Jon A., List: Indeed, Peirce's Law is one of several possible formalizations of excluded middle within classical logic, although it seems likely that Peirce himself would have objected to referring to it as such since he denied the underlying assumption.
CSP: Logic requires us, with reference to each question we have in hand, to hope some definite answer to it may be true. That *hope *with reference to each case as it comes up is, by a *saltus* [leap], stated by logicians as a *law *concerning all cases, namely, the law of excluded middle. This law amounts to saying that the universe has a perfect reality. (NEM 4:xiii, no date) In a 2013 paper (in Spanish, https://www.academia.edu/36792040/Cuadernos_de_Sistem%C3%A1tica_Peirceana_5, pp. 5-24) Arnold Oostra discusses how Peirce's 1885 article, "On the Algebra of Logic: A Contribution to the Philosophy of Notation" (CP 3.359-403), furnishes an axiomatization of classical propositional logic (CPL); and the last of the five axioms is what today we call Peirce's Law. As Oostra notes, "With this axiomatization of CPL, Peirce anticipated the development of mathematical logic by about 40 years" (p. 21). Oostra goes on to show that (ironically) by omitting the "law" that now bears his name and adding several axioms defining conjunction and disjunction without excluded middle accordingly, Peirce also could have provided an axiomatization of intuitionistic propositional logic (IPL) well in advance of Brouwer. In Oostra's words, "his axiomatization of 1885, omitting Peirce's Law that he included as a last resort to prove the completeness of CPL, hides the nucleus of an axiomatization of the IPL" (p. 22). Regards, Jon Alan Schmidt - Olathe, Kansas, USA Structural Engineer, Synechist Philosopher, Lutheran Christian www.LinkedIn.com/in/JonAlanSchmidt - twitter.com/JonAlanSchmidt On Sun, Dec 20, 2020 at 8:00 AM Jon Awbrey <jawb...@att.net> wrote: > Peircers, > > Pursuing the discussion of many things: of laws — and graphs — and > reasoning — of contradictions — and abducations — and why the third is > given not — and whether figs have wings — > > It might not be non sequitur to remember that place in Peirceland where we > walk the line between classical and intuitionistic logic, namely, the > boundary marked by the principle we have come to call Peirce's Law. > > Here's a link to a bit of fol-de-rule, with graphs and everything — > > Peirce's Law > https://inquiryintoinquiry.com/2008/10/06/peirces-law/ > > Regards, > > Jon >
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