List: Recognizing continuous predicates and leading principles as "indecomposable elements" that marry Semes into Propositions and Propositions into Arguments, respectively, led me back to the original source of the marriage metaphor that I have been employing routinely in recent posts.
CSP: The process [of semeiosis] rather reminds one of the reproduction of a population,--sufficiently so, indeed, to furnish a convenient store of metaphors requisite for the expression of its relations ... There is a science of semeiotics whose results no more afford room for differences of opinion than do those of mathematics, and one of its theorems increases the aptness of that simile. It is that if any signs are connected, no matter how, the resulting system constitutes one sign; so that, most connections resulting from successive pairings, a sign frequently interprets a second in so far as this is "married" to a third. Thus, the conclusion of a syllogism is the interpretation of either premiss as married to the other; and of this sort are all the principal translation-processes of thought. (R 1476:36[5-1/2]; 1904) By simple substitution, I would add that the *predicate *of a *Proposition *is the interpretation of either *subject *as married to the other. Each subject *indexically denotes an Object* of the Proposition, which must already be known to an interpreting Quasi-mind from previous Collateral Experience (or, I should add, current Collateral Observation); while the continuous predicate *iconically signifies the Interpretant*, which is all that the Proposition *itself *can convey--sometimes strictly by means of *syntax *reflecting "the flow of causation," as in "Cain killed Abel" (cf. R 664:9-13; 1910 Nov 26-27). I have mentioned at least a couple of times on-List my curiosity about the *axioms *or *postulates *of the science of semeiotics, from which the *theorem *that Peirce asserted in the passage quoted above could be derived with the same kind of necessity as the results of mathematics. Presumably they would comprise a complete Speculative Grammar, together identifying "what *must be* the characters of all signs used by a 'scientific' intelligence, that is to say, by an intelligence capable of learning by experience" (CP 2.227; c. 1897). I now suggest that a "proof" of the theorem might look something like this. - Every Seme is one Sign, every Proposition is one Sign, and every Argument is one Sign. - Any system of connected Signs constitutes either a Seme, a Proposition, or an Argument. - Therefore, any system of connected Signs constitutes one Sign. I trust that the major premiss is uncontroversial, such that the soundness of this Argumentation hinges on the truth of the minor premiss. I consider it to be fully consistent with my hypothesis from a few weeks back that all Signs are *material parts* of a *perfect continuum*, in accordance with the definitions that Peirce provided in two different manuscripts from 1908, one of which was "The Bedrock Beneath Pragmaticism." CSP: Whatever is continuous has *material parts* ... The *material parts* of a thing or other object, *W*, that is composed of such parts, are whatever things are, firstly, each and every one of them, other than *W*; secondly, are all of some one internal nature (for example, ... are all external representations, etc.); thirdly, form together a collection of objects in which no one occurs twice over and, fourthly, are such that the Being of each of them together with the modes of connexion between all subcollections of them, constitute the being of *W*. (R 300:82-83[40-41], CP 6.174) CSP: ... my notion of the essential character of a perfect continuum is the absolute generality with which two rules hold good, first, that every part has parts; and second, that every sufficiently small part has the same mode of immediate connection with others as every other has. (CP 4.642; May 26) All "sufficiently small" Signs have not only the same "internal nature," but also the same "mode of immediate connection" between them--i.e., *logically indecomposable* *relations*; namely, continuous predicates and leading principles. As I summarized last week ... JAS: A mere collection of Semes is not a Proposition; rather, a Proposition "marries" those Semes (as its subjects) by means of a continuous predicate. The only thing that a Proposition *itself *can convey is this very *relation *among its subjects. Likewise, a mere collection of Propositions is not an Argument; rather, an Argument "marries" those Propositions (as its premisses) by means of a leading principle. The only thing that an Argument *itself *can convey is this very *relation *among its premisses, from which the conclusion follows. And as I stated a couple of days ago, a complex Seme can *also *be analyzed into simple Semes joined by a continuous predicate, often as a hypostatic abstraction of a Proposition. Going one step farther, rather than threatening to *destroy *Peirce's Semeiotic, this approach promises to *unify *it as the basis of a truly *scientific *Metaphysics--the result of accepting its principles "not merely as regulatively valid, but as truths of being" (CP 1.487; c. 1896). CSP: ... the explanation of the phenomenon lies in the fact that the entire universe--not merely the universe of existents, but all that wider universe, embracing the universe of existents as a part, the universe which we are all accustomed to refer to as "the truth"--that all this universe is perfused with signs, if it is not composed exclusively of signs. (CP 5.448n1p5, EP 2:394; 1906) The "universe of existents" consists of discrete Instances of the Signs that comprise "all that wider universe" as a *semeiosic* continuum--Tokens of Types, individual actualizations of real and inexhaustible *potential *Instances--which are determined by their *Dynamic *Objects to determine Quasi-minds to produce *Dynamic *Interpretants as Feelings, Exertions, and further Instances of Signs (cf. CP 4.536; 1906). Such effects *tend toward* each Sign's *Final *Interpretant, which is what it *would* produce in the Ultimate Opinion after infinite inquiry by an infinite community--the marriage of Semes into *facts*, and the marriage of all those Propositions into the vast Argument that is "the entire universe" *itself* (cf. CP 5.119, EP 2:193-194; 1903). CSP: What we call a "fact" is something having the structure of a proposition, but supposed to be an element of the very universe itself. The purpose of every sign is to express "fact," and by being joined with other signs, to approach as nearly as possible to determining an interpretant which would be the *perfect Truth*, the absolute Truth, and as such (at least, we may use this language) would be the very Universe. Aristotle gropes for a conception of perfection, or *entelechy*, which he never succeeds in making clear. We may adopt the word to mean the very fact, that is, the ideal sign which should be quite perfect, and so identical,--in such identity as a sign may have,--with the very matter denoted united with the very form signified by it. The entelechy of the Universe of being, then, the Universe *qua *fact, will be that Universe in its aspect as a sign, the "Truth" of being. The "Truth," the fact that is not abstracted but complete, is the ultimate interpretant of every sign. (EP 2:304; 1904) This is the *telos *of semeiosis, the *summum bonum* that is admirable in itself, the regulative hope that sustains all inquiry. Regards, Jon S. On Wed, Mar 27, 2019 at 9:26 PM Jon Alan Schmidt <[email protected]> wrote: > List: > > It occurs to me that a complex Seme can be analyzed into simple Semes > joined by a continuous predicate. For example, just as the copula "is" > corresponds to the latter in a categorical Proposition, the preposition > "of" plays that role in the Seme "the mortality of man," such that a more > explicit translation is "the character of mortality possessed by anything > belonging to the class of man." This amounts to a hypostatic abstraction > of the Proposition, "Anything belonging to the class of man possesses the > character of mortality." > > Moreover, while further exploring the images of R 284 (1905) in the > Digital Peirce Archive ( > https://rs.cms.hu-berlin.de/peircearchive/pages/home.php), I came across > these additional interesting remarks. > > 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. All other symmetrical relations are > compounded and involve asymmetric elements ... In existential graphs,--that > is, in the usual, "Beta," form of the system,--there are equally these two > modes of connection, the lines signifying identity and the absence of lines > coexistence. But, of course, no relations other than these can be > expressed except by giving relative significations to spots; and if a spot > signifies an asymmetric relation, it is necessary to distinguish connection > with one part of it as meaning something different from connection with > another side. Of course, if a great variety of colors or other qualities > of lines were recognized, although their two ends were alike, a > corresponding variety of asymmetric relations could be built up, since, for > example, a friend of a cousin is not necessarily a cousin of a friend. (R > 284:88,94-96[83,89-91]) > > > The standard interpretation of EGs treats a Line of Identity as an > indefinite subject to which discrete predicates may be attributed by > attaching Spots. Here Peirce instead described a Line of Identity as > *itself *a "mode of connection," presumably *between *subjects, > consistent with his later concept of a continuous predicate; specifically, > "is identical to." He then acknowledged that a Spot for "an asymmetric > relation" requires each of its connections (i.e., Pegs) to be distinguished > by its location, but also noted that "colors or other qualities of lines" > could serve a similar purpose. These comments suggest an alternative way > of scribing and interpreting EGs, as follows; see attached for updated > examples. > > - Represent each discrete dyadic or higher predicate with a Predicate > Spot ("stands") whose number of Pegs matches the number of subjects, > including the relation itself. > - Represent each monadic predicate, including the relation itself, > with a Subject Spot that is attached to a single Line of Connection. > - Use color and font to reflect the nature of the Dynamic Object of > each Subject Spot--red and bold for an Abstractive, green and italic for a > Concretive, blue and underlined for a Collective, or black and plain for a > Relation. > - Use the same color for the attached Line of Connection, which > represents the corresponding continuous predicate--"possesses the character > of" for an Abstractive, "is identical to" for a Concretive, "belongs to the > class of" for a Collective, or "(stands) in the relation of" for a > Relation. > - Arrange the Subject Spots around a Predicate Spot by attaching the > subject nominative on the left side, the relation itself above, the direct > object on the right side, and any others below (cf. R 670:8[7]; 1911 June > 9); i.e., read the Graph *clockwise* in accordance with the principle > that syntax ought to be consistent with "the flow of causation" (cf. R > 664:11-13; 1910 Nov 27). > - Translate each Peg of the Predicate Spot--except the one for the > relation itself--and each Point where a Line of Connection changes color, > branches, or crosses a Cut as an indefinite subject ("something"). > > I should add that I am by no means claiming that we *must *implement this > new approach, or even that anyone *ought *to do so; only that it is > *valid*, reflecting a different analysis of a Proposition--the one that > throws everything possible into the subject. As such, it appears to > confirm that a Seme can be a monad (one-Peg Subject Spot) and a continuous > predicate is at least a dyad (Line of Connection); but does it reveal > anything about the valency of a leading principle? In EGs, the latter > corresponds to a *transformation rule*, which brings to mind part of what > Gary F. quoted in the "Phaneroscopy and logic" thread earlier today. > > CSP: Suppose then a Triad to be in the Phaneron. It connects three > objects, *A*, *B*, *C*, however indefinite *A*, *B*, and *C* may be. > There must, then, be one of the three, at least, say *C*, which > establishes a relation between the other two, *A* and *B*. (EP 2:364; > 1905) > > > Can we say that *A* is the initial Graph, *B* is the subsequent Graph, > and *C* is the convention that permits the change from *A* to *B*? If > so, does this confirm that a leading principle is at least a triad? When I > wrote the post below, that felt like its most speculative and least secure > assertion, so I am open to being *shown *(not merely *told*) that I am on > the wrong track here. In fact, that goes for just about anything that I > propose on-List, including all of the above and below; "since in scientific > inquiry, as in other enterprises, the maxim holds, *Nothing hazard, > nothing gain*" (EP 2:410; 1907). > > Thanks, > > Jon S. > > On Mon, Mar 25, 2019 at 9:39 PM Jon Alan Schmidt <[email protected]> > wrote: > >> Gary F., List: >> >> I changed the thread topic so as not to derail what is supposed to be a >> discussion of Phaneroscopy into Semeiotic. >> >> The notion of an "indecomposable element" is obviously quite prominent in >> the quoted excerpt. CP 1.288-299 includes similar passages from three >> other manuscripts, which the CP editors dated c. 1908, c. 1894, and c. >> 1905--the last of which is from a *different *draft for "The Basis of >> Pragmaticism." I was curious to see what came next in that text, but was >> omitted from CP. While browsing through the Peirce Digital Archive images, >> I came across the following, which caught my eye instead. >> >> CSP: Among the preliminary questions the first (which is only rendered >> necessary on account of our study of medads, monads, dyads, etc.) will be, >> Can an indecomposable element of the phaneron be a medad? The answer must >> be, *no*. For a medad is a proposition, and a proposition essentially >> contains two elements, its subject and predicate. This is true even of the >> simple proposition 'It rains,' that is the environment is rainy. (R >> 284:42[39]; 1905) >> >> >> A Proposition is *not *an indecomposable element, because it can *always >> *be analyzed into a subject and predicate. Moreover, a "discrete" >> predicate is also *not* an indecomposable element, because it can *always >> *be analyzed into *another *subject and a *continuous *predicate. >> However, "a continuous predicate obviously cannot be a compound except of >> continuous predicates, and thus when we have carried analysis so far as to >> leave only a continuous predicate, we have carried it to its ultimate >> elements" (SS 72; 1908). >> >> Likewise, an Argument is *not *a indecomposable element, because it can >> *always >> *be analyzed into Propositions--premisses and conclusion--and a leading >> principle; but the latter, like a continuous predicate, *is *indecomposable. >> As I have acknowledged before, Francesco Bellucci called attention to this >> parallel in his 2018 book, *Peirce's Speculative Grammar: Logic as >> Semiotics*, crediting List founder Joseph Ransdell with being "The first >> to perceive the similarity between" them (p. 351 n. 30). >> >> FB: Just like a continuous predicate, a logical leading principle is >> proved valid through itself, and adding it as a further premise does not >> modify its primitive logical structure ... Leading principles and >> continuous predicates behave precisely the same with respect to logical >> analysis: they are "elementary" or "unanalyzable" logical forms that are >> found to enter intact into the parts into which we try to analyze them. (p. >> 333) >> >> >> What about the Signs that serve as the *subjects *in such an >> analysis--namely, Semes? Some are decomposable into *more basic* Semes, >> such as Peirce's example of "The mortality of man"; but I suggest that >> logical analysis can *never *decompose a Seme into any *other *kinds of >> parts. This is what I take to be the upshot of your observation below that >> a Seme is only a "first" *relative to* a Proposition or an Argument; >> i.e., it is the *simplest *class of Signs according to the relation to >> the Final Interpretant. When we have carried logical analysis of *any *Sign >> to its ultimate elements *in that respect*, we will find that we have >> only *Semes*, *continuous predicates* that marry those Semes in >> Propositions, and *leading principles* that marry those Propositions in >> Arguments. >> >> Now, consider each of these elements from the standpoint of *valency*. >> A Seme can be a monad, but a continuous predicate is *at least* a dyad >> joining two Semes as subjects in a Proposition, and a leading principle is >> *at >> least* a triad joining three Propositions as premisses and conclusion in >> an Argument. Consistent with Peirce's classification of the sciences, >> logical analysis (*logica utens*) thus confirms that this aspect of >> Speculative Grammar--the first branch of the Normative Science of logic >> (*logica >> docens*)--fully conforms to the principles provided by Phaneroscopy. >> >> Regards, >> >> Jon Alan Schmidt - Olathe, Kansas, USA >> Professional Engineer, Amateur Philosopher, Lutheran Layman >> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >> >> On Mon, Mar 25, 2019 at 9:55 AM <[email protected]> wrote: >> >>> List, >>> >>> First I’d like to thank Jon A.S. and Francesco Bellucci for their posts >>> in another thread which help to clear up a basic misconception about >>> Peirce’s application of his categories to his semiotic analysis. To further >>> my aim of getting “back to basics” in this thread, I’ll try to state one >>> key point in more general terms: >>> >>> Each of the ten trichotomies in Peirce’s late classification of signs >>> can be (and usually is) arranged in order of increasing complexity. Within >>> each trichotomy, the simplest sign type is “first” *in relation to the >>> other two*. Thus *Seme* is first in the trichotomy Seme/Pheme/Delome. >>> But that is the *only* sense in which “A Seme is a First” (as John S. >>> put it). Only one trichotomy of signs — Qualisign/Sinsign/Legisign (as >>> Peirce called them in 1903) — is made according to the “mode of being” or >>> ontological nature of the sign itself as possible/actual/necessary. All the >>> other trichotomies classify signs according to their various relations >>> to the other correlates within the basic triadic relation >>> Sign-Object-Interpretant. Within the Seme/Pheme/Delome trichotomy, which >>> (as Jon said) is made according to the sign’s relation to its interpretant, >>> the Seme is certainly *not* First in an ontological sense as claimed by >>> John S. >>> >>> This feature of Peirce’s trichotomic analyses should be borne in mind as >>> we look further into his development of the “valency” analogy. The next >>> Peirce text I’m selecting from here was “probably written in December 1905” >>> according to EP2, where it is Selection 26, “The Basis of Pragmaticism in >>> Phaneroscopy.” I have highlighted certain key terms by using *bold* >>> type; the *italics* are Peirce’s (i.e. they mark words he underlined in >>> the manuscript). >>> >>> [[ I propose to use the word *Phaneron* as a proper name to denote the >>> total content of any one consciousness (for any one is substantially any >>> other), the sum of all we have in mind in any way whatever, regardless of >>> its cognitive value. This is pretty vague: I intentionally leave it so. I >>> will only point out that I do *not* limit the reference to an >>> instantaneous state of consciousness; for the clause “in any way whatever” >>> takes in memory and all habitual cognition. The reader will probably wonder >>> why I did not content myself with some expression already in use. The >>> reason is that the absence of any contiguous associations with the new word >>> will render it sharper and clearer than any well-worn coin could be. >>> >>> I invite the reader to join me in a little survey of the Phaneron (which >>> will be sufficiently identical for him and for me) in order to discover >>> what different *forms of indecomposable elements* it contains. On >>> account of the general interest of this inquiry, I propose to push it >>> further than the question of pragmaticism requires; but I shall be forced >>> to compress my matter excessively. It will be a work of observation. But in >>> order that a work of observation should bring in any considerable harvest, >>> there must always be a *preparation of thought*, a consideration, as >>> definite as may be, of what it is possible that observation should >>> disclose. That is a principle familiar to every observer. Even if one is >>> destined to be quite surprised, the preparation will be of mighty aid. >>> >>> As such preparation for our survey, then, let us consider what forms of >>> indecomposable elements it is possible that we should find. The expression >>> “indecomposable element” sounds pleonastic; but it is not so, since I mean >>> by it something which *not only is elementary, since it seems so*, and >>> seeming is the only being a constituent of the Phaneron has, as such, but >>> is moreover *incapable of being separated by logical analysis into >>> parts*, whether they be substantial, essential, relative, or any other >>> kind of parts. Thus, a cow inattentively regarded may perhaps be an element >>> of the Phaneron; but whether it can be so or not, it is certain that it can >>> be analyzed logically into many parts of different kinds that are not in it >>> as a constituent of the Phaneron, since they were not in mind in the same >>> way as the cow was, nor in any way in which the cow, as an appearance in >>> the Phaneron, could be said to be formed of these parts. We are to consider >>> what *forms* are possible, rather than what *kinds* are possible, >>> because it is universally admitted, in all sorts of inquiries, that the >>> most important divisions are divisions according to form, and not according >>> to qualities of *matter*, in case division according to form is >>> possible at all. Indeed, this necessarily results from the very idea of the >>> distinction between *form* and *matter*. If we content ourselves with >>> the usual statement of this idea, the consequence is quite obvious. A doubt >>> may, however, arise whether any distinction of form is possible among >>> indecomposable elements. But since a possibility is proved as soon as a >>> single actual instance is found, it will suffice to remark that *although >>> the chemical atoms were until quite recently conceived to be, each of them, >>> quite indecomposable and homogeneous, yet they have for half a century been >>> known to differ from one another, not indeed in internal form, but in >>> external form.* Carbon, for example, is a tetrad, combining only in the >>> form [CH4] (marsh gas), that is, with four bonds with monads (such as >>> is H) or their equivalent; boron is a triad, forming by the action of >>> magnesium on boracic anhydride, [H3B], and never combining with any >>> other valency; glucinum [the old name for beryllium] is a dyad, forming >>> [GCl2], as the vapor-density of this salt, corroborated by many other >>> tests, conclusively shows, and it, too, always has the same valency; >>> lithium forms LiH and LiI and Li3N, and is invariably a monad: and >>> finally helion, neon, argon, krypton, and xenon are medads, not entering >>> into atomic combination at all. We conclude, then, that there is a fair >>> antecedent reason to suspect that the Phaneron's indecomposable elements >>> may likewise have analogous differences of external form. Should we find >>> this possibility to be actualized, it will, beyond all dispute, furnish us >>> with by far the most important of all divisions of such elements. ]] >>> >>> A *tetrad* (valency 4) is called so because it forms four bonds with >>> *monads*, i.e. with atoms that form only single bonds with anything >>> else. A *triad* (valency 3) forms three bonds with monads, and a *dyad* >>> (valency 2) forms two bonds with monads. Peirce is proposing that this >>> division of the chemical elements according to their *external form* >>> (i.e. their mode of combination with other atoms) can serve as a >>> hypothetical model for a division of indecomposable elements of the >>> phaneron. This is the preparation which (we hope) “will be of mighty aid” >>> for the *observation of the phaneron* which is the inductive stage of >>> the science of phaneroscopy. >>> >>> In practice, the key to such observation of the phaneron is the *control >>> of attention*. “Thus, a cow inattentively regarded may perhaps be an >>> element of the Phaneron,” but since it can be analyzed in many ways, it is >>> certainly not an *indecomposable* element. This shows that Peirce’s >>> phaneroscopic observation leads us directly into logical analysis — so >>> directly that, in my view, logical analysis is in practice *part* of >>> phaneroscopy. (There are other versions of *phenomenology* in which >>> such analysis is not so directly involved — which is why I have described >>> Peirce’s brand of phenomenology as more analytical than others.) If we ask >>> how logic, or logic as semeiotic, can *depend* on phaneroscopy as >>> Peirce says it does, the only way we can avoid circularity is to say that >>> *logica >>> docens* does depend on phaneroscopy, but the latter makes use of a *logica >>> utens* as part of its process. (Or, as has been suggested, we can give >>> other names to parts of the process; but personally I’d rather not >>> introduce even more terminology into an already jargon-filled discourse.) >>> >>> There are probably other questions raised by the excerpt above, or by my >>> commentary, so I’ll stop here for today to see if anyone wants to raise >>> them before we continue. >>> >>> Gary f. >>> >>
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