Re: [PEIRCE-L] Problems in mixing quantifiers with modal logic (was Delta Existential Graphs
John, I have been following this exchange between you and Jon Alan with considerable interest. Thank you both for discussing these most interesting -- and I think, important matters relating to modals, Delta graphs, etc. -- in the generally collegial manner in which you have been proceeding. You wrote: And please read what Peirce was writing to William James around that time. He was talking about a Big Book with some rather complex requirements for the logic -- far more than alpha graphs, even with modality. And the content of the Big Book had a large overlap with L231 of June 1911. That letter mentioned his goal of a logic for representing moving motion pictures. That's not possible with Alpha graphs. I would like to suggest that it would be helpful if, instead of suggesting that, for example, Jon (and, I assume, anyone reading this exchange) should "read what Peirce was writing to William James around that time," that you offer exact quotations, something you've not infrequently have suggested is 'best practice' in considering what Peirce actually said, actually had in mind. In truth, I haven't seen many exact quotations in your posts in this exchange (something Jon famously -- or infamously, depending on your perspective -- can't be accused of) and this has often made it difficult to discern exactly what your critique of Jon's position is nor, for that matter, what your's is in certain given cases. I doubt that many, following this recent exchange, have the time or inclination to hunt for quotations that are only *very generally* pointed to. Again, I have found your exchange most interesting and valuable. But on a listserv such as Peirce-L, it would be more than helpful to have exact quotations provided in posts to the List, especially in consideration of the topics which you and Jon have been discussing. Best, Gary On Tue, Mar 5, 2024 at 6:24 PM John F Sowa wrote: > Jon, > > The first point to emphasize is that Peirce's primary goal in the last > decade of his life was to provide a proof of pragmatism. That would > require a system of logic that could express and analyze rather > sophisticated texts about science. The metalanguage of the IKL logic in > 2006 is very close to Peirce's EGs supplemented with the operator that he > specified in R514 (June 1911), which seems to be very similar to what he > was specifying in L376 (December 1911). > > Alpha graphs for Boolean logic are a trivial subset of EGs. Peirce made > an important contribution to Boolean logic by adding the symbol -< for > implication. He also made a few other important modifications. But that > was a very early project. In 1903, he presented his version of modal > logic, which included EGs with lines of identity. As far as I know, there > was never a reason for him to say anything further about Alpha graphs other > than the fact that they were a simple subset that could be freely mixed > with Beta graphs. > > JAS> I am still wondering exactly how your candidate would represent the > five modal propositions that Peirce wrote in his Logic Notebook, if not > exactly as he scribed them on that page (R 339:[340r], 1909 Jan 7. > > Did you read my response? I showed that the five EGs on the excerpt you > included were *not *modal. They were simple first-order (Beta) EGs. And > I included a translation of all five to English sentences that did not > require a single occurrence of the words 'possible' or 'necessary'. > > As far as I know, Peirce never used the modal logic of 1903 for any > purpose in any MSS after 1903. If you can find any examples, please send > us a copy. But he did write quite a bit about modality, including his > tinctured graphs of 1906. He did criticize them in L376 for their > *notation*, but not their goal of representing rather sophisticated modal > content -- much more than modal alpha graphs. > > And please read what Peirce was writing to William James around that > time. He was talking about a Big Book with some rather complex > requirements for the logic -- far more than alpha graphs, even with > modality. And the content of the Big Book had a large overlap with L231 of > June 1911. That letter mentioned his goal of a logic for representing > moving motion pictures. That's not possible with Alpha graphs. > > Since Risteen had considerable experience with Cayley's trees, that is an > excellent reason for his visit, and for Peirce to be constructing a tree of > "papers". It's inconceivable that he would have invited Risteen (a former > collaborator who had an excellent understanding of his 1885 logic of first > order and higher order logic) to discuss some trivial work with a subset of > the modal logic of 1903. > > Four points: (1) there is evidence of metalanguage (postulates in the > margin about nested graphs) in R514 and L376: (2) there is no evidence that > Peirce intended to adopt a subset of his 1903 modal notation, which he had > not used in any MSS after 1903; Risteen's
Re: [PEIRCE-L] Problems in mixing quantifiers with modal logic (was Delta Existential Graphs
Jon, The first point to emphasize is that Peirce's primary goal in the last decade of his life was to provide a proof of pragmatism. That would require a system of logic that could express and analyze rather sophisticated texts about science. The metalanguage of the IKL logic in 2006 is very close to Peirce's EGs supplemented with the operator that he specified in R514 (June 1911), which seems to be very similar to what he was specifying in L376 (December 1911). Alpha graphs for Boolean logic are a trivial subset of EGs. Peirce made an important contribution to Boolean logic by adding the symbol -< for implication. He also made a few other important modifications. But that was a very early project. In 1903, he presented his version of modal logic, which included EGs with lines of identity. As far as I know, there was never a reason for him to say anything further about Alpha graphs other than the fact that they were a simple subset that could be freely mixed with Beta graphs. JAS> I am still wondering exactly how your candidate would represent the five modal propositions that Peirce wrote in his Logic Notebook, if not exactly as he scribed them on that page (R 339:[340r], 1909 Jan 7. Did you read my response? I showed that the five EGs on the excerpt you included were not modal. They were simple first-order (Beta) EGs. And I included a translation of all five to English sentences that did not require a single occurrence of the words 'possible' or 'necessary'. As far as I know, Peirce never used the modal logic of 1903 for any purpose in any MSS after 1903. If you can find any examples, please send us a copy. But he did write quite a bit about modality, including his tinctured graphs of 1906. He did criticize them in L376 for their notation, but not their goal of representing rather sophisticated modal content -- much more than modal alpha graphs. And please read what Peirce was writing to William James around that time. He was talking about a Big Book with some rather complex requirements for the logic -- far more than alpha graphs, even with modality. And the content of the Big Book had a large overlap with L231 of June 1911. That letter mentioned his goal of a logic for representing moving motion pictures. That's not possible with Alpha graphs. Since Risteen had considerable experience with Cayley's trees, that is an excellent reason for his visit, and for Peirce to be constructing a tree of "papers". It's inconceivable that he would have invited Risteen (a former collaborator who had an excellent understanding of his 1885 logic of first order and higher order logic) to discuss some trivial work with a subset of the modal logic of 1903. Four points: (1) there is evidence of metalanguage (postulates in the margin about nested graphs) in R514 and L376: (2) there is no evidence that Peirce intended to adopt a subset of his 1903 modal notation, which he had not used in any MSS after 1903; Risteen's expertise suggests that trees of "papers" are very likely to be involved in the representation and reasoning with and about Delta graphs; and (4) IKL or some version of metalanguage for representing trees of papers can represent a significant amount of computer science and AI today. That is the topic of the article about Delta graphs, which I am writing. John From: "Jon Alan Schmidt" John, List: JFS: One reason why I did not respond in detail to your previous note (copied below) is that your citations to the writings by Dunn and Goble only apply to PROPOSITIONAL modal logic (no quantifiers). I have acknowledged this all along--my candidate for Delta EGs is an extension of Alpha EGs, not Beta EGs. After all, the various modal axioms are formulated as extensions of classical propositional logic, not first-order predicate logic (FOPL). The heavy lines of compossibility (LoCs) in my Delta EGs represent possible states of things (PSTs) in which propositions denoted by attached letters would be true, while the heavy lines of identity (LoIs) in Beta EGs represent indefinite individuals to which general concepts denoted by attached names are attributed. Roberts suggests that these two notations could be combined, with LoCs attached to the top of names that are also attached to LoIs (1973, pp. 99-100); but as you rightly observe later in your post, this "opens up a huge can of worms." I have mentioned previously an exception to this cautionary note, which is implementing system P with no iterated modalities. LoCs are then attached to letters for propositions on the one sheet for the actual state of things (AST), which are keyed to different Beta graphs with LoIs on the various sheets for PSTs. This demonstrates the sense in which formal propositional logic as implemented by Alpha EGs is a simple metalanguage for reasoning about propositions, each of which can then be more informatively
