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<http://www.LinkedIn.com/in/JonAlanSchmidt> - twitter.com/JonAlanSchmidt<http://twitter.com/JonAlanSchmidt> On Thu, Sep 5, 2019 at 1:46 PM John F. Sowa <[email protected]<mailto:[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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