SYSTEM DUALITY: BIRATIONAL HIERARCHY

Abstract

System theory, and most particularly hierarchy theory, must be consistent with philosophy. In his book “Logic in Reality”, Brenner reinforces the traditional philosophic position that an entity can only exist in relation to its non-existence. This leads to a duality in system theory which is consistent with the selective division of Nature into entity and ecosystem, where the two depend on different criteria and even different logics. A fascinating aspect of such a birational approach is that representations and properties only exist as intermediates between pairs of ideal extremes. Quantum logic, for example, no longer replaces post-Newtonian classical logic; it complements it, identifying all real entities as compromises between the two. This albeit philosophically non-traditional included middle is identical to that of the philosophical logic of Stéphane Lupasco, and to the implications of Brenner’s “Logic in Reality”. This presages a major philosophical change in the way Science can be carried out. What we wish to do is to bring all of Science under a generalized umbrella of entity and ecosystem, and then characterize different types of entity by their more or less important relationships with their relevant ecosystems. The most general way to do this is to move the ecosystemic paradigm up to the level of its encompassing logic, creating a complementary pair of conceivably different logics – one for the entity we are focusing on; one for the ecosystem within which it exists – and providing for their quasi-autonomous birational interaction. We present a representation of natural hierarchy which is itself dual in character, and counsel that monorational constructions are ineffective. As an example, we present a dual formulation of entropy. We conclude with an application of the model to large Organizations.