|Bertalanffy, Ludwig von (1968). General System Theory. Foundations, Development, Applications. New York: George Braziller. S. 84f.|
The isomorphism found in different realms is based on the existence of general system principles, of a more or less well-developed „general system theory.“ The limitations of this conception, on the other hand, can be indicated by distinguishing three kinds or levels in the description of phenomena.
At first, there are analogies—i.e., superficial similarities of phenomena which correspond neither in their causal factors nor in their relevant laws. Of this kind are the simuiaera vitae, popular in previous times, such as when the growth of an organism was compared to the growth of a crystal or of an osmotic cell. There are superficial similarities in the one or other respect, while we are safe to say that the growth of a plant or an animal does not follow the pattern of crystal growth or of an osmotic structure, and the relevant laws are different in both cases. The same applies to the consideration of a biocoenosis (e.g., a forest) as an „organism,“ with the obvious difference between the unification of an individual organism and the looseness of a plant association; or the comparison of the development of a population with birth, growth, aging and death of an organism where the comparison of life cycles remains highly dubious.
A second level are homologies. Such are present when the efficient factors are different, but the respective laws are formally identical. Such homologies are of considerable importance as conceptual models in science. They are frequently applied in physics. Examples are the consideration of heat flow as a flow of a heat substance, the comparison of electrical flow with the flow of a fluid, in general the transfer of the originally hydrodynamic notion of gradient to electrical, chemical, etc., potentials. We know exactly, of course, that there is no „heat substance“ but heat is to be interpreted in the sense of kinetic theory; yet the model enables the stipulation of laws which are formally correct. It is logical homologies with which the present investigation is concerned. We may express this as follows: If an object is a system, it must have certain general system characteristics, irrespective of what the system is otherwise. Logical homology makes possible not only isomorphy in science, but as a conceptual model has the capacity of giving instrucdons for correct consideration and eventual explanation of phenomena.
The third level finally is explanation—i.e., the statement of specific conditions and laws that are valid for an individual object or for a class of objects. In logico-mathematical language, this means that the general functions ƒ of our equation (3.1) are replaced by specified functions applicable to the individual case. Any scientific explanation necessitates the knowledge of these specific laws as, for example, the laws of chemical equilibrium, of growth of an organism, the development of a population, etc. It is possible that also specific laws present formal correspondence or homologies in the sense discussed; but the structure of individual laws may, of course, be different in the individual cases.