Gödel and the limits of logic (2006)

I highly recommend getting Godel&#x27;s proof[1] and reading it. It&#x27;s an amazing journey and quite understandable from the start (the first half of the book is introduction), and I&#x27;ve never been able to read proofs very well. It takes concentration, but once you get it (at &#x27;17 GenR&#x27;) it&#x27;s almost like a symphony going off. The crystalline brilliance of the &quot;System P&quot; decomposition is worth it just to see how math as a process could be reduced to a such simple, clear and concise set of symbol manipulations...and then the rest shows how that could be used topple itself. Incredibly philosophically insightful.<p>[1] <a href="https:&#x2F;&#x2F;www.amazon.ca&#x2F;Undecidable-Propositions-Principia-Mathematica-Mathematics-ebook&#x2F;dp&#x2F;B00A44R3E8&#x2F;ref=sr_1_1?ie=UTF8&amp;qid=1489447527&amp;sr=8-1&amp;keywords=on+formally+undecidable+systems+godel" rel="nofollow">https:&#x2F;&#x2F;www.amazon.ca&#x2F;Undecidable-Propositions-Principia-Mat...</a>

A light take on the subject can be found in Logicomix: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Logicomix" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Logicomix</a> - a cool blend between the dry topic and comics.

Are there any Gödel-like problems that does not involve self references?

This reminds me of the Berry Paradox: <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Berry_paradox" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Berry_paradox</a>

I like very much the program x virus example&#x2F;citation.. but I would put it in the other way around: &quot;A program can find all virus, unless the operating system is a virus itself.&quot;

&quot;Digital Physics&quot; (the movie) is now free on Amazon Prime. It is also available for rent&#x2F;purchase on iTunes and Vimeo, in case you are kind enough to support an independent filmmaker:) Come explore the world of self-reference, infinity, complexity, Gödel &amp; Turing, and psychedelics with Khatchig!!

Why have I never had to debug a Gödel paradox in my day-to-day programming? Is it because of types? Finite memory? Can someone enlighten me? Thanks

Isn&#x27;t Gödel&#x27;s incompleteness a consequence of overly ambitious material implication properties? When you look at the truth table:<p>A | B | A -&gt; B<p>0 | 0 | 1<p>0 | 1 | 1<p>1 | 0 | 0<p>1 | 1 | 1<p>I fail to see why all except for 1 -&gt; 0 = 0 aren&#x27;t undefined. I understand reasoning behind why this was done, but mixing unrelated predicates seems like a generally bad idea, even if it allows mechanical proofs.<p>Aren&#x27;t there already &quot;complete&quot; systems like relevance logic? Now with computers we can perhaps make proofs we need &quot;relevant&quot; instead of being based on fundamentally incomplete though &quot;simpler&quot; logic?