List, I must apologize to the list for introducing the term "dot" into this discussion, as Peirce actually uses that term not in Lowell 2, but in some of his other explanations of existential graphs, notably CP 4.438:
"Let a heavy dot or dash be used in place of a noun which has been erased from a proposition. A blank form of proposition produced by such erasures as can be filled, each with a proper name, to make a proposition again, is called a rhema, or, relatively to the proposition of which it is conceived to be a part, the predicate of that proposition." In Lowell 2.13, Peirce refers to this heavy dot as a "decidedly marked point": "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'." (The dot between "that" and "should" may not even be visible in some mail readers, which could cause even more confusion!) With this in mind, I will copy 2.14 here again, but with some interpolations of my own (in a contrasting font) that will try to clear up the confusion regarding the analysis of propositions as represented in EGs. Gary f. Continuing from Lowell 2.13, https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low ell-lecture-ii/display/13620 You will ask me what use I propose to make of this sign that something exists, a fact that graphist and interpreter took for granted at the outset. Gf: The point marked with a dot, . , like a blank in a rheme, represents some individual which can serve as a subject of a proposition. In that respect it is equivalent to a demonstrative pronoun, or a proper name the first time it is heard, in ordinary language. But in this lecture Peirce introduces this "decidedly marked point" . before introducing the rheme or spot which represents the predicate. This has the effect of emphasizing the fact that . denotes an individual subject within the universe of discourse. CSP: I will show you that the sign will be useful as long as we agree that although different points on the sheet may denote the same individual, yet different individuals cannot be denoted by the same point on the sheet. Gf: This entails that a line made up of . points can denote a single individual, and this becomes the "line of identity" in EGs. CSP: If we take any proposition, say A sinner kills a saint and if we erase portions of it, so as to leave it a blank form of proposition, the blanks being such that if every one of them is filled with a proper name, a proposition will result, such as ______ kills a saint A sinner kills ______ ______ kills ______ where Cain and Abel might for example fill the blanks, then such a blank form, as well as the complete proposition, is called a rheme (provided it be neither [by] logical necessity true of everything nor true of nothing, but this limitation may be disregarded). If it has one blank it is called a monad rheme, if two a dyad, if three a triad, if none a medad (from μηδέν). Gf: In the linguistic expression of a proposition, a "proper name" (or a pronoun) can serve as a subject while the rest of the sentence is the predicate. In the "blank form" of a proposition, the "blank" occupies the place of the subject which in EG notation is a "marked point" .. But notice that a common noun, such as "sinner" or "saint" in Peirce's examples above, is not a subject but is part of the predicate, or rheme. Thus a complete proposition which includes only general terms is still a rheme, a medad with no blanks. The number of blanks is the "valency" or 'adicity' of the rheme, the number of individual subjects it can take (such as Cain or Abel or .. Translating this into ordinary language about propositions, common nouns and verbs together (along with some structure words and modifiers) make up the predicate, and it can take any number of subjects, but each of these must be an individual denotable by a proper name or a demonstrative pronoun. CSP: Now such a rheme being neither logically necessary nor logically impossible, as a part of a graph without being represented as a combination by any of the signs of the system, is called a lexis and each replica of the lexis is called a spot. (Lexis is the Greek for a single word and a lexis in this system corresponds to a single verb in speech. The plural of lexis is preferably lexeis rather than lexises.) Gf: After this, Peirce very rarely used the term "lexis", but consistently used both "rheme" (or rhema) and "spot" to denote this aspect of the EG system. (That's why I made my parenthetical remark about not confusing the "spot" with the "dot", which appears to have caused the very confusion I was trying to avoid!) CSP: Such a spot has a particular point on its periphery appropriated to each and every one of its blanks. Those points, which, you will observe, are mere places, and are not marked, are called the hooks of the spot. But if a marked point, which we have agreed shall assert the existence of an individual, be put in that place which is a hook of a graph, it must assert that some thing is the corresponding individual whose name might fill the blank of the rheme. Gf: In existential graph-replicas, the "spot" (rheme, predicate) generally takes the form of a word or phrase such as "is a pear" or "is ripe" or "kills" or "loves". The "hooks" (sometimes called "pegs", as John mentioned) are invisible unless they are marked by a point which is one end of a line of identity. A line of identity is considered a graph in itself, but all it can say in propositional form is "something exists," which is not very useful. In order to predicate anything else of this subject, you have to attach the . or line-end to a spot, at one of its hooks. CSP: Thus . gives . to . in exchange for . will mean "something gives something to something in exchange for something." Gf: I'll follow this up with 2.15 where the "line of identity" is defined; I found that I had to use the term in this post in order to explain the difference between the . and the "spot", which represent subject and predicate respectively in the logic of relations. I should mention that "subject" and "predicate" are not rigid ontological categories when applied to the language in which propositions are expressed. As Peirce observed later on, the subject/predicate distinction is contingent on one's analysis of the given proposition, so that "all that words can convey" may be "thrown into the predicate" (CP 5.525), giving us a medad rheme. (I won't venture to say what the result would look like if everything is "thrown into the subject.") Gary f. http://gnusystems.ca/Lowell2.htm }{ Peirce's Lowell Lectures of 1903 https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low ell-lecture-ii
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