John, List: JFS: I already answered these points.
I could say the same thing, but I will likewise give it another try. JFS: Please look at the example in RLT. A line of identity by itself is a complete, fully formed EG. There is no line of identity in that one-of-a-kind EG. The line connecting "is much to be wished" to the oval is lightly drawn, just like the oval itself; and in the very next EG, there is no line at all connecting the oval with "is false." At this point in the lecture, Peirce has not even introduced the line of identity yet. When he subsequently does so, he calls it "a heavy line" (RLT 153) and then consistently draws it accordingly. Here are the relevant manuscript images so that you can see the difference for yourself. [image: image.png] [image: image.png] [image: image.png] JFS: According to the way Peirce defined that notation and translated it to English, he chose the word 'that' as the English word that represents that construction (an oval with an attached line of identity). Please look at the actual text of RLT 151. Again, Peirce himself does not provide an English translation of that one-of-a-kind EG; and again, the line attached to the oval is *lightly *drawn, not a *heavy *line of identity. Why do you keep claiming otherwise? JFS: I am not asking you to believe anything I say. But I am asking you to look at the references I cited. I am asking you to look carefully at Peirce's own texts, and to set aside your preconceptions about what they say and show. JFS: The postulates of geometry are asserted to be true of whatever version of geometry they define. Peirce explicitly states in R 514 that "in the margin outside the red line, whatever is scribed is merely asserted to be possible. Thus, if the subject were geometry, I could write in that margin the postulates, and any pertinent problems stated in the form of postulates ..." Geometry falls within pure mathematics, which is a strictly hypothetical science that draws necessary conclusions about pure possibilities, as you yourself have observed on multiple occasions. JFS: All the evidence shows that L376 is the definition of Delta graphs. He is clearly defining a new version of modal logic in the same document in which he said that he needed to define a new version of modal logic. To deny that he was defining Delta graphs just does not make any sense of what he was writing. Peirce never says or implies in R L376 (1911) or elsewhere that he needs "to define a new version of modal logic." He simply states, "I shall now have to add a *Delta* part in order to deal with modals," because he was dissatisfied with his earlier attempts--first broken cuts in Gamma (1903), then tinctures (1906). To claim that he was defining Delta graphs in the 19 manuscript pages that are extant goes far beyond anything that he actually wrote on them. Perhaps he did go on to define Delta graphs in the subsequent pages that are missing, but unless and until someone finds them, we can only speculate. Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sun, Feb 25, 2024 at 4:44 PM John F Sowa <s...@bestweb.net> wrote: > Jon, > > I already answered these points. I'll restate them more clearly: > > JAS> "X is something to be wished" is not a proposition, it is a rheme. X > is a variable, logically equivalent to a blank. The proposition within the > oval replaces X, i.e., fills the blank. > > Please look at the example in RLT. A line of identity by itself is a > complete, fully formed EG. It may be translated to the English sentence > "There exists something X." When attached to a verb phrase, the complete > fully formed EG states "Something X is much to be wished." While looking > at the example in RLT, hold you hand over the oval, and the remainder that > you see is a complete EG. > > Now hold your hand over the verb phrase "is much to be wished." What you > see is a line of identity attached to an oval that contains another EG. As > Peirce explained, that is his convention for designating a proposition p, > and the line of identity attached to the oval represents p. When you raise > your hand that has the effect of a ligature that connects two lines of > identity. That has the effect of asserting p=X. > > According to the way Peirce defined that notation and translated it to > English, he chose the word 'that' as the English word that represents that > construction (an oval with an attached line of identity). Not by > coincidence, the same word 'that' was chosen by the nine logicians and > computer scientists who specified the IKL logic for an exactly equivalent > process in 1906. > > I am not asking you to believe anything I say. But I am asking you to > look at the references I cited. They include quite a few professional > logicians who agree with each other and with what I showed them in Peirce's > own writings. > > JAS> Again, the notation of R 514 effectively turns the entire sheet into > a *conditional *proposition, with its physical edges serving as a cut and > the red line serving as another cut nested within it. Any propositions in > the margin belong to the antecedent and are thus "merely asserted to be > possible," such as the postulates of geometry, while any propositions > inside the red line belong to the consequent and are thus asserted to be > true... > > No. The postulates of geometry are asserted to be true of whatever > version of geometry they define. > > All the evidence shows that L376 is the definition of Delta graphs. He is > clearly defining a new version of modal logic in the same document in which > he said that he needed to define a new version of modal logic. To deny > that he was defining Delta graphs just does not make any sense of what he > was writing. > > John >
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