Or at least had a profound influence on my life. This post doesn’t have much to do with writing, but I ran into a comic that serves as an excellent illustration of Gödel’s Proof. This proof also revolutionized mathematics, but that’s another story, which I’ll tell a little of next.
Kurt Gödel was a German mathematician who escaped Germany in time to miss being there for the second world war. He moved to Princeton and he and Albert Einstein were best of friends. A famous British mathematician, Alfred North Whitehead, and philosopher Bertrand Russell had an ambition at the time to write a book that unified all of mathematics, beginning to end. The title was Principia Mathematica. The multi-volume book is extremely dense reading and I don’t recommend it. It’s not finished either. Kurt Gödel proved that they couldn’t do it. When the Brits learned of it, (long story short), after trying to figure a way around the Proof, they gave up.
Fortunately for me and non-mathematicians everywhere, Gödel’s proof, although is is not light reading, it can be understood if you’re willing to stop and think, and sometimes re-read parts. I recommend that you give it a read in you’re into this sort of thing.
It was back in my college days. (Paul Fosmark, you might remember me mentioning this in one of our U of M campus evangelistic street meetings.) I was asking a lot of questions about the meaning of life, what is true, and so on, as people that age are wont, and I ran into an article about this piece of mathematics (later I found the book, but I loaned it so someone, and it, shall we say, went into the ministry) and, as I mentioned in the first line of this post, it had a profound effect on me.
What he proved, among several other things, was that no logical system can be complete. You can always ask questions within a system that the system can’t answer.
Another way of putting this is that all systems contain statements that are true within the system but you can’t prove that they are true. A corollary of this was that you could generate contradictory statements and still be following the rules of the system.
(Still with me?) Gödel showed that a logical system gets into trouble when it makes self-referential statements. Statements that refer to themselves. And that’s what this comic contains an example of.
Two outcomes of this proof (of many): You will never have 100% bug-free software, and the problem of free will versus God’s sovereignty will never be solved by any living theologian. Whitehead and Russell did figure a way around the proof, but it’s not very practical for us here on earth. You can get around the incompleteness if the system is infinite. Think about that!
I’ll do my best to make the next post lighter reading.
PS—Here’s a simpler example. Is it breaking news or not?