From: skinner@sp94.csrd.uiuc.edu (Gregg Skinner)
Subject: Re: Christianity and Logic, take 2
Reply-To: g-skinner@uiuc.edu
Organization: UIUC Center for Supercomputing Research and Development
Date: Wed, 6 Jan 93 21:21:06 GMT

Kent Sandvik writes:

>Let's give another example where I indeed agree that premises don't
>matter concerning the final logical conclusion:

I'm confused.  Just yesterday he asked,

     OK, if we can't state that a premise is true or false, how could
     we then draw a conclusion about the logical validity of the
     outcome?

Today he's giving "another" example where he agrees that "premises
don't matter".

>Tautologies - "God is eternal because God is eternal".
>This is certainly false because you can't show that something is something
>based on itself.

Tautologies are always true, by definition.  Thus, the above compound
statement is true.  As an argument, it is fallacious, however, because
it begs the question.  The conclusion, "God is omnipotent", may be
either true or false; the fallacious argument does not contribute to
discerning which is the case.

>Contradictions - "God is eternal so God is not eternal".
>Here this is false as well, because something can't be and not be at
>the same time.

A contradiction is a compound statement that is always false.  Though
it seems a bit counter-intuitive, the above is not always false, because
of the way implication is defined,

A	~A	A -> ~A
-----------------------
F	T	T   <----- For this set of truth values, the above is true.
T	F	F

If the above were "God is eternal and God is not eternal" it would
indeed be a contradiction:

A	~A	A and ~A
-----------------------
F	T	F   
T	F	F

Looking at the original wording as an argument, we see that is an
invalid argument, as the conclusion does not follow from the premise.
Note that it is not necessary for us to know the truth value for "God
is eternal" to determine the argument is invalid.

>I would like to know if you could present more similar logical constructs
>based on a frame model, and then if Mr. Skinner for instance could map
>his statement into one of the agreed models, then I indeed agree that
>I was wrong.

We need a definition for "frame model".  If you're looking for more
definitions like "tautology" and "contradiction", check for these in
the index of the book you've found:

   conditional   (if, then)
   biconditional (if and only if)
   equivalence

The argument I gave relies exclusively on two of these: Conditional
and Equivalence.

>I don't mind learning the truth, and I agree, I don't know
>logic

It is with a great deal of disbelief that I read these words.  Mr.
Sandvik recently claimed to be an "expert in logic".  I am forced to
conclude he purposefully lied.

Further, I have to wonder how can Mr. Sandvik be so sure Christianity
lacks logic if he has not studied logic.

>Sorry, but if you can't resolve this clear
>Christian logical construct, then my point that 'something's rotten
>with Christian logic' is still a valid one.

Mr. Sandvik is the only one who is claiming that the construct to
which he refers is a "clear Christian logical construct".  If he
wishes to knock down a straw man, so be it.  He is in error to think
that in doing so he supports his argument.

Apparently we're getting through, though, because the claim has
changed from "There's nothing logical about Christianity" to
"Something's rotten with Christian logic."  Shall we interpret this
change as a retraction of the former claim?  



                                 Gregg Skinner


	     An argument can be valid even though its
	     premises and its conclusion are all false or
	     the premises false (or one or more premises
	     false) and the conclusion true.  As long as
	     we must say that if the premises were true,
	     the conclusion would have to be true as well,
	     validity is not affected by the actual truth
	     or falsity of the argument's component parts.

	     D.B. Terrell
	     "Logic: A Modern Introduction to Deductive Reasoning"



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