Amazing!

I've been harping on this theme for what seems to be ages now in this forum.

We evaluate abstract relations using consistency as the criteria, and we evaluate direct experiences using repition as the criteria, for linguistic expressions of each respectively. These comprise logical relations and semantic relations respectively.

Logical realations may be completely known, but semantic relations (empirical) involve an unknown, so cannot be completely known.

But I would NOT align these with "Aristotelian" and "non-Aristotelian" respectively.


HOA = Horribly Obscure Acronym.

No.
1. For logic.
For all P, P -> P.
For all P, P or ~P -> T.
For all P, P and ~P -> F.
F or T -> T.
F and T -> F.
Where P is a proposition and T and F are arbitrary values which we may instantiate as "true" and "false". No "semantics" is involved.

2. For hypothetical mappings that have to be tested, (empirical), the third rule is

The map "reflects" the map maker.

A great many maps are NOT "self-reflexive", but all maps have a map maker.

A: A hypothetical relation set (map) constructed to represent an unknown territory is not (is different from) the unknown territory.
B: A hypothetical relation set (map) constructed to represent an unknown territory does not cover all the unknown territory.
C: A hypothetical relation set (map) constructed to represent an unknown territory reflects the choices and abstractions of its constructor. (The "C" of General Semantics)

Russell, in Russell's paradox, shows that NO map is truly "self" reflexive, because every supposed circular reference is at a higher level of abstraction. The map cannot contain itself, and any part of the map that is supposedly about itself, cannot incude the part of itself that it is supposed to be about, or infinite regress without limit, which cannot be physically implement, would result.

A map, which contains a key, which itself may contain another key, comprises a multi-level structure about the object of the map, presuming that the map (higher level object) may be included in that territory, but the territory covered by the map often does not contain the map, so the relation is false-to-fact.

My map of California is not in California, and it certainly does not cover the physical area in California taken up by the key. There is no map key physically present in California.

If you aim a television camera at the monitor showing what the camera is looking at, you see infinite regression that does not include self-reflexitivy, because the tv-camera is not in the picture. If you stand between two parallel mirrors, you can see each reflecting the other, and it takes two levels for one mirror to show itself; it only does so by refelecting the other mirror's content. It is not self-reflexion, but A reflecting B's reflection of A. All are created and determined by the human setting the situation up - the map maker.

Maps are not, in general, self-reflexive; only a few contain keys about themselves.

Maps "reflect" the map maker. But a better way of saying this is that the map structure shows the implementation of the maker's choices.

It's only in a very metaphorical sense that the word "reflect" "reflects" (pun intended) the relation between the map and its maker.

The basic thrust of Russell's paradox hangs on showing that when Frege allowed a set to be a member of itself it lead to a contradiction - inconsistency. Since this was "pure" set theory, that is hypothetical relations with no specific content, it meant that the structure of allowing anything to be "in" itself (self-reflexivity) is self-contradictory - inconsistent. Consequently the whole notion of "self-reflexity" can only be solved (saved) by insuring that each "reflection" is at another level of abstraction.

Map A can contain F(A-f(A)), but it can not contain F(A), because then it would have to contain F(F(A)), F(F(F(A))), ...
Physically, we are limited, so no map can be constructed with successively smaller inserts within inserts.

Even the TV camera pointed at the monitor fades off into oblivion through loss of information at each level.

Simply applying "the map covers not all the territory" shows that we eventully run out.

I answered that question "No", because the hypothesis involved is not acceptable.

The rules for "avoiding the types of logical fallacies encountered while evaluating "relations of ideas"" are:

1. For Logic:
For all P, P -> P.
For all P, P or ~P -> T.
For all P, P and ~P -> F.
F or T -> T.
F and T -> F.
Where P is a proposition and T and F are arbitrary values which we may instantiate as "true" and "false". No "semantics" is involved.

And, for matters of "fact", while two of the rules are acceptable - with reservations - the third rule, that you expressed, not only is not suited for avoiding the types of fallacies encountered when evaluating "matters of fact", it actually contributes to committing some such fallacies.

I expressed the correction or revision as:

C: A hypothetical relation set (map) constructed to represent an unknown territory reflects the choices and abstractions of its constructor.

But, just to be inclusive, I also chose to express the other two in a similar vocabulary:

A: A hypothetical relation set (map) constructed to represent an unknown territory is not (is different from) the unknown territory.
B: A hypothetical relation set (map) constructed to represent an unknown territory does not cover all the unknown territory.

A little similarity of structure.

While the second half of your division can be called "non-Aristotelian", the first half really cannot.

Aristotle's laws of thought:
Whatever is is itself. (A is A.)
It cannot be that something is and that it is not. (~(A and ~A))
It is not possible to be and not to be the same thing. (~(A(x)) and ~A(x)))

(The first is basically the consistent and repeatable use of symbols. This is "relative invariance".)
(The second is propositional logic)
(The third is predicate logic.)