There are seven. The original medieval city is laid out like a peninsula with the river as a sort of natural moat. On the other side of the river is more land. Thus, the seven bridges connected old Bern with the other side of the river. When it was first built, the idea was that the river acted as a natural moat. Apparently they overcame their fear of invasion, since bridges kind of defeat the purpose of a moat. Especially seven of them.