Principles (of thought)
Total nothingness=propertieslessness not prevails, because if total nothingness prevails, for example this text cannot be read:
Properties (x’) exists, at least in this now, if for example this text can be read (experienced):
x={x’}; {x’} is a cluster of x’ (properties), which characterize, constitute, define x, then in that way that x (identically) is {x’}.
If "different" x "have" exactly, identically the same {x’}, then it (rationally) is the matter of the same, unique x:
Up) x=y=[unique x]; [{x’}Î x]=[{x’}Îy]:
Ip) x=x=[unique x]; [{x’}Îx]=[{x’}Îx].
Kp) x≠y; [{x’}Îx]≠[{x’}Îy].
Ip and Kp follows implicatively identically from Up, Up is implicatively identically Ip and Kp:
Up=Ip,Kp.
Implicative identity more commonly defined:
Ii) x=x’; x’Îx in intensional, meaningwise meaning (as evident [x properties]=x’Îx).
Iiphenomena/x are as identities superpositionalities, they exists at one and the same time, "timewise", but not necessarily "roomwise", Iix needs so to speak not (be seen to) exist in the same place, position, "point", p (nonextension with position), by which Iix not are psuperpositionalities, which both "timewise" and "roomwise" exists in the same "p", which are defined:
Sx=x(p)+y(p); x,y=[x(={x’}),x’].
Such strict psuperpositionalities, thus that x is several different x at one and the same time in (the same) "p", where x then can be an x(={x’}) or an x’, a property, are intuitively commonly absurd, but given forthcoming Etheory there is rationally a (big) exception, namely that stable mx momentarily (principally during time≤tp; tp=timep) can exist superpositionally with other mx/mv, which Etheoretically are the only possible psuperpositionalities (which not verify the Nothingsuperpositionality below, which is assumed to define/prove T1, because the Etheory presupposes T1).
Ii almost directly clarify that symmetry, that x=x’ and that x’=x (x’≠x, commonly also y≠x, but in the latter case it is commonly (per definition) not excluded that y=x may be valid, so when the analysis wants to be clear about that it is about nonx(≠x), then x’ is used), not is valid in general, but an example: (x « y)=(x ® y), and (x ® y)≠(x « y), unless x « y given(/presupposed) is valid: (x ® y)=(x « y); (x « y).*
Transitivity in the meaning x=y=z is valid in accordance with Ii, can be stated, transitivity however not is valid if x=y and z=y, thus x=z is in general not valid in that case, and that of course because symmetry not is valid in general, which also is entirely intuitive, because different x (commonly) very well implicatively identically may define (implicate) the same x. These basic principles present (which are in the convention), the concept of reflexivity also can be mentioned, which here (approximatively) is equivalent to Ip.
What an x is implicatively identically to may require its reasoning, even in terms of properties, indeed, something, x’, which is seen to follow from x can also be defined to be a property of x: x has the property (to be able to implicate) x’ (x ® x’), so what are to be seen as properties of x requires (may require) its discussion, perhaps implying that some properties are seen as direct (more categorical), others as indirect (less categorical, more loose).
Iix are more categorical, "strong" x (phenomena) than ("weaker") implicationx, where the binding, relation between x and y thus not is as strong (x ® y, x gives y (or: if x, then y, or: x implicates y)). For the implication it is commonly valid that [((x))=[perhaps(/maybe(/possibly)) x (x perhaps(/maybe(/possibly)))]]:
Ia) ((x,z,å,..)) ® y; If several x gives y in the same moment ("tp") it happens in different locations; Up.
Several, maybe very many x can give, "produce" y, or maybe just one (unique) x in some exceptional case (if x not implicates (any) y, then it of course not is a matter of an implication, or if x anyway is defined to implicate (any) y, then it of course is false definition).
Ib) x ® ((y,z,å,..)); How many y x can give in the same moment ("tp") depends (naturally) on x constitution.
An x can give, "produce", different, maybe many different y, or in some exceptional case maybe just one (unique) y.
Iix can (rationally) weaker be defined as implicationx:
(x=y)=(x ® y).
The reverse however, is not valid:
(x ® y)≠(x=y).
If it not is given that x=y is valid:
(x ® y)=(x=y); x=y.
Kp (the Contradiction principle, which then Up (the Uniqueness principle) implicatively identically defines) is especially useful, because Kp defines that if x is (assumed to be) true, then all y(≠x), as "replacers" for (the phenomenon) x (defined by x), are false:
All y are false; x is true; Kp.
If x is assumed to be false, then it either is to completely reject x, declare x to be completely false:
x is completely false if x=0=[no x(≠0)] ex post; x≠0 ex ante.
A completely false x is implicatively identically to there being no "replacer" y≠0 to x, y=0:
x is (only) false if it at least exists one "replacer" y(≠0) to x (which (by assumption) makes x true, which is the second falsehood alternative (oralternative)):
Only one (unique) y can replace x, at a time; Up.
x+y=[unique x](; Up), where x defines the phenomenon y (linguistically or nonlinguistically/factually/"empirically"/empirically; "Empiri" is perception that are perceived to correspond to empiri, to something that exists per se, independent of "empiri" or other perception/experience/apprehension) defines (y so to speak is in place for to perform/define).
Or: x*+y≠x*+y’, where x* defines the (basic) phenomenon that x false and y and y’ true defines.
Ip (the Identity principle) defines that x are the properties x has (owns), or are, with which the question can be asked if {x’} per se, as a function of itself, can change, become more x’ (holism) or less x’ (meridioism):
x={x’}±q?
If for example (meridioistically) x={x’}q it not contradicts Ip (if {x’}q={x’}q), and can thus not be ruled out as a contradiction in accordance with Kp, but what is valid regarding this must consequently be analysed in another way:
If the "original" {x’} is unchanged, no x’ is exogenously added to {x’}, or subtracted, taken away from {x’}, or x’Î{x’} not separate anything off, divides itself, then q(=x’≠0) arises from Nothing respectively disappears into Nothing. More specifically, the following can be defined: x=nx’; n≤m, and x=nx’±q; n>m, thus at a limit one to x added x’ gives rise to ±q, q which thus must arise from Nothing (+q), or disappear, "dissolve" in to Nothing (q). With which of course the question is if that is possible? If Nothing exists, then there principally is the possibility for that (just through the existence of Nothing), but not if Nothing not exists, because it is excessively irrationally, absurd to assume that something can arise from something that not exists, or to assume that something can turn into something which not exists at all. So the ruling is thus primarily about the existence of Nothing, can that existence be determined? Yes, if that psuperpositionality that Nothing=propertieslessness defines is assumed to be absurd, which is assumed, then the existence of Nothing can be excluded:
Nothing=[propertieslessness (propertiesless x)]:
The property propertieslessnessÎ[existing Nothing].
Because if the property propertieslessnessÎ[nonexisting Nothing], then of course Nothing not exists (given Ip; (nonexisting Nothing)=(nonexisting Nothing)(; Ip)).
An existing Nothing which as propertiesless (having the property propertieslessness) not has any properties:
The property propertieslessnessÏ[existing Nothing]:
T1) Nothing not exists (at all):
Up’’) x={x’}:
x≠{x’}±q.
Holism/meridioism thus not exists, thus provided/given that Nothing defines an absurd psuperpositionality.*
Given Up’’ the following further directly (implicatively identically) can be stated:
FT) Undecidable/independent (nonaxiomatic nonderivable, holistical) sentences x’=qÎ[theory x] not exists.
No x is (in accordance with Up’’) given as just only the sum of other sentences:
The cluster of (sentences) x’ in itself defines nothing, but it is the one who defines, interprets and argues for x’ that defines x’ and what implicatively identically follows (is seen to follow) from x’. So it is almost necessary to be overclear in the definition of what is seen to follow (to be possible to derive) from x. If the "jump" (between x and x’) is too big, even the definer not sees the "connection" between x and x’, the ("continuous") logic that brings from x to x’, then it simpliciter not is a matter of (rational) logic; Rationally the whole "process" from x to x’ must be seen(/realized), and be motivated (be given clear reasons for), exceptions from that must thoroughly be motivated, for example when a (deriving)principle (of inference) is assumed, which moves the analysis forward, to results, but it not is (really) possible to see how it (the principle) "procedurally" does when it leads to (derives) conclusions.
Further given Up it is (implicatively identically) valid that:
Up’) ¦(x)=x.
That there not exists (functions of) superclones, different identical x, all x are then unique given Up, different only if they not have identically the same x’ (in accordance with Kp).
Are there some other principles than the foregoing which can be assumed generally? Which is analysed in the next section.
__________ * If it is valid, it is assumed, defined, that x=y and that y≠x, then x=y only can be insubstituted in Ip (x=x) on the right side: x=x=y, because insubstitution 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 insubstituted 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 insubstitute in x=x, without symmetry being assumed.
** Given the Etheory 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 Etheoretically principally also material, although of course not as tangible as mx, se further the Esection.
