Gary F, List,
The texts to which you are drawing our attention are fascinating. Let me ask a question that we should be able answer in a yes or no way, even if we don't see all of the implications of the competing answers. In "Prolegomena to an Apology to for Pragmaticism," Peirce makes some comments about "The Bedrock beneath Pragmaticism." The remarks are found in the CP in footnote 1 to 4.553 (on page 443 of Vol. 4). He says: "It is chiefly for the sake of these convenient and familiar modes of representation of Petrosancta, that a modification of heraldic tinctures has been adopted. Vair and Potent here receive less decorative and pictorial Symbols. Fer and Plomb are selected to fill out the quaternion of metals on account of their monosyllabic names." When he refers to the "quaternion" of the metals, it is clear that he means to use the term in the first of the sense that he articulates in the Century Dictionary, which is something that belongs to a group of four. In making the point, would it also make sense to say that the representation of these modes in the gamma system can be interpreted in the third sense of the term as well, where we employ a mathematical system of numbers that are understood to be in four dimensions--one real and three imaginary? In a number of places, both in the earlier writings on the symbolic systems of logic and the later writings on the existential graphs, Peirce applies the mathematical system of the quaternions for sake of thinking about the values of the variables where the values are (1) continuous in their variation (and not merely binary T or F), and (2) related as part of a system having more than three dimensions. As such, I think that the answer may be "yes", that we might interpret the relations between the tinctures that are used to designate the boundaries around different sheets as related in manner that is analogous to a four dimensional system of quaternions. The reason I point this out is that it has a direct bearing on the way we might interpret the improvement offered on the gamma graphs where the relation between the recto and verso is taken to represent a relation between existential facts and possibilities of different kinds (depending on the tint of the outer boundary on the verso side)--where a cut in a page is conceived to go down through subsequent pages in a book that represents other kinds of possibilities depending upon the tint of the recto and verso of each of those pages. In the system of the quaternions, the relations between the dimensions is different in a number of respects from that which is represented in an algebra of multiple dimensions where all of the dimensions are understood in terms of rational or real systems of number. One of the big differences is that in the system of quaternions, the multiplication of values in two of three imaginary dimensions (say i and j) takes you directly to a value in the other dimension (say k). Why possible basis might I have for suggesting that Peirce may drawing on the Hamiltonian system of quaternions as a possible model for interpreting the relations between what is asserted on different pages have different tinctures? The straightforward reason is that Peirce is well aware that, in systems of number that are not complex (e.g., the integers, rationals or reals), there is no closure over the inverse operation of multiplying something by itself (i.e., raising it to a power). The inverse of this operation (e.g., taking the square root), requires the use of a system of complex numbers in order to have closure for the system. One of the things that the system of gamma graphs allows--which the alpha and beta systems do not--is the representation of the operation of hypostatic abstraction. In logical terms, this allows the introduction of objects that are formed on the basis of abstractions of predicates--such as with a lambda operator in logics of Church or a Hilbert operator in the systems of Hilbert. As such, I think that Peirce sees that a modal logic--such as he is exploring in the gamma graphs--may need something that has the formal properties of the quaternions as a basis for interpreting the possible values of the variables. That, at least, is the guess I'd like to explore. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: [email protected] <[email protected]> Sent: Monday, April 1, 2019 10:22:07 AM To: 'Peirce List' Subject: RE: [PEIRCE-L] Phaneroscopy and logic Jerry C, You’re right that my perspective on the role of chemistry in Peirce’s work has changed quite a lot since a decade ago — but then, so have many other ideas I had about Peirce then. I daresay my ideas even about the ‘basic framework’ of his philosophy are still changing as I read and re-read more of his work. I do think he meant the word “bedrock” in his title as a metaphor, but I also think that he found the object of that metaphor less “solid” than he hoped it would be when he started that 1908 essay, and that’s why he left it unfinished. To me, though, it’s no less interesting to follow his train of thought in these drafts than to follow it through his more finished and famous essays. I’d like to quote here one more text that offers a clue to Peirce’s feelings about organic chemistry at the time he wrote it (1906). It’s an excerpt from “PAP”, MS 293 (NEM 4:313-30), one of Peirce’s drafts for his “Prolegomena to an Apology for Pragmaticism.” [[ What, in a general way, does the Diagram of Existential Graphs represent the mode of structure of the Phaneron to be like? The question calls for a comparison, and in answering it a little flight of fancy will be in order. It represents the structure of the Phaneron to be quite like that of a chemical compound. In the imagined representation of the Phaneron (for we shall not, as yet, undertake actually to construct such a Graph), in place of the ordinary spots, which are Graphs not represented as compound, we shall have Instances of the absolutely Indecomposable Elements of the Phaneron (supposing it has any ultimate constituents, which, of course, remains to be seen, until we come to the question of their Matter; and as long as we are, as at present, discoursing only of their possible Forms, their being may be presumed), which [are] close enough analogues of the Atoms in the Chemical Graph of “Rational Formula.” Each Elementary Graph, like each chemical element, has its definite Valency,—the number of Pegs on the periphery of its Instance,—and the Lines of Identity (which never branch) will be quite analogous to the chemical bonds. This is resemblance enough. It is true that in Existential Graphs we have the Cuts, to which nothing in the chemical Graph corresponds. Not yet, at any rate. We are now just beginning to rend away the veil that has hitherto enshrouded the constitution of the proteid bodies; but whatever I may conjecture as to those vast supermolecules, some containing fifteen thousand molecules, whether it seems probable on chemical grounds, or not, that they contain groups of opposite polarity from the residues outside those groups, and whether or not similar polar submolecules appear within the complex inorganic acids, it is certainly too early to take those into account in helping the exposition of the constitution of the phaneron. Were such ideas as solid as they are, in fact, vaporous, they ought to be laid aside until we have first thoroughly learned all the lessons of that analogy between the constitution of the phaneron and that of chemical bodies which consists in both the one and the other being composed of elements of definite valency. ]] In our time, of course, “the veil that has hitherto enshrouded the constitution of the proteid bodies” has long gone, thanks to advances in microscopy, so that research into “the proteome” and the various functions of various proteins within the body seems to be overtaking genetic research at the cutting edge of the biological sciences. Peirce would have been very interested in this, I’m sure, but I’m equally sure it would not serve his phaneroscopic (or logical) purposes at all, any more than his phaneroscopy has any direct applications in such specialized sciences. To me, the importance of Peircean thinking today appears not so much in the laboratory as in the relations we live by every day, i.e. the subject matter of cenoscopy — for which, as he said, no special equipment is required, just a willingness to ask deep questions and try to work out answers to them. Gary f. From: Jerry LR Chandler <[email protected]> Sent: 31-Mar-19 22:40 Subject: Re: [PEIRCE-L] Phaneroscopy and logic GaryF., List: Thank you for your comments and perspectives. Your perspective on the role of chemistry in CSP writings has changed in the past decade, has it not? Next, a comment on a critical historical facet of chemistry. Inorganic chemistry developed from mining, smelting, coinage, weaponry, etc. Organic chemistry developed from food preservation, fermentation, dyestuffs and natural healing agents and the like. Relatively little cross-over between the two practices because of different ends and different methods. Conceptually, inorganic chemistry became the study of transformations by fire and heat, acids, bases and salts as electrical combinations of cations and anions that combined by pairings. Organic chemistry was defined in terms of Life and destruction of organics by heat and fire to form acids bases and salts. In both forms, the nature of chemical transformations was largely unfathomable. Mysterious. How this did “this” become “that”? This mystery remains in public mindset yet today, does it not? WRT the term, medad, it seems that CSP used the term in a grammatical sense in respect to the completeness of a sentence, in logical terms in the sense of completeness of propositions, in a chemical sense with regard to the inert gases and in a different chemical sense with regard to completeness or saturation of hypothetical valences. Context appears to determine the desired meaning. With regard to your sentences: In that post, was not trying to say anything about the chemical sciences as they exist today; and Peirce himself was not trying to inform his readers about chemical science when he adopted the “valency” analogy to construct a hypothesis about the elements of the phaneron. This thread is about phaneroscopy, and about Peirce’s development of that science. When I use the term “chemistry” in this thread, I am referring to the universe of discourse from which Peirce drew the concept of valency — which was, of course, the chemical science of his time. my only comment is to wish you luck for the following reasons. CSP’s knowledge of math, physics, chemistry, logic, philosophy and languages are intermingled and interbraided and interlaced and intermixed in such ways that I am skeptical that we will be able to untangle them. Was he justified in creating so many new words? Probably. But, without comparable knowledge of late 19 th Century math, physics, chemistry, logic, philosophy and languages, each reader searches for an interpretation that fits their individual philosophy. Will anyone ever recreate the linguistic space that he created and mined and extended and bastardized? At least that’s my opinion this evening because it is now clear that several related symbol systems and logics are needed to make manifest the exact representation of things as forms and/or as information about things. With regard to the Bedrock paper, why did CSP use this word, “bedrock”? Is it merely a metaphor? Or, is it an analogy for sensible connects between the terminology of organic chemistry and his notions of existential graphs? Clearly, it is not homologous usages of organic terms between then and now. I remain very grateful for your transcription of this paper because it substantially clarifies the underlying roles of chemistry in his logic WITHOUT necessitating any direct relationships or propositions or connections or functions or mappings. Cheers Jerry
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