In the
town of Saints and Sinners about half the inhabitants are
Saints and the rest are
Sinners.
Indistinguishable in their outer appearance, Saints
always tell the truth and
Sinners always lie
- about what they believe is true. However, there is an
Asylum in
town where many of
the residents are totally insane and completely deluded
in their
beliefs: all true
propositions they believe to be false and all false
proposition they believe
to be true! So,
there are residents and staff of four types at the Asylum:
(1) sane Saints
(who tell the truth),
(2) insane Saints (who always lie) (3) sane Sinners (who
lie) (4)
insane Sinners (who
tell the truth). For example, an insane Sinner believes
that the moon
is made of green
cheese. But if you ask him "Is the moon made of
green cheese?" he'll
lie to you and say
that it's not - so he winds up telling the truth! For
speaker X, let sX
denote the
statement "X is sane." The consistency test for
the Asylum is the truth of the
statement: a Saint
and only a Saints tells the truth if and only if he or
she is sane.
This is shown in
the fourth column of the truth table, below. After
examining the truth
table, scroll down
and solve a problem involving residents of the Asylum.
No support for LM Objects
A conversation overheard at the Asylum:
While visiting the Asylum you overheard a conversation
between two residents A and B.
A said to B, "I'm sane and you're an insane Sinner." B replied,
"If I'm insane, then
you're insane!", to which A countered, "If I'm insane, then
you're a Saint!!" What can
you deduce about A and B? See the truth table, below.
Suppose instead that the conversation had gone like this: A said to B,
"I'm sane and
you're an insane Saint." B replied as before, to which A countered,
"If I'm sane, then
you're a Saint!!" Highlight two words below and press the Delete
key twice. What can
you deduce about A and B?