Tp is a tautological principle Classical logic assumes, which then especially defines that y=(y Ú y); Tp is not identical whit Up’; Tp defines (possible) existence of superclones, Up’ excludes existence of superclones.

 

Classically logically "N*’" is over-interpreted to define N*’, N*’ in which it not is given that x’=y and that y’=x, which then is valid in accordance whit N. Such over-interpretation (which is legion in Classical logic) is not the big problem with Classical logic, but that is the assumption of the equivalent to the immensely restricted N*, then contradicting Ia and Ib, and then defined through N. N that Classical logic more rigorously can be stated to assume through that Classical logic assumes the so-called Law of double negation (Dl), because N is a necessary presumption för (the validity of) Dl (provided that Dl not is assumed ad hoc (to assume Dl ad hoc is unserious)), which the following proof of Dl shows given N, because given N it is then valid that:

 

x’=y and that y’=x (both sentences symmetrically valid, thus also reversely valid):

 

(y’)’=y, (x’)’=x (x=y’ in-substituted in x’=y, and y=x’ in-substituted in y’=x):

 

Dl) x’’=x, y’’=y.

 

It is thus (the assumption of) N that results in Dl (proof-wise).

 

The foregoing is enough to confute Classical logic, and for that matter of the so-called Intuitionistic logic, which weaker than Classical logic defines the following concerning N:

 

N’) x=y; ((y=x)).

 

Thus that x implicatively identically is (implicates) y, bur that y not necessarily implicatively identically is (implicates) x, the reversed can also be defined, for which there is no (conventional) name:

 

N’’) ((x=y)); y=x.

 

Given Ia and Ib both N’ end N’’, except N then, are false, a binding, relation between different x in the way that N/N’/N’’ defines simpliciter not exists (other than as a false x in the brain convolutions), an example:

 

x can give z, or nothing at all (x ® x), if x at all be to hand, prevails, x ® y can only be a rule/"law" which not is fulfilled (for the moment (x=0)). And y can be given(/implicated) by å, which overall can be defined:

 

(x ® y)_o=((å ® y)_u Ù ((x ® z))), where o defines unfulfilled rule and u defines fulfilled rule.

 

This then especially to compare with the Classically logical equivalent to N*’ ("N*’").

  

Classically logically it complicates in the most horrible way, why the foregoing Classically logically simply not is seen, which can be exemplified by Jan Łukasiewicz's proof of Dl (then to be compared with the Dl-proof above) at https://en.wikipedia.org/wiki/Double_negation, it presupposes in particular the following four sentences:

 

1) x=(y ® x).

 

2) (x ® (y ® z ))=((x ® y) ® (x ® z)).

 

3) (x’ ® y’)=(y ® x).

 

4) x=((x ® y) ® y).

 

1 and 3 trivially directly follows from N:

 

1) N=x,(y ® x), so x=(x ® y).

 

3) Well, it is then valid that x’=y and y’=x in accordance with N, with which 3 (the "Transposition") trivially follows.

 

4 presupposes Tp as well, except then N:

 

4) x=y=(y ® y)=((x ® y) ® y)(; N=y,(x ® y), so y=(x ® y)).

 

And then 2:

 

(x ® y)=(x ® y)(; N=(x ® y)=N; N, so (x ® y)=(x ® y)):

 

(x ® (y ® y))=((x ® y) ® (x ® y)); Tp:

 

2) (x ® (y ® z))=((x ® y) ® (x ® z)); z=y.

 

z, or any other x (ex ante) ≠x,y, which given N (ex post, after assumption of N) of course is x or y:

 

z=x,y.

 

Especially this is "hidden" or simply not is seen in N-logic, because it complicates, so that then this that z=x,y is kept hidden. With which z is believed to be something other than x or y, which of course defines something much more complex than if it only is about x and y, which it then only is given N, N-logic (Classical logic) commonalize (over-interpret) thus in a treacherously way, because it doesn't understand better (hopefully, otherwise it is of course a matter of fraud).

 

To also take the two "hypothetical syllogisms" at https://en.wikipedia.org/wiki/Hypothetical_syllogism#As_a_metatheorem that Łukasiewicz presupposes in his proof of Dl, for the sake of enlightenment:

 

(y ® y)=(((x ® y) ® (x ® y)):

 

HS1) (y ® z)=(((x ® y) ® (x ® z)); z=y.

 

(x ® y)=((x ® y) ® (x ® y)):

 

(x ® y)=((y ® y) ® (x ® y))(; N):

 

HS2) (x ® y)=((y ® z) ® (x ® z)); z=y.

 

That Lp-formulas, to lastly also take two distributive formulas:

 

x=(x Ù x)=(x Ù y)=(x Ù (y Ú y))=(x Ù (y Ú z)); z=y.

 

x=(x Ú x)=((x Ù x) Ú (x Ù x))=((x Ù y) Ú (x Ù y))=((x Ù y) Ú (x Ù z)); z=y.

 

So:

 

(x Ù (y Ú z))=((x Ù y) Ú (x Ù z)).

 

x=(x Ú x)=(x Ú y)=(x Ú (y Ù y))=(x Ú (y Ù z)); z=y.

 

x=(x Ù x)=((x Ú x) Ù (x Ú x))=((x Ú y) Ù (x Ú y))=((x Ú y) Ù (x Ú z)); z=y.

 

So:

 

(x Ú (y Ù z))=((x Ú y) Ù (x Ú z)).

 

All this (which then follows from primarily N) then Łukasiewicz presupposes before he even so to speak begins to prove Dl, with which the whole of course appears to be very complicated, and in its own way it of course is, but then self-created complexity, because directly starting from N it is thus easy as a pie to prove Dl.

 

Anyway, the foregoing shows that extremely much can be defined based on/given N, but N is thus (rationally) completely false, with which these derivations are equally false, however much they may seem to define something that makes sense. But if any of these formulas are to be used in logical analysis, then they have to be argued for per se, each formula (ex ante) be ascertained if it is relevant to assume in some context, or not. To assume them valid on the basis of N is (rationally) simpliciter not possible, but they then must so to say stand on their own legs, (ex ante) be argued for to do so, be rational (intuitive) in the context in which they perhaps are assumed (to be valid); Such "simple" principle as Lp for example is extremely complicated to see (analyse) the validity of in specific contexts, for example if [x+z=y+z]=[x=y], because directly interpreted this sentence is naturally not valid, the left term is de facto not identically the right term, unless y=x, in which case the relation trivially is valid (given Up/Ip), but what if y≠x ‒ the more normal regarding this with x and y. If y=x, then it mostly is meaningless to define "y", mostly just confusing, if now then y=x, in which case it then most rationally is to stick to x(=y=x), the only exception is when rewriting identities, especially mathematically a common method of arriving at conclusions, simply then by rewriting identities (with help of the principles which are assumed to fit for that) ‒ is the [x=y]-relation in some meaning remaining if z is added to x and y respectively? For example, is father+mother=child+mother identically father=child? No, hardly, but it really needs to be analysed if this Lp-principle can be seen as valid/rational in some context.

 

By way of conclusion concerning Classical logic, it defines the following "Truth table" in accordance with N, to be compared with the rational table in the introduction section:

 

   x        y

 true  false

false   true

 

This table which then shall be interpreted in accordance with N, which primarily is irrational in two ways: the N*-perspective, that (unique) x ® (unique) y, then contradicting Ia and Ib, and the (x,y≠0)-perspective, that there always is a unique true y if x is false, then contradicting that there can be completely false x; The assumption that x,y≠0 can Classical logic be argued to make because N is difficult to justify if x or y can be 0: x’=0 or 0’=x; x≠0, for which x’(=non-x) defines 0, and which x defines (is defined by) 0’(=non-0)? Secondarily there is an "eye"-perspective underlying N, that the "eye" finds, sees the relevant non-x among all the irrelevant non-x, which Classically logically usually is defined: If x is a proposition, then also x’ is a proposition, for example defined on page 68 of Language Proof and Logic, or page 97 of Principia Mathematica (â1.7), which only is absurd. There is no such connection/relation between different x, neither mentally (in that case it is about some prejudice) nor "platonistic", that it only (eternal) is so, which just only is even more absurd than that there is a mental connection between different words, concepts, that there in the language are eternally given connections between different words, concepts. Which not prevents especially Kurt Gödel (1906-1978), with his incompleteness theorems (contradicting FT), from still being a platonist, commonly in the meaning that theories X can exist equivalent empirically, thus per se (beyond especially the human's consciousness), and certainly, if the existence of platonistical X is thought, it is a fairly given thought that these X just only may define (undecidable/independent) x, without them being either provable or disprovable, without being axioms. But rationally, again (more rigorously of course in accordance with FT), this is only nonsense, it is the consciousness that defines X, nothing is determined/defined before it is determined/defined, see further the section Concerning FT in Addition II.

 

 

Given the E-theory the only rational alternative for 0=[no x(≠0)] is void/room ({mv}), with which it for example (superclonically, contradicting Up’) can be defined that x-x=0, with the evident interpretation that if x is excluded from itself only empty space remains. For 0 to not cause problems in analysis, the best is to assume 0 to be idempotent, so that the right side in following example still is 0:

 

∞(x-x)=∞0=0.

 

Because if 0 for example is assumed to be p (principally, as part of empty space p's are empty space), then of course ∞0=dp, something unintuitively arises; And of course even more so if 0>p, for example a volume, non-idempotent volume, with which of course x0>0; x>1.

 

With this it is into mathematics (again), which it especially given the E-theory is easy to slip into, because it is evident that the E-theory defines a fundament for development of mathematics, especially geometry, and the E-theory also defines (uses) certain basic mathematical concepts. But not much, because this work primarily (of course) not is mathematics (then it simpliciter not would be able to define what it does). More developed mathematics is so to speak a later issue, a problematic issue, which already has been discussed, especially Lp's unreliability shows. Lp which indiscriminately is used in mathematics. For example for proving the equivalent to Dl in mathematics, roughly as follows, given this work:

 

A) x-x=0:

 

I) -(x-x)=-0; Lp, [-]=[-1]:

 

-x--x=0; -(x-x)=-x--x (distributive principle), -0=0, which is valid given that 0 is idempotent:

 

--x-x=0; -x--x=--x-x (commutative principle):

 

II) --x=x; A(, Up).

 

Because it is the matter of manipulation of two superclones (of course contradicting Up’, but without the assumption of superclones there is no mathematics; Mathematics specifically assumes the existence of superclones through the assumption of the Axiom of extensionality), where then x superclonically is excluded from itself, the assumption of distributivity and commutativity is (intuitively) no problem (because (especially as) it is about summation (of (purely abstract) superclones) to 0), it is however in no way intuitive that exclusion of x-x (-(x-x)) is the same as x-x,* which it then given Lp is (for A to be identically (to) I). Neither is the result, II, intuitive, intuitively exclusion (--x) of an exclusion (-x) simply is a (tautological, pleonastic) double rejection (throwing away) of the exclusion, but primarily then given Lp, it brings back to x, just as if N had been assumed (x=-x).** N which definitely not is assumed to be generally valid in (pure) mathematics, in which it not is one if x is plus or minus (in applied mathematics it can be one, for example for length differences):

 

II can also be proved without Lp (and other complexities), because in accordance with A (A:s intension) it also is valid that:

 

A’) -x+x=0.

 

So if x=-x, it in-substituted in A gives:

 

-x--x=0:

 

--x=(+)x; A’.

 

But in any case is Lp mathematically extremely important, so not mathematically wrong to prove II whit the help of Lp, and in a way lucky that Lp given this later proof of --x=x leads to just that, not leads to, proves something else.

 

Well, Lp leads, as already been touched upon, to strange conclusions (although Lp in its specific formulation in this case of course brings in negation, which of course N also is about), albeit of course, concerning II, a practical conclusion, whose practical validity simply has to be tested, and in that II has turned out to satisfaction, obviously, otherwise II (of course) would not (mathematically) be used. And given the latter proof, given A’, it (rationally) simply must be valid, completely independent of Lp.

 

 

All in all, perhaps the most important this work teaches is that no x is given (determined before it is determined), but it is all about assumptions, definitions, interpretation of reality which results in assumptions, primarily in first x, basic x, "axioms" (".." because rationally truly fundamental "axioms" are almost given, given true, especially then Up, but can they, especially then Up, be disproved, then of course they not are given, but disproving especially Up is (rationally) completely impossible, because every proof, whichever, must presuppose Up (or equivalently) simpliciter for the proof to be the proof (x=x; x=[the proof]), not being something else (x≠x)), and secondarily especially important is about Ii-interpretations/derivations based on these basic x, or perhaps concerns derivations given/provided some assumed principle of derivation (rule of inference, such as then for example Lp), theorems:

 

basic-x ® theorem.

 

Another "empirical" possibility is that basic-x sees, interprets as the (causal) basis for something "empirically" out-interpreted:

 

e) basic-x ® hypothesis.

 

If an Ii-interpretation ("continuous logic") is difficult to find out in this, it has to be content with that, especially (pragmatically) if it is a practical implication. But naturally, the best is to try to find an Ii-interpretation, even if it not always is possible, take for example that that thrusted mx "empirically" seems to move reasonably in the thrusting mx "jump"-direction, which it then is no Ii-interpretation in/for.***

 

Only e may rationally be left unexplained, if it is about purely abstract theory, it can rationally not be left unexplained, in accordance with FT.

 

__________

* -(x-x)=x-x (implicatively identically, just like -(x-x)=) for example, but this then with no deeper meaning than that the right term is in the left term), but x-x is not given =-(x-x) (exactly as x=x’ not is given, but then x’=x (because x is in the left term)).

 

** Given that x’=-x, which without further ado can be stated to be what Classical logicians means that N defines, and it also is intuitive in one case, namely if it is defined that x’=E-x, thus that x’ is All exclusive (except) x, in which case excluding x (-x) intuitively defines x’: -x=x’=E-x, which defines that E=0’’; x±0’’=x, where 0’’ intuitively closest is 0*: 0’’=0*, which can be proved if Lp is assumed (which is done in section E), but Lp is then unreliable, so it has to suffice whit this intuition, which defines 0* to be a duality, both the largest (E, which 0* then can be interpreted as, as positionless) and the smallest (0’’, which it is evident that 0* is, interpreted as non-extension, only), which adds nothing to x, which argues for 0 to be defined to be (idempotent) void (empty space) ≠E, for the sake of distinction.

 

*** Given that mx "jumps" (with which it rationally then is that thrusted mx "jumps" unconditionally stochastic), which then is the rational/logical (continuous movement (p-long movements) is irrational/illogical). However, if continuous movement is (irrationally) assumed anyway, then it is rationally (intuitively) that thrusted mx’ moves depending on how thrusting mx moves into mx’, collides with mx’. So in some sense the alternatives must be weighed against each other, even if the basic problem of continuous/discontinuous movement is more fundamental than how the phenomenon of collision between mx looks like, is defined. And as for that, it only is valid that discontinuous movement is rational/logical, continuous movement not. "The empiri" will probably never give a hint here, because it has to go down to the utmost micro level for this to be "seen":

 

Given the E-theory it is regarding "empirical" knowledge, when it really concerns empirical (objective) knowledge, (outmost) incident mx which hit receptors which send signals (even that outmost mx of course) to the brain (in humans, which of course also outmost are mx (including the brain)). The brain interprets these signals, and can never know, firstly whether it really is a matter of (objectively) incident mx, because it might just as well be the brain per se that invents an impression, a thought, and secondly the brain can never, if it is the matter of incident mx (which then per se never can be known), know if these incident mx, given the process of the brain and the process between receptors and brain, correctly depicts, corresponds to empirical objects. It can only be ASSUMED that that is the case, the "empiri" only gives a hint of what empirically is valid. De facto it is the brain that determines what is "empirical"/empirical valid, simpliciter because the brain in accordance with the foregoing never can be sure if it really is about empirical knowledge.

 

Given this the only rational is to perhaps believe in clear "empirical" information, which mostly is about information that seems to come directly from the empiri, not mediated through/by instruments. E-theoretically it especially important is about the assumption that x attracts each other, hold together, "empirically" it appears to be so, despite it rationally is absurd, outmost then that mx (just only) can attract each other (that an invisible hand can bring mx towards each other). The brain is faced with a dilemma here, which should it believe, the rational or the irrational/absurd (some other options not exists, given an assumption of mx)? Also the assumption that thrusted mx "jumps" reasonably in thrusting mx "jump"-directions is then an "empirical" assumption, because thrusted mx then rationally "jumps" unconditionally stochastic. But "empirically" thrusted x moves more determinate (for example a billiard ball), unequivocally so, to deny that requires that the brain's "empirical" perception completely be rejected, declared strictly false, which well is to take it too far.

 

Direct "empirical" information is thus highly problematic, and even more problematic it becomes when instruments (devices) are involved, when an instrument (according to "empirical" perception), a "machine", mediates (is assumed to mediate) "empirical" information. For it is evident that the machine especially can deliver information just only created in the machine, any empirical input in/to the machine (which of course also is about (incident) mx (with an angle of incidence)) is so to speak lost (or non-existing), the machine simply ignores it perhaps, the machine just only delivers the information it (by the engineers) is programmed/created to deliver. But even if the machine actually processes input, incident mx, then of course the question is whether this process can be trusted, that the machine not distort the information incident mx perhaps provides (about the empiri).

 

But most important in any case is the interpretation of direct (by the (human) brain interpreted as being direct) as well of indirect (by machines/instruments mediated, which then the (human) brain interprets to be) "empirical" information, all such information can almost always, if not always, be differently interpreted, especially if it is about subtle experiments, where perhaps numbers, plots and graphs which a machine prints out must be interpreted. In the foregoing especially two interpretations of experiments have been made which differ from conventional interpretation, the first:

 

Einstein assumes that light not is captured/glued by attraction(/gravitation), which then gives rise to the theories of relativity, given that measuring instruments firmly anchored on (to) the Earth's surface not can measure relative speed of light of incident light that the instrument measures the speed of, which they also cannot according to actual experiments. E-theoretically light is captured/glued by (mx-)attraction, with which such firmly anchored measuring instruments simpliciter cannot measure relative light speed of incident light, for that the measuring instrument must be set in motion.

 

The second:

 

Quantum physicists assumes that small particles can interfere with themselves (why that would cause particles to take different paths?), to explain particle scattering, that small particles not moves linearly (especially in the "Double-slit experiment"). E-theoretically it simpliciter is so that small particles (consisting of fewer mx) moves wobbly, non-linearly. For more linear movement the "particles" must be larger (consist of more mx), and this is exactly what especially the Double-slit experiment shows, directly interpreted, without the introduction of "interference"; This concept of interference, including the concept of waves, probably was adopted given a continued assumption of the classical assumption that particles moves linearly, instead of simpliciter assuming that (small) particles moves non-linearly, they entangled (complicated) it with this with interference and particles being waves. Distinction must be made between attraction-movement and thrust-movement, thrust-movement as it is about in the Double-slit experiment, the particles are shot(/thrusted/pushed) through slits against a plate behind the slits. Attraction-movement on the other hand gives almost evident rise to more linear movement, towards the attracting mx. Of course depending on how the attracting mx moves, if they moves, then of course (rationally) the attracted mx bends their paths in the direction the attracting mx moves.^

 

^ This is a good example of that phenomena rationally almost gives themselves, of course it is possible to assume otherwise, but it is clearly irrational, at least in my mind, and I am convinced that most people see it that way, thus (with ones "inner eye") sees that by mx’ attracted mx cannot move in any direction other than the direction of attraction (towards mx’).^^ This rationally intuitive is so to speak everywhere in the E-theory, there is so to speak a rational (given) path to walk, at least concerning the most basic. Take for example further E, given T1, there is, given T1, as well as no alternative to the assumption of space-contractions (eternal mx excluded (T2 assumed)), the conventional that points, positions ("virtual particles") in E can "suck up" space, the (rational) intuition directly says no to, it simply expressed makes positions being something categorically more than pure space, or then a point (p) if it is about that. Even the most irrational probably hesitate to assume that a p can be a "space sucker" (which of course not hindered the physicists from nevertheless assuming roughly equivalently that, but that can be blamed on a confused, far too complicated definition, so that they lost their way, not sees clearly). Well, this then examples of rationally thinking, which then more or less given, leads to conclusions (on the "path").

 

^^ "Empirically" it is only possible to make indirect assumptions about mx, if any mx, because the human brain "empirically" has no access to the outmost (mx-)micro-level. The human brain "empirically" only sees "big splotches" as objects (when it interprets incident mx in the chain that perhaps were started by incident mx in to an eye), even when it comes to what it thinks it sees in instruments, it is far from perhaps "seeing" mx. And consequently it is a matter of from the "splotches" interpreting what perhaps is valid for mx, if any mx. With which man never can be sure that what she (indirectly) assumes for mx by observing the "splotches" is valid. For certainty direct access to mx is required. And even if it seemingly is present, it is in accordance with the foregoing then in any case only a matter of the brain's perception of the "empiri"/the empiri. But the "hint" can in any case be assumed to be more relevant if it is about "mx-level" than about "splotch-level".

 

An "mx-level" which then not is present, and probably never will be present, because given/provided that it is about mx, mx must be examined, "dissected" with other mx, other materially is too big, rough to be able to examine mx with. That mx literally can be seen is out of the question, the only thing that in that case can be seen is from mx reflected, bounced off mx, small "points", in order for an image to be created many "points" are required, which an mx simpliciter not can give rise to as being a "point", which then perhaps other incident mx after a collision can bounce away from, and of course only give the "image" of a "point", if these bouncing away mx can be "captured". Seeking to destroy mx, by bombarding it with (other) mx, in which case then mx (E-theoretically) is completed, requires that mx somehow can be "seen" to disappear/complete, just because mx completes, thus just only disappears, turns into being mv (again), there is nothing (no "energy")^^^ to measure (out), but this disappearance must then somehow be literally "seen". Regarding any attraction force (or other force), it is about "seeing" mx attracting other mx (or not), thus that mx in the vicinity of each other move towards each other, without any other (exogenous) force being involved, it only (perhaps) is about attraction. In groups/clusters of mx (especially then in slightly larger particles) thrusts also are involved, which are impossible to isolate, but for a categorical statement of attraction force of mx, an ("empirical") proof of it should consist of only two mx. And perhaps individual mx attraction force is too weak, so that only two mx not moves towards each other, with which of course no conclusion can be drawn, well, the direct conclusion would of course be that mx are neutral, a wrong conclusion of course if it is so that mx has attraction force, but that it takes mx in a group for it to have an impact. This as said only hypothetically, that mx-level can be reached is as said almost out of the question.

 

^^^ Yes, the mx-"energy" from completed mx flows so to speak out into the room, becomes one with it (mx diffuses (out into the room) so to speak (and with that then becomes one with the room)), with which the "energy" from the completed mx then principally are the (pure) volume mx has passed into being, with which the whole becomes extremely difficult to measure in any way, without going further into that. Physically measurable can without further ado (outmost) be claimed to be about (non-completed) mx, the "energy" are mx, a {mx}, not a {mv} as "energy" actually is (the "energy" that then can create mx, and mx then again transitions into when they completes).