Thursday, September 22, 2011

The wealth of ambiguity

When we read these lines by Robert Burns (1759-1796),

     Oh my luv is like a red, red rose,
     That's newly sprung in June . . .
we don't know whether he compares a woman he loves to a flower or whether it is his own emotion he describes.  And the multiplicity of meanings is a good and pleasing thing.  Similarly, when we read the problem,

     Solve the equation, x² + 4 = 0 

we have several interpretative possibilities.  If x should be an integer, the equation has no solutions.  Likewise if x is a real number.  But if we admit complex numbers, the equation has two solutions, both imaginary.

     The existence of multiple contexts and multiple meanings is a characteristic shared by good mathematics and poetry.  It makes both of them both difficult and rich.  Such is the case for this logic-poem by Michael Palmer:

   Prose 31     by Michael Palmer

              The Logic of Contradictions

   A logical principle is said to be an empty
   or formal proposition because it can add
   nothing to the premises of the argument it
   governs.  This leads to the logic of contra-
   dictions.  It is an anacoluthon to say that
   a proposition is impossible because it is
   self-contradictory.  (It is also ambiguous.)
   The definition of the possible as that which
   in a given state of information (real or
   pretended) we do not know not to be true
   conceals another anacoluthon.

"Prose 31" may be found in Palmer's collection The Lion Bridge, (New Directions, 1998).

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