David Liebesman Associate Professor of Philosophy & Linguistics University of Calgary (and former BU Assistant Professor of Philosophy) Abstract: Counting and measuring seem quite different: one requires enumerating distinct entities, while the other requires assigning a particular value along a conventional scale (e.g. weight). This seeming difference is reflected in most semantic accounts of number words ("three") and measure phrases ("three pounds"). I argue that when we examine the nature of counting with mixed fractions ("two and a half") we discover that our semantic accounts of counting and measuring should be continuous. I then propose a semantics of number words that incorporates this discovery.