The Man said:
Not ‘A’ or not ‘black’ would also be blue, green, white, yellow ect.. everything that is ‘not black’. By defining ‘A’ as ‘back’ you also define everything else as not ‘A’. We can ‘generalize’ (to correctly use one of Dorons’s favorite words) this consideration by defining what constitutes ‘black’.
It is not a generalization. All you did is to force A and not-A (that can be interpreted also as two arbitrary different things) to fit to your one A's reasoning.
ETA:
Let’s take another example a coin one side defined as ‘heads’ and the other as ‘tails’. A proper coin by that definition must have a ‘heads’ side AND a ‘tails’ side, that is not a contradiction but a complementation of that definition of the sides on a proper coin. For any one flip of the coin the result ‘heads’ AND ‘tails’ is a contradiction while ‘heads’ OR ‘tails’ is a tautology. So again Doron it comes down to being very specific in what you are talking about and using terminology in the applicable context.
Very good example The Man.
In The Man's example we deal with already existing and researched things, and avoid any ontological viewpoint of the fundamental terms that enable their existence.
Let us follow this limited viewpoint (where Ontology is avoided).
In this case, we have an existing thing, called coin that has two properties.
The properties (called ‘heads’ AND ‘tails’) are observed by flips. Each flip returns one and only one result out of two possible results.
OM calls the ability to return one and only one result out of
n possible results, Locality.
Local result A AND not-A is indeed a contradiction, because Locals cannot be simultaneously in more than a one state (as The Man says: "
For any one flip of the coin the result ‘heads’ AND ‘tails’ is a contradiction").
But this is not the one and only one way to get A AND not-A.
Alternative 1: A AND not-A is the superposition of the possible results of each flip, and by superposition A AND not-A is not a contradiction.
Since OM uses Distinction as its first-order property, alternative 1 holds at OM.
Alternative 2: The researched thing is non-local. In this case the coin's flip example has to be replaced by another one, for example Line's location.
If we draw a line segment on a particular location that is determined by a point, the line segment is on AND not-on the point, and there is no contradiction because on AND not-on is the very nature of Non-locality (represented by a line segment, in this case) exactly as the coin's flip represents Locality.
Since OM defines Non-locality as one of its building-blocks in addition to Locality, then, again, A AND not-A is not necessarily a contradiction at OM.
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Let us carefully research A by using an ontological viewpoint.
A's existence is the result of an interaction of two opposites.
For example, OM's researchable universe is the result of the complementation between Emptiness AND Fullness, where Emptiness is the opposite of Fullness and vice-versa.
The result, called A, is not totally empty AND not totally full, which enables the research.
At this non-total state (A) one defines the concept of collection, which its existence is stronger than Emptiness AND weaker than Fullness.
By using a collection as a research tool, one defines Emptiness as "that has no predecessor" (value 0) and Fullness as "that has no successor" (value
∞).
These values are the magnitudes of existence of the researched and they are taken indirectly by the intermediate level of existence of collection (the non-total state A). These values cannot be defined directly because Emptiness on its own is too weak and Fullness on its own is too strong.
At A one defines the researchable states of Locality AND Non-Locality, where Locality AND Non-locality are mutually independent of each other, and together they are used in order to define A's researchable universe.
At A's researchable universe, P AND not-P is necessarily a contradiction iff P is Local.
Jsffisher's and The Man's "nothing more, nothing less" reasoning must be local, because P is "nothing more AND nothing less" (nothing beyond P is researched and we get a closed entropic reasoning that is too weak in order to deal with Non-locality or Distinction as its first-order properties).
