I'm going to assume that some members of the Peirce list are still interested in reading what Peirce had to say about phenomenology, phaneroscopy, philosophy, logic as semeiotic, pragmaticism, maybe even metaphysics, and maybe even hoping to learn something new from it. Perhaps these subjects, to which Peirce devoted most of his time, are not “of true lasting importance,” but I must confess to finding Peirce’s work in these areas more interesting, more informative, and even more empirical than such esoterica as the thermodynamics of majority-logic decoding in information erasure.
I don’t have time right now to study closely Jon's suggestions regarding the "Logical Analysis of Signs," but i can't help noticing that his thread dovetails with this one in several ways. For instance, his most recent post deals with connectedness between signs at various levels of semiosis, considered as manifestations of continuity. This is related to the Peirce text I’m posting today, which again deals with the “valency” hypothesis in phaneroscopy, but makes an important distinction between that and the kind of valency we find in Existential Graphs. This text is from from “πλ” (MS 295), CP 1.292; according to the CP Bibliography and the Robin list, this is part of a draft of the “Prolegomena” published in the Monist for October 1906. (This text in CP 1.288-92 is dated “c. 1908,” but that is a mistake, probably a typo for “1906”.) [[ If, then, there be any formal division of elements of the phaneron, there must be a division according to valency; and we may expect medads, monads, dyads, triads, tetrads, etc. Some of these, however, can be antecedently excluded, as impossible; although it is important to remember that these divisions are not exactly like the corresponding divisions of Existential Graphs, which have relation only to explicit indefinites. In the present application, a medad must mean an indecomposable idea altogether severed logically from every other; a monad will mean an element which, except that it is thought as applying to some subject, has no other characters than those which are complete in it without any reference to anything else; a dyad will be an elementary idea of something that would possess such characters as it does possess relatively to something else but regardless of any third object of any category; a triad would be an elementary idea of something which should be such as it were relatively to two others in different ways, but regardless of any fourth; and so on. Some of these, I repeat, are plainly impossible. A medad would be a flash of mental “heat-lightning” absolutely instantaneous, thunderless, unremembered, and altogether without effect. It can further be said in advance, not, indeed, purely a priori but with the degree of apriority that is proper to logic, namely, as a necessary deduction from the fact that there are signs, that there must be an elementary triad. For were every element of the phaneron a monad or a dyad, without the relative of teridentity (which is, of course, a triad), it is evident that no triad could ever be built up. Now the relation of every sign to its object and interpretant is plainly a triad. A triad might be built up of pentads or of any higher perissad elements in many ways. But it can be proved — and really with extreme simplicity, though the statement of the general proof is confusing — that no element can have a higher valency than three. ]] In chemistry, a medad is an atom of valency zero, i.e. an “inert” element, one that does not combine with others to form new molecules. In Existential Graphs, a medad represents a rhema with no open blanks or unsaturated bonds or “loose ends”; thus a complete proposition is a medad because its predicate already has all the subjects its valency allows, with no openings for more. But in phaneroscopy, “a medad must mean an indecomposable idea altogether severed logically from every other” — and it is “impossible,” according to Peirce, for the phaneron to contain a medad, because it would have no relation to anything (not even to itself, being “instantaneous”). “A medad would be a flash of mental “heat-lightning” absolutely instantaneous, thunderless, unremembered, and altogether without effect.” In other words it would not “appear” “before the mind” at all, I suppose because appearing before the mind necessarily implies having some effect on it. Together with the “proven” fact that no element can have a higher valency than three, this leads to the a priori conclusion that the three indecomposable elements of the phaneron must correspond to chemical elements of valency one, two, and three, i.e. to monads, dyads and triads. It seems to follow that a Priman, or First, would be represented in Existential Graphs by a Spot with one Peg, which may have a line of identity attached to it, but only if the other end of that line is a loose end. For instance, a Priman such as the color of a stick of sealing wax could be represented by a Spot (labelled “red”) with a line of identity (meaning “something exists”) attached to its one Peg, so that the graph may be translated as “Something is red.” But this only goes to show that a monad in EGs is different from a monad in phaneroscopy. In the latter, a monad is a First, and “Firstness is that which is such as it is positively and regardless of anything else” (EP2:267). In its mode of being, it is a possibility. But the EG monad, asserting that something is red, represents more than a possibility; moreover, it has an evident duality, as there is some kind of Secondness or difference between the Spot and the line of identity. This, I take it, is why Peirce observes that “these [phaneroscopic] divisions are not exactly like the corresponding divisions of Existential Graphs.” The nature of this difference will be explored in the rest of this series. One other problem arises in Peirce’s paragraph above, concerning “the relative of teridentity (which is, of course, a triad).” My next post or two will have more to say about this, but for now I’d just like to point out that the graph of teridentity (i.e. three-way identity), which occurs when a line of identity branches, cannot represent the basic triadic sign relation, because the Sign, Object and Interpretant are not identical to one another. — Or are they, in some sense? Perhaps we should leave this question open, for now. Gary f.
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