Mediaeval logicians often wrote about changes between contradictory states, for example a switch’s changing from being on to not being on. One of the questions discussed in these writings was whether at the moment the change occurs the changing thing is in the earlier or the later state. The present paper investigates the general setting for that question, and discusses the answer given by Walter Burley, an important early-fourteenth century author whose theory was a standard one. Burley’s theory at first (...) seems arbitrary, and moreover committed to serious theoretical problems. The last part of the paper therefore considers what unspoken factors may have motivated Burley. Certain causal principles are suggested that would remove the apparent arbitrariness and avoid the theoretical problems with his theory, but only at the expense of revising it in a substantive way. (shrink)

_More Precisely_ provides a rigorous and engaging introduction to the mathematics necessary to do philosophy. It is impossible to fully understand much of the most important work in contemporary philosophy without a basic grasp of set theory, functions, probability, modality and infinity. Until now, this knowledge was difficult to acquire. Professors had to provide custom handouts to their classes, while students struggled through math texts searching for insight. _More Precisely_ fills this key gap. Eric Steinhart provides lucid explanations of the (...) basic mathematical concepts and sets out most commonly used notational conventions. Furthermore, he demonstrates how mathematics applies to many fundamental issues in branches of philosophy such as metaphysics, philosophy of language, epistemology, and ethics. (shrink)