John, List: JFS: But in R670. Peirce definitively rejected the idea of defining negation in terms of implication and falsity.
Also JFS (https://list.iupui.edu/sympa/arc/peirce-l/2021-05/msg00045.html): In discussions about Peirce and his writings, anything other than an exact quotation by Peirce is an opinion ... any statement about what Peirce meant by anyone other than Peirce is an opinion ... nobody can claim that anything other than an exact quotation is what Peirce intended. Please provide "an exact quotation by Peirce" in which he "definitively rejected the idea of defining negation in terms of implication and falsity." Otherwise, in accordance with these recent methodological assertions, it is just an opinion and cannot be claimed as "what Peirce meant" or "what Peirce intended." There is certainly no such quotation in R 670, and *omitting *the derivation of negation from the implication of falsity in that manuscript (and others) does not constitute *rejecting *it, much less *definitively *rejecting it. As I have said before, and as Francesco Bellucci fully agreed, a much more plausible interpretation is that Peirce merely *simplified *his presentation of EG for an audience (National Academy of Sciences) that was not previously familiar with them. As I have also said before, what Peirce *does *definitively reject is his 1906 *description *of EG in "Prolegomena to an Apology for Pragmaticism"--*not *the system itself, nor its underlying philosophical basis. CSP: To more completely dissect deduction I use a diagrammatic syntax that I *described *very badly and with unbearable language in The Monist of October 1906 ... (RL 378, 1911 Sep 29; my translation, bold added) CSP: The *description *was, on the whole, as bad as it well could be, in great contrast to the one Dr. Carus rejected. For although *the system itself* is marked by extreme simplicity, the *description *fills 55 pages, and defines over a hundred technical terms applying to it. (RL 376, 1911 Dec 6; bold added) CSP: Nine years later [in 1906], having found that *system *of expressing assertions that I had given my rejected article to have been a perfect Calumet mine in my own work, I undertook to write such an *account *of that system as no *stultus stultorum* could refuse to print; and, as a natural consequence, it was far the worst I ever perpetrated. (RL 477, 1913 Nov 7; bold added) Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Tue, May 18, 2021 at 9:59 PM John F. Sowa <[email protected]> wrote: > Jon AS, > > I'm writing an article about Peirce's writings on logic in 1911, which > I'll post to P-list soon. And I'm glad that we can agree on that point. > > JFS> However, Peirce and Brouwer were on opposite sides of fundamental > issues about the nature of mathematics. ... In general, Brouwer's > assumptions were diametrically opposed to Peirce's fundamental assumptions. > > JAS> I wholeheartedly agree. > > But in R670. Peirce definitively rejected the idea of defining negation in > terms of implication and falsity. I show that in my article. > > JAS> Peirce anticipates aspects of the formal system that is now known as > intuitionistic logic--e.g., defining negation as the implication of > falsity... > > Nobody knows what Peirce would have said about the less dogmatic treatment > of intuitionistic logic by Heyting and others, including Oostra. But it's > doubtful that he would have approved of the drastic reduction in acceptable > mathematical theories. He was always highly suspicious of any attempt to > block the way of inquiry. > > John >
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