From: kibo@world.std.com (James 'Kibo' Parry)
Subject: Paradoxes: THREE-WAY ARGUMENT
Organization: A room filled with typography (in Boston's Back Bay)
Date: Sun, 12 Apr 1992 02:10:34 GMT

Remember, every one of my "Spot & Einstein" stories is modelled on a
Bach fugue for unaccompanied no-hole nose-flute.

                                             -- Douglas "Kibo" Hofstadter



THREE-WAY ARGUMENT
==================

(Achilles, Einstein, and Spot are in discussing meta-logic.)

ACHILLES:  So, Herr Professor Einstein, I do believe you were about to
tell us about some rib-tickling PARADOXES.

SPOT:  What's a paradox?

EINSTEIN:  Vell, Spot, a good example is the EPIMENEDES PARADOX,
forumlated by Epimenedes, a philosopher from Crete.  He said "All
Cretans are liars."

SPOT:  So he was a liar, then?

ACHILLES:  Oh, I get it... if he were lying, then the statement would
be false, and thus he would NOT be a liar... I say, this is a real
knee-slapper!

SPOT:  Whine!  I don't get it.

EINSTEIN:  It's equivalent to saying "I AM LYING," which is what
Captain Kirk said to make that android's head explode.  Zee, if Kirk is
telling the truth, he is lying.  If he is lying, he is telling the
truth.  Thus, Kirk cannot be either lying or telling the truth.

(Smoke comes out of Spot's ears as the Professor continues.)

EINSTEIN:  Then there is the RUSSELL PARADOX, named for you-know-who.

ACHILLES:  Dear old Bertrand R., co-author of the PRINCIPIA
MATHEMATICA!

EINSTEIN:  The one and the same.  Envision, if you will, all possible
sets, sets of anything.

ACHILLES:  Okay.

SPOT:  Huh?

EINSTEIN:  Now imagine the SET OF ALL SETS.  It is a member of itself,
right?

ACHILLES:  Okay.

SPOT:  What?  It can't be...

ACHILLES:  Trust us, it is.  What next, Herr Professor?

EINSTEIN:  Since some sets contain themselves, but most do not, think
of the SET OF ALL SETS WHICH CONTAIN THEMSELVES.  Logically, there must
be a set of all the other sets, THE SET OF ALL SETS WHICH DO NOT
CONTAIN THEMSELVES.  Now, which of those two sets does the latter set
belong IN?

ACHILLES:  Oh!  Gosh!  That's simply stunning!

SPOT:  Waaaaah!  I don't get it!  I guess it's because I'm just a
stupid little puppy.

EINSTEIN:  Okay, Spot, I vill try to give you a simpler example, one
even a stupid little puppy like you may understand.  It is THE SPOT
PARADOX!

SPOT:  Wow, my own paradox?

ACHILLES:  Lucky you!

EINSTEIN:  THE SPOT PARADOX says "Spot is a stupid little puppy."

ACHILLES:  Hmm... oh yeah... I like that!  Very sutble, yet mordant.
You have a true gift, Herr Professor.

SPOT:  Wait... how can that be a paradox?  It's TRUE!  There's nothing
inherently contradictory about it!  THE SPOT PARADOX isn't a paradox at
all!  I don't understand any of this!

EINSTEIN:  Shall I draw you a diagram, stupid little puppy?

(Just then, Achilles stubs his heel on a discarded syringe which is
contaminated with rabies, because they are sitting in Spot's back
yard.)

ACHILLES:  Arrr!  Arrrrr!  Grrrrr.  (He kills Einstein and Spot.)


..................    ...................................................
James "Kibo" Parry    271 Dartmouth St #3D, Boston MA 02116 (617)262-3922
kibo@world.std.com    Independent graphic designer and typeface designer.
Newsgroups: alt.religion.kibology