Re: Tautologies Then and Now
From: Chris Menzel (cmenzel_at_remove-this.tamu.edu)
Date: 12/09/04
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Date: 9 Dec 2004 16:24:42 GMT
On Thu, 09 Dec 2004 11:38:06 GMT, Stephen Harris said:
> ...
>> In pretty much any logic text in existence, a tautology is a sentence in
>> the language of propositional logic that is true regardless of the
>> assignment of truth values to its atomic components. "Tautology" used
>> in any other way, in the context of mathematical logic, is, well, wrong.
>> The more general notion that covers both propositional logic and
>> first-order (and higher-order) logic is that of a logical truth, i.e., a
>> sentence of a given language that is true in all interpretations of the
>> language. So, alternatively, a tautology is a logical truth of
>> propositional logic.
>>
>> Chris Menzel
>
> Would you comment on these quotes? * is my emphasis..
No, I'll comment on the fact that you want me to comment on them.
Apparently you think these quotes show that truth tables applied to
"truth-functional proxies" of quantified argument schemas provide a
*general* method for testing first-order validity. They don't. In
*some* cases they do, namely, if you restrict your attention to
arguments consisting of formulas of monadic predicate logic (i.e.,
formulas that involve only 1-place predicates), or if the argument in
question is invalid and has a *finite* countermodel. This information
is pretty much in the link you provide:
> http://www.lawrence.edu/fast/boardmaw/analytic_essay.html
Have a look at the penultimate paragraph and footnote 4.
> SH: I quoted Peter Suber because your fame has not preceded you to
> my limited knowledge of who is a quotable authority in logic.
Shows what you know. ;-)
Chris Menzel
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