Jon (and list), I can’t honestly say that I find this post (or your follow-up to it) very useful for explicating the relationship between EGs and phaneroscopy — but I’ve had a few distractions in recent days and haven’t had time yet to prepare a better alternative. For one thing, I’m not finished reading the Atkins book, and since he’s obviously thought through these issues very thoroughly I don’t want to waste time reinventing the wheel until I have something better to propose. What I will do in this post is provide a link to the context of the quote you include from SS 198 (since this text is not widely available and has a lot to say on the topic). This 1906 letter to Welby is rather obscure, so I’ll put it out there before commenting on it: http://gnusystems.ca/PeirceWelbyMarch1906.htm
You also mention “The Bed-Rock beneath Pragmaticism” (R 300), which I’m currently reading in manuscript because there’s only one existing transcription that I know of (in Bisanz, The Logic of Interdisciplinarity) and I don’t have access to that. I haven’t started a transcription of my own yet, but I’m studying it as part of Peirce’s unpublished MSS attempting to follow up on the 1906 “Prolegomena to an Apology for Pragmaticism” in the Monist, all of which have a direct bearing on our subject line, and on Peirce’s “proof” of Pragmaticism. In his Introduction to EP2, Nathan Houser cites this group of MSS (although none of them is included in EP2): [[ Midway through his third Monist series, Peirce changed his mind and decided to base his proof on his Existential Graphs. He never completed his graph-based proof, but there are many manuscript pages indicating what he had in mind. In one draft (MS 298) Peirce explained: “You ‘catch on,’ I hope. I mean, you apprehend in what way the system of Existential Graphs is to furnish a test of the truth or falsity of Pragmaticism. Namely, a sufficient study of the Graphs should show what nature is truly common to all significations of concepts; whereupon a comparison will show whether that nature be or be not the very ilk that Pragmaticism (by the definition of it) avers that it is. . . .” That proof, as represented in preliminary form in Peirce’s 1906 “Prolegomena to an Apology for Pragmaticism” (CP 4.530–72) and in MSS 296– 300, is extremely complex. It depends heavily on establishing that the system of Existential Graphs provides a working model of thought and that experimenting with the Graphs amounts to experimenting with concepts themselves. … ] Peirce Edition Peirce Edition Project. The Essential Peirce: Selected Philosophical Writings (1893-1913) (p. xxxvi). Indiana University Press. Kindle Edition. ] I doubt that R 300 is as late as 1908; anyway it clearly belongs with the group Houser refers to. This gives me a lot of material to work through and I’m in no hurry to draw conclusions from it all, so it may be awhile before I have anything much worth posting under this head. But meanwhile, I’m interested in what you or other list members have to say on the subject — and especially I’d like to know if anyone has a transcription of “The Bed-Rock beneath Pragmaticism” (R 300) that they’d care to share. I don’t want to reinvent that wheel either. The Peirce letter to Welby that I mentioned at the top is rather long to include in a post, so here’s a link to the version on my website: http://gnusystems.ca/PeirceWelbyMarch1906.htm Gary f. From: Jon Alan Schmidt <[email protected]> Sent: 11-Feb-19 14:41 To: [email protected] Subject: Re: [PEIRCE-L] EGs and phaneroscopy Gary F., List: Your points are well-taken. As I have admitted in the past, I am by no means intimately familiar with EGs, but I have been trying to get more up to speed on them in light of recent discussions. I now finally have a better understanding of why John Sowa has been so persistent about advocating the standard modern analysis of propositions that throws everything into the predicate. Since that was Peirce's approach at the time when he invented EGs, it is what they reflect--Spots represent predicates, the number of Pegs represents their valency, and Lines of identity between them represent individual subjects (variables) to which they apply. Obviously this interpretation also makes perfect sense when using EGs to teach first-order predicate logic today, as John does. GF: Your proposal is to reverse what Peirce says in that last sentence, to read the Spots as Subjects and the Lines of Identity as (continuous) Predicates. Indeed; as I have pointed out repeatedly, in 1908 Peirce introduced the concept of the Continuous Predicate as what remains when everything else is instead thrown into the subject--specifically, everything that requires Collateral Experience on the part of the interpreting Quasi-mind in order to be understood. John's protestations notwithstanding, Peirce explicitly endorsed this approach as "the proper way in logic" (NEM 3:885), presumably because it carries the analysis "to its ultimate elements" (SS 72). Bellucci actually provides a quote from 1906 as the first hint in this direction, where Peirce briefly discussed the proposition, "Something is an animal." CSP: If l throw off from this the "Something is" still what remains is "Something is an animal," because the conception "Something is" is continuous. That is, it is the same as "Something is something that is," or "Something is Something that is Something that is," and so on ad infinitum. (SS 198) When we represent the same proposition in an EG, this is perfectly consistent with interpreting the Line of Identity as a continuum of Dots--i.e., potential individuals, an inexhaustible supply of "Somethings," all of which are identical in the relevant sense. CSP: The line of identity is not, however, arbitrarily conventional nor purely conventional. Consider any portion of it taken arbitrarily ... and it is an ordinary graph for which "---is identical with---" might perfectly well be substituted ... The line of identity is, moreover, in the highest degree iconic. For it appears as nothing but a continuum of dots, and the fact of the identity of a thing, seen under two aspects, consists merely in the continuity of being in passing from one apparition to another. (CP 4.448; c. 1903) I now suspect that Peirce's further insight in 1906 about this continuity of the Line of Identity, as well as that of the blank Sheet of Assertion, was what eventually led him to formulate the concept of the Continuous Predicate two years later. Consider this relevant statement in "The Bed-Rock Beneath Pragmaticism," which Robin dated 1905 and the Collected Papers dated 1906, but the Commens Bibliography <http://www.commens.org/bibliography/manuscript/peirce-charles-s-1908-bed-rock-beneath-pragmaticism-ms-r-300> now (tellingly) dates 1908, citing Christian Kloesel and Elize Bisanz. CSP: … every Subject must denote a single individual object, whether that individual be an electron, a man's body composed of a million cells, the sum total of mankind, past, present, and future, a single undetermined multitude (maniness), an ens rationis or creature of thought, such as a quality, a relation, or a word, or any object of a given description that the interpreter may choose, or of whatsoever other thing or idea or figment. (R 300:66[64]; 1908) I believe that this development may also be linked with Peirce's contemporaneous discussions of "three Universes of Experience" (CP 6.455, EP 2:435; 1908) and "three Universes, which are distinguished by three different Modalities of Being" (EP 2:478-479; 1908). My hypothesis is that just as the Categories of predicates are the irreducible elements that we discover in Phaneroscopy based on valency grounded in Mathematics, perhaps these Universes of Subjects are the irreducible elements that we discover in Metaphysics as "the results of the absolute acceptance of logical [i.e., semeiotic] principles not merely as regulatively valid, but as truths of being" (CP 1.487; c. 1896). If this is correct, or even just useful for some purpose (as I find it to be), then the question becomes whether and how we can reinterpret EGs accordingly--without changing their appearance, transformation rules, or natural language equivalents at all, since there is no doubt about the validity of the underlying logic. I suggest four specific adjustments. 1. Understand each Spot as representing a Subject, rather than a predicate; and each Line as representing a Continuous Predicate, rather than a continuous individual. 2. Call the latter a Line of Predication accordingly, rather than a Line of Identity; and conceive it as continuous through any Spot for a hypostatically abstracted relation, rather than interrupted by it. 3. Recognize each Subject Spot as having exactly one Peg, such that valency is represented by multiple branches of the Line of Predication, rather than multiple Pegs on a Spot. 4. Treat each Relation Spot accordingly as "shorthand" for multiple Spots--one for the Subject itself, and one for each Spot of Teridentity that is required to give the Line of Predication the correct valency; i.e., one for a dyadic relation, two for a triadic relation, etc.--such that the Subject Spot for the relation is attached to one of these branches, and each additional branch for triadic and higher relations is attached to one of the other Subject Spots. This avoids the more radical revision that I mentioned previously--explicitly scribing the additional Spots in order to show the entire continuous Line of Predication, which would then require any Cut enclosing a Relation Spot also to enclose all of its associated Spots of Teridentity, and might have other unintended consequences. Instead, we can still scribe (for example) "Cain---killing---Abel," but understand "Cain," "killing," and "Abel" as three Subjects; the Line of Predication as continuous through "killing"; and "killing" as a Spot of Teridentity with the resulting branch attached to the Subject Spot for that relation. GF: But that would amount to eliminating the difference between identity and relation. Identity is a relation--specifically, a degenerate dyadic relation. Other examples include "possessing a character" and "belonging to a class." Each of these could be expressed as "_____ is in the dyadic relation of _____ to _____," but that would be redundant, since they are already Continuous Predicates--which is why they are typically represented instead by a single Line of Identity between two Spots. The interesting thing that occurred to me while contemplating all of this yesterday is that according to the standard interpretation, one such Continuous Predicate is hidden within every Spot. Since anything scribed in an EG is existentially quantified (hence the name), "A---B" translates most literally to "something that is A is identical to something that is B." However, in this context, the predicates "is A" and "is B" can have different meanings, depending on the nature of the labels that replace A and B. For an adjective, "is A" means "possesses the character of A-ness"; for a proper name or other Index, "is B" means "is identical to B"; and for a common noun, "is C" means "belongs to the class of C's." If we now take two Spots connected by a Line as representing two Subjects connected by a Continuous Predicate, which of these alternatives expresses the latter? Again, the solution is recognizing the nature of the Subjects. Consistent with existential quantification, the first Subject--in English grammar, typically the "subject nominative"--must always be interpreted as a particular individual (some A), so the appropriate translation of the Continuous Predicate depends on how the second Subject is classified. Recalling Peirce's 1908 trichotomy for the Mode of Being of the Dynamic Object, that Subject will be Abstractive for a hypostatically abstracted quality, Concretive for a concrete existent, or Collective for a general class; and these obviously correspond to "possesses the character of," "is identical to," and "belongs to the class of," respectively. With this approach, the only situation in which a Continuous Predicate must remain concealed within a Spot is when the first Subject is a quality; e.g., round---red translates to "something that possesses the character of roundness possesses the character of redness." With this in mind, I suggest one more adjustment, the addition of a simple convention. 5. Designate a quality as the first Subject of a Continuous Predicate only when this is unavoidable; i.e., when all of its Subjects are qualities. Regards, Jon Alan Schmidt - Olathe, Kansas, USA
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