- being honest to others about your thinking (e.g. your real reasons for holding a particular position)
- being honest with yourself about what the available evidence indicates
It is possible to be honest without being intellectually honest.
- Conservapedia defines it as "willingness to advocate positions one knows to be correct, even when expression of those positions is unpopular or could lead to negative consequences for the expresser" -- which is one consequence, but not the whole thing.
dKosopediano information as of 2010-10-16