John, yes, Peirce in 1903 seems fully committed to the principle of excluded middle where "necessary reasoning" is involved.
The reason I'm flagging this definition of "not" as problematic (for me) is that in Peirce's next lecture it plays the key role in the evolution from the "scroll" (read as a conditional) to the "cut" (read as negation) in Existential Graphs. And then Peirce realizes in 1906 that this way of reading becomes a problem in the construction of gamma graphs. Anyway, we'll come to that soon enough, in Lowell 2 ... which was also left unpublished by the CP editors, probably for the same reason! Gary f. -----Original Message----- From: John F Sowa [mailto:s...@bestweb.net] Sent: 9-Oct-17 16:38 To: peirce-l@list.iupui.edu Subject: Re: [PEIRCE-L] Lowell Lecture 1.8 On 10/9/2017 2:28 PM, g...@gnusystems.ca wrote: > I never would have guessed that “what we mean by “/not/” is “every > proposition would be true if it were.” That comment can only be true if there is no middle option -- i.e., a stone is either hard or not hard AND there is no possibility of being neither hard nor not hard. From http://www.digitalpeirce.fee.unicamp.br/lane/p-trilan.htm > Charles Peirce was the first logician to define logical operators for > a many-valued system of logic.[1] In February 1909, on three pages of > a notebook in which he recorded his thoughts on logic (MS 339) Peirce was probably troubled by that comment himself. Or perhaps somebody who attended the lecture asked a question that caused Peirce to rethink the issue for 3-valued logic. In fact, that question may have puzzled the editors -- and that's why they did not publish the final paragraph in the CP. It's significant that Peirce wrote the Lowell lectures in 1903 but didn't write the truth tables for 3-valued logic until 1909. He may have been thinking about the issue for some time, but hadn't worked out the details. John
----------------------------- 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 .
