List, Mary,
Lowell 2.14 introduces the spot (which must not be confused with either the dot or the blot!), and in this connection is worth comparing with MS 439, the third of the Cambridge Lectures of 1898 (RLT 146-164, NEM4 331-46). In this lecture given five years before Lowell 2, Peirce began with a sketch of his "categories" (Firstness, Secondness and Thirdness), then applied them to formal logic (more specifically to the "Logic of Relatives"), which he then explained "by means of Existential Graphs, which is the easiest method for the unmathematical" (or so he claimed - RLT 151). In this post I'll include two paragraphs from that 1898 lecture. First, from RLT 154: Any part of a graph which only needs to have lines of identity attached to it to become a complete graph, signifying an assertion, I call a verb. The places at which lines of identity can be attached to the verb I call its blank subjects. I distinguish verbs according to the numbers of their subject blanks, as medads, monads, dyads, triads, etc. A medad, or impersonal verb, is a complete assertion, like "It rains," "you are a good girl." A monad, or neuter verb, needs only one subject to make it a complete assertion, as -obeys mamma you obey- A dyad, or simple active verb, needs just two subjects to complete the assertion as -obeys- or -is identical with- A triad needs just three subjects as -gives-to- -obeys both-and- The main difference between this and Lowell 2 is the terminology: what Peirce calls a "verb" here is called a "spot," "rheme" or "predicate" in the Lowell lectures. (Compare the usage of "rheme" in the semiotic trichotomy rheme/dicisign/argument as given in the Syllabus, EP2:292 or CP 2.250.) The "subject blank" or "line of identity" here represents the individual "subject of force," as does the "heavy dot" in Lowell 2, where the sheet of assertion represents "the aggregate" of those "subjects of the complexus of experience-forces well-understood between the graphist, or he who scribes the graph, and the interpreter of it." The other paragraph which I'll quote from the Cambridge lecture (RLT 155-6) relates the existential graph system both to semiotics and to the Peircean "categories" - and I think these relations also hold in the Lowell presentation of the graphs. Notice here that the line of identity is classed among "verbs" here, although the ends of the line (the "dots" of Lowell 2) represent "individual objects" which would be the "subjects" of the "verbs" in the graph. As a verb, though, all the line of identity can mean is "is identical with," its subjects being those ends, which in Lowell 2 occupy the "hooks" of the "spots." In the system of graphs may be remarked three kinds of signs of very different natures. First, there are the verbs, of endless variety. Among these is the line signifying identity. But, second, the ends of the line of identity (and every verb ought to [be] conceived as having such loose ends) are signs of a totally different kind. They are demonstrative pronouns, indicating existing objects, not necessarily material things, for they may be events, or even qualities, but still objects, merely designated as this or that. In the third place the writing of verbs side by side, and the ovals enclosing graphs not asserted but subjects of assertion, which last is continually used in mathematics and makes one of the great difficulties of mathematics, constitute a third, entirely different kind of sign. Signs of the first kind represent objects in their firstness, and give the significations of the terms. Signs of the second kind represent objects as existing,- and therefore as reacting,- and also in their reactions. They contribute the assertive character to the graph. Signs of the third kind represent objects as representative, that is in their Thirdness, and upon them turn all the inferential processes. In point of fact, it was considerations about the categories which taught me how to construct the system of graphs. One last comment: the usage of the word "individual" in logic can be confusing, but Peirce's definition of the term in Baldwin's Dictionary - http://gnusystems.ca/BaldwinPeirce.htm#Individual -is helpful for understanding Peirce's usage. Gary f. Sent: 23-Nov-17 16:38 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. 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. 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). 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.) 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. Thus . gives . to . in exchange for . will mean "something gives something to something in exchange for something." 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
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
