List , John: I wrote:
"Because it violates the common sense of the meaning of natural language terms in the premise.” John, your introducing the issue of the "Law of the Excluded Middle” is a red herring to me. Let me add a word or two to clarify my intent. My concern is rather esoteric from the attempt of mathematical / logical reasoning to reduce meaning to empty symbols. My concern is founded on the nature of the meanings of signs / signals / icons / indexes and symbols. The usage of the term “Everything” includes, I presume, all possible premises, irrespective of the symbolic origin of the premise. “Everything”, in my opinion, goes far beyond the ultra-simple notions mathematical logic, mathematical formalisms, and physical units of representations (abstractions from nature). The universe is what it is and the CSP writings challenges us find representations of all its emanations, not merely those that are concerned to the well-worn paths of predicate logic and ridiculous functions that ignore the observable nature of nature. If one wishes to explore the pragmatic nature of “everything”, one could choose a significant concern, such as the practice of medicine or molecular biology. Cheers Jerry > On Oct 11, 2017, at 1:20 AM, John F Sowa <s...@bestweb.net> wrote: > > Jerry LRC, Jon AS, List, > > Jerry >>> [JFS] Since a contradiction is always false, a contradiction >>> implies everything. >> Everything? While this assertion is widely repeated in >> the literature, I think it is highly problematic. > > It's widely repeated because it is a fundamental assumption > of most versions of formal logic -- i.e., of every logic that > assumes the Law of Excluded Middle (LEM). > > But it is indeed problematic. Brouwer, for example, rejected > LEM for intuitionistic logic. > > And even for systems that are based on LEM, nobody actually claims > that everything has been proved. Instead, they recognize that there > is a mistake somewhere, and they start searching for it. > > Jon >> [JFS] For modal logic, there are three options: >> necessary, possible, and contingent (not necessary and not impossible). >> Did you mean to say necessary, impossible, and contingent? > > Yes. I wrote that too hastily. "not impossible" is a synonym > for "possible". For the three options, I should have written > necessary, impossible, and contingent (possible and not necessary). > > But after I sent that note, I did some googling, which led me > to the article "Peirce and Brouwer" by Conor Mayo-Wilson: > http://mayowilson.org/Papers/Peirce_Brouwer.pdf > > Some excerpts: > > page 1 >> In his 1908 "The Unreliability of the Logical Principles" Brouwer >> rejected the law of excluded middle (LEM)... >> Five years earlier, Peirce had reached similar conclusions... > > p. 2 >> Peirce and Brouwer's common rejection of LEM is not simply a >> coincidence, but rather, stems from a deep underlying similarity >> in their respective philosophical analyses of the continuum. > > p. 3 >> Peirce and Brouwer seemed to have no knowledge of each other's work. >> Brouwer might have learned of Peirce's ideas on semiotics in the >> 1920's through his association with Lady Welby... However, the two >> most likely worked independently... > > Fernando Zalamea also discusses Peirce and Brouwer in connection > with the continuum. But he doesn't mention Lady Welby: > http://uberty.org/wp-content/uploads/2015/07/Zalamea-Peirces-Continuum.pdf > > In any case, these sources indicate that Peirce began to reconsider > his ideas about LEM around the same time as the Lowell lectures. > His thoughts about the continuum seem to be the original reason. > But by 1909, his thoughts led to 3-valued logic and a new way > of representing and describing existential graphs. > > John > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu > . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu > with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at > http://www.cspeirce.com/peirce-l/peirce-l.htm . > > > >
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