open-mindedly

You listen to song after song—attentively, open-mindedly, optimistically.

This means to look the situation squarely in the face, to study it calmly, open-mindedly, and thoroughly.

But if you search open-mindedly, you will probably find some underlying agreement.

I ask you to look at the matter fairly, honestly, open-mindedly.

"He's an able fellow," he said once, apparently most open-mindedly.