  Gupta and Belnap 1993 characterize the difference between stability and near stability as follows: “Stability simpliciter requires an element [in our case a sentence] to settle down to a value x [in our case a truth value] after some initial fluctuations say up to [an ordinal η]… In contrast, near stability allows fluctuations after η also, but these fluctuations must be confined to finite regions just after limit ordinals” (p. 169). Gupta and Belnap 1993 introduce two theories of truth, T* and T#, based on stability and near stability. Theorems 3.12 and 3.13, below, illustrate an advantage of the system T#, i.e., the system based on near stability. 