Jon, The word 'instance' is an OPTIONAL term that may be added to almost any noun in the English language. As I'm now looking out the window, I see three tree instances nearby and many more instance of trees farther down the hill. But the word 'instance' may be dropped when there is no need to emphasize that distinction. Most English speakers never use the word 'instance'. They would just say "I see three trees nearby and many more down the hill"
In mathematics, everything is abstract (a "might be" as Peirce would say). But when mathematicians who speak any language draw instances of geometrical entities (circles, triangles, hexagons...) on a blackboard or whiteboard or paper..., they do not refer to them as circle instances, hexagon instances, etc. They just call them circles or hexagons. Nobody gets confused by that convention. JAS: 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." On that point, we are in total agreement. And since Peirce is trying to teach his readers a totally new notation for expressing a new form of diagrammatic reasoning, he uses that OPTIONAL word 'instance' to emphasize the distinction. But I suggest that you look at any book on mathematics. To make the comparison more obvious, look at books on geometry from Euclid to the present. Most authors rarely or never use the word 'instance' when they talk about circles or triangles they draw. JAS: Peirce also acknowledges the convenience of talking only about graphs (or words), not graph-instances (or word-instances). Thank you for acknowledging what I have been saying. The only point where there may be some disagreement is over the word 'convenience'. In English, the default form (what linguists call the "unmarked form") does not use the word 'instance'. They would call the addition of the word 'instance' a "marked form" that is used for emphasis. Except for an introductory tutorial, I believe that Peirce is being unnecessarily pedantic. 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) Mathematicians have been choosing brevity since Euclid, and they still do. As for the question about how many identical graph instances occur on the phemic sheet, that is a moot point -- because the rules of inference allow copies in the same area to be made or erased at any time. It's irrelevant how you count them, because you can change the count without changing the meaning of what is on the phemic sheet. JAS: 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. No. In a letter to Welby, he explicitly adopted the word 'mark' as a replacement for 'potisign' (possible sign). That shows that he recognized a standard practice in the English language: Use exactly the same word for the abstract "may be" and the actual instance. He also admits that option for its "value as brevity." 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. JAS: 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. We agree with everything except the tag end "or one utterance from another". The word 'tone' is a special case of an auditory mark. It may be used to distinguish the sound of two different flutes or certain auditory marks of an utterance. But it is not a word that anyone would use to distinguish marks by any other senses. Even for a spoken utterance, it would not be used to distinguish differences in the subject matter. Even for Peirce's example of a camel, the sound of a camel has been compared to a toilet flushing. Nobody would call that a tone. But it is certainly a prominent mark of a camel. JAS: 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). I agree that Peirce chose the word 'tone' for that distinction. But all of those examples are visible marks. A word that is normally used to describe sounds is a poor choice. The fact that Peirce himself vacillated on this choice indicates he was not completely satisfied. His choice of 'mark' is more consistent with his definition in Baldwin's dictionary and other English dictionaries. We acknowledge that the definition of the word 'mark' generally refers to a physical instance. But any English word that refers to something physical can also be used to refer to the abstract form of that thing. In conclusion, we have discussed a huge number of different issues in Peirce's writings and in other examples. In every example (with the possible exception of certain kinds of sounds), the word 'mark' is more general and more intelligible for a wider audience than the word 'tone'. Re wider audience: Our most important audience are people in the 21st C who do not realize the value of Peirce's writings for issues today. That is far better topic to discuss. John ---------------------------------------- From: "Jon Alan Schmidt" <jonalanschm...@gmail.com> 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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