Mary, list,
In turning our attention to beta graphs, Peirce is addressing the problem of how to represent an individual In the logical sense, or an existing thing in the ontological sense. In ordinary language it can be represented by a proper name (as opposed to a common noun, which is a general term). In the alpha graph system, the universe of discourse “is a collection of individuals” or “subjects of force,” but there is no way to represent a specific member of that collection. In beta graphs we could represent such an individual by a letter such as A (which Peirce calls a “selective”), but his preferred and more iconic way is to represent it by a heavy dot. As we will see shortly, a line made up of a continuum of these dots is a line of identity. Your question about the “blot” has me thinking again about “the two peculiar graphs” which are “the blank place which asserts only what is already well-understood between us to be true, and the blot which asserts something well understood to be false” (earlier in Lowell 2). They are peculiar in several ways, and each is in some sense the opposite of the other. For instance, the blank cannot be erased, but any graph can be added to it on the sheet of assertion; while the blot can be erased, but nothing can be added to it, because it “fills up its area.” For the same reason, the blot (meaning “Everything is true”) cannot be scribed on the sheet of assertion, because asserting it would blot out the distinction between true and false, on which logic itself is grounded. The blot is a pseudo-graph because it cannot be added to the blank as any real graph can. It can only function within a cut, or a nest of cuts, and its only function amounts to negating the contents of the enclosure within which its own enclosure is enclosed. It works like the blank turned inside out, if you can imagine that. In terms of the communication between graphist and interpreter, we might say that the blank sheet of assertion represents the commens of tacit knowledge which they share. What then does the blank represent when enclosed in a single cut? Everything tacitly known to be not true, or everything not tacitly known to be true? By the conventions of EGs, it seems to be the former, and thus equivalent to the blot, “which asserts something well understood to be false.” This explains Peirce’s last “Alpha Fundamental Permission,” that “A vacant cut may be treated as a pseudograph.” (Peirce may be understating the case when he says that these permissions, as presented in Lowell 2, are “somewhat confusing”!) If I have that right, more or less, I don’t think the blot can work as a way to begin “the play of musement.” In this lecture at least, the blot is part of a system for the analysis of “necessary reasoning,” and musement is at the other (more spontaneous) end of the spectrum of thought. Gary f. From: Mary Libertin [mailto:[email protected]] Sent: 21-Nov-17 12:04 To: Peirce List <[email protected]>; Sharon Hattrick <[email protected]>; [email protected] Subject: Re: [PEIRCE-L] Lowell Lecture 2.13 To clarify the start of my previous post, the 4th paragraph I mention is Peirce’s 4th paragraph. Rather than retype it here, I’ll just point to it: “There is nothing to prevent ...” Please reread it and Peirce’s surrounding paragraphs. Thanks. On Tue, Nov 21, 2017 at 11:48 AM Mary Libertin <[email protected]> wrote: I am interested in the 4th paragraph below. I am presenting the following as an attempt to continue this interesting discussion. Peirce In para 4 states that the first use should be in bold to designate it as the first. This is similar in some ways to the type/token distinction, and designating the first a type whenever a second appears is useful (and even necessary in law, as his example suggests). But there is often no first. In perception, for one example ... one knows there is a (type) only after gradually coming to an awareness that two or more constitute a type. This awareness may take a lifetime to establish or may never occur. Peirce is being very particular theoretically, establishing a blackboard and a grapheous and graphist, and may I pause to say Peirce somewhere states that any given word example he is using (the mark once it is formed by an interpreter?) is neither written nor spoken. This makes sense since it is a discussion of existentiality / existential graphs. This paragraph I’ve written above raises so many possible problems and questions. Is the blot that he discusses earlier in his Harvard lecture a way to begin an enactment of the play of musement or process of semiosis at an elemental level — In perception? Or, how is Peirce’s above paragraph related to nominalism? I know the thanksgiving-hiatus ensues and provides us a time to give and receive the harvest. Enjoy... Mary Libertin On Tue, Nov 21, 2017 at 10:10 AM <[email protected] <mailto:[email protected]> > w Continuing from Lowell 2.12: https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii/display/13617 I now pass to the beta part of the system of existential graphs. It is far more interesting and important than the alpha part but incomparably less so than the gamma part. When one hears a proper name mentioned for the first time, one generally learns of the individual person or thing denoted by that name that it exists. It may, of course, be identified with a subject of force already well-known; but that will be exceptional. It will frequently be apparent that it is a thing quite different from any hitherto mutually recognized. In this case, it will make an addition to the universe of discourse, brought about by means of the assertion of a real relation of it to an object previously recognized. Sometimes, it will be doubtful whether it is one of the recognized subjects of force or not. But what I want to focus your attention upon is that at the first mention of a proper name, apart from any special information about its subject that may then be conveyed, the name merely tells us that something exists, that is, is a factor of the entire complexus of forces that we partly have known by experience. But at any subsequent mention of the proper name, though this assertion of existence is reiterated, yet that being know[n] already is of no importance. The importance of the name at all occurrences after the first is that it identifies what is mentioned with something we had heard of before. If you bear in mind these characteristics of proper names, you will perceive that when lawyers and others use the letters A, B, C as a sort of improved relative pronouns, saying for example that if A owes B money and C owes A money, then B may “trustee” C for the debt (as you say in Massachusetts), these letters differ from new proper names only in the accidental circumstance that they are first introduced in the antecedent of a conditional proposition while proper names are first introduced in positive assertions. I call such improvised proper names selectives. There is nothing to prevent our using the capital letters as such individual names, provided we distinguish the first replica by scribing it heavily or otherwise. I cannot say that this is a bad way; it serves the purpose of putting out of view confusing [trifles?]. But I do say that it requires rather complicated rules, and from every other point of view except that of putting unimportant circumstances out of view and convenience in printing, is usually inferior to another way of fulfilling the same purpose, which I proceed to describe. Since the blackboard, or the sheet of assertion, represents the universe of discourse, and since this universe is a collection of individuals, it seems reasonable that any decidedly marked point of the sheet should stand for a single individual; so that • should mean “something exists.” We cannot make this • • to mean that two things exist, since this would conflict with our convention that graphs on different parts of the sheet shall have each the same meaning as if each stood alone, so that consequently the second point merely reiterates that something exists. <http://gnusystems.ca/Lowells.htm> http://gnusystems.ca/Lowells.htm }{ Peirce’s Lowell Lectures of 1903 https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii
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