 This raises the question, how can we understand second-order validity from the second-order perspective? In view of the above theorem we cannot understand second-order validity as something that can be expressed in second-order logic on some structure which itself can be characterized in second-order logic. The reference to set theory seems inevitable in understanding second-order validity. Let us discuss what this might mean from the point of view of structuralism. Parsons defines structuralism as follows: