Tulsi Prajna 2000 04

SR No.: 524603
Original Sutra Author: N/A
Author: Shanta Jain, Jagatram Bhattacharya
Publisher: Jain Vishva Bharati
Publication Year: 2000
Total Pages: 152
Language: Hindi
Classification: Magazine, India_Tulsi Prajna, & India
File Size: 7 MB

Page 116

propositional function carries statement which involve certain variables. These variables may have some values which may be either true and remaining may be false. Thus the calculus of propositions and that of propositional functions got evolved, transforming pure logical forms into mathematical symbols, as in the Labdhisāra treating all that which is beyond that in the Gommaṭasāra, Pierce divided the foredicate into three parts, monadic, dyadic and polyadic, leaving blanks to be filled by relations, maintaining syllogism as an original inference and logic as the science of general laws of symbols. Then the mathematical logic was given a well known form, "Principia Mathematica" by Whitehead and Russell,17 after the work of Frege who regarded numerals as abstract and objective, existent as concepts and not as ideas as the anka samdrsti in Jaina School. Peano, however went on to analyze the mathematical methods, transforming them into a logical calculus, employing symbols and formulas for developing algebraic derivations. All this show how the Jaina Karma Theory had a objective, and all their methods in mathematical efforts led to their theory of emancipation. We find that Cantor's and Zermelos works were rejected by Poincore and Kronecker, so also was the case with the Jaina theory of karma, in the logical struggles in India. Brouwer, the successor of Kronecker's criticism, found the intuitionism, parallell to logisticism of Russell. It restricts the cultural development of mathematics in the regions of the logical universe lying outside the domain of sensical experiences.
Apart from the above two schools, there is the third school of 'formalism' founded by Hilbert, follower of Peano, 1862-1943 A.D.) regarding symbols and operations as the core of mathematics. He felt that the method of consistency proof of developed to assure whether a model was free from antinomies or contradictions. He fused the axiomatic method with the logistic method, for proving consitency of formulas for finite and transfinite sets. Godel, however, evolved a method for proving a system as consisting of theorems which could be neither proved nor disproved, paving the way for finding out the incompleteness of a system. For a bios, in Jaina school, the Karmic System, actually is incomplete, since beyond this system, exists the system of operations, capable to keep the soul free, for ever, from the karmic state of phenomena. To the logical trends we need add the trends of other sciences, pioneered by Maxwell, Einstein and others who have contributed to the field theories which are moving faster to cope with the brain fields of a bios, which are still in the darker ranges of study.
110 ZZ
तुलसी प्रज्ञा अंक 109