Re: Tautologies Then and Now

From: Stephen Harris (cyberguard1048-usenet_at_yahoo.com)
Date: 12/12/04 

Date: Sun, 12 Dec 2004 10:57:20 GMT

"Chris Menzel" <cmenzel@remove-this.tamu.edu> wrote in message
news:slrncro4fr.11s.cmenzel@philebus.tamu.edu...
> On Sun, 12 Dec 2004 02:30:55 -0500, paul <paul8801@on-ramp.nl> said:
>> 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.
>
> Because it usefully picks out a certain class of logical truths, viz.,
> those that are true simply in virtue of their truth functional
> structure. If its meaning were broadened to include the logical truths
> of predicate logic, it would serve no purpose. We already have "logical
> truth" and "universal validity" (though the latter is rather less
> common; indeed, I can only recall seeing it in the LTF Gamut text --
> whose actual authors, BTW, are the frighteningly prolific Dutch logician
> Johan van Benthem and a couple of his colleagues).
>

"Logic: The Art of Persuasion and the Science of Truth"
I think by Vann McGee

"Monadic Predicate Calculus

Normal Truth Assignment = N.T.A.
Definition: "A sentence is tautological iff it is assigned the value1
by every N.T.A. A sentence is valid iff it is true under every N.T.A.
For the sentential calculus,the words "tautological "and" valid" were
different words for the same thing. Now that we've started on the
predicate calculus, we need to distinguish them. Validity is the notion
we're really interested in,but we need the notion of tautology as a
technical notion. Proposition. Every tautology is valid, but not vice
versa. [SH: He provides a proof, and then continues:]

A tautological sentence is a valid sentence whose validity is determined
by the sentence's truth functional structure. If, instead,the validity of
a sentence depends upon the meaning of the quantifiers,the sentence won't
be tautological.

We can test whether a sentence is tautological by the method of truth
tables, examining each possible way to assign a truth value to the
sentence's basic truth functional components."
---------------------------------------------------------

SH: You have provided similar statements to McGee who is
teaching an online class at MIT. He apparently considers it
important to mention truth tables and tautologies as part of
the background information leading into discussing FOPL.
I have found several references to Monadic Predicate logic
on the net which mention truth tables.

When you teach (or taught) this logic class which goes into PL,
did you provide the same background as McGee? Or did you
perhaps omit it (full discussion of MPL) because you thought it
might be confusing? What I'm trying to get at, is McGees
decision to include the material I quoted a fairly standard decision,
or would some qualified instructors choose to dismiss the material
that McGee deems important enought to include in his lectures, re MPL?

http://aka-ocw.mit.edu/OcwWeb/Linguistics-and-Philosophy/24-241Logic-IFall2002/Readings/index.htm

Introduction. The Place of Logic Among the Sciences (PDF)
Sentential Calculus Introduction (PDF)
Sentential Calculus Semantics (PDF)
Extension Theorem (PDF)
State Descriptions, Disjunctive Normal Form, and Expressive Completeness
(PDF)
SC Substitutions (PDF)
The Search-for-Counterexample Test for Validity (PDF)
Compactness Theorem (PDF)
SC Translations (PDF)
Trouble with "If"s (PDF)
Monadic Predicate Calculus (PDF) ***** lecture 11
Derivations in the Monadic Predicate Calculus (PDF) ***** lecture 12
Completeness in the Monadic Predicate Calculus (PDF)
Predicate Calculus (PDF)
Predicate Calculus Derivations (PDF)
Identity (PDF)
Russell's Theory of Definite Descriptions (PDF)
Sense and Reference (PDF)
Function Signs (PDF)
Sentential Calculus Revisited: Boolean Algebra (PDF)

Regards,
Stephen

Relevant Pages
Quantcast