Robert, List: RM: When we put the last lines of CP 3.559 before your eyes, do you look away?
I honestly do not understand what prompted this question, since I *directly quoted* the last lines of CP 3.559, and I have previously pointed out that the entire referenced paragraph is the central passage of my series of articles about the logic of ingenuity. I also do not understand the rest of the post that follows, since I have repeatedly acknowledged that formulating a pure hypothesis falls within the scope of pure mathematics. It is Peirce himself who describes this as a "quite fictitious problem" such that the resulting mathematical objects are "pure artifacts," not realities that are as they are regardless of what anyone thinks about them. Please note again the last quotation that I provided, especially these sentences to that effect. CSP: Mathematical reasoning has for its object to ascertain what would be true in a hypothetical world which the mathematician has created for himself,--not altogether arbitrarily, it is true, but nevertheless, so that it can contain no element which he has not himself deliberately introduced into it. All that his sort of reasoning, therefore, has to do is to develop a preconceived idea; and it never reaches any conclusion at all as to what is or is not true of the world of existences. (CP 8.110, c. 1900) Regards, Jon S. On Tue, Aug 17, 2021 at 11:40 AM robert marty <robert.mart...@gmail.com> wrote: > Dear Jon Alan, > > When we put the last lines of CP 3.559 before your eyes, do you look away? > > "… *Thus, the mathematician does two very different things: namely, he > first frames a pure hypothesis stripped of all features which do not > concern the drawing of consequences from it, and this he does without > inquiring or caring whether it agrees with the actual facts or not; and, > secondly, he proceeds to draw necessary consequences from that hypothesis"* > (CP > 3.559) > > Why does Peirce write this? Because it is obvious that the famous > mathematics of which you say that ADT "*explicitly affirms the dependence > of phaneroscopy (and every other positive science) on mathematics for > certain principles, including formal deductive logic"* [emphasize mine ], > are for him pure artifacts. Indeed, he does not exhibit any of them, and > neither do you. They are empty argumentation factors, "elements of language > without denotation," like "unseen characters" are in the theater (sorry, I > have to repeat myself). Thanks to them, one can sing the great merits of > ghosts without risking being contradicted to better exclude realities, like > every mathematical object. > > Moreover, Peirce (mathematician) wrote this makes sense: how to recognize > "mathematical principles" and abstract them from complex phanerons if one > does not have them, either in one's mind or if one does not have the > capacity to construct them? > "A*t the same time, it frequently happens that the facts, as stated, are > insufficient to answer the question that is put. Accordingly, the first > business of the mathematician, often a most difficult task, is to frame > another simpler but quite fictitious problem (supplemented, perhaps, by > some supposition), which shall be within his powers, while at the same time > it is sufficiently like the problem set before him to answer, well or ill, > as a substitute for it*." (CP 3.559, again) > > But maybe it is "tribalistic" to remind it? > > Regards, > Robert Marty > Honorary Professor; Ph.D. Mathematics; Ph.D. Philosophy > fr.wikipedia.org/wiki/Robert_Marty > *https://martyrobert.academia.edu/ <https://martyrobert.academia.edu/>* > > Le mar. 17 août 2021 à 17:38, Jon Alan Schmidt <jonalanschm...@gmail.com> > a écrit : > >> John, List: >> >> JFS: They show that De Tienne has misunderstood the role of mathematics >> in Peirce's philosophy. >> >> >> On the contrary, those three quotations show that anyone >> accusing André of hostility toward mathematics and mathematicians has >> completely misunderstood his point. He *explicitly affirms* the >> dependence of phaneroscopy (and every other positive science) on >> mathematics for certain principles, including formal deductive logic. >> Nevertheless, he rightly distinguishes *pure *mathematics as the science >> which draws necessary conclusions about strictly hypothetical states of >> things from *applied *mathematics as an integral part of every other >> science, including phaneroscopy. We cannot count on *pure *mathematicians >> to help figure out what goes on in experience, because they only formulate >> and explicate a *pure *hypothesis "without inquiring or caring whether >> it agrees with the actual facts or not" (CP 3.559, 1898). >> >> JFS: In the second sentence, the phrase "rest of us", which is intended >> to exclude mathematicians, is extremely insulting to Peirce and the many >> mathematicians quoted in ppe.pdf. >> >> >> There is no reason to take this remark by André so personally. As with >> his hyperbolic statement on slide 23--"The world could stop existing, but >> to pure mathematicians that would at most be an inconvenience"--he is >> clearly referring here only to the idealization of someone who *never >> *inquires >> or cares about actual facts. Peirce was indeed a mathematician, but he was >> not *only *a mathematician, and he was certainly not a *pure *mathematician >> in this extreme sense. >> >> JFS: Diagrams are the form of mathematics where the mathematicians and >> the people who claim they know nothing about mathematics share common >> ground. >> >> >> I agree--for Peirce, all necessary reasoning is mathematical reasoning, >> and all mathematical reasoning is diagrammatic reasoning, so all necessary >> reasoning is diagrammatic reasoning. >> >> CSP: For mathematical reasoning consists in constructing a diagram >> according to a general precept, in observing certain relations between >> parts of that diagram not explicitly required by the precept, showing that >> these relations will hold for all such diagrams, and in formulating this >> conclusion in general terms. All valid necessary reasoning is in fact thus >> diagrammatic. (CP 1.54, c. 1896) >> >> CSP: All necessary reasoning is strictly speaking mathematical reasoning, >> that is to say, it is performed by observing something equivalent to a >> mathematical diagram ... (EP 2:36, 1898) >> >> >> CSP: ... I declare that all necessary reasoning, be it the merest >> verbiage of the theologians, so far as there is any semblance of necessity >> in it, is mathematical reasoning. Now mathematical reasoning is >> diagrammatic. (CP 5.148, EP 2:106, 1903) >> >> >> Nevertheless, the distinction between mathematics as a *hypothetical *science >> and all the *positive *sciences must be carefully maintained. >> Accordingly, I believe that what Peirce says in the following passage about >> metaphysics and metaphysicians is equally applicable to phaneroscopy and >> phaneroscopists. >> >> CSP: Metaphysicians have always taken mathematics as their exemplar in >> reasoning, without remarking the essential difference between that science >> and their own. Mathematical reasoning has for its object to ascertain what >> would be true in a hypothetical world which the mathematician has created >> for himself,--not altogether arbitrarily, it is true, but nevertheless, so >> that it can contain no element which he has not himself deliberately >> introduced into it. All that his sort of reasoning, therefore, has to do is >> to develop a preconceived idea; and it never reaches any conclusion at all >> as to what is or is not true of the world of existences. The metaphysician, >> on the other hand, is engaged in the investigation of matters of fact, and >> the only way to matters of fact is the way of experience. ... It follows, >> that deductive, or mathematical, reasoning, although in metaphysics it may >> oftener "take the stage" than in the drama of special research, yet after >> all, has precisely the same *rôle *to enact, and nothing more. All >> genuine advance must come from real observation and inductive reasoning. >> (CP 8.110, c. 1900) >> >> >> Regards, >> >> Jon Alan Schmidt - Olathe, Kansas, USA >> Structural Engineer, Synechist Philosopher, Lutheran Christian >> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >> >> On Sun, Aug 15, 2021 at 11:37 PM John F. Sowa <s...@bestweb.net> wrote: >> >>> Robert, List, >>> >>> I strongly agree with your approach, and I would like to add three >>> quotations by Peirce (copied below). They show that De Tienne has >>> misunderstood the role of mathematics in Peirce's philosophy. >>> >>> But I am not claiming that ADT does not understand Peirce, People were >>> doing mathematical thinking for thousands of years before anyone knew they >>> were doing mathematics. What they were doing is diagrammatical reasoning, >>> which creative mathematicians, especially Peirce, have always known is the >>> foundation for mathematics. >>> >>> For quotations that emphasize that point, see the first 10 slides of a >>> talk I presented at a Peirce session at an APA meeting in April 2015 and >>> extended for a workshop hosted by Zalamea in Bogota: Peirce, Polya, and >>> Euclid: Integrating logic, heuristics, and geometry, >>> http://jfsowa.com/talks/ppe.pdf >>> >>> In the first sentence of ADT's slide 25 (see the attached file >>> ADT25.jpg), he belittles Peirce's life's work: "we cannot count on >>> mathematicians to help figure out what goes on in experience." >>> >>> That is contrary to all three quotations by CSP. There are indeed some >>> mathematicians (pedantic, non-creative ones) whose guidance would be >>> unreliable. But Peirce, Polya, Euclid, Archimedes, Einstein, and others >>> quoted in ppe.pdf aren't among them. >>> >>> In the second sentence, the phrase "rest of us", which is intended to >>> exclude mathematicians, is extremely insulting to Peirce and the many >>> mathematicians quoted in ppe.pdf. >>> >>> In the third sentence, the question "how do we transition" is answered >>> by Peirce: use diagrams! Diagrams are the form of mathematics where the >>> mathematicians and the people who claim they know nothing about mathematics >>> share common ground. >>> >>> John >>> _____________________________________ >>> >>> Three quotations by Peirce: >>> >>> Phaneroscopy... is the science of the different elementary constituents >>> of all ideas. Its material is, of course, universal experience, -- >>> experience I mean of the fanciful and the abstract, as well as of the >>> concrete and real. Yet to suppose that in such experience the elements >>> were to be found already separate would be to suppose the unimaginable and >>> self-contradictory. They must be separated by a process of thought that >>> cannot be summoned up Hegel-wise on demand. They must be picked out of the >>> fragments that necessary reasonings scatter; and therefore it is that >>> phaneroscopic research requires a previous study of mathematics. (R602, >>> after 1903 but before 1908) >>> >>> My trichotomy is plainly of the family stock of Hegel’s three stages of >>> thought, -- an idea that goes back to Kant, and I know not how much >>> further. But the arbitrariness of Hegel's procedure, utterly unavoidable >>> at the time he lived, -- and presumably, in less degree, unavoidable now, >>> or at any future date, -- is in great measure avoided by my taking care >>> never to miss the solid support of mathematically exact formal logic >>> beneath my feet.... (R318, 1907, p. 37) >>> >>> The little that I have contributed to pragmatism (or, for that matter, >>> to any other department of philosophy), has been entirely the fruit of this >>> outgrowth from formal logic, and is worth much more than the small sum >>> total of the rest of my work, as time will show. (CP 5.469, R318, 1907) >> >>
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