Although the thermodynamic concept of entropy goes back to the work of Rudolf Clausius in 1865, physicists have yet to reach consensus on its meaning or its definition in statistical mechanics. In discussions with other scientists, I have found strongly held opinions that differ widely. In most cases, the differences seem to arise from unstated assumptions, which can make the reconciliation of opposing opinions difficult. To make these assumptions explicit, I will discuss some of the views I have encountered, as well as the principles that have guided my own thinking about the foundations of statistical mechanics, the microscopic origins of thermodynamics, and the definition of entropy. My purpose will be fulfilled if this discussion paves the way to a final consensus, whether or not that consensus agrees with my point of view.