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).