Problems of conceptual uncertainty have been dealt with in theories of formal logic. Such theories try to accommodate vagueness in two main ways. One is fuzzy logic that introduces degrees of truth. The other way of accommodating formal logic to vagueness is super valuations and its descendants. This paper studies a more inclusive class of reasoning support than formal logic. In the present approach, conceptual uncertainty, including vagueness is represented as higher order uncertainty. A taxonomy of epistemic and conceptual uncertainty is provided. Finally, implications of conceptual uncertainty for reasoning support systems are analyzed.