Logical XOR
If there is always an excluded middle is there a form of the dialectic that permits a complete polarisation of opinion? Clearly the only form we have seen thus far is the refusal to shift identity from ones fixed view; in giving no time to the views of others (with other choices of identity) can it be possible to actually place ones own self unintentionally in the role of the facilitator in the centre?
Clearly to have no time for other opinions would place someone in the role where there is no agreement: Then we would be in the facilitator's negative position, and a new synthesis would arise: unless of course that the method itself is negated: We can not be blamed for others adjusting their fixed views to ours if they see that they are in truth, corrected!
We have a synthetic 'XOR' in the use of the sides of "negation" using the dialectic's 'NOT' operation. These alternatives take their place again as thesis/antithesis in a new dialectic balance recovering the use of the dialectic 'OR' instead - (again with an excluded middle), so XOR is not, as it were a possibility. Where can we find the logical XOR operation? Clearly it is not in view in the dialectic other than in the division of oil and wine disjoint as in the previous page:
What we actually have is the choice between movement "to the left or right" found in the left and right handed forms of the octal. Without considering addition for the moment, a choice of unity, "d" say separates the "left hand" into {e,f,g} and the "right hand" into {a,b,c}.
Then we could fashion our exclusive OR to {a,b,c} v {e,f,g}.
Now the synthesis in the dialectic has been upon a fixed coset of (a,b,c) in the octal; {a,b,c} as correxponding to unity is also "taken off the table" in the process and is always excluded in preference to unity (as 'd' here).
If the method itself is contradicted then choosing (a,b,c) in place of 'd' or {e,f,g} as the desired result is surely preferable: it being the one fixed "quantity" in view amongst the four seals of revelation's possible shift of unity from one of {d,e,f,g}.
In view in the left and right hands we could have the association with a = 1 and (b,d,f) static
e = (a,b,c)
g = (a,d,e)
c = (a,f,g)
Which would result in the possible dialectic in the symbols {a,c,e,g}.
But the separate K4 form would be
a = 1 = (a,b,c)
b = (a,d,e)
c = (a,f,g)
with NO dialectics in the symbols (d,e,f,g) or any other.
Now both sets, (a,b,c) and {c,e,g} with a=1 are clearly found to have correspondence to the K4 groups spanning the octal; The former would be the "left and right hands" in the Father, and the latter those as in His Son Christ. There is no ability to construct the dialectic in the K4 form only,.. only in the left handed elements (cosets of K4 groups) in the octal (The Father).
So there is no real reason to suppose that there would be an XOR operation on the dialectic: Because one could hold true in faith to every stipulation of faith using the dialectic only, and never encounter Jesus Christ. (Not a proof if you think that is what I am saying!)
Clealy the relation of inverses true/false requires either only two such balances to construct the red horse of the second seal example, or it requires that the dialectic be shown to be inconsistent. The only recourse then is that the method become null: and the only element outside of the static K4 group remaining is unity, which is the fixed position.
Aside from examples of "chicken and the egg" arguments, there are no didactic opposites in the method of the dialectic. In order for there to be no possible synthesis, by the nature of the dialectic the method must be invalidated or refused. The result is to employ the freedom of the K4 form, where unity is in place of the absolute truth, as before and the freedom of multiplicative inverses {b,c} is to those things that may be truthfully debated: There is no sense denying what is always correct, with arguments that themselves are null; There is the clear sense of correctness found in the unity element, and in the inverses of multiplication the symmetry of freedom of choice.
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