On 9/19/2018 4:28 PM, Jerry LR Chandler wrote:
A chemical atomic number, as a unique form of matter, is composed of
polar opposite electrical charges that generate a special (polar)
logical operation called valence that operates only on one of the pair
of polar opposites.
That is an empirical issue about the application.
It can never be a variable in the sense of the Cartesian axis system,
which is the sense of Quine categorical error.
See below for the method for removing all references from an applied
theory to derive a theory of pure math. The method for applying
a pure theory to chemistry would reverse that mapping.
Note step #2 below. It would map chemical entity names to symbols
such as E1, E2, E3... Those are not variables. They are just
names of abstract entities in the mathematical theory.
Then, if you apply that pure math theory to chemistry, you would
map those names E1, E2... of abstract entities back to the names
of entities in the subject matter (in this example, chemistry).
The purpose of this discussion is to illustrate the mappings
of mathematical theories to and from any empirical subject.
There are infinitely many theories of pure math.
For every theory (precise, approximate, or mistaken) in any empirical
subject, there is a corresponding theory of pure math. The theory of
phlogiston, for example, has a counterpart in pure math. It makes
some true predictions, but most of its predictions are wrong.
But the converse is not true. There are infinitely many pure math
theories that have no application to anything in the universe.
Some of them are logical possibilities that are physically
impossible. Others are just irrelevant to anything real.
Others are so weird that they aren't even imaginary -- no human
could imagine them.
John
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1. Start with whatever applied theory you have. Let's assume
that it's stated in some mixture of mathematical formulas,
chemical symbols, chemical formulas, and English statements.
2. Leave every name or symbol in pure math unchanged. Replace
every name or symbol in the application with some distinct, but
non-obvious name -- for example, relation names R1, R2, R3...;
function names F1, F2, F3...; and entity names E1, E2, E3....
For variables, use non-obvious names: x1, x2, x3...
3. Then translate every statement or formula in any notation
to predicate calculus (Peirce-Peano algebra). This would be
systematic for the formulas in math & chemistry, but it may
take some thought and rewriting to force raw English into
predicate calculus. But if the English is precise (or can
be restated precisely), the translation can be done.
4. But your theory probably depends on many other theories
of chemistry and physics. Repeat the above steps with all
of those theories -- and be sure to maintain a record of
the way each name was translated -- consistent translation
across all the theories is essential.
5. After you finish that, throw away the crib sheet that says how
the original names were mapped to the R, F, E, and x symbols.
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