John, List: JFS: He uses exactly the same word with no change whatsoever for the abstract "might be'' (the formal pattern of spots, lines, and ovals) and the visible graph as it is written on a phemic sheet.
It is remarkable that someone can read a short paragraph and then seriously claim that it says *exactly the opposite* of what it plainly says. Peirce *only *uses the word "graph" for "a mere form, an abstraction, a 'general' or as I call it a 'might-be'"; and he states explicitly that "it would be incorrect to say that the graph *itself *is put upon the sheet. For that would be an impossibility." What, then, *is *put upon the sheet? Peirce does not give it *any *name in R L376, but in various other texts, he repeatedly calls it a "graph-instance"; and in a published article, he presents this as a *paradigmatic *example of the distinction between a *type *and a *token *that is an *instance *of a type (CP 4.537, 1906). Again, there is nothing at all in the letter to Risteen about the *other *member of this trichotomy, whether we call it a "tone" or a "mark." JFS: Teachers who are explaining how to draw, use, and talk about EGs call them graphs, not graph instances. Indeed, because what they are discussing (for the most part) are graphs as *general *types, not graph-instances as *individual *tokens. Peirce also acknowledges the *convenience *of talking only about graphs (or words), not graph-instances (or word-instances). CSP: Any shape or combination of shapes that put on the Sheet of Assertion would be an assertion, I term a *graph*, and your act of putting it on any surface by writing or drawing or a mixture of the two I express by saying that you *scribe *that sign on that *area*; and the result of doing so, that is any single one among the inexhaustible multitude of possible embodiments of the graph, I call a graph-instance. To illustrate the utility of this distinction, I call your attention to the fact that we most commonly use the word "word" with a meaning analogous to that of "graph,"--for we say that hounds, beagles, curs, mastiffs, spaniels, terriers, poodles, and an incredible variety of other stocks are alike included under the *single word*, *dog*. Yet when an editor asks me to write him a paragraph of a hundred words on some subject, he means to count every occurrence of "the" as a separate word. He does not mean *words*, but *word-instances*; but in this case the value of brevity outweighs that of accuracy. In the case of graphs and graph-instances, it is quite the other way. (R 650:10-11, LF 1:164-165, 1910 Jul 23) Note well Peirce's last remark here--the value of accuracy in *distinguishing *"graphs" (types) and "graph-instances" (tokens) outweighs that of brevity in simply using "graphs" for both. For example ... CSP: "The father g.o." [g.o. = goes out] is a *graph*, even if it is not scribed on the sheet. For a graph is what is true or false, and its being scribed does not make it so. Also suppose we have on the Sheet of Truth The mother g.o. The mother g.o. The mother g.o. The mother g.o. Then there is only *one *graph on the sheet, but there are *four graph-instances*. This is a very useful distinction to prevent misunderstandings. A *graph-instance* is a single scribing according to this System of that which must either be true or false. A *graph *is the one *form *of all possible graph-instances which express the same meaning in precisely the same way. Thus The MOTHER g.o. and The mother goes out are two instances of the same graph because their differences are entirely *insignificant*, that is do not amount to different ways of expressing the fact, but only to different ways of writing. But The mother g.o. and The mother g.o. The mother g.o. are two different graphs, though their meaning is the same. (R 514:7-8, LF 1:478-479, 1904) Again, a graph is a *type*, "a definitely significant Form"; while a graph-instance is a *token*, "A Single event which happens once and whose identity is limited to that one happening or a Single object or thing which is in some single place at any one instant of time, such event or thing being significant only as occurring just when and where it does" (CP 4.537). Also ... CSP: A *Graph*, then, as the word is used when it is plain that an *Existential *Graph is meant, is not a sign or mark or any other existent or actual individual, but is a *kind *of sign which if scribed on the Phemic Sheet (i.e. if an *Instance *of it stood on the Sheet) would make an assertion. The individual sign that results from the scribing of a Graph has been called an "*Instance*" of the Graph. This word "Instance" might conveniently be introduced into ordinary parlance. For example, only two words in our language are called articles; but one of these, the definite article, *the*, will commonly occur, on an average page of novel or essay, over twenty times. They are reckoned by the editor who asks for an article of so many thousand "words" as distinct words; but in fact they are only twenty or more *instances *of the same word; and if the editor takes any pleasure in speaking accurately he should call for an article of so many thousand "word-instances." At any rate, it would be highly inconvenient to call "Graph-instances" Graphs. (R 669:9-10, LF 1:579, 1911 May 27) Here Peirce explicitly *denies *that a graph is a "mark," which he explicitly *equates *with an "existent or actual individual," i.e., a token--so "mark" is plainly unsuitable for naming a *different *member of the same trichotomy. In any case, the bottom line is that when a graph is scribed on the sheet, what actually stands on the sheet as a result is *not *a graph, but a graph-instance. GR: 1. She preferred the tone of her flute to that of the first flautist in the orchestra. 2. Her tone of voice changed dramatically when she was angry. Those two sentences are normal sentences that any English speaker would understand, whether or not they had read anything by Peirce. JFS: Yes, they are normal sentences because the word 'tone' in these examples is used to refer to the actual sound that is heard, not to some mark that might distinguish one tone of voice from another. No, the word "tone" in Gary's examples is used to refer to a certain *quality *of the actual sound that is heard, which *can *distinguish one flute from another or one utterance from another. Likewise, in my own example, all lowercase, all caps, bold, italics, and color *can *be employed to distinguish different instances (tokens) of the same word (type) from each other such that they have different dynamical interpretants in their different contexts. Such an "indefinitely significant character" is *exactly *what Peirce defines as a "tone," the possible counterpart of existent "token" and necessitant "type" (CP 4.537). JFS: Nobody has found anything later (or better at any time) on this topic. Later, maybe not; better is obviously a subjective judgment. I have quoted several passages in this post alone, as well as in my previous posts, that I believe are *better *in the sense that they are *clearer*. JFS: My primary concern is that you and Jon have made claims abut Peirce without showing any justification. Anyone who alleges that we have offered no justification for our claims about Peirce is either not paying attention or willfully ignoring the *considerable *evidence that we have provided. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Thu, Apr 18, 2024 at 6:14 PM John F Sowa <s...@bestweb.net> wrote: > Jon, Gary, List, > > Please reread the paragraph below by Peirce from L376 (December 1911). > The example he uses is 'existential graph'. He uses exactly the same word > with no change whatsoever for the abstract "might be'' (the formal pattern > of spots, lines, and ovals) and the visible graph as it is written on a > phemic sheet. > > CSP: Any visible form which, if it were scribed on the phemic sheet would > be an assertion is called a *graph*. If it actually be so scribed, it > would be incorrect to say that the graph *itself* is put upon the sheet. > For that would be an impossibility, since the *graph* itself [is] a mere > form, an abstraction, a "general," or as I call it a "might-be", i.e. > something which might be if conditions were otherwise than they are; and in > that respect it [is] just like a "*word*,"--*any* word, say *camel*. (R > L376:14-15, 1911 Dec 8) > > This is Peirce's final word on the subject: the word 'graph' (or the > longer phrase 'existential graph') is the correct term to use for *BOTH *the > abstract form and for the visible drawing on a phemic sheet. If you need > more examples, look at how Peirce writes about the EGs he is using to > *SOLVE *problem or *PROVE *a theorem. In every such example, he calls > them graphs, not graph-instances. The only cases when he might talk about > a graph instance is in *METALANGUAGE *about the theory. If anybody finds > such examples, please let us know. > > JAS: However, this *contradicts* John's claim instead of corroborating > it, by explicitly stating that we *cannot* say that what is being > observed is the [mark] itself--we need a *different* word for the > embodiment of the [mark], such as "graph-instance" in lieu of "graph." > Alternatively, if "mark" is the right word for the embodiment, then we need > a *different* word for the form itself. > > No. That claim confuses two very different ways of talking about two very > different topics. Teachers who are explaining how to draw, use, and talk > about EGs call them graphs, not graph instances. However, philosophers who > are distinguishing theory and practice, use a metalanguage for > distinguishing the abstract form (a might-be) from the actual visible > drawings. > > Just look at any book on geometry from Aristotle to the present. The > words such as 'circle' or 'triangle' refer to abstract forms. And > *EXACTLY *the same words are used to describe the drawings in a book or > computer screen (or even on sand, as they often did in the olden days). > > But as a philosopher, Plato made a very sharp *METALEVEL* distinction > between the abstract Platonic forms and the visible patterns drawn in ink, > chalk, wax, or sand. Nevertheless, all working mathematicians use the > simple words circle, triangle, square... when they're solving problems, > proving theorems, and writing explanations for both experts and students. > Please note how Peirce writes about EGs when he's using them to solve > problems. He does not call them graph-instances. > > In an earlier note, I commented on the last phrase by Peirce in the above > quotation: "in that respect [a graph is] just like a "*word*,"--*any* word, > say *camel*." Then I gave the following examples to show why the word > 'mark' is better than 'tone' in the trichotomy of (Mark Token Type): > > 1. A hump is a mark of a camel. > 2. A trunk is a mark of an elephant. > > Those two sentences are normal sentences that any English speaker would > understand, whether or not they had read anything by Peirce. Now consider > the following two sentences: > > 1. A hump is a tone of a camel. > 2. A trunk is a tone of an elephant. > > Those two examples not only sound silly, they show why a word like > 'tone', which is limited to sounds is much more confusing than the word > 'mark', which may be used for any sensory modality. > > GR: > 1. She preferred the tone of her flute to that of the first flautist in > the orchestra. > 2. Her tone of voice changed dramatically when she was angry. > > GR: "Those two sentences are normal sentences that any English speaker > would understand, whether or not they had read anything by Peirce. > > Yes, they are normal sentences because the word 'tone' in these examples > is used to refer to the actual sound that is heard, not to some mark that > might distinguish one tone of voice from another. > > GR: Now consider the following two sentences: > 1. She preferred the mark of her flute to that of the first flautist in > the orchestra. > 2. Her mark of voice changed dramatically when she was angry. > > In these two sentences, the word 'mark' is incorrect because the literal > word 'tone' would be appropriate. > > GR: Indeed your consistent insistence that you are right -- no discussion > needed, your seemingly claiming to be the final arbiter in all Peircean > terminological matters > > Au contraire, please note that I have not claimed any authority of my > own. In my comments about Peirce's position, I have used his own words, as > he stated them in L376. Nobody has found anything later (or better at any > time) on this topic. > > To reinforce Peirce's claims, I have also added explanations based on > traditional usage in geometry from the Greeks to the present. Benjamin > taught Charles those topics from a very early age. > > My primary concern is that you and Jon have made claims abut Peirce > without showing any justification. That is why I believe that the analysis > above, which is based on Peirce's last words on the matter and on standard > practice in mathematics from Euclid to the present, is indeed the last word > on this topic. > > Nobody has found anything to the contrary. > > John >
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