Exploration of General Systems Theory GST and Jainism may provide new frontiers of knowledge and evolution

SR No.: 269185
Original Sutra Author: N/A
Author: Surendra Singh Pokharna
Publisher: Surendra Singh Pokharna
Total Pages: 37
Language: English
Classification: Article
File Size: 504 KB

Page 8

Syntropy 2013 (2): 243-279
ISSN 1825-7968
construct a sentence S in the simple mathematical language of elementary numbertheory 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.
4.2. 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.
In these examples, Godel's theorems are applied to some cases in abstract mathematics, but they are now being explored in various other branches of sciences. However, as discussed above, a concept of consciousness is required to go beyond the current scientific thinking.
5. Limitations of the physical sciences as they apply to living systems:
Actually all living beings are essentially irreversible in nature, that is they grow and decay and they are also open systems compared to the physical system's which are closed systems. They constantly interact with the environment like, human beings take oxygen from atmosphere and releases carbon di-oxide. Hence biological and social systems cannot be subjected to the process of measurement and hence they are not exactly describable in the strict terminology of the physical, sciences, in addition, human systems have a memory which makes it impossible to do any scientific experimentation on them. Hence such systems are studied in a different way by using statistical procedures. In such methods only some rough trends or patterns can be found.
Now this type of experimentation is not possible in case of present phenomena because as shown above human system has memory, free will, creativity, tendency to interact strongly with other fellow beings and the environment. Furthermore there are micro controls in the form of thought processes which cannot be easily adjusted in any planned "scientific experiment". Hence it is impossible to perform experiments on human systems and predicting events about them from a purely scientific point of view.
250