Logical AND

The dialectic method clearly results in a synthesis of two opposing viewpoints; We have simply shown that in the finite field GF(8) the book of revelation defines the four seals with these rules of shifting identity: The presence of one stable viewpoint in the presence of two others that oppose each other (in conflict) with a fixed position results in the agreement in principle of both views once the antagonism of the fixed position is removed from the discussion, or even the environment.

The dialectic as a method of satan for synthetic logic as opposed to correctly grounded logic based on facts, is an untethered system that has at its heart the idea that every opposing viewpoint is reconcilable as long as there is a shift of identity - a compromise made by each party.

We simply denoted the static triples for each choice of unity from the singletons in the octal (from cosets of a K4 group, also static) as simply

d = {e,f,g}
e = {d,f,g}
f = {d,e,g}
g = {d,e,f}

Only one row could be static or could be unity, but the unity position itself may be caused to "shift".

For three parties there is a common element that becomes the basis for synthesis, say g = {d,e,f} that takes its place as "wine" common to all the other three. If then we choose two opposites of thesis/antithesis, their common element is "taken off the table" as if it were absorbed like unity. The result is that the remaining triple of the other three corresponds to that choice of unity and is "static" and contains both elements not in common to the opposing two.

{e,f,g} => {d,f,g} <= {d,e,g} with 'g' as "wine" and 'e' as "oil" or unity.

{d,f,g} takes the place of the synthesis of the two viewpoints of {e,f,g} and {d,e,g}, it for all intents and purposes becomess the logical "AND" of the two.

For the three parties themselves we have conflicting unity, we would require that;

d => (e = 1) <= f

That the fixed views of 'd' and 'f' resolve into the fixed view of "e"; Of course, "e" is the fact which is actually agreed upon, and although this seems contradictory, that the "agreement" is taken off the table, what is actually in view is that the relation of e = {d,f,g} which is static.

The first three seals of revelation relate respectively to a fixed view, a meeting of views where neither concedes their point, and this balancing of views seen here. The ability to find a common synthesis equivalent to the "fact" (as 'e' here) on the basis that the same fact be taken off the table is mirrored in that the common ground of this method is found amongst the remaining views (as 'g' here).

That with acceptance of what is agreed upon ('e') is as a non-issue the opposing viewpoints of 'd' and 'f' that must shift to 'e' are shown to be "compatible" with the "wine" ('g') in a position {d,f,g} equivalent to {e}. The shift from 'd' and 'f' to 'e' is the synthesis of finding a "commonality" or conjunction of the two.

Logically, any difference of opinion ({e,f,g} or {d,e,g}) upon a "fact" (e) that results in two opposing fixed views (d or f) may shift those fixed views to what is held in common (e), resulting in a synthesis of the opposing views ({d,f,g}) into one viewpoint that may be in support of the "fact" (e). The remaining element 'g' that is common to both opinions as well as the synthesis is always on the table: It can either be the "willingness to continue" or the place of the method itself, or even in effect, the logical disjunction of the two opinions, rather than the fixed views ('d' and 'f') themselves and their logical conjunction "e".

This is what was wanted: That 'g' = {d,e,f} is excluded, (the oil and wine is not "hurt" or contradicted by order), and that the synthesis ({d,f,g}) of the two opinions ({e,f,g} and {d,e,g}) takes the place of the (perhaps non-existent) logical conjunction of the two fixed views (d and f). Whereas in the case 'd' v 'f' are exclusionary, 'e' becomes as it were, the apparently reached conjunction. In the case where there is indeed an excluded middle, the dialectic would enable the logical conjunction of 'd' and 'f' to be 'e' without trouble. The logical disjunction would simply be our "wine" 'g'.

Effectively then we have in the dialectic method itself an appropriate form that supplies the requirements of a logical "AND" operator: That any two opposing opinions A and B have their conjunction in the (synthesis) result of the process C, and any two totally exclusionary arguments (as fixed views 'd' or 'f') have a conjunction (as arrived at in 'e') in the method;

The "wine" or 'g' results in the method bringing 'd' and 'f' together - if 'd' and 'f' are irreconcilable then the method itself may continue with unity as 'g' as in the previously excluded fourth balance: Then 'e' would become "wine" - we have a simple inversion where the conjunction is the method: When the method itself fails to provide a conjunction, it itself takes the place of the conjunction with its own "in built" inconsistency.

In that case, the inversion from 'e' to 'g' does not contradict the method on the basis that the synthesis is invalid: Likewise if two views have a logical conjunction, there is in the process the wine 'g' that will continue the relationship based upon the conjunction ('e') which is the logical AND required.

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