Continuity Theorems

There may be an an underlying organisational principle to the survival and overall running-of-the-gauntlet of existential selection criteria that allows an idea or an organism plausible continuity and indefinitely extended access to a means of self-propagation. Perhaps this underlying structure or systems-symmetry is uncannily coincident with the notion of the proving of a theorem; a set of procedurally-aggregated (and thus temporally-bound) logical relationships and inductive steps on an endless evolutionary staircase and in which proof of validity (but not of truth or falsity) is intimately bound to a probability of existential continuity. At the level of truth or falsity we might find the binary switch of life and death, of gain and loss; an abstraction which in any specific circumstance or context is not reliant upon the success or failure of any specific instance or implementation of the theorem from which successful continuity is made (in the gestalt) a more probable outcome.

On paths of labyrinthine continuity and the living mysteries of ambiguous self-reference: survival may not be so much of self as of patterned consequence and influence, of context or global-systems (extensivity). The logic and semantics of explanation or description of this principle are also subject to their own continuity proof.