on Sep. 30, 2018 :
With a marketing image (which I have learned from Smashwords not to call a book cover) of two pairs of shoes ensconced in a shallow box of red bricks and a title page photograph of a swamp with hundreds of dead trees, I can say Fathoming Gödel lives up to these aspects of its innovative promotion.
Is Gödel’s mathematical logic like picking up sticks in a forest? The forest is littered with sticks, but you convince yourself that you can pick up enough sticks to create a park that you and other people can enjoy. Then you lower your expectations and hope to create a small clearing that you alone might enjoy. Time passes, tinged with madness, and all that remains is the forest and sticks.
Is Gödel’s mathematical logic like The Beatles’ album "Sargent Pepper’s Lonely Hearts Club Band"? It’s not actually a concept album, but since so many people claim that it is one, and not only that, but the first concept album in rock and roll, then in a way it is a concept album notwithstanding that it is not a concept album.
If you read "I Am a Strange Loop" by Douglas Hofstadter, he seems to admit that Gödel’s first incompleteness proof is invalid, but then he seems to go on to say that it is true by analogy. And, perhaps, he makes the further claim that all truth comes from analogy. This neatly sidesteps the claim that I believe was made by Aristotle that analogy is the weakness form of argument.
Perhaps, the explanation of a lesser mystery will shed light on the greater mystery of Gödel and his proofs. For years, I wondered why the rock and roll group The Band had managed to accrue such overwhelming accolades from their peers as well as from the critics in the music press. The Band put out a few fine albums, but I think the actual reason they were so lauded is that they were too obscure to be appreciated by the average rock music fan. It is difficult to believe that being too obscure for the average fan would be of paramount importance to the elite, but it seems it is. So it is with Gödel. It is the impenetrable obscurity of his proofs that by far makes the greatest contribution to his mystique. Those who claim to understand his work and can convince others of this fact have an automatic elevation in their status. And, to rise in the pecking order is the most sublime achievement society can offer. I recently learned that snapping turtles spend the winter months buried in mud at the bottom of ponds. This act would seem to rival Gödel in the obscurity competition.
It seems no one ever bothers to ask of Gödel and his proofs and other creators of obscure theories why wouldn’t friendly individuals produce at least one and perhaps several straightforward explanations of their complex ideas. Sometimes it seems that in the past, famous people were little more than gimmicks. If we ever achieve the world depicted in the "Star Trek" universe, the question will not be why was there a book probing Gödel’s proofs, but instead the question will be why weren’t there many books written suspecting his proofs.
(review of free book)
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.
(review of free book)