AbstractThe paper examines a single, apparently simple argument for the existence of incompatibilities between the virtues as traits of character. This argument appeals not to empirical truths about human psychology or human nature but to the possibility of conflict between the exercise of different virtues in action. There are, for example, situations in which we can exercise the virtue of truthfulness only at the expense of not exercising the virtue of tact, as when we are asked a question to which the straightforward answer will pain our questioner. The person who in these situations would give a straightforward answer possesses the virtue of truthfulness to a higher degree than the person who would respond more evasively, whereas the latter person possesses the virtue of tact to a higher degree than the former. But since the two responses are mutually exclusive, it follows that the degree to which we possess the virtue of truthfulness must, at least in some measure, correlate inversely with the degree to which we possess the virtue of tact. And similarly for many other pairs of virtues. My paper focusses on the two cardinal assumptions of this argument, viz., (i) that sometimes the exercise of one virtue can conflict with the exercise of another, and (ii) that the degree to which a person possesses a virtue correlates directly with the extent of its exercise, and defends both assumptions against a variety of objections which allege that, in different ways, they are insensitive to the complexity of the virtues.