John, List: JFS: I appreciate your comments, even though they disagree with what I believe Peirce intended. But I can see that I need to respond to the questions you raise in the article I'm writing.
Likewise, I appreciate your responses and the ongoing dialogue. As I see it, what we are discussing is not so much a matter of discerning what Peirce intended as adhering carefully to what he actually wrote. JAS: In the RLT example, what is written outside the "lightly drawn oval" *does not* govern what is written inside the oval, at least not in the same sense. After all, what is written outside the oval is not a *proposition *at all ... JFS: It most certainly is a proposition. Outside the oval, there is a line of identity attached to a verb phrase "is much to be wished." That forms a complete sentence "X is something to be wished." The other end of the line is attached to the oval which contains the proposition that is to be wished. Your response here *confirms *exactly what I said and *contradicts *your first sentence. "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. By contrast, a postulate is not a rheme, it is a complete proposition from which other propositions follow necessarily. In Peirce's own words, "A *Postulate *would be a proposition necessary as a premiss for a course of deductive reasoning and predicating a contingent character of the hypothetical subject of that course of reasoning; and any proposition of that description would be a Postulate" (NEM 4:386, 1904). JFS: To express the complete graph, Peirce introduced the word 'that' to create the complete sentence "That you are a good girl is much to be wished." Actually, Peirce never introduces the word "that" and never states the complete sentence, "That you are a good girl is much to be wished." This is your own (correct) translation of his one-of-a-kind EG that comes right after a single sentence introducing it in the text--"When we wish to assert something about a proposition without asserting the proposition itself, we will enclose it in a lightly drawn oval, which is supposed to fence it off from the field of assertions" (RLT 151, 1898). He then presents another EG, for "That you are a good girl is false," and goes on to state, "let it be understood that if a proposition is merely fenced off from the field of assertion without any assertion being explicitly made concerning it, this shall be an elliptical way of saying that it is false" (RLT 152). This is followed by the standard EG for negation, with "You are a good girl" inside the oval and nothing outside it. JFS: You could express the same point in the notation of R514. In the margin, you write an EG that states "The proposition stated below is much to be wished," Inside the content circled in red, you write "You are a good girl." In R 514, Peirce states 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 ..." Accordingly, the EG that you describe here asserts that (a) "The proposition stated below is much to be wished" is merely possible, and (b) "You are a good girl" follows necessarily from "The proposition stated below is much to be wished." Obviously, this is *not at all *logically equivalent to what the one-of-a-kind EG in RLT asserts, namely, "That you are a good girl is much to be wished." 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 if the antecedent is true, such as theorems deduced from the postulates. That being the case, a further improvement would be *shading *the entire margin instead of drawing a red line just inside it, iconically conveying that it is a different surface--"as the main part of the sheet represents existence or actuality, so the area within a cut ... represents a kind of possibility" (CP 4.577, 1906). "It is a help to shade the oddly-enclosed areas and omit the lines that represent the cuts" (R 670:[16], 1911 Jun 12). JAS: the sole reason that Peirce expresses for needing to add a Delta part to EGs is "in order to deal with modals," which for him are propositions involving possibility and necessity. JFS: Please do not make any assumptions about what Peirce did or did not intend. I am not the one making any such assumptions, I am simply drawing reasonable interpretive conclusions based on exact quotations. Peirce explicitly and repeatedly *defines *modal propositions as those involving possibility and necessity, i.e., "proposition A is possibly true" and "proposition B is necessarily (or certainly) true." As far as I know, he *never *refers to propositions involving other expressions like "proposition C is written in Holy Scriptures" or "proposition D is much to be wished" as "modal." Can you provide any exact quotations where he does so? Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt / twitter.com/JonAlanSchmidt On Sat, Feb 24, 2024 at 11:12 PM John F Sowa <s...@bestweb.net> wrote: > Jon, > > I appreciate your comments, even though they disagree with what I believe > Peirce intended. But I can see that I need to respond to the questions you > raise in the article I'm writing. > > JAS> In the RLT example, what is written outside the "lightly drawn oval" > does not govern what is written inside the oval, at least not in the same > sense. After all, what is written outside the oval is not a proposition at > all. > > It most certainly is a proposition. Outside the oval, there is a line of > identity attached to a verb phrase "is much to be wished." That forms a > complete sentence "X is something to be wished." The other end of the line > is attached to the oval which contains the proposition that is to be wished. > > To express the complete graph, Peirce introduced the word 'that' to create > the complete sentence "That you are a good girl is much to be wished." > > You could express the same point in the notation of R514. In the margin, > you write an EG that states "The proposition stated below is much to be > wished," Inside the content circled in red, you write "You are a good > girl." > > As for my description in the slides presented in 2020, I was not lecturing > to Peirce scholars. I started with a summary of the EG notation of 1911. > Then slide 30 is stated in the terms introduced in slides15, 16, 17... > Therefore, > my later discussion is stated in those terms. > > JAS> the sole reason that Peirce expresses for needing to add a Delta part > to EGs is "in order to deal with modals," which for him are propositions > involving possibility and necessity. > > Please do not make any assumptions about what Peirce did or did not > intend. As you know, Peirce had the most complete collection of MSS on > medieval logic in the Boston area -- he had more than the Harvard > libraries. Among the authors were logicians call the "Modistae". They had > a huge number of modes, including "written in Holy Scriptures". We don't > know exactly what Peirce read, but It's quite likely that he had read > something by or about them. And we don't know what he thought about them. > > In any case, such modes may be possible, actual, or necessary. The > additional information, such as "written in Holy scriptures" or "is much to > be wished" is descriptive, but it's independent of the state of those > worlds as possible, actual, or necessary. > > As more examples, look at the three ways of describing the diagrams in > slide 31. To start, let's assume that Pierre is sitting in the actual > world. The content of the thought balloons may be actual or possible. His > thoughts about them, such as wishing or hoping, add information, but they > don't change their status as actual or possible. > > John >
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