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Newsgroups: sci.logic
From: Chris Menzel <cmen...@remove-this.tamu.edu>
Date: 12 Dec 2004 12:16:07 GMT
Local: Sun, Dec 12 2004 7:16 am
Subject: Re: Tautologies Then and Now
On Sun, 12 Dec 2004 10:57:20 GMT, Stephen Harris said:
> SH: You have provided similar statements to McGee who is Well, truth tables are not theoretically necessary, but they provide > 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. students with a nice gentle introduction to the ideas of formal languages and their interpretation, and to the idea of logical truth -- which, as noted countless times now, is in this context indicated by the term "tautology". > I have found several references to Monadic Predicate logic That's because there is, theoretically, a way to USE truth tables to > on the net which mention truth tables. determine validity in general for monadic predicate logic. But note what seems to be a sticking point for you and paul. Although there is a way to USE truth tables for some purposes in predicate logic, truth tables are not a part of the standard *semantics* of predicate logic, even mondaic predicate logic, and in principle *cannot* provide such a semantics in general, due to their finite character. In particular, they cannot provide an adequate account of the meaning of the quantifiers. You seem to be emphasizing the fact that they can be USED in (some corners of) predicate logic. Paul seems to have picked up on the fact that truth tables are not part of the standard SEMANTICS of predicate logic, and hence, in particular, on the idea that "tautology" -- which has essentially to do with the semantical methods of propositional logic -- is an inherently propositional notion. > When you teach (or taught) this logic class which goes into PL, I introduce predicate logic via monadic predicate logic. But I don't > 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? talk about the TT method for deciding validity because, at that point, I'm focusing on the meaning of the quantifiers, not validity, and I do so by talking about simple interpretations. I do eventually introduce a method of demonstrating invalidity that uses TTs, but only as a way station en route to the destination of a predicate logic countermodel. Chris Menzel You must Sign in before you can post messages.
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