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Logic

Axiomatic logic is a monoid.

The only possible formal proofs we can make are isomorphic to Peano's
arithmetic, leading to Zermelo-Fraenkel (ZF) set theory as a reduction
of historical set theory to a minimal decidable set theory.

After arithmetic, that is operation on integral numbers (0, 1, +), all
predicates are undecidable, that is the finding of Kurt Gödel. All
proofs that are made beyond arithmetic are a decision, a construction
of the person making the proof. In set theory this is called ZFC : the
Zermelo-Fraenkel set theory with the axiom of choice. This lead to the
expression that "- A proof is a social construct.".

There might be a DX's theorem, the reverse "Catch 22" of Kurt Gödel's
decidability theorem :
,______________________________________________________________________,
| We should be very careful before admitting that a theory is the only |
| possible theory for a given problem unless it can be reduced to      |
| the basic arithmetic monoid (0, 1, +). This is a self proven theorem |
| since there are also other possible proofs for different expressions |
| of this very theorem.                                                |
,----------------------------------------------------------------------,

So Berkeley was right : there is thinking matter, and a matter that is
thought, and communication is the flow of thinking from the thinking
matter towards the matter that is thought. And maybe it can be a
sufficient wording for people to enjoy, well, matter, and thinking.

References :
 
 Ernst Friedrich Ferdinand Zermelo (1871-06-27 –> 1953-05-21)  was a
 German logician and mathematician, in 1908 he completed his work on set
 theory.
 
 Abraham Adolf Halevi Fraenkel (אברהם הלוי (אדולף) פרנקל)
 (1891-02-17 –> 1965-10-15) was a German-born Israeli mathematician, he
 published two papers in 1922 and 1925 leading to the Zermelo-Fraenkel
 set theory axioms.
 
 Kurt Friedrich Gödel (1906-05-28 –> 1978-01-14) was Czech logician,
 mathematician, and philosopher. He published his incompleteness theorem
 in 1929. In 1930 Gödel attended the Second Conference on the
 Epistemology of the Exact Sciences, held in Königsberg, 5–7 September.
 There he delivered his incompleteness theorems.


Copyright 2023 TRAN-DUY Thomas "DX" de Grivel <thodg@kmx.io>
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