Organismic Set Theory and Relational Biology

Nicolas Rashevsky defined the mathematical concept of organismic sets for different levels of organization in living organisms by means of sets of several distinct types. Thus, in the case of organismic sets of zero-th order, , the elements represent genes, and a concrete is defined as the set of all genes of a specific organism or organism type (`species'); alternatively, can be defined as a set representation of any organismic genome, . The latter are then considered together with inputs from the environment, as well as their activities and relations among organismic set elements (genes in the case of ), where are indices in a countable, index set . Thus, Rashevsky's organismic set (OS) theory is part of abstract relational biology. At the next level of biological organization, cells are considered as first order organismic sets, , whereas multi-cellular organisms are represented by organismic sets of second order, , whose `elements' are the first order organismic sets, or cells, . Attempts were then made by Rashevsky to expand his theory of organismic sets to organizational models of human societies. Results from such studies of relations between sets were considered to be far more important than the numerical or quantitative aspects that play such important roles in physics and chemistry. A number of interesting results were obtained by means of standard (Boolean) logic predicates applied to organismic sets and their relations. Further details can be found in the publications listed below and the references cited therein. Subsequently, autopoietic theories have enlarged upon, and also extended, the application of organismic sets to biological systems and Ecology.

Bibliography

1

Rashevsky, N.: 1965, The Representation of Organisms in Terms of Predicates, Bulletin of Mathematical Biophysics 27: 477-491.

2

Rashevsky, N.: 1969, Outline of a Unified Approach to Physics, Biology and Sociology., Bulletin of Mathematical Biophysics 31: 159–198.