Professor Grünbaum's much-discussed refutation of Zeno's metrical paradox turns out to be ad hoc upon close examination of the relevant portion of measure theory. Although the modern theory of measure is able to defuse Zeno's reasoning, it is not capable of refuting Zeno in the sense of showing his error. I explain why the paradox is not refutable and argue that it is consequently more than a mere sophism.

In Physics 4.11, Aristotle says that changes are continuous because magnitude is continuous. I suggest that this is not Aristotle’s considered view, and that in Generation and Corruption 2.10 Aristotle argues that this leads to the unacceptable consequence that alterations can occur discontinuously. Physics 6.4 was written to amend this theory, and to argue that changes are continuous because changing bodies are so. I also discuss the question of Aristotle’s consistency on the possibility of discontinuous alterations, such as freezing.