Gary R, Robert M, Jon AS, Edwina, List, Thanks, Gary, for explaining our points of agreement. As you emphasize in bold face, we all agree with Nathan Houser and with Short that Peirce’s later taxonomy “is sketchy, tentative, and, as best I can make out, incoherent” (Short 2007, p. 260). But he [GR, Short] quickly went on to point out that it is not the inconclusiveness of Peirce’s own findings but “the kind of project” he had conceived and was pursuing that is important.
I also emphasize our agreement with Max Fisch, who pointed out, during the final six years of Peirce’s life he was engaged on a system of logic considered as semiotic which he hoped would “stand for realism in the twentieth century. I also agree with the other sentences you emphasized in bold. Since I have finished the article on phaneroscopy, I am now writing the article on Delta Graphs. That is an example where Peirce was on solid ground with his deep understanding of logic and mathematics. Next week, I'll send the abstract and preview of the new article, which shows how Peirce anticipated a version of logic that was developed in the 21st century (2006 to be exact). Since I also agree with Robert Marty's emphasis on Peirce's mathematical background, I include his note below. The emphasis on mathematics is essential. It explains Peirce's successes and the areas where he was less successful, such as the points that Short said were sketchy, tentative, and even incoherent. I agree that the questions about interpretants are important, but the answers depend on issues of cognitive science that are so complex that our best known mathematical methods are inadequate. This is still an open research area, and the most we can say is that the problems Peirce attempted to solve are still unsolved. John ________________________________________ From: "robert marty" <robert.mart...@gmail.com> List, I agree with JAS on the architectonic character of the classification of the sciences. I want to complement what he says further and be even more precise about Peirce's deeper thinking. Indeed, JAS is perfectly suitable to note that applying the principle of classification (which Peirce borrows from Auguste Comte, revisiting it as JAS mentioned) leads to placing the Special Sciences in a position to receive their principles from semiotics. But strictly speaking, applying the principle from the first trichotomy of the Sciences of Discovery (CP 1.180) must lead to the more general conclusion that semiotics itself receives its principles from Mathematics and Philosophy (or Cenoscopy). More precisely, as we progress through the successive trichotomies, we see that semiotics receives its principles from a chain of dependencies that necessarily begins with Mathematics and continues with Phenomenology, Aesthetics, Ethics, and Logic (the science of the general laws of signs), which then trichotomizes into Speculative Grammar, Critic and Methodeutic, before providing its principles to Metaphysics. Peirce is very precise on this point and on what needs to happen in the minds of the scientists concerned: I set out from Comte's well-known scheme (or schemes). It seemed to me that this embodied a most striking truth about the relations of sciences, along with some glowing falsities. That truth I conceived, and still conceive, to be that the results of one science, A, will often be applied by another science, B, as principles or tools wherewith to solve its problems (not of course, without research of its own), while science, B, will perhaps suggest problems to science, A, but will not furnish it with any great aid in solving its problems. I thought I ought to use this principle of Comte's for all it was worth, without allowing it to run away with me. For what I wish to produce is a scheme which shall exhibit, as far as possible, the most real affinities of the different branches of science as these sciences exist in the minds of those who are now actively pursuing them, or better, as these men are coming to regard these affinities. (MS 1339: p.4-5) Peirce situates this schema in the Well of Truth, a metaphor that deserves our attention, for it is in this Well that the Sciences of Discovery, and hence scientific knowledge, will be built: [ …] Auguste Comte wrote that the sciences form a sort of ladder descending into the Well of truth, each one leading on to another, those which are more concrete and special drawing their principles from those which are more abstract and general. (CP 2.119) Every systematic philosopher must provide himself a classification of the sciences. Comte first proposed to arrange the sciences in a series of steps, each leading another. This general idea may be adopted, and we may adapt our phraseology to the image of the Well of truth with flights of stairs leading down into it (MS 1345, p.001, undated, NEM, vol III.2: 1122) The first step of the ladder into the Well is the mathematical step. The application of Comte's principle, revisited and iterated, leads to the conclusion that everything that happens in the Well of Truth depends on Mathematics and that without Mathematics, one cannot claim to be working inside the Well. The result is that any formal construction, any opinion, however authoritative, that does not justify a solidly established relationship with mathematics is outside the Well. In this way, a host of informal doctrines are produced, which can nevertheless be helpful insofar as it is possible to give them a mathematized form inside the Well. I realize this is not everyone's liking, especially those bricoleurs who think they've done mathematics because they've drawn a childish picture with universal categories. It should also be clear that the mathematics Peirce refers to cannot be limited to those of his own time. A century separates us from the mathematics of which Peirce was aware, a century of mathematical production available today on the first step of the Well. No one can refuse the use of new mathematical objects, especially if they are well connected with Peirce's intuitions because they lack the training to enable them to apprehend them themselves. What's worse is that, for the same reasons, a classification of the sciences that begins with phenomenology, free of any mathematical dependency, is most often presented. The reason I intervene at the heart of this rather literalist debate on interpretants is that I have seen the notion of "sufficiently penetrating mind" appear: [CSP] "The Normal Interpretant is the Genuine Interpretant, embracing all that the sign could reveal concerning the Object to a sufficiently penetrating mind..." This notion must be considered within the Peircean social conception of science; that some minds are more penetrating than others, in general, is conceivable. But rather than posing this question in terms of particular competencies unequally distributed among the members of a scientific community, perhaps we should first ask ourselves the question of the exactitude of the thinking of the question and give ourselves the means to do so: Every science has its mathematical part, in which certain results of the special science are assumed as mathematical hypotheses. But it is not merely in this way that logic is mathematical. It is mathematical in that way, and to a far greater extent than any other science; but besides that it takes the proceedings of mathematics in all their generality and founds upon them logical principles. All necessary reasoning is strictly speaking mathematical reasoning, that is to say, it is performed by observing something equivalent to a mathematical diagram; but mathematical reasoning par excellence consists in those peculiarly intricate kinds of reasoning which belong to the logic of relatives. The most peculiarly mathematical of these are reasonings about continuity of which geometrical topics, or topology, and the theory of functions offer examples. In my eighth lecture I shall hope to make clear my reasons for thinking that metaphysics will never make any real advance until it avails itself of mathematics of this kind. (EP 2: 36) And for that, you need to have the "mathematician's sword" in our hands: I have gained an unfortunate reputation as a writer upon the algebra of logic. It is generally understood that I hold logical algebra to be the main part of logic. But that is quite a mistake. I am in the world but not of the world of formal logic. A calculus, even in mathematics proper, is like the sword that our warriors by sea and land carry at their sides. Having it there at hand marks the mathematician as the sword marks his officer. (MS 1334, 1905) And what could be more penetrating than a sword? Regards, Robert Marty
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