(These papers form the basis of the author’s subsequent papers “Beyond Gödel”)
The author attempts to retreat from the dogmatic attitude of certainty in the existence of an outright fallacy in Gödel's reasoning, as expressed forcibly in ‘The fallacy in Gödel's proof of undecidability (Mar 2000)’, and returns once again to his earlier position that there are seriously disquieting non-constructive features in Gödel's reasoning and conclusions.
These papers highlight some natural, and constructive, lines of reasoning that contradict Gödel's conclusions, but do not appear to merit serious consideration in the existing literature as tending to cast doubt on the validity of Gödel's reasoning.
My grateful thanks to Professor Gyorgy Sereny, Department of Algebra, Budapest University of Technology and Economics for patiently correcting serious errors regarding my assumptions concerning the rank of primitive recursive functions, and helping me appreciate the significance of the deeper role that their strong representability plays in Gödel's reasoning.
Finally my thanks once again to Dr. Chetan H. Mehta for his continuing encouragement, and to friends, associates and family members who continue to be sacrifice their legitimate interests so that this work might have a chance to arrive at its natural conclusion.
Bhupinder Singh Anand
Mumbai : December 2000
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