Jeff, List: Indeed, I provided the same link to the English slide presentation in my post that started this thread. Again, the papers include plenty of IEG examples, and once one figures out the Spanish terms and abbreviations, they are relatively easy to follow. Moreover, I am finding that https://translate.google.com/ does a surprisingly decent job with the text. :-)
I also previously quoted Zalamea and linked to his short article ( https://riviste.unimi.it/index.php/Lebenswelt/article/view/11113/10508) that summarizes both Oostra's IEGs and Francisco Vargas's proposal for a new mathematical model of Peirce's continuum; he calls the latter "a single stroke of genius" (p. 79). Even so, he later states, "I have had the chance of having fantastic students, which, then, with time, have become my teachers. Arnold Oostra is possibly the greatest student I have encountered, and, undoubtedly, he has now become the foremost international scholar on Peirce's mathematics" (p. 82). High praise, especially considering the source! Incidentally, as you probably know, Vargas's paper on the continuum is in volume 7 of *Cuadernos de Sistemática Peirceana* along with your own contribution, "On the Hypotheses that Lie at the Bases of Discrete Systems of Mathematics: Drawing on Peirce’s Phenomenology." Zalamea's brief synopsis in English is already well beyond my competence, so in this case I do not hold out much hope of being able to make sense of the details in Spanish. Regards, Jon S. On Thu, Sep 5, 2019 at 4:47 PM Jeffrey Brian Downard < [email protected]> wrote: > Hi Jon S, John S, List, > > Arnold Oostra gave presentations in English on his work on intuitionistic > logics and the EG at the Peirce Centennial Congress in 2014 and on related > themes at the later meeting on Peirce's work on mathematics in Bogota > (organized by Fernando Zalamea). At the latter, he was effectively the > keynote speaker. > > Having searched Google Scholar, it is hard to fund much of his work that > isn't in Spanish. Here is an example of a presentation in English to give > you a flavor of what he is doing: > https://matematicas.uniandes.edu.co/eventos/SLALM2012/slides/arnold_oostra.pdf > > Fernando has created a community of students and scholars in Bogota who > are working on Peirce and the EGs. Arnold has reproduced that model in > Tolima. The quality of the research products of his *undergraduate* > students is quite strong. It is clear that both Fernando and Arnold are > remarkable teachers as well as researchers. > > --Jeff > Jeffrey Downard > Associate Professor > Department of Philosophy > Northern Arizona University > (o) 928 523-8354 > ------------------------------ > *From:* Jon Alan Schmidt <[email protected]> > *Sent:* Thursday, September 5, 2019 1:04:55 PM > *To:* [email protected] > *Subject:* Re: [PEIRCE-L] Intuitionistic Existential Graphs (IEGs) > > John, List: > > Thanks for the additional background information. For anyone interested > in further details about Oostra's approach, attached is a combined PDF with > his relevant papers in Spanish from the first five volumes of *Cuadernos > de Sistemática Peirceana*. The first and last relate Peirce's thought to > intuitionistic mathematics and logic in general, while the middle three > specifically explain his Alpha, Beta, and Gamma systems of IEGs. He > concludes by stating that (ironically) omitting what is now known as > Peirce's Law from his 1885 article in *The American Journal of > Mathematics*, "On the Algebra of Logic: A Contribution to the Philosophy > of Notation" (CP 3.359-403), would have provided the nucleus for an > axiomatization of intuitionistic logic. > > Regards, > > Jon Alan Schmidt - Olathe, Kansas, USA > Professional Engineer, Amateur Philosopher, Lutheran Layman > www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt > > On Thu, Sep 5, 2019 at 1:46 PM John F. Sowa <[email protected]> wrote: > >> Intuitionistic logic was founded by the Dutch mathematician L. E. J. >> Brouwer. He objected to "nonconstructive" proofs by contradiction. >> >> Many mathematicians have been sympathetic, but they were reluctant to use >> Brower's logic because it made many legitimate theorems more difficult to >> prove. >> >> For more info, see https://plato.stanford.edu/entries/intuitionism/ >> >> Re EGs: Peirce's diagrammatic reasoning, which begins with diagrams and >> reasons about them is by its very nature constructive. However, Peirce's >> rules of inference also allow proofs by contradiction. >> >> The idea of making EGs intuitionistic would enforce constraints on the >> rules of inference to prohibit the options that are nonconstructive. That >> could be considered as a kind of three-valued logic with True, False, and >> Not provable. But that's different from True, False, and Unknown -- or the >> fuzzy versions with a continuous range of values. >> >> Susan Haack strongly objected to Zadeh's idea of a continuum of truth >> values. But it would be more appropriate to consider the fuzzy values as >> degrees of confidence or belief. >> >> Re EGs: It's possible to translate any algebraic notation to and from an >> EG form. Therefore, any interpretation -- fuzzy, intuitionistic, modal, >> metalanguage -- that could be expressed in an algebraic form could be >> adapted to an EG version and vice-versa. >> >> By the way, Brouwer was a member of Lady Welby's Significs group, but >> it's unlikely that Peirce and Brouwer ever communicated. >> >> John >> >
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