Self Fulfilling Beliefs
For systems, we define reflexivity to mean that for any p (in the language of the system) there is some q such that q≡(Bq→p) is provable in the system. Löb's theorem (in a general form) is that for any reflexive system of type 4, if Bp→p is provable in the system, so is p.
Read more about this topic: Doxastic Logic
Famous quotes containing the words fulfilling and/or beliefs:
“I sing, not arms and the hero, but the philosophic man: he who seeks in contemplation to discover the inner will of the world, in invention to discover the means of fulfilling that will, and in action to do that will by the so-discovered means.”
—George Bernard Shaw (1856–1950)
“If we cannot find a way to interpret the utterances and other behaviour of a creature as revealing a set of beliefs largely consistent and true by our own standards, we have no reason to count that creature as rational, as having beliefs, or as saying anything.”
—Donald Davidson (b. 1917)