I am interested in applying Godel's and Turing's arguments to systems not
ordinarily considered to be mathematical or having to do directly with
discussions of "mind". This is interesting to me since if these arguments
apply to universes and their generation then they should apply to all
processes within universes and thus to a complete discussion of the
Everything. I have made some attempts at constructing correspondences
between the workings of a FAS, the process of manufacturing a product and
the process of making rules such as the legislative process. I would like
any comments and any information relative to earlier attempts to do similar
things.
A FAS contains:
1) An Alphabet [Well Formed Formula [WFF] are sequences of alphabet
elements [symbols].]
For Manufacturing the alphabet is the elements of the Periodic Table. The
table symbols being a shorthand for actual atoms of the elements.
For Rules Making the alphabet is the elements of the periodic table
[sometimes as single or collective symbols [such as "a person"], language
symbols, and mathematic symbols.
2) Rules of Grammar: Is the formula well formed?
For Manufacturing the Rules of Grammar are the physics of the universe in
question.
For Rule Making the rules of grammar are physics, language grammar, and
mathematical grammar.
3) Rules of Inference [How to construct true WFF's from the axioms. That
is how to construct valid proofs.
For Manufacturing the rules of inference are the manufacturing process
[machines and process rules].
For Rule Making the Rules of Inference are the existing rules and the axioms.
4) Axioms - WFF taken to be true absent proof. [Some systems have none.]
For Manufacturing the axioms are the raw materials sometimes as a
collective [Cu, Ag, wood, ceramic, etc.].
For Rules Making the axioms are WFF about specific system behavior.
A correspondence:
Theorem [True WFF] same as: Well made Product; and same as: Non conflicting
Rule.
Hal
