2. For the second step of the presentation, for s = 2, we then have --

R^(2^(2)) = R^(4) = R^(2 x 2) = (R^2)^(2) = (R + T)^(2) =

(R + T)((R + T)) =

the [self-[reflexive]]function (R + T) "of" (R + T) =

( R + T )-squared = ( R + T ) confronts itself =

( R + T ) evokes its own immanent other / "intra-dual" out of itself =

R + T) "aufheben"-negates itself =

( (R + T) + delta-(R + T) ) =

( (R + T) + qtr + qtt ) =

( qr + qt + qtr + qtt ).

Thus, we see that two new possible philosophical categories have emerged, symbolically, in this "argument", in the calculation of step 2 of this "Ockhamian Dialectic", namely, the category connoted by the "connotogram" -- or
"connot-icon -- qtr, assigned to the "uninterpreted" N\Q "meta-number" qualifier q3, and the category connoted by the "connoticon" qtt, assigned to the "uninterpreted" N\Q "meta-natural meta-number" qualifier q4.

I propose that we interpret as follows --

q3 (---] qtr = qf = F:

the category of well-formed propositions of the first
intension, in which the terms of language, categorematic and syncategorematic alike, functioning together, "subsume" "reality" for those cognizing subjects/agents within Nature -- i.e., for that which we [humans] name by the term "humanity" -- who are capable of creating and using language, by "converting" that "reality" into systematic, sentential, propositional, linguistic, human descriptions of that "reality".

q4 (---] qtt = qs = S:

the category of well-formed propositions of the second intension, in which the terms of language, categorematic and syncategorematic alike, functioning together, "self-subsume", by "[self-]converting" that human,
internal, "inter-subject-ive", or "inter-agent-ive", "mental", secondary universe of "terms", of "language", of "ideas", into systematic, sentential, propositional, linguistic, human descriptions of that universe of linguistic "things", of linguistic "[idea-]objects", of linguistic descriptions themselves; that universe of the human "meme-pool", or of the self-developing "Human
Phenome", self-reflexively.

Thus, by R^(2(^2)), step 2 of the dialectic connoted by R^(2^(s)), we have generated the full regalia of the Ockhamian taxonomy, namely --

R^(2^(2)) = R^(4) = R + T + F + S =

"real things" + "categorematic and syncategorematic terms" + "propositions of the first intension" + "propositions of the second intension"

(---]

q1 + q2 + q3 + q4.

-- where F comprises the "Scientia realis",

S the "Scientia rationalis", and

( F + S ) the "Scientia Universalis".


For more on this "Dialectical Ideography", and its applications, see:

www.dialectics.org . . .


Regards,

Miguel