This entry traces the historical development of the Square of Opposition, a collection of logical relationships traditionally embodied in a square diagram. This body of doctrine provided a foundation for work in logic for over two millenia. For most of this history, logicians assumed that negative particular propositions ("Some S is not P") are vacuously true if their subjects are empty. This validates the logical laws embodied in the diagram, and preserves the doctrine against modern criticisms. Certain additional principles ("contraposition" (...) and "obversion") were sometimes adopted along with the Square, and they genuinely yielded inconsistency. By the nineteenth century an inconsistent set of doctrines was widely adopted. Strawson's 1952 attempt to rehabilitate the Square does not apply to the traditional doctrine; it does salvage the nineteenth century version but at the cost of yielding inferences that lead from truth to falsity when strung together. (shrink)

In this paper, I want to make two main points. The first point is methodological: Instead of attempting to give a classical analysis or reductive definition of the term “expertise”, we should attempt an explication and look for what may be called symptoms of expertise. What this comes to will be explained in due course. My second point is substantial: I want to recommend understanding as an important symptom of expertise. In order to give this suggestion content, I begin to (...) develop an account of understanding. Finally, I will draw attention to some consequences of this approach. (shrink)