Re: Tautologies Then and Now

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

Date: Sun, 12 Dec 2004 02:30:55 -0500

On Sun, 12 Dec 2004 02:51:47 GMT, "Stephen Harris"
<cyberguard1048-usenet@yahoo.com> wrote:

>> "If an argument contains n different predicate symbols, then if it is
>> valid for a model containing 2^n individuals, then it is valid for
>> every model or universally valid."
>>
>> Copi, I.M. "Symbolic Logic." p. 81.
>>- Paul

>I think Copi's definition that you quote is a broad definition outside the
>range "tautology" applies. Shortly, you have shown how it is correct
>to use "universally valid" in describing all of general predicate calculus.
>Your quote does not show that it is incorrect to use "tautologous"
>for specific decidable fragments.

 It should be clear to you from numerous quotes you posted previously
that, with the one exception of Barbara Partee, most authors are
careful when discussing logics to restrict their use of the term
"tautology" to propositional/sentential logic. For example your oft
quoted

http://www.lawrence.edu/fast/boardmaw/analytic_essay.html

says on top: "Corresponding to tautologies in Sentential Logic are
analytic sentence schemata in First Order Predicate Logic. You will
remember that a tautology is a sentence schema which is true under any
consistent interpretation of its sentential letters;"

Clearly the author indicates the term "tautology" is used uniquely in
sentential logic. Numerous other quotes you have presented also
indicate that same limit. Which matches Gamut and Copi:

* "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." p. 99.

* "If an argument contains n different predicate symbols, then if it
is valid for a model containing 2^n individuals, then it is valid for
every model or universally valid." Copi, I.M. "Symbolic Logic." p. 81.

If you google "universally valid" wrt predicate logic you'll find many
instances of its application to always valid predicate statements
versus the one example of Partee. My question is why is "tautology"
not normally used outside sentential logic? There must be a reason.

- paul

Relevant Pages

  • Re: Tautologies Then and Now
    ... careful when discussing logics to restrict their use of the term ... "tautology" to propositional/sentential logic. ... * "If an argument contains n different predicate symbols, ... If you google "universally valid" wrt predicate logic you'll find many ...
    (sci.math)
  • Re: Tautologies Then and Now
    ... proposition that is true in every row of its truth table or in every ... tautology; syntactic tautology. ... I don't think I was posting quotes which support his conclusion. ... predicate logic and it is foundational to modal logics. ...
    (sci.logic)
  • Re: Inconsistent = all sentences provable?
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    (sci.logic)
  • Re: Tautologies Then and Now
    ... topic in two recent posts regarding Modal logics, ... let paul get away which this stubbornly fanciful summary of your earlier ... Now I have provided several examples of the term "tautology" used in modal ...
    (sci.logic)
  • Re: question regrading tautology and valid formula
    ... Modal Logics: Theory and applications thoroughly, ... A valid formula is a well formed formula. ... between tautology and valid formula? ...
    (sci.logic)