John,
> Op 30 augustus 2020 om 20:55 schreef "John F. Sowa" <s...@bestweb.net>: > > > Auke, I agree with you about the issues and priorities. > > AvB> Peirce is multi facetted. Each of us looks from a particular > angle... I am not interested in what might be the final version Peirce wrote > on the negation vs scroll issue... I can agree with you if we are discussing > EG as a formal system. > > Yes. Formal EGs are the foundation. As Peirce himself said, logic as > semiotic is much broader. It includes the methodeutic for analyzing and > developing the immense variey empirical sciences. > We have discussed this point before. It seems to me that you forget about speculative grammar and only recognize critic and speculative rethoric. But if we abstract from the apprehension of the sign as an object when we look with the detached eye of the logician (the realm of critic), we must take care when going to speculative rethoric to again direct our attention to the role the apprehension of the sign as an object plays in our processes of interpretation. We must acknowledge that each interpreter has its own verso sheet. And, that this sheet determines as what sign a representamen gets interpreted. Auke > > AvB> In a sense when we interpret we look at the input from all logical > perspectives. Box-X running from 0000 to tttt, or from doubt to belief. > > Yes. All versions of classical first-order logic are sufficiently > expressive to define all the patterns of mathematics. But the eg1911 version > (as stated in L231) has a simplicity and symmetry that makes the definitions > easier to state and the proofs easier to discover. > > For examples, see the slides I presented at an APA conference in 2015 and > extended with more examples for another workshop: "Peirce, Polya, and > Euclid: Integrating logic, heuristics, and geometry," > http://jfsowa.com/talks/ppe.pdf . > > Note that the two-dimensional shaded areas of eg1911 can be generalized > to 3-D shaded regions for proofs in solid geometry. They could even be > generalized to 4-D regions for "stereoscopic moving images", which Peirce > mentioned in L231. Those generalizations are not possible with the 1903 > scrolls or the 1906 recto/verso sides of a 2-D sheet. > > Another important example is an unsolved research problem that was stated > in 1988 and remained unsolved until 2010. Good logicians failed to find the > proof because they made the same mistake that Peirce stated in 1893 (CP > 4.76): "For [the reader] cannot reason at all without a monstrative sign of > illation." See the proof with EG rules in slide 65 ff of ppe.pdf. > > Examples of signs of illation (or inference) include Peirce's claw > symbol for if-then in Boolean algebra or his scroll in EGs. Those > symbols are asymmetric, but the critical step for solving the problem of > 1988 is easier to discover with the symmetric EG "permissions". > > As for the time and date when Peirce discovered the simplicity and > generality of the eg1911 rules, compare R669, which ends abruptly > shortly after 7:40 pm on 2 June 1911, to the completely rewritten R670, > which begins on June 7. On June 22, he began L231, which contains a > complete and polished version of the logic in R670. > > The date of the discovery is interesting for Peirce scholars. But the > power and generality of eg1911 is demonstrated by the applications. For > more examples, see "Diagrammatic reasoning with EGs and EGIF", > http://jfsowa.com/pubs/diagrams.pdf ; "Reasoning with diagrams and > images", http://www.collegepublications.co.uk/downloads/ifcolog00025.pdf > > 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 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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