Gödel's Theorem: An Incomplete Guide to Its Use and Abuse
"Among the many expositions of Gödel's incompleteness theorems written for non-specialists, this book stands apart. With exceptional clarity, Franzén gives careful, non-technical explanations both of what those theorems say and, more importantly, what they do not. No other book aims, as his does, to address in detail the misunderstandings and abuses of the incompleteness theorems that are so rife in popular discussions of their significance. As an antidote to the many spurious appeals to incompleteness in theological, anti-mechanist and post-modernist debates, it is a valuable addition to the literature." --- John W. Dawson, author of Logical Dilemmas: The Life and Work of Kurt Gödel
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The author fails to clearly see the other side of the story. Take his stance on applying the IT to objectivism: Well, at first argues that objectivism is not a formal system in the mathematical sense. This means that you cannot present objectivist axioms with symbols (think language) and derive rules from them by way of logical inference. Well, does that not mean that there's no objective system of ethics derivable by logical inference from the 3 axioms she gives? In a sense, he's saying her theory is subjective! Either the IT doesn't apply and "objectivism" is somewhat subjective (*gasp), or the IT does apply and objectivism is either inconsistent or incomplete. Then he goes on to make an argument that misses the point. He talks about whether objectivism can tell you something about space. According to him it cannot and so it's "trivially" incomplete. That might be true, but it's also incomplete in a much more important sense: it cannot tell you how you should act in every given situation. There are infinitely many different situations that an individual might find himself in (I can list different situations for the rest of eternity), and applying the objectivist axioms won't tell him how to act. So maybe there is something to relating the IT to objectivism, maybe it's a misuse of the IT. Nevertheless, the auther does not have me convinced either way.