It is natural to say that when we acquire a new concept or concepts, or grasp a new theory, or master a new practice, we come to see things in a new way: we perceive phenomena that we were not previously aware of; we come to see patterns or connections that we did not previously see. That natural idea has been applied in many areas, including the philosophy of science, the philosophy of religion, and the philosophy of language. And, in reflecting on the character of philosophy itself, Wittgenstein himself associates the introduction of a new concept in philosophy with the discovery of a new way of looking at things (PI §401), and says that the point of presenting us with an imagined example may be to change our way of looking at things (P...