Kirsti, List: John Sowa almost always gives very good answers in his posts here when viewed from the traditional views of the philosophy of Vienna Circle.
But, a very good answer is not necessarily a mathematically, or logically or scientific COMPELLING answer for the science, logic, or mathematics of today. Cheers Jerry > On Sep 20, 2018, at 12:17 AM, [email protected] wrote: > > The answer offered here to Jerry Chandler by John Sowa I find a very good > answer. > > Cheers, Kirsti > > > > John F Sowa kirjoitti 19.9.2018 17:33: >> Jerry LRC, >> As Kirsti said, the subject line about categories and modes was >> a long thread about Peirce's 1903 classification of the sciences. >> I plan to post a copy that text, my diagram about it, and related >> quotations by Peirce on my web site. >> But I changed the subject line for the topic of pure & applied math. >>>> everything that is imaginable can be described by some theory >>>> of pure mathematics. >>> How can one describe a “feeling” in pure mathematical terms? >> You can't. That would require applied mathematics. >>> How can one describe a large bio-molecule, such as Nicotinamide >>> Adenine Dinucleotide (NAD) in pure mathematical terms?" >> For any theory of applied math, there is a simple procedure for >> finding a corresponding theory of pure math. And it's based >> on the point you mentioned: >>> Simply quote W.O Quine: “To be is to be a variable.” >> 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. >> You now have a theory about which Bertrand Russell would say >> "We don't know what we're talking about or whether what we're >> saying is true." >> That's pure math. >> Of course, nobody would ever attempt to translate a complex >> theory with many complex dependencies by the above procedure. >> Scientists and engineers normally adopt and adapt pure math theories >> one at a time, as they are needed. They often create applied theories >> from scratch, without looking for a prefabricated theory in pure math. >> But all such theories can be translated to pure math by the above >> method or some variation of it. >> John > > > ----------------------------- > 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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