John, List: Unfortunately, your post revealed another double standard.
JFS: What I'm about to say may sound like nitpicking, but Peirce was the supreme artist of nitpicking ... Since Peirce is no longer with us, somebody has to pick the nits. No, since Peirce is no longer with us, *no one* can presume to speak *for him*; at least, that is what you have been persistently maintaining. JFS: If a 21st c. logician said that to Peirce, he would instantly agree and say that the modern term 'atom' represents what he called an indivisible EG. He would then show how his EGs map to and from modern notations (predicate calculus and the many variations implemented in digital computers). In accordance with your own ground rules for others, please do not put words in Peirce's mouth unless they constitute a verbatim quotation. You have no authority to state *definitively *what he would say in this hypothetical conversation; it is pure conjecture on your part, and should be clearly presented as such. JAS: As helpfully diagrammed by Existential Graphs, every assertion is the attribution of general concepts (Spots) by means of continuous predicates (Pegs) to indefinite individuals (Lines of Identity). JFS: Peirce would not agree with Jon's sentence above. There you go again. JFS: His first objection would be that 'assertion' is not a synonym for 'proposition'. A proposition is an ens rationis, but an assertion is a "speech act" (to use Austin's term) that adds a claim that the proposition happens to be true. Every EG *asserts *a proposition, claiming it to be true in the Universe of Discourse, and thus is accurately characterized as an *assertion*. That is why Peirce called the surface on which EGs are scribed the "Sheet of Assertion," not the "Sheet of Proposition." JFS: The words 'spot' and 'line' were Cayley's choices for naming the two kinds of parts in a graph. But graph theory was invented and reinvented many times by mathematicians working in different branches ... Nobody today uses the word 'spot'. I do, and I suspect that there are other Peirce scholars who do. You are welcome to use more "modern" terms if you like, but there should be no danger of misunderstanding once "Spot" and "Line" (and "Peg") are defined in this context--which is often necessary when utilizing verbatim quotations from Peirce's own explanations of EGs, your preferred 1911 version being a relatively rare exception. In fact, he still used "Spot" in R 670, written only days earlier. JFS: The phrase "appropriated to denote" is unclear, but the translation to the algebraic form shows exactly what Peirce intended. That phrase is not unclear at all--each Line that is attached to a Spot by means of a Peg *denotes *an indefinite individual, which is one of the *subjects *of the proposition that the EG expresses. JFS: He never said nor implied that a peg is a continuous predicate. Indeed, and I have never claimed that he did; rather, it is *my own* interpretation of EGs in accordance with Peirce's late 1908 analysis of propositions that throws everything possible into the *subject*. That includes not only each Line (indefinite individual), but also each Spot (general concept), leaving *only *the Pegs as the *continuous predicates* that marry them--"possessing the character," "standing in the relation," etc. JFS: The sentence "A cat is on a mat" is indefinite about the referents of the two subjects, but neither Peirce nor any modern logician would say that it's vague. The context was denoting an indefinite/vague *individual *(subject) with a Line of Identity, not characterizing an entire *sentence *(proposition) as indefinite/vague. Lane's (and Peirce's) point is that "a cat" is indefinite/vague, such that the principle of contradiction does not apply, because both "a cat is black" and "a cat is not-black" might be (and, in fact, are) *true*; likewise for "a mat." I discussed this on the List in my post <https://list.iupui.edu/sympa/arc/peirce-l/2019-06/msg00012.html> last month about "Modes of Being and Modes of Meaning," extensively quoting R 641-642 (1909 Nov 3-28), where Peirce consistently used "indefinite" rather than "vague." JFS: For more examples and discussion, see "What is the source of fuzziness?" Again, as Lane observes, Peirce's "idea of vagueness is quite different from the contemporary one" (p. 139); in particular, "by 'vague' he did not mean exactly what is exemplified by terms having borderline cases or 'fuzzy' boundaries" (p. 10). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Professional Engineer, Amateur Philosopher, Lutheran Layman www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sun, Jul 21, 2019 at 4:19 PM John F Sowa <[email protected]> wrote: > Gary R and Jon, > > I agree that Jon has done a lot of good work in analyzing > Lane's book and digging through Peirce's MSS to relate RL > and CSP. I appreciate his work, and I thank him for it. > > But the way Jon is using Peirce's logic is not the way Peirce > defined it. What I'm about to say may sound like nitpicking, > but Peirce was the supreme artist of nitpicking. He insisted > that his logic be used with absolute precision. Since Peirce > is no longer with us, somebody has to pick the nits. > > We should also respect Peirce's ethics of terminology. For a > 21st c. audience, his ethics would require us to use whatever > terminology has become standard in the 21st c. When I pick nits > or suggest changes in terminology, I have several goals: > > 1. Be constructive: help clarify the discussions in a way > that is as accessible as possible for a 21st c. reader. > > 2. Be faithful to Peirce: prefer verbatim selections from > his writings and state precise equivalences for any of his > terminology that should be updated for a modern audience. > > 3. For teaching students and to clarify ambiguities for anybody, > every logical point should be stated in two ways: (1) EGs > and (2) Peirce-Peano algebra. > > Point #3 is required by Peirce's ethics of terminology. I agree > with Peirce that EGs are "the logic of the future". But a good > teacher always begins with something familiar to the students > before leading them to any recommended improvements. And the > overwhelming majority of people who have taken any course in > logic have been taught Peirce-Peano algebra, but not EGs. > > I won't go through the details of Jon's note of July 13 (most > of which I agree with or sympathize with). But I believe it's > necessary to pick the nits of the following quotation: > > > CSP: Truth belongs exclusively to propositions. A proposition has > > a subject (or set of subjects) and a predicate. The subject is a > > sign; the predicate is a sign; and the proposition is a sign that > > the predicate is a sign of that of which the subject is a sign. > > If it be so, it is true. (CP 5.553, EP 2:379; 1906) > > > > JAS: As helpfully diagrammed by Existential Graphs, every assertion > > is the attribution of general concepts (Spots) by means of > > continuous predicates (Pegs) to indefinite individuals (Lines > > of Identity). > > First point: All modern logicians and their students would agree > with Peirce's first sentence above. But they would say that the > second sentence is a special case of an atom, and they would add > that a general proposition links one or more atoms with Boolean > operators (AND, OR, NOT, IF...) and uses proper names or quantified > variables to represent the subjects. > > If a 21st c. logician said that to Peirce, he would instantly > agree and say that the modern term 'atom' represents what he > called an indivisible EG. He would then show how his EGs map > to and from modern notations (predicate calculus and the many > variations implemented in digital computers). > > Next point: Peirce would not agree with Jon's sentence above. > His first objection would be that 'assertion' is not a synonym > for 'proposition'. A proposition is an ens rationis, but an > assertion is a "speech act" (to use Austin's term) that adds > a claim that the proposition happens to be true. > > For Peirce, a proposition is a type in the trichotomy of > mark/token/type. The same type may be expressed in an open- > ended variety of tokens in different versions of natural languages > and formal logics. And different tokens may be expressed in an > open-ended variety of spoken, written, printed, or signed ways. > > And any token may be used in an open-ended variety of speech > acts: asserting, judging, mentioning, discussing, claiming, > doubting, hoping, fearing, wishing, lying, persuading... > > Another extremely important point is that any proposition p > expressed in Peirce's algebra of 1885 may be mapped to and > from an EG that expresses exactly the same proposition p. > > The converse is not true because Peirce's Gamma graphs can > express propositions that cannot be expressed in his 1885 > notation. However, there are modern extensions to predicate > calculus that can express Gamma graphs. For some discussion > of the issues, see http://jfsowa.com/pubs/5qelogic.pdf > > The equivalence in expressive power of EGs and the algebraic > forms implies that syntactic differences have no semantic > meaning whatsoever. Therefore, any syntactic feature that is > lost in translation in either direction is *meaningless*. > > Re spot, peg, and line: The words 'spot' and 'line' were > Cayley's choices for naming the two kinds of parts in a graph. > But graph theory was invented and reinvented many times by > mathematicians working in different branches. Euler was the > first with his solution to the problem of the Seven Bridges > of Königsberg. His words were 'island' and 'bridge'. Other > mathematicians used different pairs: vertex/edge, node/arc, > node/link, point/line. > > Nobody today uses the word 'spot'. And Peirce himself rarely > drew an actual spot in his examples of EGs. He just attached > lines of identity to the words that named his predicates. I > believe that's the reason why he avoided the word 'spot' in > his 1911 intro to EGs. See http://jfsowa.com/peirce/eg1911.pdf > > Re peg: The number of pegs of a predicate corresponds to the > number of blanks used in defining the predicate by blanking out > names in a sentence that states a proposition. In the algebra, > a predicate is represented by a name such as Q followed by a list > of names or expressions. A triadic predicate, for example, > could be represented in the algebra as Q(x1,x2,x3). > > As Peirce said in eg1911.pdf (NEM 3:164) "Individual graphs usually > carry 'pegs', which are positions on their periphery appropriated > to denote, each one of them, one of the subjects of the graph." > > In short, a peg is a *position* on the periphery of an EG predicate > that maps to a *position* in the list of the algebraic predicate. > The phrase "appropriated to denote" is unclear, but the translation > to the algebraic form shows exactly what Peirce intended. He never > said nor implied that a peg is a continuous predicate. > > Re "indefinite individuals (Lines of Identity)": A line of identity > maps to an existentially quantified variable in the algebra. The EG > cat—on—mat maps to (∃x)(∃y)(cat(x) & mat(y) & on(x,y)). The English > sentence "A cat is on a mat", the existential graph, and the algebra > are indefinite in exactly the same way: They just say that there is > an indefinite cat and an indefinite mat in a relationship named 'on. > > JAS > > [Incidentally, Lane observes in chapter 6 that Peirce's "idea of > > vagueness is quite different from the contemporary one" (p. 139); > > accordingly, I wonder if it would be more perspicuous to employ > > the term indefinite rather than vague when referring to Peirce's idea.] > > No. The sentence "A cat is on a mat" is indefinite about the > referents of the two subjects, but neither Peirce nor any modern > logician would say that it's vague. > > Peirce wrote "The vague might be defined as that to which the > principle of contradiction does not apply" (CP 5.505, see below). > The sentence "A cat is on a mat" is not vague because it must > be either true or false. It can't be both or neither. > > For more examples and discussion, see "What is the source of > fuzziness?": http://jfsowa.com/pubs/fuzzy.pdf > > John > _____________________________________________________________________ > > Peirce (CP 5.505) > > Logicians have too much neglected the study of vagueness, not > > suspecting the important part it plays in mathematical thought. > > It is the antithetical analogue of generality. A sign is objectively > > general, in so far as, leaving its effective interpretation > > indeterminate, it surrenders to the interpreter the right of > > completing the determination for himself. "Man is mortal." "What > > man?" "Any man you like." A sign is objectively vague, in so far > > as, leaving its interpretation more or less indeterminate, it > > reserves for some other possible sign or experience the function > > of completing the determination. "This month," says the almanac- > > oracle, "a great event is to happen." "What event?" "Oh, we shall > > see. The almanac doesn't tell that." The general might be defined > > as that to which the principle of excluded middle does not apply. > > A triangle in general is not isosceles nor equilateral; nor is a > > triangle in general scalene. The vague might be defined as that to > > which the principle of contradiction does not apply. For it is > > false neither that an animal (in a vague sense) is male, nor that > > an animal is female. >
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