Fathoming Gödel

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The conclusion reached in "Fathoming Gödel" is that Gödel's 1931 paper is a shell game. It is based on several errors that are well camouflaged. Some shortcomings in the paper are openly admitted although they are downplayed, and errors are also produced in an effort to force a particular conclusion. This critique is limited to Gödel's first incompleteness theorem as translated by Martin Hirzel. More
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About Jim Spinosa

Born in 1955,Jim Spinosa remembers,as a youngster,
being entranced by the science fiction novels he
perused in a small,corner bookstore in Denville,
NJ. The cramped confines of that store had claimed
to contain the largest selection of books in Northern New Jersey. His penchant for science fiction engendered an interest in physics. Often daunted by the difficulty of physics textbooks,he
questioned whether physics could be presented as clearly and concisely as science fiction,without sustaining any loss in depth Nuts and Bolts:Taking
Apart Special Relativity is an attempt to answer that question.

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Review by: James R Meyer on March 25, 2016 :
Unfortunately, Spinosa has jumped in at the deep end, and it is clear that he has failed to do the necessary research and has jumped to conclusions that are completely wrong due to his failure to understand the basics of what he is talking about. Two examples will suffice to demonstrate this:

Spinosa uses Hirzel’s English translation of Gödel’s proof. In Hirzel's translation, words in all capitals such as 'VARIABLE', 'FORMULA', 'AXIOM', etc do not actually designate variables or formulas or axioms of the formal system, but they denote natural numbers, where the natural numbers correspond (by Gödel numbering) to expressions of the formal system; and relations between these numbers correspond (by Gödel numbering) to relationships between expressions of the formal system. This is explicitly explained in Hirzel’s translation on his page 6, just before section 2.3, and the distinction is indicated by capitals (Note: in Meltzer’s translation, the distinction is indicated by italics.) Spinosa has completely failed to comprehend this distinction between expressions of the formal system and numbers that correspond to such expressions, and his article is full of examples of this misunderstanding.

Spinosa also fails to understand that in Hirzel’s paper, there are two completely different functions that have the same name: "subst", and he manages to completely confuse the two (This is partly why I recommend Melzer's translation over Hirzel's, since Meltzer uses two different names, as does Gödel’s original paper). It is true that Gödel does not assist the reader by his assertion that his relation 31 is the concept Subst that he referred to previously, but had Spinosa understood the distinction referred in the above paragraph, this would have not presented a problem.
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