List: EGs express Propositions that correspond to *instantaneous states* of Arguments, which are *entia rationis* for the sake of analysis, since the real "inferential process" of semeiosis is *continuous*. The transformation rules for EGs correspond to the leading principles of valid Arguments, and ultimately permit either deletion or insertion of an EG at each discrete step.
CSP: The following is a fundamental condition, (worthy of Italic dress,) of a perfect analysis of the legitimate transformations of Graphs: *Every undeduced permission to transform a Graph should be a permission under defined conditions either to delete an indecomposable Graph or to insert an indecomposable Graph in a defined place.* For such a transformation can evidently never be resolved into a series of simpler steps. But any other can, since a transformation of one complex Graph into another can be resolved into a series of transformations of simple Graphs, and since if it be permissible to transform one simple Graph, A, into another, B, it is permissible to transform A into AB, which is merely the copulate of A and B, and then to transform AB into B, thus resolving the transformation into an inclusion followed by a deletion. (R S30 [Copy T:3-4]; c. 1906) Notice Peirce's claim here that there are *indecomposable *EGs. He implied something similar about Propositions in the sentence that I omitted at the ellipsis in the very first long CSP quote in my initial post of this thread. CSP: As for a Proposition, it is represented in this System by a Graph; and the smallest significant bit of a Graph is still a Graph, that is to say, *the smallest constituent of a Proposition is a Proposition*. (R 295:117[102]; 1906, bold added) This appears to be in direct contradiction with another passage that I have quoted previously, which he wrote at about the same time. CSP: ... 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. (R 490:43-44, CP 4.583; 1906, bold added) Fortunately, Peirce went on to clarify what he meant by "an indecomposable Graph." CSP: But two remarks are called for by way of explanation of the adjective "indecomposable" in the above maxim. One is that *it is not meant that the meaning is unanalyzable*, but merely that the graph in question is not a Copulate of other Graphs. Indeed, I should have used the participle "undecomposed," if I had not thought that that might prove still more perplexing. The other remark relates to the application of the adjective to *continuous* Graphs, like the Blank and the Line of Identity, the essential property of which is that any portion of an Instance of such a Graph is itself an Instance of the same Graph ... From this it follows that the Graphs of Coëxistence (the Blank) and of Identity are "indecomposable," i.e. partless, in the sense of the maxim, although they and their Instances can be separated into parts of any multitude we like, whenever we like, and with such boundaries as we choose to impose. (R S30 [Copy T:4-5&8]; c. 1906, bold added) An EG is indecomposable--or rather, undecomposed--if it cannot be broken down into *simpler *EGs, even though its *meaning *as a Proposition can still be analyzed into subjects and predicate. The two *continuous *EGs (Blank and Line of Identity) are *always *indecomposable/undecomposed/partless in this sense, even though they and their Instances can still be analyzed into as many parts as necessary in order to make them sufficiently *determinate* for some purpose. A Seme (unattached Spot) is a non-propositional Sign that only exists as a *constituent of *Propositions (EGs), but it serves there as a substitute for its Object (cf. CP 4.538), which is a *concept*. CSP: 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." (R 490:44, CP 4.583; 1906) Every concept thus *corresponds to* a Proposition--one that affirms a *possibility*, rather than asserting an *actuality*. CSP: An abstraction is a creation of thought; but the real fact which is important in this connection is not that actual thinking has caused the predicate to be converted into a subject, but that this is *possible*. The abstraction, in any important sense, is not an actual thought but a general type to which thought may conform. This general type is not a creation of actual thinking, but is an inevitable result of sufficient thought. Now that is the sort of stuff that truth is made of. (NEM 3:918; 1904 Nov 21) The word that labels a Spot functions as a proper name, *indexically denoting *an abstract general concept as a *subject* of the Proposition that the EG expresses. The Spot itself has a certain number of Pegs, *iconically signifying *its valency as a *predicate* that the Proposition *attributes *to its other subjects--the indefinite individuals denoted by Lines of Identity--thereby making them *more determinate*. Those connections are *continuous* predicates, such as "possesses the character of" or "belongs to the class/collection of" for Spots with one Peg, and "stands in the relation of" for Spots with two or more Pegs. Regards, Jon S. On Fri, May 3, 2019 at 9:23 AM Jon Alan Schmidt <[email protected]> wrote: > List: > > Semes are creations of thought for the purpose of representing > Propositions, which are creations of thought for the purpose of describing > Arguments. By contrast, the *continuity* of the latter as the > "inferential process" of semeiosis--i.e., thought itself--is *real*. > > CSP: ... I conceive that a Continuum has, IN ITSELF, no definite parts, > although to endow it with definite parts of no matter what multitude, and > even parts of lesser dimensionality down to absolute simplicity, it is only > necessary that these should be marked off, and although even the operation > of thought suffices to impart an approach to definiteness of parts of any > multitude we please.* > *This indubitably proves that the possession of parts by a continuum is > not a real character of it. For the real is that whose being one way or > another does not depend upon how individual persons may imagine it to be. > It shows, too, that Continuity is of a Rational nature. But it conveys no > gleam of evidence that Continuity itself is Unreal ... (R S30 [Copy T:6-7]; > c. 1906) > > > The continuity of a line is fundamental, such that it cannot be *built up* of > points, or even of *definite *line segments. Likewise, the continuity of > semeiosis is fundamental, such that a Proposition cannot be *built up* of > Semes, and (especially) an Argument cannot be *built up* of definite > Propositions. Nevertheless, those parts can be "marked off" as needed or > desired, up to "any multitude that we please." But what about Peirce's > subsequent characterization of a continuum as something that is > *composed *of "material parts"? > > 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 places, > or all times, or all spatial realities, or are all spiritual realities, or > are all ideas, or are all characters, or are all relations, or 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; 1908) > > > Taking *W* as the real *semeiosic *continuum--the entire Universe as a > vast Argument (cf. CP 5.119, EP 2:193-194; 1903), which "is perfused with > signs, if it is not composed exclusively of signs" (CP 5.448n1p5, EP 2:394; > 1906)--Propositions certainly meet the first two requirements to be its > material parts, as well as the third since every *occurrence *of > a Proposition is a different *Instance *of it. As for the fourth, Peirce > affirmed elsewhere that "the mode of being of the composition of thought" > is "always of the nature of the attribution of a predicate to a subject" > (CP 6.341; 1908)--which is precisely the nature of a Proposition. > Returning to the quote above, he even went on to acknowledge the element of > *arbitrariness* in identifying any continuum's material parts. > > CSP: Almost everything which has material parts has different sets of > such parts, often various *ad libitum*. Nothing which has an Essence > (such as an essential purpose or use, like the jackknife of the celebrated > poser) has any material parts in the strict sense just defined. (R > 300:83-84[41-42], CP 6.174; 1908) > > > He then affirmed that those parts are either vague (i.e., indefinite) or > *entia > rationis* corresponding to some *state *of the whole when something > prevents the latter "from having any material parts in the strict sense." > > CSP: But the term "material parts" may, without confusion (if a little > care be exerted), be used in a somewhat looser sense. Namely, if the Being > (generally, a Concept) of an object, *T*, essentially involves something > *C* which prevents it from having any material parts in the strict sense, > and if there be something, *W*, which differs from *T* only in the > absence of *C* and of any other such hindrances, so that *W* has material > parts, then the material parts of *W* may loosely be termed material > parts of *T*; but in such case the concept of *W* so derived from *T* is > nearly or quite always somewhat vague, so that either the material parts > will be so too, or else they must be conceived as merely the parts of some > *state* of it, and very likely of an instantaneous state that is an *ens > rationis* closely approximating to the nature of a fiction. It will be > seen that the definition of Material Parts involves the concept of > *Connexion*, even if there be no other connexion between them than > co-being; and in case no other connexion be essential to the concept of > *W*, this latter is called a *Collection* … (R 300:84-85[42-43], CP > 6.174; 1908) > > > Still taking *W* as the real *semeiosic *continuum, a candidate for an > example of *T* is the System of Existential Graphs, with Propositions as > its material parts in the *loose *sense; i.e., the Graphs *themselves*, > since "Every graph expresses some proposition" (R 490:36; 1906). This > includes the Blank as the Graph of Coexistence--everything taken for > granted at the outset--along with any number of Graphs that are explicitly > scribed on the Sheet of Assertion. They can only ever be the parts of a > *hypothetical* "instantaneous state" of a *real* Argument for the purpose > of analysis--a *Collection *of Propositions connected *only *by co-being, > since leading principles correspond to the transformation rules governing > "Thought-motion" from one state to another. > > Regards, > > Jon S. > > On Wed, May 1, 2019 at 2:52 PM Jon Alan Schmidt <[email protected]> > wrote: > >> List: >> >> Nearly four months ago, I posted the following. >> >> JAS: I have been musing recently on the well-known remark by Peirce that >> "just as we say that a body is in motion, and not that motion is in a body, >> we ought to say that we are in thought, and not that thoughts are in us" >> (CP 5.289n1, EP 1:42n1; 1868). He also asserted in the same series of >> articles that "all thought is in signs" (CP 5.253, EP 1:24; 1868), so by >> substitution we ought to say that our individual (Quasi-)minds are in >> semiosis, and not that signs are in our individual (Quasi-)minds. As >> Peirce recognized, despite not having the benefit of Einstein's insights, >> Zeno's famous paradoxes are dissolved by understanding *continuous *motion >> through space-time as a more fundamental reality than *discrete *positions >> in space and/or moments in time. We arbitrarily *mark *the latter to >> facilitate measurement and calculation for particular purposes, but space >> is not *composed *of points and time is not *composed *of >> instants. Likewise, I suggest that semiosis is *continuous*, and we >> arbitrarily isolate *discrete *signs--or rather, Instances of Signs--to >> facilitate analysis for particular purposes. We can say that a Dynamic >> Object determines a Token of a Type to determine a Dynamic Interpretant in >> an individual (Quasi-)mind, treating this as an actual event "occurring >> just when and where it does" (CP 4.537; 1906). Nevertheless, the Type is >> not *composed *of its Tokens. >> >> >> In the wake of our various discussions since then, I believe that these >> comments still hold up quite well. In fact, I recently came across a >> passage in a discarded manuscript draft for the end of "Prolegomena to an >> Apology for Pragmaticism" (CP 4.572) that sheds further light on the matter. >> >> CSP: [I mentioned on an early page of this paper that this System leads >> to a different conception of the Proposition and Argument from] the >> traditional view that a Proposition is built up of Names, and an Argument >> of Propositions. It is true that of the four meanings of the term Argument >> (for the Middle Term, for the Copulation of Premisses, for the setting out >> of Premisses and Conclusion, and for the Logical operation of converting >> Premisses into Conclusion), the second and third justify the traditional >> account. But in the last sense, which alone is the essential one, an >> Argument is no more built up of Propositions than a motion is built up of >> positions. So to regard it is to neglect the very essence of it ... Just as >> it is strictly correct to say that nobody is ever in an exact Position >> (except instantaneously, and an Instant is a fiction, or *ens rationis*), >> but Positions are either vaguely described states of motion of small range, >> or else (what is the better view), are *entia rationis* (i.e. fictions >> recognized to be fictions, and thus no longer fictions) invented for the >> purposes of closer descriptions of states of motion; so likewise, Thought >> (I am not talking Psychology, but Logic, or the essence of Semeiotics) >> cannot, from the nature of it, be at rest, or be anything but inferential >> process; and propositions are either roughly described states of >> Thought-motion, or are artificial creations intended to render the >> description of Thought-motion possible; and Names are creations of a second >> order serving to render the representation of propositions possible. (R >> 295:117-118[102-103]; 1906) >> >> >> Semeiosis is a continuous "inferential process," analogous to *motion*; >> definite Propositions are "artificial creations" for the purpose of >> describing that Argument, analogous to *positions*; and Semes are >> "creations of a second order" for the purpose of representing those >> Propositions--perhaps analogous to coordinates? I suspect that Peirce had >> something similar in mind when he wrote another passage less than two years >> earlier, which I have quoted previously. >> >> 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. But this is hardly more than a phrase; for *creation >> *and *thought *have different meanings as applied to the two … That the >> abstract subject is an *ens rationis*, or creation of thought does not >> mean that it is a fiction. (NEM 3:917-918; 1904 Nov 21) >> >> >> An Argument can be *analyzed *into definite Propositions married by a >> logical leading principle, and a Proposition can be *analyzed *into >> abstracted subjects married by a prescinded predicate. However, >> these parts are all "creations of thought," *entia rationis*, Perceptual >> Judgments rather than Percepts themselves--which is presumably why "A >> proposition can be separated into a predicate and subjects in more ways >> than one" (NEM 3:885; 1908 Dec 5). >> >> Regards, >> >> Jon Alan Schmidt - Olathe, Kansas, USA >> Professional Engineer, Amateur Philosopher, Lutheran Layman >> www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt >> >
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