List: After stating that "the only way of directly communicating an idea is by means of an icon" (R 787:23[27], CP 2.278), Peirce proceeds to describe algebraic formulae as "icons in which the likeness is aided by conventional rules" (23-24[27-28], 2.279-280). Near the end of the manuscript, he revisits the specific example of an assertion that he had discussed earlier and reformats it algebraically.
CSP: Now our word "is," the copula, is commonly expressed in Old Egyptian by a demonstrative pronoun. It is evident that this demonstrative has in such sentences the force of a relative. Where is the verb? We feel that it is contained in the general words. In short "man is mortal" is expressed in Old Egyptian in a form which expresses the following psychological process of thinking, "What is spoken of is man, which what is spoken of is mortal." This is precisely the way in which the same idea is conveyed in my general algebra of logic, where, putting *h* for man and *d* for mortal, I write Π*i hi* –< *di* This form equally serves for a universal categorical or a conditional proposition ... (42[46], 2.354) Here *h* and *d* are indices denoting the two abstract general subjects, *humanity* and *mortality*, although Peirce calls them "singular" because they are "directly indicated" (19[23], 2.339). The subscript *i* is also an index denoting a concrete individual subject, while Π is "the *universal quantifier*, which allows any object, no matter what, to be chosen" (20[24], 2.339) as this third subject. Finally, "the sign of inclusion" (43[47], 2.356) is a symbol serving as the "*copula*, or asserting verb" (25[29]); but it also has an iconic aspect that *communicates the idea* of inclusion, which "makes the relation of subject to predicate of a categorical proposition, *precisely the same* as the relation of antecedent to consequent of a conditional [or hypothetical] proposition" (RLT 130, 1898) such that they are "one in essence" as Peirce's title for the manuscript affirms. Now consider how the same example is expressed in an existential graph (see attached). In this case, the copula is not a *part* of the assertion; instead, it corresponds to the convention that *anything* scribed is thereby asserted, since the sheet itself is an icon of the continuum of all true propositions. The two labeled spots and one line of identity are the indices denoting the three subjects, but where is the icon that signifies the predicate? It is the *syntax*, because "in the syntax of every language there are logical icons of the kind that are aided by conventional rules" (R 787:24[28], CP 2.280). For EGs, this includes the scroll as an icon of the logical relation of implication, which asserts a conditional necessity rather than an actuality. As Peirce put it years later ... CSP: [T]his syntax is truly *diagrammatic*, that is to say that its parts are really related to one another in forms of relation analogous to those of the assertions they represent, and that consequently in studying this syntax we may be assured that we are studying the real relations of the parts of the assertions and reasonings; which is by no means the case with the syntax of speech. (NEM 3:164-165, 1911 Jun 22) Despite his last remark here, Peirce elsewhere recognizes that "the syntax of speech" *can* be diagrammatic; e.g., in an English sentence like "Cain killed Abel" where *all* the words are indices of subjects. Here the syntax alone signifies the predicate, serving as an icon of "the flow of causation." CSP: Take the Proposition "Cain killed Abel." This is identically the same Proposition as "Abel was killed by Cain": It is only the grammatical dress that is different. Other things being equal, everybody will prefer the former. Why? Because it is simpler; but why is it simpler? Because in putting the cause before the effect, it in that respect diagrammatizes the truth. (R 664:10-11, 1910 Nov 27) This is presumably why Peirce consistently maintains that every proposition has two parts, subjects (indices) and predicate (icon), but goes back and forth on whether to treat the copula (symbol) as a distinct third part. Regards, Jon S. On Wed, Jun 17, 2020 at 7:25 PM Jon Alan Schmidt <[email protected]> wrote: > List: > > According to Peirce in this manuscript, each *index* in an assertion > denotes one of its *subjects*, either by a word or by "a mere look or > gesture" (R 787:19[23], CP 2.338, c. 1895-6). How we distinguish those > subjects is somewhat arbitrary. > > CSP: Thus, in the assertion, "all men are mortal," we may say that the > subject is *every man*, or we may say that it is the *collection of men*, > or that *every man* and *some mortal* are the two subjects, or that > *everything* is the subject (the predicate being "is either not man or is > mortal"), or that *everything* and *humanity* and *mortality* are the > three subjects, or a hundred other dispositions. But if it is desired to > adopt one constant canonical form, the best rule will be to use a separate > index for everything which is indifferent from a logical point of view. > That is, in this case to take *everything*, *humanity*, and *mortality* > as the indices. (ibid) > > > What Peirce here calls "the best rule" is what he describes more than a > decade later as "the proper way in logic," which leaves "the *pure* > predicate a mere form of connection" (NEM 3:885, 1908 Dec 5). The basic > principle is "to throw into the subject everything that can be removed from > the predicate," and then "all that it remains for the predicate to > represent is the form of connection between the different subjects as > expressed in the propositional *form*" (SS 71, 1908 Dec 14). When we > have done this, "we have carried it [the analysis] to its ultimate > elements" (SS 72). > > Consequently, "all men are mortal" becomes "everything either does not > possess the character of humanity or possesses the character of > mortality." Removing the three indices leaves that which is *not* > "indifferent from a logical point of view"; namely, "_____ either does not > possess the character of _____ or possesses the character of _____." This > is the *icon* in the assertion that signifies its *predicate*. As Peirce > notes, "A proposition has properly but a single predicate; but this is > frequently compound" (R 787:24[28]). > > Finally, the *symbol* in the assertion is whatever "gives the listener > reason to believe that the speaker endeavors to represent that he feels the > compulsion" (ibid). Traditionally it is the *copula*, but after analysis > it consists of the words that represent the pure (or continuous) > predicates--"either _____ is true or _____ is true," and "_____ possesses > the character of _____." Peirce eventually calls such signs "copulatives" > or "*Copulants*, which neither describe nor denote their Objects, but > merely express universally the logical sequence of these latter upon > something otherwise referred to" (EP 2:484, 1908 Dec 25). > > CSP: The *Copulants* are likewise indispensable and have the property of > being *Continuant*. What I mean is that the sign "*A* is red" can be > decomposed so as to separate "is red" into a Copulative and a Descriptive, > thus: "*A* possesses the character of redness." But if we attempt to > analyze "possesses the character" in like manner, we get "*A* possesses > the character of the possession of the character of Redness"; and so on *ad > infinitum*. So it is, with "*A* implies *B*," "*A* implies its > implication of *B*," etc. So with "It rains and hails," "It rains > concurrently with hailing," "It rains concurrently with the concurrence of > hailing," and so forth. I call all such signs Continuants. They are all > Copulants and are the only *pure* Copulants. These signs *cannot be > explicated*: they must convey Familiar universal elementary relations of > logic. We do not derive these notions from observation, nor by any sense of > being opposed, but from our own reason. (EP 2:485) > > > Put another way, the subjects of an assertion are "whatever there is of > which sufficient knowledge cannot be conveyed in the proposition itself, > but collateral experience on the part of its interpreter is requisite" (NEM > 3:885). However, we cannot observe or experience "universal elementary > relations of logic," so we cannot *indicate* them to someone else. > Instead, "the only way of directly communicating" them "is by means of an > icon" (R 787:23[27], CP 2.278). > > Regards, > > Jon S. > > On Sat, Jun 13, 2020 at 10:02 PM Jon Alan Schmidt < > [email protected]> wrote: > >> List: >> >> Since a couple of you have expressed interest, attached is my complete >> transcription of R 787 >> <https://rs.cms.hu-berlin.de/peircearchive/pages/search.php?search=%21collection846> >> (c. 1895-6), along with the two pages of RS 787(s). The latter are marked >> as 6 and 7 in the upper-right corner, and there are no pages marked 8 and >> 9, but it could be that they were simply discarded; page 7 concludes with >> the end of one paragraph and page 10 starts with the beginning of another, >> which plausibly could have come next. I have indicated all the page breaks >> in the manuscript and the paragraph breaks in CP where applicable. >> >> Pages 1-4 are about the nature of mathematics and echo other writings by >> Peirce on that topic from the 1890s. Pages 5-7 include the paragraph about >> "scientific intelligence" that Gary F. recently quoted >> <https://list.iupui.edu/sympa/arc/peirce-l/2020-05/msg00160.html> and >> suggest a rudimentary classification of the sciences--listing only >> mathematics, logic, metaphysics, and the special sciences. Pages 10-17 >> focus on logic, generalizing it to encompass both speculative grammar and >> speculative rhetoric. Pages 18-29, including CP 2.332-229 and 2.278-280, >> provide a detailed analysis of assertions. Pages 29-35, including CP >> 1.564-567 and 2.340-341, seek to correct some errors that Peirce >> acknowledges in his previous treatments of signs, especially "On a List of >> New Categories" (1867). Finally, pages 36-49, including CP 2.342-356, at >> last address the subject stated in the title, "That Categorical and >> Hypothetical Propositions are one in essence." >> >> There are a number of interesting passages that we could discuss, but for >> now I will stick to the thread topic as originally prompted by Robert's >> quote from CP 2.278. Again, the context of that sentence is a detailed >> analysis of assertions, and Peirce sets the stage as follows. >> >> CSP: The assertion consists in the furnishing of evidence by the speaker >> to the listener that the speaker believes something, that is, finds a >> certain idea to be definitively compulsory on a certain occasion. There >> ought therefore to be three parts in every assertion, a sign of the >> occasion of the compulsion, a sign of the enforced idea, and a sign >> evidential of the compulsion affecting the speaker in so far as he >> identifies himself with the scientific intelligence. (R >> 787:15-16[19-20], CP 2.335) >> >> >> The text proceeds over the next ten pages to identify these three parts >> respectively as indices denoting the subjects, an icon signifying the >> predicate--which is the kind of idea that can *only* be communicated by >> means of an icon--and a symbol (such as the copula) serving as the >> "asserting verb" (25[29]). Along the way, Peirce anticipates some key >> logical developments in his later writings--most notably (for me), throwing >> everything possible into the subject, leaving only pure or continuous >> predicates, sometimes (as in existential graphs) conveyed strictly by the >> syntax. More to come on all that. >> >> 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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