> 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 >> >> _ _ _ _ _ _ _ _ _ _ >> ⺠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 . >> ⺠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 . >> ⺠PEIRCE-L is owned by THE PEIRCE GROUP; moderated by Gary >> Richmond; and co-managed by him and Ben Udell. >> >
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