Re: Tautologies Then and Now

From: paul (paul8801_at_on-ramp.nl)
Date: 12/10/04 

Date: Thu, 09 Dec 2004 20:16:03 -0500

On Thu, 09 Dec 2004 23:40:28 GMT, "Stephen Harris"
<cyberguard1048-usenet@yahoo.com> wrote:

>>> http://www.lawrence.edu/fast/boardmaw/analytic_essay.html
>>
>> Have a look at the penultimate paragraph and footnote 4.
>>
>
>I read the whole essay. Which is why I changed my mind about Paul being
>right about the truth tables; I had doubts about it and kept researching.

 You mean paul's professors. As I wrote: "Can you cite a text that
extends truth tables beyond propositional logic? My professors always
said that doesn't happen, and it certainly didn't in any of my texts."

 Owen's apparently new analysis notwithstanding, can you or someone
cite a logic textbook that uses truth tables in predicate logic? I'm
not refuting that such a text exists, I'd just be interested to know.

>Paul also wrote: ... "...I said -- that the term "tautology" is not applied
>outside propositional logic."
>
>SH: But I don't think that can be exactly correct either in part because
>Paul posted,
>
>"In predicate logic ... Formulas @ such that V_M(@) = 1 for all models
>M for the language from which @ is taken are called universally valid
>formulas (they are not normally called tautologies)."
>
>L.T.F. Gamut. "Logic, Langauge, and Meaning: Volume 1, Introduction to
>Logic." The University of Chicago Press. p. 99.
>
>SH: I don't think the author of the book would have used the qualifier
>"normally" (they are not normally called tautologies) if it were strictly
>true that the term "tautology" never applied to predicate logic which is
>"outside propositional logic", the boundary paul claimed, "not applied".
>
>I'm not actually faulting paul, because this exception seems rather
>technical.

 You're assuming that what is abnormal is inherently also appropriate.
I believe that what Gamut means by "not normally called tautologies"
is that some may use the term "tautology" within predicate logic, but,
strictly speaking, it is abnormal and inappropriate. That view is
supported by what I was taught in school, and by reading Gamut, which
finds no exception to the restriction of the term "tautology" to
propositional logic, and as I recall other utterances stipulating the
limitation of the term "tautology" to propositional logic.

 You ought to just post a genuine counter example to the limit rather
than every ambiguous description you find. Which of course is not to
say that even some .edu site does not have posted notes that say
something that's normally considered inappropriate. That's why I'm
asking for TEXTBOOK sources, which are most likely less likely to err.
You should not assume you can get the best logic education via google.

- paul

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