Concept of universality within the framework of the second order cybernetics

Abstract

Ideological essence of the second-order cybernetics is generally understood as a “view from within”. This requires certain conceptual revision of most fundamental notions. Particularly, an interpretation of a ‘universal law’ is subject to such a revision. Formally speaking, any universal law may be coded in the form АхР(х), where Ax is the universal quantifier. However, its meaning changes significantly, for it could be shown that it must be treated probabilistically. The reason for this is in that the standard phrase ‘for any x’, which discloses the meaning of the formula Ax, must be seen here as an arbitrariness of choice, while ‘the choice arbitrariness’ must be seen as a constructive procedure within the second-order cybernetics. Otherwise, basic presumption of the second-order cybernetics will not hold. Indeed, classical science assumes that when one says ‘Let us pick up an arbitrary x from the model M’ then the very procedure of ‘picking up an arbitrary x’ is not assumed to be a part of model M. Classical scientists think of this act as of some agent’s act who is completely external to model M. Second order scientists take it differently. All agent’s acts — observations, measurements, picks, experiment organizations, etc — must be seen as a part of an appropriate model. This is the core of the ‘view from within’: theoretical agents, their acts as well as their theories must be considered as internal events, or properties, of the intended models. Going back to formula Ax, it is easier to see now that an intention ‘to pick up an arbitrary x’ must be treated as a real process within an appropriate model M. The only way to do it is to assume that such models have (truly) random events generators G as a necessary part of their structure. All above implies that an interpretation of AxP(x) within the framework of the second-order cybernetics must be the following: P(x) is universally true on M iff there exists G in M such that at any time t G may randomly choose any element from M with probability р(х)≠0, and P(x) will appear to be true. As a result of this, we may claim that the very idea of justifiable universality is inconsistent with deterministic ontologies (in the second-order science framework). Indeed, deterministic ontologies do not assume that at any time t it is possible to pick up an arbitrary x from the model M, for, by definition, they are limited only to certain choices through time, which are pre-determined by deterministic schedule of choices.