True or False

6/30/2015

63,015 is a 602-gonal, 6,303-gonal, and a 21,006-gonal number.  It is a composite, deficient, Harshad, odd, Smith, sphenic, square-free, and unprimable number.

Have you ever heard the rule that "There is an exception to every rule."?

Is that rule true or false?

If a rule had an exception then that rule would be false.  Take the spelling rule "i before e, except after c".  I think it is a weird rule.  In the word "weird" the i does not come before the e, and there is no c.  There are many exceptions to that rule.  Are there any rules that don't have exceptions?

The rule listed above does not say it has an exception.  It does not say "There is an exception to every rule, except this rule."

But this rule is a rule, and it says that every rule has an exception.  So it must have an exception too!  And since the rul has to have an exception it must be false.

Owwww ... my head is starting to hurt.

Can you help me out?  What do you think?  Is the rule true or false?  Or can we even determine if it is true or false?  What do you think?



David