Re: [PEIRCE-L] Pure and applied mathematics
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 peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
Re: [PEIRCE-L] Pure and applied mathematics
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 peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
Re: [PEIRCE-L] Pure and applied mathematics
John, List: > On Sep 19, 2018, at 9:33 AM, John F Sowa wrote: > >> >> 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.” > 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. It can never be a variable in the sense of the Cartesian axis system, which is the sense of Quine categorical error. This is factual realism. Cheers Jerry - PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
RE: [PEIRCE-L] Terminology of Peirce's final sign classification
Jon, a few brief responses inserted: From: Jon Alan Schmidt Sent: 19-Sep-18 13:07 Gary F., List: I was not previously aware of Peirce's marginal note about "Replica," so thank you for bringing it to my attention; the CP editors dated it "c. 1910," not 1904. He used "Replica" quite extensively before that--including in "New Elements"--for each enduring embodiment of a Sign within a particular Sign System, such as each appearance of "the" on a printed page of English text. GF: The date of the note is of no importance. What I said was that Peirce did not use the term “replica” after 1904 in a semiotic context. You have not cited an example to refute that observation, nor have you cited an instance of Peirce ever using the term “Sign-Replica.” I am proposing to retain it for this purpose, mainly to differentiate it from an "Instance" of a Sign as he defined that term in 1906, which is an occurrence at exactly one time and place. As long as a book is closed and sitting on the shelf, it contains many Replicas of "the," but an Instance of that Sign only happens each time someone actually reads one of them. Also, for the record, Peirce definitely did not use "replica" as a synonym for "sinsign" in 1903. CSP: Every legisign signifies through an instance of its application, which may be termed a Replica of it. Thus, the word "the" will usually occur from fifteen to twenty-five times on a page. It is in all these occurrences one and the same word, the same legisign. Each single instance of it is a replica. The replica is a sinsign. Thus, every legisign requires sinsigns. But these are not ordinary sinsigns, such as are peculiar occurrences that are regarded as significant. Nor would the replica be significant if it were not for the law which renders it so. (CP 2.246, EP 2:291; 1903) GF: True, the two words are not synonyms in the strictest sense of the word. But a “replica is a sinsign” and a sinsign is a sign in this classification, which means that the replica is a sign. This is not the case in your systematization, because all signs are Types, and a Replica is not a Type, is it? In this scheme, every Replica was a Sinsign, but not an ordinary one, such that not every Sinsign was a Replica; and a Replica was only significant because it was rendered so by the Legisign that it embodied. I acknowledge that my current approach is different--I am proposing that all Signs are what Peirce called Legisigns in 1903 (Types in 1906 and later), because as he wrote elsewhere, a Sign only exists in Replicas; in itself, it is an Entelechy (3ns), not a Matter (2ns). We can (and Peirce often did) call the Replicas "Signs" in the same way that we can talk about "the" both as one word and as 15 to 25 different words on a page. However, for the sake of clarity--especially within technical discussions of Speculative Grammar--I continue to advocate reserving "Sign" for the former, calling the latter "Replicas," and using "Instance" for each individual event of semiosis that produces a Dynamic Interpretant. GF: But it makes less sense to speak of written, printed or pronounced instances of the word “the” as “replicas”, because they differ radically in perceptible form ... I have addressed this before. Replicas of the same Sign within the same Sign System will resemble each other; it is precisely their significant characters (Tones) that make them recognizable as Replicas of Signs at all. However, Replicas of the same Sign in different Sign Systems--e.g., written/printed English vs. spoken English, not to mention other languages--may indeed "differ radically." GF: Sorry, this rationalization of your usage does not address the issue. Peirce said that there is only one word “the” in the English language, only one Type, regardless of whether Tokens of it are spoken or printed. A language is one Sign System, regardless of the variety of media used to utter the signs. Again, none of this amounts to an exegetical claim about Peirce's writings; rather, it is a systematic proposal for understanding Signs and their relations today. I would be glad to consider any purported cases of "existing things or events which turn out to be significant," but allegedly cannot be analyzed as Replicas/Instances of general Signs. I have already explained in other threads why I do not view ripples on a lake, weathercocks, thermometers, barometers, etc. as counterexamples. GF: Yes, I’ve seen those explanations, which mainly demonstrates your skill at rationalizing. The footprint I saw in the mud just now is not a replica of any other sign or a Token of any Type. The fact that we have a general concept of “footprint” does not constitute an analysis of that sign in the mud, or indeed of any genuine index. I just don’t see how such repurposing of Peirce’s terms contributes anything but confusion to the understanding of signs today. Gary f. Regards, Jon Alan Schmidt - Olathe,
[PEIRCE-L] Pure and applied mathematics
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 peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
RE: [PEIRCE-L] Terminology of Peirce's final sign classification
Jon, list, I agree with you (and Gary R) that “sign-vehicle” is an unfortunate choice of term, for the reasons you’ve given. But similar reasons apply to your term “Sign-Replica,” another term that Peirce himself never used (with or without the hyphen), as far as I can tell. He did use the term “Graph-replica” to distinguish between a graph that visibly existed on paper and the imagined diagram that it “replicated”; but he stopped using the term “replica” in reference to EGs in 1904, for reasons given in a marginal note to CP 4.395: “I abandon this inappropriate term, replica, Mr. Kempe having already (‘Memoir on the Theory of Mathematical Form’ [Philosophical Transactions, Royal Society (1886)], §170) given it another meaning. I now call it an instance.” Peirce also stopped using the term “replica” in reference to signs generally, and I doubt that you can find an instance of it in his semiotics after 1904. In the 1903 classification, he was using it as a synonym for “sinsign.” Since qualisign/sinsign/legisign is a trichotomy of signs — as is tone/token/type — a sinsign, or token, or replica, is a kind of sign. So is a legisign, or Type; in which case it makes no sense to say that all Signs are Types; which is probably why Peirce never said that, not even in “Kaina Stoicheia.” Likewise the term “Sign-Replica” makes no sense because a replica is a sign in the only classification system where Peirce actually used the word “replica,” that of 1903. And besides that, many of the examples Peirce gave of sinsigns at that time do not actually replicate anything; they are simply existing things or actual events which are determined by objects to determine interpretants. (The fact that you have to use a symbol in order to name or denote these things is irrelevant to their functioning as signs.) I’m inclined to think that Peirce’s use of “replica” in the 1903 classification of signs was already a mistake. It is misleading because for all ordinary purposes, a replica is a copy of something, usually of an existing thing. This is not necessarily the case with sinsigns, or with tokens as defined by Peirce in 1906: “A Single event which happens once and whose identity is limited to that one happening or a Single object or thing which is in some single place at any one instant of time, such event or thing being significant only as occurring just when and where it does.” Peirce does not say here, or anywhere that I know of, that a Token of a Type is a “replica” of that type, because that would be misleading: the relationship between a Token and the Type that it ‘betokens’ is not the same as the relation between a replica and what it replicates, because the latter two are ordinarily in the same mode of being. It makes sense to speak of a “replica” of a graph which has been imagined but not scribed, because both graph and replica are essentially visual. But it makes less sense to speak of written, printed or pronounced instances of the word “the” as “replicas”, because they differ radically in perceptible form — which is probably why Peirce didn’t use that term for them after 1904, not even when he was using the word as his paradigmatic illustration of the Type-Token distinction. For your “systematic” revision of Peircean terminology you could, I suppose, follow Peirce’s example and replace “replica” with “instance.” But that would be a band-aid solution to the deeper problem, which is your claim (or proposal) that all Signs are Types. For Peirce, an existing instance of a word is a sign (albeit a fragmentary and incomplete one), and calling it a “sign-instance” or “sign-replica” as if it were only an instance of a Sign is at best redundant. As for existing things or events which turn out to be significant, calling them “sign-replicas” is deeply misleading — more deeply than the notion of a “sign-vehicle.” Gary f. From: Jon Alan Schmidt Sent: 18-Sep-18 21:07 To: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Terminology of Peirce's final sign classification Gary R., List: I agree with your comments about Atkins's unfortunate take on the trichotomy according to the Sign itself. It certainly does not pertain to "the Sign-Vehicle," since this is a term that Peirce himself never used. The closest that he came was when he wrote in an unidentified fragment, "A sign stands for something to the idea which it produces, or modifies. Or, it is a vehicle conveying into the mind something from without" (CP 1.339). On the other hand, he clearly distinguished a Sign from a vehicle when discussing the "somewhat imperfect example" of a mosquito transmitting a disease. CSP: ... the active medium is in some measure of the nature of a vehicle, which differs from a medium of communication in acting upon the transported object and determining it to a changed location, where, without further interposition of the vehicle, it acts upon, or is acted upon by, the
