I decided to buy this book, and at 50 pages in (of about 700 pages total) I can already say it will be worth the full price. Here's a quote to show what I mean (chapter 2.6.2, pp. 45-46):
To understand [Gödel's incompleteness theorem], the essential point is the principle of elementary logic that a contradiction A and not-A implies all propositions, true and false. -- Then let A = {A1, A2,..., An} be the system of axioms underlying a mathematical theory and T any proposition, or theorem, deducible from them:
A => T.
Now, whatever T may assert, the fact that T can be deduced from the axioms cannot prove that there is no contradiction in them, since, if there were a contradiction, T could certainly be deduced from them!
This is the essence of the Gödel theorem, as it pertains to our problems. As noted by Fisher (1956), it shows us the intuitive reason why Gödel’s result is true. --
Recommended.
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