I had some problem with my email, and I'm using a different system that has terrible formatting. I attached a better copy of my previous note. John
Jon and Gary R, I had some work that kept me from spending time on email. But that delay gave me some time to put these issues into perspective. I realized that Jon is constantly looking for Peirce's "considered" answers. But Peirce didn't have final answers. He developed a scientific framework for asking questions, analyzing guesses, and refining hypotheses into theories. But no theory is final. Every answer generates more questions. There is no stopping point. Re classification of the sciences: I originally drew that diagram for some discussions in the Ontolog Forum email list. I wanted to show how Peirce's classification, which is still the best available, can relate the many theories of science, engineering, law, art, and everyday life. Since then, I discussed that diagram with several Peirce scholars. They made helpful suggestions, which led me to make some revisions. Three points: (1) It's my diagram, not Peirce's; (2) Every feature of that diagram is consistent with what Peirce wrote; (3) It does not make any assumptions that go beyond what he wrote. See http://jfsowa.com/peirce/cspscience.png Re Cosmology: Peirce learned mathematics, physics, and astronomy at his father's knee. Until he lost his position at USCGS and JHU, his knowledge of those fields was at the forefront of research, and that research is reflected in his cosmology. No one knows what he might have thought about quantum mechanics. It supports his Tychism, but it poses a challenge to his preference for Synechism. Re physical and metaphysical cosmology: In RLT p. 267, Peirce wrote "The subject of mathematical metaphysics, or cosmology, is not so very difficult, provided it be properly expanded and displayed." But there are infinitely many theories of math. With his blackboard metaphor in RLT, Peirce illustrated his views of continuity. But that metaphor is not consistent with quantum mechanics. For these reasons, I'm skeptical about using Synechism to support claims about cosmology. Peirce's logic and semeiotic are still at the forefront of research today. But his physics is obsolete, and so is any mathematical metaphysics that is inconsistent with QM. JAS > Logic as the third branch of Normative Science is "the science of > the general laws of signs"--i.e., Semeiotic--and depends on Ethics > (which depends on Esthetics), as well as Phenomenology and > Mathematics. Speculative Grammar, which I assume corresponds to > "Formal Semeiotic," is the first branch of Logic. No. CP has 119 occurrences of 'formal logic'. Peirce used the term for the mathematical notations by logicians from Boole to himself. He also used it for the logics from Aristotle to the Scholastics to Kant. Logic as a normative science is Peirce's update of the Greco- Roman Trivium: the Liberal Arts of Grammar, Logic, and Rhetoric. See CP 1.159, which defines logic as the second "of a trivium of conceivable sciences." He later called it Critic. In CP 1.185, he wrote "Mathematics may be divided into a. the Mathematics of Logic; b. the Mathematics of Discrete Series; c. the Mathematics of Continua and Pseudocontinua." But that is the only context where he used the term 'mathematics of logic'. However, CP has 16 occurrences of 'the logic of mathematics'. Most of them are in CP 1.417 to 1.519, which has the subtitle "An attempt to derive my categories from within." (c 1896), The last occurrence, CP 8.171, is in Peirce's 1903 Review of Bertrand Russell's book _Principles of Mathematics_. That shows Peirce considered Russell's version of formal logic to be an example of the logic of mathematics. For more, see his definition of 'formal' in the Century Dictionary: "1. According to form, rule, or established order; according to the rules of law or custom; systematic; regular; legal." He also defined 'formal logic' as "the theory of the relations of different forms of propositions and syllogisms." By adopting De Morgan's term 'formal logic', Peirce followed his own ethics of terminology. Since it is still the most common term in the 21st c, anyone who accepts Peirce's ethics would also have an obligation to use it. GR quoting JAS > Moving to another matter, [JAS] wrote regarding John Sowa's > diagram of Peirce's classification of the sciences: > > JAS: This is very disappointing -- despite all of the recent > on-List complaints about attributing 's views to someone apart from > verbatim quotations, the attachment still falsely claims that it > presents Peirce's classification of the sciences. As I pointed > out several months ago, it does not -- there is no passage > whatsoever where he employed the term "Formal Semeiotic," and > also no passage whatsoever where he situated any aspect of > Semeiotic under Phenomenology." No. Please note CP Vol 1, Book 3. Its title is "Phenomenology", and its major topic is the use of formal logic to derive the categories. That is the foundation for Peirce's semeiotic. The title of Book 4 is "The Normative Sciences". Summary of the issues: 1, I agree that phenomenology is a single subject, whose major product is the semeiotic categories (sometimes called phenomenological). See CP Vol 1, Book 3, 1.284-572. 2. In his classificatiion of the sciences, Peirce omits his most famous achievement: semeiotic. Since I believe that it should be mentioned in that diagram, I put one line under Phenomenology and added the label Formal Semeotic. 3, The single line and label show that phenomenology is a single subject, which consists of the use of formal logic to analyze and classify signs. But then I needed a label for it. There are several options: Semeiotic Categories, Phenomeological Categories, Semeiotic, or Formal Semeiotic. 4. Since Peirce's CD definition of the word 'formal' is also appropriate for the way he derived his semeiotic categories, that would suggest the label 'formal semeiotic'. That term would be defined as the method of derivation in Book 3. In Book 3, the logic he uses is his own formal logic, not the normative branch. For example, in CP 1.293, he wrote "A thorough study of the logic of relatives confirms the conclusions which I had reached before going far in that study. It shows that logical terms are either monads, dyads, or polyads," Therefore, the term 'formal semeiotic' is consistent with Peirce's definitions and practices, I'm not claiming that he used the term or that he would approve of my use. But I believe that it's pedagogically useful for helping students remember how the trichotomies ere derived. GR > [JAS makes] it clear enough that not only was the latter Peirce's > ... considered view that continuity, "the tendency to take habits," > 3ns, was first, that is, original before time was, so to speak... > > Then, in the last of the 1898 Lectures (RLT), ... Peirce > makes this explicit such that the 'sporting' of 1ns 'occurs' upon > a pre-cosmic blackboard, so to speak, representing a kind of > ur-continuity, that "principle of habit," a primordial continuity > which is the sine qua non of Peirce's early cosmology in my view. > > Finally, in his last, or at least penultimate, thinking on the > matter Peirce would write that the development of laws occurred > "... under a certain universal tendency toward habit-forming..." 1908 No. Everything Peirce wrote was his considered view at the moment. But his First Rule of Reason implies that anything considered as a final view would block the way of inquiry. His writings after 1910 show that his own views were still growing and evolving. 1914 was a stopping point, but it was not the completion. With a few more years and better access to contemporary science, he would have been actively debating with Einstein, Bohr, and others. Lecture 8 of RLT is a good illustration of the issues. In that lecture Peirce expressed his hopes for the future developments of cosmology. His own contributions were tentative, speculative, and vague. Some quotations: CSP from RLT, pp 261 to 263. > I object to having my metaphysical system as a whole called > Tychism... I like to call my theory Synechism, because it > rests on the study of continuity... Let the clean blackboard > be a sort of Diagram of the original vague potentiality, or > at any rate of its determination. (p 261) > > Where does this continuity come from? It is nothing but the > original continuity of the black board... Continuity, as > generality, is inherent in potentiality, which is essentially > general. (p 262) > > all this, be it remembered, is not of the order of the > existing universe, but is merely a Platonic world... (p 263) In Lecture 8 of RLT, Peirce said that he had more math to support his claims, but what he wrote is "sufficiently vague" to be acceptable. Quantum mechanics does not contradict everything he wrote about continuity, but it would make Tychism just as important, if not more important than Synechism. JAS > I have never claimed that Peirce denied CP 1.412. What I have > maintained is that we should interpret it in light of later > passages, which presumably reflect Peirce's more considered views. Unfortunately, nobody knows what Peirce was considering in his later years. When he visited Harvard to give lectures, he may have learned snippets of what was going on. His Neglected Argument of 1908 was "sufficiently vague" to be consistent with anything. But the lack of detail is a warning. He was acutely aware of major new developments about which he couldn't say anything definite. Conclusion: Peirce's work in progress Peirce adopted objective idealism from Schelling, and added some modifications of his own. But I believe that a version of logical idealism, as proposed by Helmut Pape, is closer in spirit to Peirce's logic and semeiotic. It's consistent with objective idealism, but it requires fewer assumptions, and it can be interpreted as a formal verion of Peirce's informal claim that everything is a sign. See https://www.academia.edu/371730/The_Logical_Structure_of_Idealism_CS_Peirces_Search_for_a_Logic_of_Mental_Processes Logical idealism supports a kind of monism with just one category of primordial entities: signs. Abstract entities, mathematical entities, mental entities, and physical entities are kinds of signs. The three universes of possibilities, actualities, and necessities consist of signs. Logic expresses the laws, facts, and relations among signs. Objective idealism makes the dubious assumption that mental entities have a privileged status in comparison to physical entities. But logical idealism implies that all signs are really real. It explains how mathematicians can claim that mathematical entitie are real, and it explains how Peirce could say that possibilities are real. Finally, Peirce's First Rule of Reason implies that all science is work in progress. And he took great pleasure in one critic's recognition of that point: CSP, CP 1.10 > Only once, as far as I remember, in all my lifetime have I > experienced the pleasure of praise -- not for what it might bring > but in itself. That pleasure was beatific; and the praise that > conferred it was meant for blame. It was that a critic said of me > that I did not seem to be absolutely sure of my own conclusions. John
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