 A possible solution is to specify the constraint that it is illegal to measure the information content of an object in terms of partial descriptions, but this would destroy our theory of descriptive complexity. Note that the complexity of an object is the length of the shortest program that produces an object on a universal Turing machine. In this sense the phrase “the first number that violates Goldbach’s conjecture” is a perfect description of a program, and it adequately measures the descriptive complexity of such a number. The short description reflects the fact that the number, if it exists, is very special, and thus it has a high possibility to occur in some mathematical context. 