Intellectual education has been frequently criticized in education as if it were one kind. However, the term “intellectual education” is ambiguous, whose target of criticism is sometimes confused. The purpose of this study is to clarify the ambiguous use of the term “intellectual education”. The notion of “intellectual education” is used at least in three different ways in educational discussions. By distinguishing three kinds of intellectual education we can clarify the point of criticism, avoiding confusions or logical leaps in educational arguments about intellectual education. Intellectual education in the first sense refers to teaching theoretical disciplines, neglecting other kinds of human activities. Discussions on intellectual education in this sense deal with the question what kinds of human activities are worthwhile to teach in education. That is to say, they deal with a curriculum question of what to teach and how to justify them. When one has chosen a certain activity to teach, one can emphasize to teach one specific aspect, namely, theoretical propositions, regarding other elements of the activity as secondary. This is the second sense of the term “intellectual education.” In this case, one can discuss whether theoretical or propositional parts of an activity could dominate other aspects of the activity such as the aspect of emotions, that of skills, that of virtues, etc., and whether teaching propositions could be a fundamental aim of education. When one tries to teach each aspect of an activity, one can ask how to teach it whether it is a skill, a virtue, an emotion or anything else. If one believes that procedural rules or maxims have to be taught first, it can be called the third type of intellectual education. In other words, the third kind of intellectual education deals with the pedagogical question of how to teach each aspect of an activity. This distinction is simply a logical distinction, which shows how different concerns and questions can be recognized in educational discussions. It is a philosophical approach to provide a conceptual framework to distinguish different kinds of educational discussions even though they are called by the same name of “intellectual education.” After clarifying the target of crificism, we further need to study about how different discussions on “intellectual education” can be developed.