Basing the Riddle coma on an objection against Lucas' arguments, I propose an
alternate hypothesis that the Riddle coma stems from a "stop rule" to avoid
inconsistency.
Lucas does an extensive job at explaining the stop rule. The basic concept of
this rule is that "by having a rule that whenever two inconsistent formulae
appear we were to reject the one with the longer proof." Lucas is against
such a rule, and with good reason. This rule is illogical because it allows
for an axiom to be true in one instance and false in another.
However, I think that this could be applied to the Riddle problem.
Suppose that upon entering the spiral that is the Riddle, a person would be
confronted with a question of their own consistency. This is very much like
the C. H. Whitely sentence "Lucas cannot consistently assert this sentence."
If the Riddle presented such a question to the person reading it, then the
person may feel inclined to defend him/herself and attempt to assert his/her
own consistency. Yet, because of the never-ending nature of the Riddle, the
person is confronted again and again when finally the person "avoids being
brought to acknowledge his own inconsistency by stonewalling" (Lucas).
And even if the person does not "stonewall" and try to keep asserting his/her
consistency, then he/she runs into the risk of "becoming a self-contradictory
belief system" (Hoftadter). Having one's beliefs, consistency, and
rationality relentlessly questioned may bring one to an internal state of
chaos where the mind shuts down and goes into a state of coma.
Hmm...this idea sounded good in my head, but now I am wondering if it may be a
bit too far-fetched.
=Katherine Loo=
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