John, List: Just a brief response this time. No, really! :-)
JFS: Peirce's classification of the sciences is fundamental for both the Bedrock thread and for the proposition thread. I revised the attached cspscience.png, which can be used as a map of the Bedrock. The diagram shows *Sowa's *classification of the sciences, not Peirce's. In the latter, Semeiotic replaces Logic as the third branch of Normative Science, rather than being the sole branch of Phenomenology. JFS: The word 'context' is sufficiently vague to include what Peirce called collateral experience. The full 46 slides show the many thorny issues that create problems for any theory of context or collateral experience. Thanks for this, I will review it carefully since Collateral Experience is a major focus of my Peirce-related thinking these days. JFS: The subject could be indicated by pointing (index), by an indexical word such as 'that', by a name on a portrait, or by some mark or letter on a diagram. What should we call the class of Signs to which such an Index belongs, according to its relation to its Final Interpretant or the Nature of its Influence? Peirce's name for it was "Seme," and by definition it broadly encompasses *any *Sign that is not a Proposition (Pheme) or an Argument (Delome). That includes not only predicates and quasi-predicates, but also subjects--e.g., Lines of Identity in EGs and variables in modern predicate logic--as well as *anything else *that serves as a substitute for its Object. CSP: By a Seme, I shall mean anything which serves for any purpose as a substitute for an object of which it is, in some sense, a representative or Sign. The logical Term, which is a class-name, is a Seme (CP 4.538) JFS: In logic from Aristotle to the present, 'term' means predicate. Indeed, and as stated there by Peirce, every term (or predicate) is a Seme; but I understand that copula as signifying the continuous predicate of *belonging to a class*, rather than *identity*--so not every Seme is a term (or a predicate). After all, Peirce's ethics of terminology constrained him to introduce "Seme" *only *because he needed a *new *name that was "much widened" relative to "Term." Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Fri, Mar 8, 2019 at 1:15 PM John F Sowa <[email protected]> wrote: > Gary F, Gary R, and Jon AS, > > GF > > the text... in which Peirce explains the relationship between > > his Existential Graphs and his phenomenological “categories” > > or experiential Universes > > Peirce's classification of the sciences is fundamental for both > the Bedrock thread and for the proposition thread. I revised the > attached cspscience.png, which can be used as a map of the Bedrock. > For a copy of CP 1.180 to 202, see https://www.textlog.de/4257.html > > > CSP: Mathematics may be divided into a. the Mathematics of Logic; > > b. the Mathematics of Discrete Series; c. the Mathematics of > > Continua and Pseudo-continua. (CP 1.185) > > Mathematical logic, as a branch of pure mathematics, is independent > of phaneroscopy. It supplies diagrams for reasoning about everything, > including the phaneron. Normative logic, which is much more extensive > than mathematical logic, "must appeal to ethics for its principles. > It also depends upon phenomenology and upon mathematics" (CP 1.191). > > cspscience.png is slide #23 of a talk about contexts. The word > 'context' is sufficiently vague to include what Peirce called > collateral experience. The full 46 slides show the many thorny > issues that create problems for any theory of context or collateral > experience. For example, slides 11 to 21 discuss situation semantics, > a 20-year attempt to define contexts in terms of physical situations. > Slides 19 to 21 summarize a post-mortem study that shows why the > methods of situation semantics have been abandoned. Slide 45 > summarizes Peirce's approach to these issues. For all 46 slides, > see http://jfsowa.com/talks/contexts.pdf > > GF > > The three Universes correspond in logic to the modalities of > > the propositions represented by the Graphs. > > GR > > whether the Three Universal Categories are transmuted into Three > > Universes of Experience > > Nominalists claim that actuality is the only universe. For them, > possibility and necessity are just "ways of talking". Carnap, who > vehemently rejected metaphysics, followed Ernst Mach in claiming > that the laws of science are nothing but "summaries of observations". > > Most mathematicians are realists about math, and most scientists > are realists about the laws of science. Einstein, for example, > criticized Carnap's "Angst vor der Metaphysik", and he called Mach > "a good experimental physicist, but a miserable philosopher". > > Peirce's strong realism implies that all three universes are really > real. Possibility is 1ns, actuality is 2ns, and necessity is 3ns. > By itself, formal logic (pure mathematics) can determine what is > logically possible (all diagrams) and logically necessary (all > theorems that are provable about those diagrams). > > Phaneroscopy is the source of knowledge about actuality. Methodeutic > determines how anybody (not just scientists) can and should discover > what aspects of logical possibility can or must exist in actuality. > > The real possibilities include all diagrams that describe anything > that may be experienced in actuality or in imagination. Mathematics > can even state theories about things that humans can't imagine, such as > quantum mechanics, Cantor's infinities, and undecidable propositions. > > GF > > I say that Peirce abandoned the gamma graphs — which he had said > > in 1903 were far more important than the alpha and beta. > > He was dissatisfied with what he had written, but he did not abandon > the goals. He left some hints about "Delta graphs", but they're too > fragmentary to draw any conclusions about what aspects of Gamma he > would keep, reject, or modify. > > Furthermore, some prominent 20th c logicians were inspired by Peirce's > Gamma graphs to develop fruitful versions of modal logic. They include > C. I. Lewis, who specified the most widely used axioms for modal logic. > For a short survey, see http://jfsowa.com/pubs/5qelogic.pdf > For more, see http://jfsowa.com/pubs/worlds.pdf > > I should also emphasize that the major topic of Peirce's 1911 letter > was probability. The EG part is only 8 pages of a 53-page letter. > But it's important because he said that probabilistic logic is just > ordinary logic about probabilities. > > In 5qelogic.pdf, I recommend a version of modal logic that follows > the same guidelines: Modal logic should be treated as ordinary > logic about the laws that determine what is necessary or possible. > In fact, that might be what Peirce intended for Delta: ordinary > logic (just the version in eg1911.pdf) about laws and facts. > > GF > > Peirce does not deal with the cuts in the text I quoted, but > > he does in other parts of the “Bedrock,” in a way that spells > > trouble for the whole system of EGs. > > In 1911, he did not mention cuts, recto, or verso. Instead, he talked > about shaded or unshaded areas. To clarify the implications, I added > NEM 3:191 and some commentary to http://jfsowa.com/peirce/eg1911.pdf > > Page 191 contains Peirce's comments about stereoscopic moving images. > I suspect that Peirce himself was aware of that "trouble", and he was > looking for ways to extend EGs to a wider range of diagrams or images. > > GF > > This could also explain why Peirce abandoned the attempt to base > > his proof of pragmaticism on EGs. > > I doubt that he abandoned it. Instead of rejecting the Bedrock, > he may have been searching for an extension of EGs to more general > diagrams. For more about including visual images and even auditory > images in EGs, see slides 29 and 45 of contexts.pdf. > > JAS > > I believe the footnotes [to CP 4.538] to be incorrect. > > The CP editors were not infallible... > > Hartshorne and Weiss were sufficiently vague that those three > footnotes are correct and informative. For the triad of Term, > Proposition, Argument they cited Rheme, Dicisign, Argument. But > they did not claim that the two triads are identical. For Seme > and Pheme, they merely said "or Rheme" and "or Dicisign". > > JAS > > we can infer that [Peirce] must have had very specific reasons for > > introducing "Seme" and "Pheme," rather than sticking with "Rheme" > > and "Dicisign." I am by no means breaking new ground here; for > > example, Francesco Bellucci... > > FB supports what I have been saying. Compare his phrase "something > that has the structure of a proposition" to CP 2.250: "a Dicisign > or Dicent Sign (that is, a proposition or quasi-proposition)" . > > > FB: A "pheme" is not simply a dicisign. A dicisign is something > > that has the structure of a proposition, and that can be used to > > make an assertion. A pheme is, more generally, something that > > has the structure of a proposition and that can be used to perform > > several speech acts ... the grammatical notion of dicisign is > > further enlarged to that of pheme by including non-assertoric > > dicisigns. Given the taxonomic investigations I have documented > > above, this should come as no surprise. To signalize the further > > extension, Peirce re-names the locutionary trichotomy <rheme, > > dicisign, argument> into <seme, pheme, delome>. > > I agree with FB that speech acts other than assertion are significant. > Peirce also discussed icons, images, and percepts as source material > for the "widened" aspects of semes and phemes. Given Peirce's fondness > for the prefix 'quasi-', I doubt that he would ever reject it. > > As predicates, semes refer to indefinite possibilities. But a > proposition or pheme must include a subject that makes a definite > reference. The subject could be indicated by pointing (index), > by an indexical word such as 'that', by a name on a portrait, or > by some mark or letter on a diagram. > > JAS > > While the later notion of "Seme" is certainly not synonymous > > with "Index," it is not incompatible with it, either--a Seme > > can be Index, and it can also be an Icon or a Symbol. > > No. EP 2:274 (1903) said "Index or Seme", but the footnote to that > page said the 1906 definition was "a very different sense". The EP > editors are as trustworthy as H & W. One might disagree, but the > evidence from CP 4.538 ff supports them. > > > CSP: A familiar logical triplet is Term, Proposition, Argument... > > By a Seme, I shall mean anything which serves for any purpose as > > a substitute for an object of which it is, in some sense, a > > representative or Sign. The logical Term, which is a class-name, > > is a Seme (CP 4.538) > > In logic from Aristotle to the present, 'term' means predicate. > As Peirce noted, a class-name is a predicate. Examples include > elephant, flower, or -- to take one of Peirce's own examples -- > "lover of women with bright green complexions". > > All these examples could be used as a term in an Aristotelian > syllogism. When translated to an EG, each of them would be > a predicate (monad) with an unattached peg. To be a subject, > that peg would have to be attached to a line of identity. > > Thanks for quoting the following excerpt from a 16-page letter to > Professor E. H. Moore. When writing to a mathematician, Peirce was > careful to state every point precisely. > > > CSP: Experience is first forced upon us in the form of a flow of > > images. Thereupon thought makes certain assertions. It professes to > > pick the image into pieces and to detect in it certain characters. > > This is not literally true. The image has no parts, least of all > > predicates. Thus predication involves precisive abstraction. > > Precisive abstraction creates predicates. Subjectal abstraction > > creates subjects. Both predicates and subjects are creations of > > thought. (NEM 3:917-918; 1904) > > Yes, of course. Both predicate terms and subject terms are > predicates. But the logical predicates represent an indefinite > possibility, and the logical subjects have an index or line of > identity that designates a particular individual. > > Look at page 907 in the same letter: > > CSP: Such things are much more lucidly expressed in my > > old universal algebra of logic... every letter on the line > > expresses predicates whose individual subject or subjects are > > indicated by the subjacent indices. > > Those indices (AKA variables in other systems of logic) correspond > to lines of identity in EGs -- or to EG selectives, which may be > used to show ligatures without drawing lines that cross. > > Near the bottom of p. 907, Peirce wrote "using x to denote the > hypothesis that ..." That is an example of what he called > "subjectal abstraction" in p. 917. The "subjacent index" x is > the equivalent of a line of identity in EGs. The word 'hypothesis' > refers to a monad that was derived by converting the following > sentence to a monadic predicate. > > Other nominalizations in that letter are the noun 'collection', > which is derived from the verb 'collect', and his widely quoted > example of dormitive virtue (top of p. 917). Every such example, > creates a monadic predicate, which requires some index (of line > of identity) to make it a logical subject. > > In CP 4.539, compare the phrase "crystal clear" to the phrase > "much more lucidly expressed" in NEM 3:907. They show that Peirce > is thinking in math/logic. After saying "a percept is a Seme", > he adds "I must be understood as talking not psychology, but the > logic of mental operations." > > In summary, > > 1. In the first step, "Experience is first forced upon us in the > form of a flow of images... Precisive abstraction creates > predicates." (NEM 3.917) > > 2. In that step, the perceptual semes are converted to predicates > in some symbolic form, such as language or logic. > > 3. Subjectal abstraction is the next step of converting one predicate > to another: e.g. the dyad -collect- becomes the monad -collection. > > 4. But another step is needed to convert that monadic predicate to > a logical subject: attaching an index or a line of identity. > > 5. The ten pages of eg1911 are central to the Bedrock. The first > page (NEM 3:159) mentions "the shocking levity and looseness of talk" > that Peirce was trying to correct. Pages 2 to 9 present a revised > version of EGs that can accommodate diagrams in 3D or 3D plus time. > And page 10 adds "But I am convinced there is a far better [method], > capable of wonders... It consists in thinking in steroscopic moving > pictures. (NEM 3:191). See http://jfsowa.com/talks/ppe.pdf > > 6. Finally, the attached cspscience.png is a map that shows how all > these aspects of the Bedrock are related. > > John >
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