From Magnus Ellingsen
I was successfully fooled by the four tests designed to demonstrate the power
of the illusions the mind can create. I think, though, that it may be an element
of confusion rather than illusion that fooled me.
All the tests start with the statement, “There is a pin and/or a bolt on the
table, or else there is a bolt and a nail on the table.” The “or else” is
supposed to be read as “exclusive or” or just XOR for short.
Here’s the statement, rewritten without changing the meaning: (There is a pin
and/or a bolt on the table) XOR (there is a bolt and a nail on the table). If
the left side of the statement is true, the right side must be false—and
vice versa. The left side contains these two possibilities: (There is a pin and
a bolt on the table) and (There is a pin or a bolt on the table). The latter
contains two possibilities: (There is a pin on the table) and (There is a bolt
on the table). All these possibilities are exclusive to the right side of the
statement, and the last one leads to an intrinsic contradiction: (There is a
bolt on the table) XOR (there is a bolt and a nail on the table). This
possibility forces the “or else” to be read as “or”—in which case this
very interesting article’s test-analysis will contain a potential for
adjustments.
Oslo, Norway
