Journal of Gyansagar Science Foundation 2013 04 01

Author(s): Sanjeev Sogani, Vimal Jain
Publisher: Gyansagar Science Foundation

Page 32

Dr. Surendra Singh Pokharna, Volume 1 Issue 1 April 2013
For biological systems which are so strongly interacting with each other, this type of formalism cannot be applied in a satisfactory way in a real sense.
General Systems Theory can bridge science with religion
Godel's incompleteness theorems
Hence to handle all the above problems mentioned above, we look for a new discipline which has recently emerged (John Gigch, 1978) and is called General Systems Theory (GST). It has been developed to handle such complex systems and issues. Different sets of rules are there to describe and understand such systems.
The most attractive aspect of scientific knowledge is its mathematical basis. We generally feel that this mathematical representation of various scientific facts make our knowledge more precise and accurate. However, from the following theorems which have been put forward by the great mathematician Kurtz Gödel, we find that any mathematical representation of any physical reality limits our knowledge of that reality. Not only this but the theorem also imply that none of the languages or representation can express the reality of nature with perfection. Complete knowledge must necessarily have its foundation in an unexpressed, unmanifest field of intelligence. Let us begin with the theorems.
This concept takes into account both physical systems and biological and social systems. Actually systems properties depend on their domain. The domain of systems is the field over which they extend. It can be classified as to whether: (a) Systems are living or nonliving, (b) Systems are abstract or concrete, (c) Systems are open or closed, (d) Systems exhibit a high or low degree of entropy or disorder, (e) Systems display organized simplicity, unorganized complexity or organized complexity, (f) Systems can be ascribed a purpose or not, (g) Feedback exist or not, (h) Systems are ordered in hierarchies and/or Systems are organized. (See Pokharna 2010 for details)
Gödel's first in-completeness theorem
This theorem says that the truth of a formalism (which describes any phenomenon) cannot be proved. Thus no finite expression of mathematical knowledge can ever provide a basis for comprehensive knowledge even of the elementary properties of the counting numbers. Thus if one starts with a collection C of symbolic mathematical (or any other) axioms which is specifiable by a finite number of mechanical rules, and if C is consistent, then there will be a true statement about the counting numbers which can not be proved from the axioms C, using the standard rules of mathematical logic. The proof of this theorem shows that from C one can construct a sentence S in the simple mathematical language of elementary number theory whose meaning is : This sentence is not provable from C. Once S is constructed it follows easily that S must be true but not provable from C. Thus on the basis of any finitely specifiable collection of axioms C, one cannot prove all true propositions about the counting numbers.
In this analysis pure physical sciences are now categorized as hard systems and subjects like sociology, religion, psychology, biology etc are classified as soft systems. (Bertalanffy 1976). It has been developed to handle such diverse systems and is a serious attempt to reconcile physical sciences with social sciences. As per this theory, all systems are characterized by transfer of information, knowledge and entropy/order which are much more important than any other attribute. Even energy comes next to them.
Need to realize that scientific knowledge is only a subset of the total knowledge system and actual knowledge is structured in the consciousness
Gödel's second incompleteness theorem A formal language (mathematical or any other) if consistent cannot define its own truth i.e. the definition of truth for a theory must be of a higher order than the theory itself. We can also say that the consistency of any specifiable collection of axioms can never be established on the basis of mathematical arguments which can be justified by these axioms. Thus to establish the validity of any single mathematical system one must necessarily utilize a more comprehensive system, to validate the latter system one has to investigate an even more comprehensive system.
With the advent of science and the resulting technology, a misunderstanding and misconception has developed among the masses that the scientific knowledge is the only ultimate knowledge in the world. Not only this, it also presumed that the knowledge which is experimentally verifiable and repeatable at any place and at any time alone is the actual knowledge. This is far from the truth. The fact is that the so called science is just around 200 years old and the concept of knowledge existed much before that for several centuries. Vedas, Upnishads, Puranas, Agamas, Mahabharat and Ramayana, Koran, Bible have lot of knowledge about life and controls to be followed. Similarly technology of gold manufacturing