List, John: Comments on “technical” aspects of Law of Excluded Middle (LEM) are inserted.
> On Oct 12, 2017, at 3:15 PM, John F Sowa <s...@bestweb.net> wrote: > > Jerry and Kirstima, > > Jerry >> the issue of the "Law of the Excluded Middle” is a red herring to me. > > Kirstima >> LEM presents one of the three basic misassumptions in modern logic. > > LEM is a convention used in a technical (mathematical) sense. > It's important to keep the conventions distinct from ordinary > (non-technical) uses of words. LEM plays a central role in triad, the logic of logic, the logic of mathematics and the logic of science. It is far more important then just a notational convention or a traditional usage of a mathematic symbol which is free to substitution for another symbol with the same definition. LEM has profound geometric inference for continuity. > > Jerry >> “Everything”, in my opinion, goes far beyond the ultra-simple notions >> mathematical logic, mathematical formalisms, and physical units of >> representations > > Yes, of course. You have to keep technical terms in logic distinct > from words in ordinary language that are spelled the same. ??? My view is rather different, perhaps because economic considerations are suppressed. If the usage of a word is not that of ordinary language, then one is obligated to distinguish the technical usage and explain to the reader what it means. CSP was very careless in this area and, often, the modern reader is very hard put to make any sense of his techno - babble. At least, that is how I often feel. On the other side of the coin, when CSP felt up to the task, he wrote many beautiful sentences and paragraphs with a special brilliance that is seldom matched. > > The term 'universe of discourse' is a technical term, which Boole > introduced in his famous book, _Laws of Thought_ (1854): >> Now, whatever may be the extent of the field within which all the >> objects of our discourse are found, that field may properly be termed >> the universe of discourse. Furthermore, this universe of discourse >> is in the strictest sense the ultimate subject of the discourse. > > When Peirce was talking about logic, he followed the terminology > of Boole and de Morgen. It's important to remember that context. I disagree. CSP often stated that chemistry and chemical names were intrinsic to his logical terminology. If one is fluent in the logic of chemistry (as it developed in the second half of the 19 th Century), then the augmentation of Boolean and de Morgen terminology is readily apparent in the logic of relatives. And in his development of his views on (non-mathematical?) Graph Theory. I agree that it is important to remember context, but this is possible if and only if one is looking at at all possible interpretations of “icons, indices and symbols” as used in the scientific community in his age. Cheers Jerry
----------------------------- 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 .
