From owner-conlang@diku.dk Tue Jan 30 05:15:29 1996 Received: from odin.diku.dk (daemon@odin.diku.dk [130.225.96.221]) by locke.ccil.org (8.6.9/8.6.10) with ESMTP id FAA19906 for ; Tue, 30 Jan 1996 05:15:27 -0500 Received: (from daemon@localhost) by odin.diku.dk (8.6.12/8.6.12) id KAA13843 for conlang-outgoing; Tue, 30 Jan 1996 10:22:34 +0100 Received: from mailserver.iris.firenze.it (risc_en0.iris.firenze.it [193.43.110.130]) by odin.diku.dk (8.6.12/8.6.12) with SMTP id KAA13828 for ; Tue, 30 Jan 1996 10:22:11 +0100 Received: from iris01.iris.firenze.it by mailserver.iris.firenze.it (AIX 3.2/UCB 5.64/951203) id AA09044; Tue, 30 Jan 1996 10:24:11 +0100 Date: Tue, 30 Jan 1996 10:24:11 +0100 Message-Id: <9601300924.AA09044@mailserver.iris.firenze.it> X-Sender: mmg@risc.iris.firenze.it X-Mailer: Windows Eudora Version 1.4.3 Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: conlang@diku.dk From: mmg@risc.iris.firenze.it (Maurizio M Gavioli) Subject: CONLANG: Re: Logic and Language Sender: owner-conlang@diku.dk Precedence: bulk Reply-To: mmg@risc.iris.firenze.it (Maurizio M Gavioli) Status: OR X-Mozilla-Status: 0001 Content-Length: 1614 answering to Barry Savage, PDoudna@AOL.COM writes: > The law of excluded middle (A is either >B or not-B) and the law of non-contradiction (A is not both B and not-B) are >no longer necessarily valid in three-valued logics. Well, the law of excluded middle (middle? I know of the excluded third) is by necessity no longer valid, because with three values, there is a third value! To drop the validity of the law of non-contradiction is a far step, however! Without it, it would even be difficult to construct any truth table! A small note, incidentally, multi-valued logic is what logicians used to call modal logic, about which there a huge literature. The most developped case, however, is the four-valued logic, which goes back to Aristotle (as almost anything, from logic to lawn-mowers...) and whose values interpretation is usually: false, possible, necessary, true. >I would observe also that whereas logicians consistently interpret "not" and >negation in English as part of a two-valued logic, in common usage "not" and >negation are frequently interpreted as representing what is contrary rather >than what is contradictory. And also what is opposite, according to some polarity or metrics (North, South; here, there; and so on), for which one cannot strictly speak of "negation". Maurizio M. Gavioli -------------------- Maurizio M. Gavioli Associazione IRIS mmg@risc.iris.firenze.it via di Vincigliata 26, I-50135 Firenze - Italy phone: +39 55 603 251 - fax.: +39 55 603 383