I just wanted to clarify some issues that may be unclear in what Peirce wrote in L376: "in the Monist of Oct. 1906... I made an attempt to make the syntax cover Modals; but it has not satisfied me. The description was, on the whole, as bad as it well could be, in great contrast to the one Dr. Carus rejected. For although the system itself is marked by extreme simplicity, the description fills 55 pages, and defines over a hundred technical terms applying to it. The necessity for these was chiefly due to the lines called “cuts” which simply appear in the present description as the boundaries of shadings, or shaded parts of the sheet”.
Many people interpreted this text as implying that Peirce was condemning the tinctures. But as he said explicitly, it was "chiefly due to the lines called cuts”, which in 1906 were defined as cuts through the paper from the recto side to the verso side. The last mention of recto/verso was in R669 (May 1911). From R670 (June 1911) to the last long letter in 1913, negative areas were marked by shading, not by cuts. From L231 (June 1911) to the end, Peirce also avoided the word 'cut'. In R670, he also mentioned tinctures as an option: “The nature of the universe or universes of discourse (for several may be referred to in a single assertion) in the rather unusual cases in which such precision is required, is denoted either by using modifications of the heraldic tinctures, marked in something like the usual manner in pale ink upon the surface, or by scribing the graphs in colored inks”. I'm not discussing these issues as a criticism of anybody. I'm just clarifying several points: (1) A notation for distinguishing "the universe or universes of discourse" is important. (2) Tinctures, by themselves, are not a bad way to express the distinction, but they could not be used in print in the early 20th C. (3) But methods for distinguishing the UoD are necessary in any text that happens to mention two or more. (4) This issue is important for any discussion about L376, because Peirce explicitly mentioned the division of the phemic sheet into multiple papers, which might express different opinions by an utterer and an interpreter. (5) In R670 above and in L376 below, the utterer and interpreter may refer to different UoDs and discuss entities in them. Those discussions, when expressed in EGs, would involve lines of identity (or quantified variables) that refer to universes and to entities in them that may be abstract, imaginary, possible, or impossible. Note that they may also discuss "special understandings". An understanding is another ens rations, as Peirce would say. >From L376; "If 'snows' is scribed upon the Phemic Sheet, it asserts that in >the universe to which a special understanding between utterer and interpreter >has made the special part of the phemic sheet on which it is scribed to >relate, it sometimes does snow. For they two may conceive that the “phemic >sheet” embraces many papers, so that one part of it is before the common >attention at one time and another part at another, and that actual conventions >between them equivalent to scribed graphs make some of those pieces relate to >one subject and part to another”. John
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