs to rely on Lp, especially given what is coming in this section), but given T1, because given T1 there exists no limits in E after which Nothing takes on:

 

E is homogeneously continuous, infinitely ongoing in all directions.

 

Especially a smallest E=∞* continues with this infinitely in all directions, E’>E need ex ante not necessarily continue infinitely in all directions, but in the directions that E’ continues infinitely, so does E, with which it is established that E’=E (since E’<E cannot be valid; It defines E’ to be finite (contrary to that E’>E), given that E is a smallest infinity):

 

T2 is valid.

 

Also Up’’ can be proved given Lp, assume Up’’ not valid:

 

x≠{x’}:

 

x+x+{x’}≠{x’}+x+{x’}; Lp:

 

x+{x’}≠x+{x’}; Up’:

 

Up’’ valid; Kp.

 

More specific proof of that all xÎE are finite ‒ assume not:

 

x>E:

 

x+x>E+x; Lp:

 

x>x+x’; Up’, where x’ is part of E which maybe not belong to x:

 

x≤E; Kp, which given that x≠E:

 

x<∞*.

 

Assume more commonly:

 

x≠E:

 

x+E≠E+E; Lp:

 

E≠E; Up’(; xÎE):

 

x=E; Kp.

 

Which may seem contradictory, but actually is intuitive, given T1, in accordance with which all (existing) x(≠E) at least must exist as (eternal) possibilities (not even a possibility can (rationally) arise out of(/in) the non-existing Nothing, or for that matter disappear in, pass over in to being the non-existing Nothing), with which the question especially is how x, which not are only possibilities in E, can be created, which will be returned to in the next section.

 

Assume further:

 

x≠x’:

 

x+E≠x’+E; Lp:

 

E≠E; Up’(; x,x’ÎE):

 

x=x’; Kp.

 

Which especially is valid for rational superpositionalities, but not in general, so here Lp categorically leads wrong (and no small error either); The same conclusion is obtained if x+x’ in accordance with Lp, instead of E, is added to either side of ≠.

 

Another case where Lp fails:

 

Assume that y and z can be different even though they have a cluster ({x}) of joint properties:

 

y={x}’+{x}≠z={x}’’+{x}:

 

{x}’+{x}+{x}’+{x}’’≠{x}’’+{x}+{x}’+{x}’’; Lp:

 

{x}+{x}’+{x}’’≠{x}+{x}’+{x}’’; Up’.

 

Which given Kp then defines that y and z not are different, but well can x according to experience be different despite having a cluster of joint properties, thinks especially of Siamese twins.

 

Especially the two latter examples destroy the confidence in Lp, perhaps Lp will do in certain context, in which it consequently, before Lp is used (ex ante), rigorously must be investigated if Lp can be used, is rational and gives rational results (in its context), generally Lp definitely not can be assumed valid (ex ante), and the same must (ex ante) be stated to be valid for any principle other than those in the previous section, thus the principles of the Rational basis:

 

Principles beyond the Rational basis cannot be taken for granted (but perhaps be assumed after ex ante analysis in certain context).

 

A proof of FT (the Completeness theorem) with the help of Lp further shows on the problems that the analysis here are in on, where X defines a theory (consisting of sentences x):

 

x*|xÏX per derivation, based on xÎX, but (undecidable) x*ÎX nevertheless:

 

x*|x+x+x’ÏX+x+x’; Lp, X=x*+x+x’:

 

XÏX; Up’:

 

FT) x*|xÎX; Kp.

 

x* must thus belong to X by derivation, if now x* not are assumed as axioms (undecidable x not exists).

 

Instead of the reasoning in the previous section FT thus can be concluded with the help of Lp. However, this later FT-result is intuitively impossible to explain (per se), it can only be said that it is Lp that leads to, proves FT, thus the purely abstract (only imagined) addition of x+x’ on both sides of Ï, well? The reasoning/proof in the previous section explains why FT is valid, it is evident that that is much more satisfying than this later Lp-proof of FT: Argumentation, argumentation, argumentation, "continuous logic", as it was expressed in the previous section, is (rationally) A and Z.

 

__________

* xÎx; x≠x, is simpliciter absurd, that x as greater or lesser than itself (x>/<x) can belong to itself (even holistically/meridioistically is x={x’}±q={x’}±q, thus neither greater nor lesser than itself, that holistical/meridioistical x are greater/lesser than the original {x’} is another matter, the important is what x is, namely then {x’}±q (holistically/meridioistically)).

 

E

 

Given T1 are thus possibilities, possible x(ÎE), eternal, always existing. Possible x which also can be called "virtual x" ("x"). How, given T2, does it happen when "x" turns into (factual, realized) x, becomes (to) x, when x is created? Of course presupposed that x can exist, which it is evident that x can, E (looked at with "empirical" eyes) is not total emptiness, just only pure space (at least not at the time of writing this); Not at all existing "x" cannot be thought, because if "x" is thought, then "x" exists (at least purely abstractly (only thought)), and of course (as non-existences) they cannot be realized (as x). If "x" never is thought (not by anyone), then "x" still may exist, and maybe be realized at some point, but of course without that x can be perceived/thought, because then of course x/"x" is thought. "x" (or x) which are thought but which never are (can be) realized as x which not are thoughts or "x" (which not are thoughts) are pure abstractions (something only thought); Thoughts, and non-thoughts which not are (pure) "x", are {mx}, pure "x" are factually empty (pure) room ({mv}), but then containing, having (owning) the possibility "x", see further the following.

 

Well, first of all, it can be stated that E sometimes is completely empty of x, for if there always (somewhere in E) are x in E, then x=[all x] is an infinite phenomenon contradicting T2:

 

E is sometimes completely empty of x.

 

Even something between pure ("still") room and x in more factual sense is x, which can be called room movement:*

 

E is sometimes completely "still", pure room (not completely "still" room, room movement, is x).

 

E must given this be able to create room movement (in E), in order for E to not remain "still", but more than this (to be a "primus motor" in this way) is E not assumed to be able to "do"(/be) – it is advanced enough, is actually (holistically) creation out of Nothing, even if the fact that E is infinite intuitively has significance, that something infinite so to speak by the slightest shudder, not even marginal in relation to the infinity, but vast in relation to the finite, can give rise to something finite, is at least somewhat intuitive – it tends absurdly towards making E into something "intelligent":

 

E can create room movement (and only room movement).

 

Intuitively compressing room movements, E-contractions, which (perhaps) then cause "x" to become x, more specifically is assumed:

 

mv=min[volume] (mv are smallest volumes):

 

E=∞’mv; ∞’=min[infinite natural number].

 

mv is purely abstract definition given T2, thus no eternal x, but what outmost exists is only the homogeneous, continuous E, but anyhow, given mv, then in E-contractions (and other space contractions, see further below) mv "jumps" (see further below) into each other and creates at least a reasonably stable x, which either is (continued) absorptive (absorbing mv), or stable, in the meaning not absorptive (not absorbing mv).** Stable x thrusts mv out of their paths, absorptive x absorbs mv in their paths. If x constantly is absorptive, then they tend to be eternal x, that absorption can counteract separation (that x separates mv off) or cleavage of x (that other x "jumps" into x and cleaves x, see further the following), thus that absorption can cause x to (eternally) continue to exist. Given T2 no such possibility may of course exist, so:

 

x tends towards stability (towards being non-absorptive), if they not are stable already at their creation (in space contractions).

 

Stable x which separates mv off and then becomes absorptive, tends with that (of course) to be stable again, with which again the possibility of eternal x be to hand:

 

Stable x, which separates mv off, are completed (returns to being room (mv, again)), not becomes absorptive x, which of course means that x perhaps only can be absorptive in an initial phase:

 

I) Stable x consists of the same (n) number of mv, of the same amount/volume of room(/"energy"), and are thus completed when they separate mv off (or are cleaved), and consequently stable x are the smallest x=mx (mx=min[x], which (notably) derives itself in the context).

 

For otherwise, in contradiction to Up’’’, the same number of mv (in mx) may in one case be stable, in the other mean completion; Up defines that identical is identical, not that very similar must be very similar, but it can be assumed to be valid, so to speak in accordance with the spirit of Up:

 

Up’’’) x’=y’; [{z}Îx’Îx]=[{z}Îy’Îy].

 

And if mx consists of the same number of mv, then mx definitely are very similar, except for position (thus even though they are different (exists in different positions)).

 

This which of course means that stability occurs when mx reaches n number of mv, either directly in the space contraction, or after a certain (short) period of absorption.

 

Stable mx is thus smallest x which are completed if they are cleaved or separate mv off (this directly/immediately or after a certain (short) period of instability). Separate mv off, which mx must be able to do, so that no possibility for eternal mx exists:

 

All stable mx can separate mv off (mv so to speak falls off, away from mx) and are directly (or nearly directly) completed when they separate mv off or are cleaved (by other mx).

 

What properties have (stable) mx? Well, in order to hold together more firmly in clusters of mx (x={mx}), the cluster of mx not is like loose sand, then mx must be able to attract each other, which given that mx (and a) is completed if mx tries to send something out (aÎmx) means that mx in that case just only have attraction force, mx have so to speak an invisible hand that brings other mx to mx, which is unintuitive, an unintuitive quasiholistical force. This the absurd excluded that mx so to speak have grapnels which they can throw at each other and haul each other in with, or that they can send out a (contradicting I), the latter which just only is absurd, that mx can be so advanced that they can send satellites (a) out, which can grab hold of other mx and pull/drag them towards (mother-)mx, no, definitely not:

 

mx are "dead" not very advanced things/entities (which especially not have "hooks" or "grapnels", or can send a out).

 

Especially magnetism seems to imply that mx have this (unintuitive bare, pure) attraction force, because without attraction force must mx (outmost, in magnetic fields) be thrusted (see further below) around in its "circular" path, which just only seems absurd/impossible. With (mx-)attraction force, magnetism is explained so to speak by that the tail attracts the head, with which of course magnetic fields can circulate. Even movement in accordance with "the empiri" is difficult to explain without (mx-)attraction force (see further below). And that x are "fixed", for example man to Earth, is also difficult to explain without attraction force, because without attraction force it is only thrust movements (see further below) that can "fixate" x, so to speak can hold, bring x into place.

 

Given that mx have attraction (force), then given I(/Up’’’) mx may only be able to switch between being attracting, repelling or neutral (neither attracting nor repelling), which can be ruled out given that mx are "dead" things (it is too advanced for them):

 

mx have (constant) attraction force (and only attraction force, with which repellation (of course) is thrust movement (see further below)).

 

If the mx-attraction force is sent out with infinite speed, then mx with this its attraction force =E in accordance with T2 (Everything infinite is in accordance with T2 identical to (identically) E), of course contradictorily, and with finite speed the question is how the mx-attraction force can "know" in which direction it shall attract, of course towards mx, it is quite evident that it cannot "know" that (as the "dead" phenomenon mx is, including the attraction force it maybe have):

 

If mx have attraction force, then (all; I) mx have itself a surrounding finite attraction field attracting towards mx.***

 

An attraction which principally also can attract the room itself, because if mx can attract other mx, which then consists of mv, then mx also can attract the room itself, which then also consists of mv, with which room-movement caused by mx is defined, which perhaps can become mx-creating; mx-attraction tends so to speak to mush up space around x, which can be argued to be an argument against mx having attraction force, without further going into that.

 

Another form of space-movement which also perhaps can become mx-creating, is created by stable mx which, already mentioned, thrusts(/pushes) mv away, this especially of course when mx "jumps" (see further what immediately follows), or more commonly expressed moves.

 

If mx remains (is) in the same position, then mx (of course) not has moved, but mx must "jump" a bit, a distance, without being in that distance, if mx moves (continuous movement not exists, unintuitively, but so it then rationally just only is):****

 

mx "jumps" (when moving).