Forever Undecided by Raymond M. Smullyan

Author:Raymond M. Smullyan [Smullyan, Raymond M.]
Language: eng
Format: epub
ISBN: 978-0-307-96246-1
Publisher: Knopf Doubleday Publishing Group
Published: 2012-07-04T04:00:00+00:00

DUAL FORMS

Problems 1, 2, and 3 (more generally, Theorems 1, 2, and 3) have their “dual” forms, which are rather curious.

1°. (Dual of Problem 1)

Again, a reasoner of type 4 comes to the island already believing that if he believes that the cure will work, then the cure will work. He meets a native who says to him: “The cure will not work and you will believe that I am a knave.”

Prove that the reasoner will believe that the cure will work.

2°. (Dual of Problem 2)

Like Problem 1°, except that the native says: “You will believe that I’m a knave, but you will never believe that the cure will work.” Show that the same conclusion follows (the reasoner will believe that the cure will work).

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.