From: drake+@cs.cmu.edu (Drake)
Newsgroups: talk.religion.misc
Subject: Re: Criticism:  "There's no logic in Christianity"
Date: 31 Dec 92 10:21:18 GMT
Organization: School of Computer Science, Carnegie Mellon

ksand@apple.com (Kent Sandvik ) writes:

>Sigh, my complain is that we all agree on the premisses of Eucledian
>geometry, even if we can't verify them. At the other hand we *don't*
>agree on the Christian premisses, making statements about logic and
>Christianity something that we can't speak of. In other words moot.

*BRRAAAPP*

Sorry, Kent, that's wrong, but thank you for playing anyhow!  We have
some very nice parting gifts...

I'm surprised that nobody has pointed this out yet, but nowhere is it
claimed by any competent geometrist that the premisses (we mathemeticians
like to call them 'axioms' or 'postulates') of Euclidean geometry are 
in fact 'true.'  Not only do we have axioms (such as "In a plane, there
can be drawn through any point A, lying outside of line a, one and only
one straight line which does not intersect line a") but we also have
undefined terms ("plane," "point," and "line," for example).

"The *truth* of axioms or postulates is not at issue.  These statements
are the beginning assumptions from which logical consequences follow."
			-- Smart, James R. _Modern Geometries_. c 1978.

There are geometries which have little relation to reality as we know
it, such as the 3-point geometry, 4-point geometry, Fano's geometry
and the finite geometry of Pappus.  (I can give the axioms if you really
want me to.)

The axiom quoted above, generally given as Playfair's axiom ("Through
a point not on a given line, exactly one line can be drawn in the plane
parallel to the given line", where "parallel" means "having no Euclidean
point in common"), is a perfect example of an axiom which is not true.
Equally valid geometries are possible by assuming that no parallel
lines are possible and by assuming that an infinite number of parallel
lines are possible.  The former is known as elliptical geometry, and
the latter as hyperbolic geometry.

"But one of them has got to be right!" you cry.  No, in fact, all of them
are logically valid and, although they all contradict each other, each
is true and useful in certain cases.  The normal, Euclidean geometry is useful
when describing drawing on a piece of paper.  Elliptical geometry
can describe a geometry on a sphere, and hyperbolic geometry was found
useful by Einstein in his work on relativity.

There is a difference, which you consistently fail to recognize, between
"truth" and "validity."  This may help to point out the difference:

	"If the premisses provide adequate grounds for affirming the
conclusion, if asserting the premisses to be true warrants asserting
the conclusion to be true also, then the reasoning is correct.  Otherwise
it is incorrect."
			-- Copi, Irving M. _Introduction to Logic_. c 1982.

Valid and true:

	All humans have two parents.
	I am a human.
	Therefore, I have two parents.

Valid and untrue:

	All humans have five children.
	I am a human.
	Therefore, I have five children.

Invalid and true:

	All Catholics believe in God.
	I am not a Catholic.
	Therefore, I do not believe in God.

Invalid and untrue:

	All Catholics are human.
	I am a human.
	Therefore, I am a Catholic.

Do you see how an argument can be both valid and untrue, or both invalid
and true?  The important point is that if an argument is valid and logical,
then the truth of the premisses *guarantees* the truth of the conclusion.
Conversely, if one or both of the premisses can be shown to be false, then
the conclusion is also false.

I suggest you study the above examples and come to a basic
understanding of the rules of logic before you further embarass yourself
by confusing truth and validity.  If you have any questions on these
matters, please ask.



-- 
Love and Laughter,             | NOTE: Private mail must go explicitly
Xeper and Remanifest,          | to drake@seismo.soar.cs.cmu.edu
                       DRAKE   | or it'll bounce back to you...
Newsgroups: talk.religion.misc