I knew it wasn't true, at least on an intellectual level.

At times he even found it amusing, on an intellectual level.

Such visions have been the subject of much debate, on several intellectual levels.

"All the information we were hearing was obviously very disturbing, but only on an intellectual level," she said.

I had known on an intellectual level, of course.

He found himself attracted to her as well, on a more intellectual level.

He had come to accept that, at least on an intellectual level.

He was still very active at this age both on the physical and intellectual level.

The intellectual level here is not, as you say, very high.

She's a pretty child, but hardly his intellectual level, I should have thought.