William James’s “The Will to Believe” defines a “live” hypothesis as one that resonates personally and compellingly motivates action, while a “dead” one fails to inspire. (James offers the example of religion: to a non-Arab, the existence of the Mahdi is a “dead” hypothesis.)
A “live” belief blends logic, temperament, and experience (framework of reference), often embracing comfortable uncertainty over abstract foreign certainty.