New Internet Dialogue Opens
on the F.E.D.
‘Dialectical Mathematics’.
Dear
Readers,
A
reddit participant
recently
posted, and commented upon, an F.E.D.
‘dialectogram’,
on one of our
conjectures as
to the opening triad of our version of the ‘dialectic of Nature’, at --
The ‘dialectogram’
there posted is a
variant of
the following --
This
poster’s comments included the following --
“This is true art. I
am actually in awe of how much effort this person has put into this stuff.”
I responded, on behalf of F.E.D.,
as follows --
“The 9 axioms, grounding the arithmetic/algebra for
dialectics applied in the diagram posted above, are stated, within the
www.dialectics.org web site, at --
“That these 9 axioms incorporate a version of the first
four, “first-order logic” axioms of the “[Dedekind/]Peano Postulates” for the
system of arithmetic of the “Natural” Numbers, makes this arithmetic/algebra
for dialectic a “non-standard model” of the Natural Numbers.
Such were foretold by the co-application, at
the level of “first order” logic, of the Gödel Completeness and Incompleteness
Theorems -- two of the deepest theorems of modern “mathematical logic”. An
intuitive, dialectical derivation of the system of these “dialectical meta-Natural
meta-numbers” from that of the standard “Natural Numbers” is available, within
the
www.dialectics.org web site, via
--
“That these 9 axioms suffice to deductively derive, as a
theorem, by a simple direct proof, a STRONG CONTRARY to what Boole called his
“fundamental law of thought”, or “law of duality”, which is the core “axiom” of
original Boolean algebra, makes this arithmetic/algebra of dialectic a
“contra-Boolean algebra” -- an algebraic dialectical logic.
This simple direct proof is presented, within
the
www.dialectics.org web site, here
--
“The resulting dialectical logic is a “supplementary
opposite” to Boole’s algebra for formal logic, one that “aufheben”-contains/conserves
Boole’s “fundamental law”, but which also “aufheben”-elevates and
“aufheben”-negates Boole’s fundamental law for formal logic. This new, “contra-Boolean” algebra expands
Boole’s “law of [EXO-]duality” into a more universal, more general “law of ENDO-duality”.”
“The
www.dialectics.org
site also recognizes a third axioms-system of dialectical- algebraic logic, one
which reconciles the opposition between the Boolean and “contra-Boolean”
algebras, in[to] a single ‘uni-system’ of dialectical algebra, incorporating
and integrating both.”
“For more about this third system of algebraic dialectical logic,
and about the entire, systematic “dialectic/systems-progression of the systems
of algebraic [dialectical] logic” -- of “algebras for [dialectical] logic(s)”
-- see:
