Talk:Tautology (rule of inference)

Wrong name

This seems extremly unlikely to be the most common usage of "Tautology" as a "rule of inference", or even as a "rule of replacement". The common rule is that if $A\leftrightarrow B$ is an (already established) tautology (logic), then A can be replaced by B. Furthermore, if you (collectively) can use Hurley, I should be able to use Rubin, Jean E. (1990). Mathematical Logic: Applications and Theory. Saunders College Publishing. ISBN 0-03-012-808-0., which calls these rules idempotency rules. I should add that her tautology (rule of inference) is closer to a tautology (rhetoric); if $P_{1}\land P_{2}\land \cdots \land P_{n}\rightarrow Q$ is a tautology (logic), then $P_{1},P_{2},\cdots ,P_{n}\vdash Q$ is a rule.

This is clearly the wrong name for this article. — Arthur Rubin (talk) 16:31, 3 March 2012 (UTC)

Say Arthur, I don't disagree with you! However, this is the name given in three of the most popular textbooks in the country. The vast majority of people learning this subject matter are using this terminology. I even put a little bit of a response to this embarrassing situation by explaining that tautology isn't the best name. However, I don't have sources using other names. There are two possible ones that I would propose (although, like I said --need sources)... Principle of tautology for disjunction and Principle of tautology for conjunction or Idempotency of disjunction of identity and Idempotency of conjunction of identity. Since at this point I am throwing out unsourced names that just make sense, I considered but rejected Idempotency of disjunction and Idempotency of conjunction because those describe a different theorem. Greg Bard (talk) 18:52, 3 March 2012 (UTC)

Perhaps we could put together a table of what the rules are in different textbooks. I should point out, in regard "most popular", that my mother's book really was the best-selling logic textbook in Canada for at least one year in the last century, so shouldn't be disregarded entirely. I have no idea where the general name discussion should be done: Talk:rule of inference or Template talk:rules of inference come to mind. — Arthur Rubin (talk) 19:21, 3 March 2012 (UTC)

I think a name other than Principle of tautology for disjunction and Principle of tautology for conjunction or Idempotency of disjunction of identity and Idempotency of conjunction of identity would require support from more than one substantial source. I am certainly open minded to including the more generalized principle mentioned in your mother's book. However, I really don't see a need or advantage to moving it. "Tautology", even if not perfect, is the prevailing term these days. I don't want to confuse anyone.Greg Bard (talk) 19:58, 3 March 2012 (UTC)

On second thought, I've seen it in literature, so I would be open to Idempotency of disjunction and Idempotency of conjunction and I think that is probably the best we are going to do. Greg Bard (talk) 21:25, 3 March 2012 (UTC)

Dear Arthur, I agree with you 100% that this article is not only low quality in presentation, but problematic in its conception. Unfortunately, as pointed out by @Gregbard, some textbooks include these two rules in their system of deduction alongside other equivalence rules such as contraposition, and refer to them as tautology rules in spite of the fact that all of the equivalence rules (and others) in their system are tautologies.

These are indeed examples of idempotence, as is mentioned in various places. Names as suggested by @Gregbard would be some improvement, though the contribution to world knowledge in my view would still be vanishingly small even with a less confusing name. Crisperdue (talk) 01:57, 28 July 2024 (UTC)

Who is this article for?

Gentlemen (Arthur and Greg) and anyone else involved with this article, instead of fighting over trifles, please tell us who this article is for. I have a Ph.D. in social sciences (granted, not in philosophy, but nonetheless), have published 3 books and I do not understand a single word of this article.

I can read 99.99% of articles on the topics of fields as variegated as astronomy, pharmacology, philosophy, history, biology, sociology, behavioural sciences, linguistics, jurisprudence, warfare... you name it -- without any problem. So I consdier myself educated above the average. Not the smartest or anything, but a person who can read most text (and not only in English) with comprehension.

Here I went back 3 times and couldn't get the head or tail of it -- in the article itslef, even less so in your discussion. So, please ask yourselves who this article is for. This is wikiPEDIA, not a very narrowly focused academic journal.

Anyway...