Tag Archives: Incompleteness

Known Unknowns

This month’s post may make a valid point.  Or it may not.  Or it may be impossible to tell, the concept of which itself may or may not make sense by the end of the piece!

How do we handle things we don’t know?  More precisely, how do we cope with things we know we don’t know?  All right then: how do we handle things we know we can’t know?

As is the nature of this blog, the examples we’re going to discuss are (at first, at least) taken from the fields of computer science and mathematics; but there are plenty of analogies in the other sciences.  This certainly isn’t a purely theoretical discussion.

On the whole, we like things (statements or propositions) in mathematics (say) to be right or wrong: true or false.  Some simple examples are:

  • The statement “2 > 3” is false
  • The statement “There is a value of x such that x < 4” is true
  • The proposition “There are integer values of x, y and z satisfying the equation x3 + y3 = z3” is false

OK, that’s pretty straightforward but how about this one?

  • “Every even number (greater than 2) is the sum of two prime numbers”

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