organismic sets

0.1 Organismic Set Theory and Relational Biology

Organismic setsPlanetmathPlanetmath (OSn) were defined by Nicolas Rashevsky as simple set-theoretical models of organization in living organisms at discrete integer or zero levels by means of sets of several distinct types or order beginning at the zeroth order, and having an upper limit as the fifth or sixth order of roganization. Thus, in the case of organismic sets of zero-th order, S0, the elements correspond to genes, and a concrete S0c is defined as the set of all genes [Gn] of a specific organism or organism type (understood as a stable biological species).

Alternatively, S0c can be defined as a set representation of any organismic genome, GO, consisting of the complete set of active, functionalPlanetmathPlanetmathPlanetmath genes of an organism together with controlling genes/operons. The latter are then also considered together with inputs ei from the environment, as well as their activities ai and relationsMathworldPlanetmathPlanetmath Rij among organismic set elements (genes in the case of S0), where i,j are indices in a countableMathworldPlanetmath, index setMathworldPlanetmathPlanetmath I. Thus, Rashevsky’s organismic set (OS) theory is part of abstract relational biologyPlanetmathPlanetmath (, but unlike organismic networks, metabolic-replication systems and organismic supercategoriesPlanetmathPlanetmathPlanetmathPlanetmath, Rashevsky’s OS are only endowed with the discrete topology, and are thus the simplest model whose only connectivities to organization are through the hierarchical latticeMathworldPlanetmathPlanetmath structureMathworldPlanetmath of the different types of OS, from GO to (OSn), with n>1. At the next level of biological organization, cells are considered as first order organismic sets, S1, whereas multi-cellular organisms are modeled by organismic sets of second order, S2, whose ‘elements’ are the first order organismic sets, or cells, S1. 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 predicatesMathworldPlanetmathPlanetmath 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 and ecological systems.


  • 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.
Title organismic sets
Canonical name OrganismicSets
Date of creation 2013-03-22 18:11:20
Last modified on 2013-03-22 18:11:20
Owner bci1 (20947)
Last modified by bci1 (20947)
Numerical id 28
Author bci1 (20947)
Entry type Topic
Classification msc 92C30
Classification msc 92B99
Classification msc 92B20
Classification msc 92B05
Synonym lattices or sets of organismic structures
Related topic OrganismicSet
Related topic NicolasRashevsky
Related topic AbstractRelationalBiology
Related topic GeneticNetsOrNetworks
Related topic ComplexSystemsBiology
Related topic OrganismicSetTheory
Related topic FunctionalBiology
Defines organismic set