List, John: John, the meaning of my post was unclear to you. My concerns focus on the pragmatic realism of scientific facts in relationship to mathematical narratives. This is seldom a major issue in the philosophy of physics because the very concept of variable is based on the definitions of the basic units of physics, where 6 of the 7 basic units of physics are defined in terms of artificial terms that are related with another by the notion of forces. These are mass, length, time temperature, electricity, and light. Each is considered to be a continuous variable.
Before responding to your post, which seems to contradict itself, I ask that you clear state the meaning of your notion of “pure mathematics”. I have taken it to mean the usual undergraduate level of mathematical philosophy that encompasses the mathematical structures that, stepwise, link set theory and category theory in the sense of Saunders MacLane text. This usage is much wider that predicate logic but excludes the various forms of para-consistent logics. Cheers Jerry > On Sep 19, 2018, at 6:28 PM, John F Sowa <[email protected]> wrote: > > 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 > ____________________________________________________________________ > > 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. > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to [email protected] > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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