Jon, list, Indeed our paths seem to be converging even more than I expected. You’ve covered some points here that I intended to make in my next post, and some others I hadn’t even thought of, but are fully consistent with the aspects of Peirce’s work that I’ve been exploring, as far as I can tell. I’ll need to study your post (and your posts in the other thread) in more detail, but instead of responding to this one point-by-point, I’m going to ‘cut to the chase’ and go straight to the Peirce text which announces the “major shift” I’ve been hinting at since the launch of this thread.
The text is R 490, described as follows in the Robin Catalogue: “CSP wrote on the cover of the notebook: "For the National Academy of Sci. 1906 April Meeting in Washington." Published, with omissions, as [CP] 4.573-584.” It’s the CP text I’ll be presenting here (I haven’t yet tried to find the MS to see what the omissions are). You (Jon) have seen this text before, in fact quoted from it a few months ago, so you may not be surprised by the comments I’ll insert between parts of it. The CP editors, with their usual disregard for chronological order, placed this text after the “Prolegomena to an Apology for Pragmaticism,” although it was obviously written before, and in fact must have been written shortly after the Welby letter dated March 9 of 1906 (http://www.gnusystems.ca/PeirceWelbyMarch1906.htm) which I quoted from in the previous post. I’ll try to show some of the connections with that letter in my comments between parts of the April text. [[ 573. In working with Existential Graphs, we use, or at any rate imagine that we use, a sheet of paper of different tints on its two sides. Let us say that the side we call the recto is cream white while the verso is usually of somewhat bluish grey, but may be of yellow or of a rose tint or of green. The recto is appropriated to the representation of existential, or actual, facts, or what we choose to make believe are such. The verso is appropriated to the representation of possibilities of different kinds according to its tint, but usually to that of subjective possibilities, or subjectively possible truths. The special kind of possibility here called subjective is that which consists in ignorance. If we do not know that there are not inhabitants of Mars, it is subjectively possible that there are such beings. … 574. The verso is usually appropriated to imparting information about subjective possibilities or what may be true for aught we know. To scribe a graph is to impart an item of information; and this item of information does one of two things. It either adds to what we know to exist or it cuts off something from our list of subjective possibilities. Hence, it must be that a graph scribed on the verso is thereby denied. ]] Peirce seems to be rethinking the very concept of logical negation here, looking at it as a kind of modality (subjective possibility) rather than deriving it from the structure of the scroll (representing the conditional de inesse) as he had in the Lowell lectures three years earlier. This line of thought follows up from the March letter to Welby, where he wrote near the end: [[ … now we come to the sole feature of the system which may be strongly suspected of being arbitrary. Namely, all the objects of graphs, or propositions, are of two classes. Every object is either asserted as an actuality, i.e., as an object of positive knowledge or it is merely suggested as a possibility, or as an object of ignorance i.e., an object of whose existence the proposition written leaves us ignorant. Let us write the objects of knowledge on the recto of the sheet and appropriate the verso to indications of objects of ignorance. ] SS 201] It seems clear enough to me that those “objects of ignorance” became the “subjective possibilities” of April 1906, but now the verso of the sheet of assertion has become more complicated because it is “appropriated to the representation of possibilities of different kinds according to its tint” (CP 4.573). I consider this the germ of the “tinctured” EGs that Peirce later presented in the “Prolegomena.” In April, though, only the verso comes in different colors, while the recto is reserved for assertions about things that do exist in the universe of discourse. Continuing with CP 4: [[ 575. Now the denial of a subjective possibility usually, if not always, involves the assertion of a truth of existence; and consequently what is put upon the verso must usually have a definite connection with a place on the recto. 576. In my former exposition of Existential Graphs, I said that there must be a department of the System which I called the Gamma part into which I was as yet able to gain mere glimpses, sufficient only to show me its reality, and to rouse my intense curiosity, without giving me any real insight into it. The conception of the System which I have just set forth is a very recent discovery. I have not had time as yet to trace out all its consequences. But it is already plain that, in at least three places, it lifts the veil from the Gamma part of the system. 577. The new discovery which sheds such a light is simply that, as the main part of the sheet represents existence or actuality, so the area within a cut, that is, the verso of the sheet, represents a kind of possibility. ]] This “new discovery” is at the heart of what I’ve been calling a “major shift” in Peirce’s thinking. However, now that the cat’s out of the bag, I’d better qualify that a bit, because Peirce may have been ‘April Fooling’ himself with his enthusiasm for this discovery. As he worked out the details of it over the next couple of years, his hopes that it would solve all the problems of the gamma graph system were not fulfilled (as Don Roberts points out in his book on EGs); and beyond that, his intention to base his “proof” of pragmaticism on the EGs was never realized. That doesn’t mean that Peirce’s new discovery was entirely fruitless; I think it led to some lasting changes in his approach to phaneroscopy, semeiotic and metaphysics. For now, though, I’ll focus on the April 1906 address itself. To continue: [[ 578. From thence I immediately infer several things that I did not understand before, as follows: First, the cut may be imagined to extend down to one or another depth into the paper, so that the overturning of the piece cut out may expose one stratum or another, these being distinguished by their tints; the different tints representing different kinds of possibility. This improvement gives substantially, as far as I can see, nearly the whole of that Gamma part which I have been endeavoring to discern. 579. Second, In a certain partly printed but unpublished “Syllabus of Logic,” which contains the only formal or full description of Existential Graphs that I have ever undertaken to give, I laid it down, as a rule, that no graph could be partly in one area and partly in another; and this I said simply because I could attach no interpretation to a graph which should cross a cut. As soon, however, as I discovered that the verso of the sheet represents a universe of possibility, I saw clearly that such a graph was not only interpretable, but that it fills the great lacuna in all my previous developments of the logic of relatives. For although I have always recognized that a possibility may be real, that it is sheer insanity to deny the reality of the possibility of my raising my arm, even if, when the time comes, I do not raise it; and although, in all my attempts to classify relations, I have invariably recognized, as one great class of relations, the class of references, as I have called them, where one correlate is an existent, and another is a mere possibility; yet whenever I have undertaken to develop the logic of relations, I have always left these references out of account, notwithstanding their manifest importance, simply because the algebras or other forms of diagrammatization which I employed did not seem to afford me any means of representing them. I need hardly say that the moment I discovered in the verso of the sheet of Existential Graphs a representation of a universe of possibility, I perceived that a reference would be represented by a graph which should cross a cut, thus subduing a vast field of thought to the governance and control of exact logic. ]] This is the place where Peirce changed his mind about the rule (stated in the “Syllabus”) that a line of identity could not cross a cut. I’m still not sure I ‘get’ what he means by a reference in this context, although phaneroscopically it seems to be a relation between a First and a Second which is not simply a dyadic relation. I think the later Peirce text (which you quoted) about symmetrical vs. asymmetrical dyadic relations is highly relevant here, but I’m not sure I can explain why, just yet. (Maybe you can.) Anyway, in the Prolegomena he reverted to the rule that a line of identity could not cross a cut (because of the different modalities of the areas on either side, but a ligature can cross a cut by joining two lines of identity that meet at a common point on the cut itself. I suppose this was one of the adjustments Peirce had to make as he worked out the details of his April revelation. My reason for calling it a “revelation” should become clear as I quote the last two paragraphs in Peirce’s text. (I am skipping over a long section which deals with some rather abstruse points of logic using EGs, but this section has been dealt with in great detail both by Don Roberts in his book on EGs and by Frederik Stjernfelt in Natural Propositions, and I have nothing further to say about it here.) [[ 583. The System of Existential Graphs recognizes but one mode of combination of ideas, that by which two indefinite propositions define, or rather partially define, each other on the recto and by which two general propositions mutually limit each other upon the verso; or, in a unitary formula, by which two indeterminate propositions mutually determine each other in a measure. I say in a measure, for it is impossible that any sign whether mental or external should be perfectly determinate. If it were possible such sign must remain absolutely unconnected with any other. It would quite obviously be such a sign of its entire universe, as Leibniz and others have described the omniscience of God to be, an intuitive representation amounting to an indecomposable feeling of the whole in all its details, from which those details would not be separable. For no reasoning, and consequently no abstraction, could connect itself with such a sign. This consideration, which is obviously correct, is a strong argument to show that what the system of existential graphs represents to be true of propositions and which must be true of them, since every proposition can be analytically expressed in existential graphs, equally holds good of concepts that are not propositional; and this argument is supported by the evident truth that no sign of a thing or kind of thing — the ideas of signs to which concepts belong — can arise except in a proposition; and no logical operation upon a proposition can result in anything but a proposition; so that non-propositional signs can only exist as constituents of propositions. But it is not true, as ordinarily represented, that a proposition can be built up of non-propositional signs. The truth is that concepts are nothing but indefinite problematic judgments. The concept of man necessarily involves the thought of the possible being of a man; and thus it is precisely the judgment, “There may be a man.” Since no perfectly determinate proposition is possible, there is one more reform that needs to be made in the system of existential graphs. Namely, the line of identity must be totally abolished, or rather must be understood quite differently. We must hereafter understand it to be potentially the graph of teridentity by which means there always will virtually be at least one loose end in every graph. In fact, it will not be truly a graph of teridentity but a graph of indefinitely multiple identity. 584. We here reach a point at which novel considerations about the constitution of knowledge and therefore of the constitution of nature burst in upon the mind with cataclysmal multitude and resistlessness. It is that synthesis of tychism and of pragmatism for which I long ago proposed the name, Synechism, to which one thus returns; but this time with stronger reasons than ever before. But I cannot, consistently with my own convictions, ask the Academy to listen to a discourse upon Metaphysics. ]] There is so much to say about CP 4.583 and its implications that I won’t even start here, as that would probably double the length of this post, at least. There are some other Peirce texts that throw light on it as well. But as for me, I’ve had enough for one day. Maybe you (Jon) or someone else will pick up the torch before I get back to it … I hope so! Gary f. From: Jon Alan Schmidt <[email protected]> Sent: 31-Mar-19 20:18 Gary F., List: I have been following this thread with considerable interest throughout, and am finally ready to offer a substantive contribution to it. I agree that the subject matter "dovetails" nicely with what I have been saying in the thread about "Logical Analysis of Signs." CSP: Corollaries. It follows that no line of identity can cross a cut. GF: The first “corollary” is important because Peirce will explicitly change his mind about it in the spring of 1906. Perhaps you will address this in your next installment, but I was not aware that Peirce ever changed his mind about this. My understanding is that when a Line of Identity appears to cross a Cut, it is really a Ligature--two different Lines of Identity that abut at the Cut itself, such that there are two indefinite individuals there, which are interpreted as not being identical. GF: Notice also that the extremity of a line of identity “denotes” an individual (in the strict logical sense of that word). But this is a somewhat peculiar use of “denote,” compared to its application to propositions, where the subject denotes the object of the propositional sign, and that subject is a symbol, typically a proper noun (a symbol crucially involving an index). Denotation is the function of an Index (cf. EP 2:307; 1904), so on the standard interpretation of EGs, each extremity of a Line of Identity is an Index of an indefinite individual ("something"). The Line of Identity as a whole, with no Spot at either end, is a Graph of the Proposition, "something is identical to something." GF: The upshot of this, if I understand it, is that a spot of teridentity may be regarded either as a rhema, which is a general concept, or as a denoted individual, which (by definition) is not general, but is identical to the three extremities of the graph of teridentity. I suggest that a Spot of Teridentity by itself is a Seme for the continuous predicate, "_____ is identical to _____ and to _____"; while a Graph of Teridentity--a Spot of Teridentity with three loose-ended Lines of Identity attached--represents the Proposition, "something is identical to something and to something." GF: The question then is whether this ambiguity of the term represents a vagueness built into the system of EGs or an indefiniteness which is a constituent of the phaneron itself — perhaps even a real vagueness. I suggest that this "ambiguity" simply reflects the fact that any analysis of a Proposition--which is what every EG represents--into subject(s) and predicate(s) is somewhat arbitrary, and this carries over to the interpretation of EGs. There are two different "ultimate" approaches--we can throw everything possible into the predicate, treating each Spot as a discrete predicate and each Line as an indefinite subject; or we can throw everything possible into the subject, treating each monadic Spot as a hypostatized subject, and each dyadic or higher Spot ("stands") and each Line as a continuous predicate. GF: You can’t have a predicate without a subject of which it is predicated; that subject must be an actuality or existent in the commens, and is identical to the object of the proposition; that object is denoted by the subject of the proposition while the predicate is signified by that proposition. I agree, which is why I continue to be puzzled by John Sowa's persistent attempts to do away with logical subjects altogether. Granted, modern predicate logic prefers to call them variables or identifiers, but there is nothing inaccurate about recognizing them as indefinite subjects instead. Of course, it is not necessary that each subject denote something that actually exists in the metaphysical sense; it just needs to "exist" within the Commens, the Universe of Discourse as represented by the Sheet of Assertion--i.e., it must be something already known to both Graphist and Interpreter. GF: More generally, we can recognize a First as an element of the phaneron only by prescinding it from the appearance of an existing thing, a Second which has that First as a quality. Yes--and then we can think and talk about a First as an element of the Phaneron only by (hypostatically) abstracting it, such that it can then be the Object of a Seme that serves as a subject of Propositions. GF: The semiotic corollary is that you can’t have a Sign without both an Object and an Interpretant as its correlates; you can’t have an Object (in the semiotic sense!) without a Sign which it determines and an Interpretant determined by the Object through the Sign; and you can’t have an Interpretant that doesn’t involve the Secondness between Sign and Object. Indeed, every actual Sign (Token) has both a Dynamic Object that determines it and a Dynamic Interpretant that it determines. My understanding is that none of these three correlates can be identical to either of the others, so a Graph of Teridentity with its three "spokes" is an inaccurate diagram of their relation. For one thing, identity is a symmetrical relation, as Peirce explicitly affirmed in a passage that I recently quoted in the other thread. CSP: It is, however, important to state that the relations of identity and of coexistence are but degenerate Secundan, and that these two are the only simple dyadic relations which are symmetrical, that is, which imply each its own converse. (R 284:88[83]; 1905) But he clearly held that the irreducible triadic relation in which a Sign mediates between its Object and its Interpretant is asymmetric. CSP: As a medium, the Sign is essentially in a triadic relation, to its Object which determines it, and to its Interpretant which it determines. In its relation to the Object, the Sign is passive; that is to say, its correspondence to the Object is brought about by an effect upon the Sign, the Object remaining unaffected. On the other hand, in its relation to the Interpretant the Sign is active, determining the Interpretant without being itself thereby affected. (EP 2:544n22; 1906) As such, it can only be properly scribed in EGs as a multi-Peg Spot--either "mediates" with three Pegs, or "stands" with four Pegs including one for "mediating" as a subject (see attached). This demonstrates conclusively that it is false, or at least misleading, to characterize the Sign itself as a triad; rather, it is the relation of mediating (or representing) that is a triad, since it always requires three correlates--e.g., the Sign, the Object, and the Interpretant. GF: Now, what are the phaneroscopic and/or metaphysical implications of considering every line of identity as “bristling with microscopic points of teridentity”? It brings to my mind these comments that Peirce made several decades earlier. CSP: A logical atom, then, like a point in space, would involve for its precise determination an endless process. We can only say, in a general way, that a term, however determinate, may be made more determinate still, but not that it can be made absolutely determinate. (CP 3.93; 1870) CSP: The absolute individual can not only not be realized in sense or thought, but cannot exist, properly speaking ... All, therefore, that we perceive or think, or that exists, is general. So far there is truth in the doctrine of scholastic realism ... That which exists is the object of a true conception. This conception may be made more determinate than any assignable conception; and therefore it is never so determinate that it is capable of no further determination. (CP 3.93n; 1870) Likewise, no matter how many Spots we attach to a Line of Identity by adding Points of Teridentity--i.e., no matter how many discrete predicates we attribute to whatever it denotes--it will always remain indeterminate in infinitely many other respects. In other words, even an individual is still general to some degree; hence, as you hinted below, we must prescind 2ns from 3ns before we can prescind 1ns from 2ns. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt <http://www.LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt <http://twitter.com/JonAlanSchmidt> On Sun, Mar 31, 2019 at 11:49 AM <[email protected] <mailto:[email protected]> > wrote: Gary R, list, The very concept of teridentity is intriguing, and plays a central role in the interface between phaneroscopy and Existential Graphs (and thus logic) that I am trying to explore — which also makes it central to the “major shift in Peirce’s thinking” which I see occurring in the spring of 1906. So I guess it’s time I devoted an entire post to the subject of teridentity. To get the drift of it, I think we need to regard phaneroscopy, ontology, and the conventions of Existential Graphs as three parallel universes of discourse such that an assertion in one necessarily has implications in the other two, and they frequently draw terms from one another to make those assertions. We begin with the Syllabus which accompanied the 1903 Lowell lectures: [[ Convention No. V. Every heavily marked point, whether isolated, the extremity of a heavy line, or at a furcation of a heavy line, shall denote a single individual, without in itself indicating what individual it is. A heavily marked line without any sort of interruption (though its extremity may coincide with a point otherwise marked) shall, under the name of a line of identity, be a graph, subject to all the conventions relating to graphs, and asserting precisely the identity of the individuals denoted by its extremities. Corollaries. It follows that no line of identity can cross a cut. Also, a point upon which three lines of identity abut is a graph expressing the relation of teridentity. ] CP 4.405-6 ] These definitions must be kept in mind as we proceed. The first “corollary” is important because Peirce will explicitly change his mind about it in the spring of 1906. Notice also that the extremity of a line of identity “denotes” an individual (in the strict logical sense of that word). But this is a somewhat peculiar use of “denote,” compared to its application to propositions, where the subject denotes the object of the propositional sign, and that subject is a symbol, typically a proper noun (a symbol crucially involving an index). In the EG system, the only means of denoting in that sense, i.e. ‘naming’ an individual, is a Selective, a letter placed at the extremity of a line of identity. As we know from the “Bedrock” manuscript, Peirce will by 1908 come to recognize this as a fundamental weakness of the whole EG system. Further on in the same document, we learn that a point of teridentity may also be a spot of teridentity: [[ 10. A spot is a graph any replica of which occupies a simple bounded portion of a surface, which portion has qualities distinguishing it from the replica of any other spot; and upon the boundary of the surface occupied by the spot are certain points, called the hooks of the spot, to each of which, if permitted, one extremity of one line of identity can be attached. Two lines of identity cannot be attached to the same hook; nor can both ends of the same line. 11. Any indefinitely small dot may be a spot replica called a spot of teridentity, and three lines of identity may be attached to such a spot. ] CP 4.416 ] In EGs, of course, a spot usually represents a logical rhema (or semiotic rheme) which has a valency, and is thus analogous to an element of the phaneron. The “boundary of the surface occupied by the spot” is purely imaginary and is not drawn on the graph-instance. It is visible in the graph only where a point on that boundary (a hook or peg) has a line of identity attached to it, and that point coincides with the extremity of the line, which also denotes an individual. The upshot of this, if I understand it, is that a spot of teridentity may be regarded either as a rhema, which is a general concept, or as a denoted individual, which (by definition) is not general, but is identical to the three extremities of the graph of teridentity. The question then is whether this ambiguity of the term represents a vagueness built into the system of EGs or an indefiniteness which is a constituent of the phaneron itself — perhaps even a real vagueness. I don’t know whether this investigation will arrive at an answer to (or an improved statement of) this question or not. The next stop on this guided tour is Peirce’s draft letter to Lady Welby dated March 9, 1906. I’ve placed this document on my website, http://www.gnusystems.ca/PeirceWelbyMarch1906.htm, and I would ask interested readers to view it with their browsers (rather than me trying to paste the many graphics into this email post) to see Peirce’s diagrams in their context, as many of my quotes from the letter will refer to one or more of those diagrams. You can of course keep your browser window open to facilitate moving back and forth between this post and the full version of the document. I might wish there were a better transcription of this document online, but I am not aware of its publication in any format other than the appendix of Semiotics and Significs, the source of my transcription. (A small part of it is given near the end of EP2, but that is not the part I will be focusing on.) Let me start with this remark that Peirce makes about the system of Existential Graphs: [[ If you take in all that I have said and what I am just about to say, you will begin to get an insight into the marvellous perfection and minute truth and profundity of this system. Logicians who analyze a proposition into “terms” and a “copula” are guilty of overlooking the truth I have just enunciated, that it is out of the nature of things for an object to be signified (and remember that the most solitary meditation is dialogue), otherwise than in relation to some actuality or existent in the commend. ] SS 197; I assume that “commend” is synonymous with commens and commind (a term he used earlier in the letter), which in EGs is represented by the Sheet of Assertion. ] If I may rephrase that: You can’t have a predicate without a subject of which it is predicated; that subject must be an actuality or existent in the commens, and is identical to the object of the proposition; that object is denoted by the subject of the proposition while the predicate is signified by that proposition. But that signified predicate can also be regarded as an “object,” because it can be an object of attention in phaneroscopy, namely a First, like the color of the sealing-wax in Peirce’s example that I posted earlier. The phaneroscopic point, I think, is that a color does not appear in the absence of something existent which actually has that color. More generally, we can recognize a First as an element of the phaneron only by prescinding it from the appearance of an existing thing, a Second which has that First as a quality. But also, recognition, or indeed any kind of cognition (or thought or sign), must also involve Thirdness. The semiotic corollary is that you can’t have a Sign without both an Object and an Interpretant as its correlates; you can’t have an Object (in the semiotic sense!) without a Sign which it determines and an Interpretant determined by the Object through the Sign; and you can’t have an Interpretant that doesn’t involve the Secondness between Sign and Object. In short, significance is a triadic relation — and this ‘feeds back’ into phaneroscopy because, as Peirce said in the quote I posted yesterday, it is “a necessary deduction from the fact that there are signs, that there must be an elementary triad.” I’m beginning to sense that this post is growing like Jack’s beanstalk, so I’ll end it with Peirce’s remarks about teridentity in the letter draft, and hope that readers can see how it is related to the above. [[ Introducing the graph of teridentity [diagram] … Quateridentity is obviously composed of two teridentities [diagram] but teridentity cannot be formed out of binidentity _________ where two lines merely make one longer line. Here let me point out what we mean in logic by equivalence and by composition. If one rheme, or verb, would be true in every conceivable case in which the other would be true, and conversely, then and only then those two verbs are logically equivalent. For logic has in view only the possible truth and falsity of signs. To say that a rheme is logically composed of two rhemes is to say that the first rheme is logically equivalent to the composite of the other two. It follows in the first place that every line of identity ought to be considered as bristling with microscopic points of teridentity; so that ___________ when magnified shall be seen to be ] SS 199 ] Now, what are the phaneroscopic and/or metaphysical implications of considering every line of identity as “bristling with microscopic points of teridentity”? If you’ve followed me this far, I’ll leave you with that question while I work on the next instalment. Gary f.
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