Re: clarification on the compactness theorem for sentential logic

From: shane (clearthink_at_cavtel.net)
Date: 10/22/04 

Date: 22 Oct 2004 12:00:30 -0700

> > I am using a certain mathematical-logic book whose
> > compactness theorem for sentential logic is a little
> > unclear to me. But I think it is a better proof than
> > in some other books because it does not use
> > contradiction.
Although I still want all comments on this question,
I think I have identified the source of this k-good,
very-good business. There is a far, far better explanation
of compactness at https://webspace.utexas.edu/deverj/
where you can find a MS-WORD document called sentential
logic. This teacher (from Philosophy dept.) gives the
full, unexplicated workup of truth extensions --- I
am reading it now --- in that document.

And, moreover, this teacher actually explains why
compactness is important. I mean everybody knows
that all compactness theorems make a leap from
finite subsets to infinite sets. But that's like
only having the mere intellectual understanding
that eating the menu isn't the same thing as eating
the meal. Once you actually eat the meal then the
import and context suddendly becomes far more
clear.

Why math teachers and math books don't do this as
a rule is something I'll never get. They claim
to provide a "service" for students but, in many
cases, their activities do not lead to results
and, when they do, are not results students care
about. More to the point, it sure in the hell
isn't the way I'll write or teach.

Shane

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