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one should understand different aspects of water and one should realize that whenever, one is describing a property of water then due to limitation of language and representation of knowledge and the context, it is not possible to describe all its aspects. The theory of Anekantavad and syadavad have found practical applications in almost all spheres of life such as personal, family and social relations and led to the concepts of tolerance, compromise, forgiveness, and mutual respect for each other's views and is essential for harmonious living. These aspects will not be discussed here and we will confine to the concepts of Jain philosophy in relation to the principle of knowledge, complementarity, quantum mechanics, wave-particle duality, probability and statistics.
2.1 Knowledge and Godel's incompleteness theorems:
We generally feel that mathematical representation of various scientific facts make our knowledge more precise and accurate. However, from the theorems which have been proposed by Kurtz Gödel, we find that mathematical representation of any physical reality limits and actually reduces our knowledge of that reality. Complete knowledge must necessarily have its foundation in an unexpressed, unmanifest field of intelligence. 2.2 Gödel's first incompleteness 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 axiom 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.
2.3.Gödel's second incompleteness theorem
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| SR No. | 007004 |
| Book Title | Elusive Consciousness |
| Original Sutra Author | N/A |
| Author | Narendra Bhandari, Surendrasingh Pokharana, Jitendra B Shah |
| Publisher | L D Indology Ahmedabad |
| Publication Year | 2015 |
| Total Pages | 150 |
| Language | English |
| Classification | Book_English |
| File Size | 19 MB |