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CONLANG: Re: Logic and Language

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by necessity no longer valid, because with three values, there is a third value!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

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