The Logical Magician's Card Trick

The logical magician (logician, for short) is fond of surprising
unsuspecting friends with sentences such as, "I am lying". A friend is
likely to reply, "And what are you lying about this time?"

The logician will persist with something like, "No, I am lying right
now!" The perplexed friend will likely reply, "All right then, but
just what is it that you're lying about right now?"

"Don't you get it?" the logician will continue, "I thought you were
supposed to be intelligent. If I'm telling the truth then I'm lying,
and if I'm lying then I'm telling the truth. You do see that, don't
you?"

If you don't see, your friend is likely to show you the old logician's
card trick. (All magicians have at least one card trick.) On one side
of a card there will be the sentence, 'The sentence on the other side
of this card is false', and on the other side there will be the
sentence, 'The sentence on the other side of this card is true'. "You
do see, don't you, that if the first sentence is true, then, according
to the false second sentence, which says the first sentence is true,
the first sentence is false? Is the paradox clear to you now?"

Although logicians rarely become violent, it is best to humor them
until you can find some excuse to get away from them. Head for a
sensible coffee shop, have a nice cup of coffee, and reflect on what
you have been told.

The truth is that logicians want you to believe that sentences can
refer to themselves, or to one another back and forth. But sentences
do not say or write anything. They come from the minds of the people
who, for one reason or another, speak and write them, and they express
the thoughts that such people have just been thinking.

For example, a helpful man who has just been asked if he has a
dictionary handy, might picture his own red dictionary on a cluttered
bookshelf and then reply, "My dictionary is on the shelf in my study".
If he had forgotten that he left the dictionary on his desk, then his
sentence would be false, but he would have made an honest mistake. On
the other hand, if someone tried to convince us that "Circles have
square corners", we should have serious doubts about either his
character or his sanity.

But what of the logician who shows you his paradoxical card? He wants
you to accept it at face value, as if the two sentences were referring
to one another right now. But we know that the card was once blank and
that the logician had been thinking about what he would write on the
card before he began writing. Then he wrote one of the two sentences,
e.g., 'The sentence on the other side of this card is false'. Is this
really what the logician was thinking, when he knew that the other
side of the card was blank? No, the logician was engaging in an act of
deception. He had already planned to write the two sentences so they
would have the appearance of referring to each other.

Gene Ledbetter
.

Relevant Pages

  • Re: The Logical Magicians Card Trick
    ... unsuspecting friends with sentences such as, "I am lying". ... A friend is ... The logician will persist with something like, "No, I am lying right ... (All magicians have at least one card trick.) ...
    (sci.logic)
  • Re: The Logical Magicians Card Trick
    ... unsuspecting friends with sentences such as, "I am lying". ... A friend is ... The logician will persist with something like, "No, I am lying right ... (All magicians have at least one card trick.) ...
    (sci.logic)
  • Re: The Logical Magicians Card Trick
    ... unsuspecting friends with sentences such as, "I am lying". ... The logician will persist with something like, "No, I am lying right ... Okay, okay, we get it: some logicians have stupid friends. ...
    (sci.logic)