In today’s polarised political landscape we see those we disagree with as aliens, believing in crazy ideas. Yet the moral and political convictions of both left and right can be traced  back to two ideals: harmony with the world, and individual autonomy. In turn those ideas stem from two fundamental ideas: that we can know the world, and that we can know our own minds. A third idea, that we can come to know the minds of others, could be what completes the other two ideas and enable us to overcome our conflicts, writes Linda Zagzebski.