From the list perspective: Jas wrote:
I have said it before, I will say it again--we have different purposes, so we reach different conclusions. -- Since perspective is important, it might be a good idea to explicate the differences in purpose each of you entertain. best, Auke > Op 24 januari 2021 om 5:32 schreef "John F. Sowa" <[email protected]>: > > > Jon AS, List, > > The *opinion* that the EG version of June 1911 is Peirce's best is > Peirce's own, as he stated in December, after six months of further > consideration. The fact that he stated it in a lengthy letter to a member of > Lady Welby's significs group is further evidence of its importance. > > That opinion is further supported by the development of logic in the > following century. Please read beyond slide 12 of > http://jfsowa.com/talks/egintro.pdf . See also > http://jfsowa.com/talks/ppe.pdf . Slide 2 of ppe.pdf has a link to a 76-page > article published in the Journal of Applied Logics that goes into all the > details. > > One of the most important features of the 1911 version is its ability to > serve as a foundation for Gerhard Gentzen's two systems of natural deduction > and clause form (published in 1934). Those two system have had immense > influence on modern proof procedures -- including the development of modern > methods of computational theorem proving. > > But in 1988, Larry Wos, one of the pioneers in theorem proving methods, > published an unsolved problem about relating Gentzen's two systems. This > problem is important for automatically relating two different proof > procedures. In 2011, I published the solution in Semiotica. For a quick > outline, see egintro.pdf or ppe.pdf. For the details, see the article in the > J. of Applied Logics. > > That proof is clean and clear in terms of the 1911 EGs. It's possible in > terms of the earlier versions, but it is more complex and harder to discover. > > Another important point: The 1911 EGs can be generalized beyond two > dimensions for "stereoscopic moving images". It's not an accident that > Peirce mentioned them in L231, but he had not yet decided how to proceed with > the details. ppe.pdf (and the JAL article) present a generalization. > Whether that is what Peirce was thinking is not clear, but it shows that the > 1911 EGs are sufficient to support something along the lines that Peirce was > contemplating. > > As for the point that negation must be inferred, please reread slides 11 > and 12 of egintro.pdf. Note that observing if-then is impossible (for a > lengthy discussion, see Hume and the lengthy debates that followed). > > But the inference required for negation is quite simple: If you expect > something and don't observe it, you can use the word 'not'. Children learn > to use the word 'not' sometime after their second birthday -- around the same > time that they learn to use the words 'I' and 'you' correctly. But they > don't learn to use 'if-then' and 'or' until much later. > > And the idea that children (or even adults) would learn 'not' from the > derivation that Peirce presented in 1906 or the one in R669 is absurd. > > There is much more to say about all these issues, but please read at > least to the end of egintro.pdf. It also has many references for further > study. > > 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 [email protected] > . > ► To UNSUBSCRIBE, send a message NOT to PEIRCE-L but to > [email protected] with no subject, and with the sole line "UNSubscribe > PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > ► PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary Richmond; and > co-managed by him and Ben Udell. >
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