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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