On 7/10/2018 9:27 PM, Jon Alan Schmidt wrote:
Is there any conceptual difference between defining a Proposition as a medad Rheme vs. defining a Rheme as an incomplete Proposition?
When I interpret Peirce's writings on any topic in science, math, or logic, I look at his sources and his successors. Church's lambda calculus, for example, replaces parts of an expression with variables instead of blanks. For example, see slide 15 of my introduction to existential graphs: http://jfsowa.com/talks/egintro.pdf For that example, I took an excerpt from one of Peirce's EGs, and its translation to English: "Aristotle is a Stagirite who teaches Alexander who conquers the world." By replacing two names with blanks, Peirce defines a dyadic relation: "___ is a Stagirite who teaches ___ who conquers the world." Note that I did not use the words 'rheme' or 'dicent sign' for those graphs. For an introduction to EGs, I did not want to confuse the students with those words. When I talk about EGs, I say that an EG expresses the same proposition as the sentence, and a sentence with N blanks expresses an N-adic relation. Church would replace those names with variables, and then put the Greek letter λ and the list of variables in front: (λx,y) "x is a Stagirite who teaches y who conquers the world." Church would say that a sentence has an intension (a proposition) and an extension (a truth value T or F in terms of some model). For Church's own discussion of intensions and extensions, see the first 3 pages of his 1941 book: http://jfsowa.com/logic/church.htm The terms intension/extension were introduced by Hamilton. Peirce used the older terms comprehension/extension, which I believe are preferable. One reason is the confusion caused by the pronunciation of 'intension' and 'intention'. As another example, I would cite the version of logic called Common Logic (CL), CL supports *polyadic* functions and relations, which may have a variable number of arguments (zero or more). A relation with zero arguments is a proposition: https://en.wikipedia.org/wiki/Common_Logic John
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