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diff --git a/content/entry/thoughts-on-logic.md b/content/entry/thoughts-on-logic.md index b5dc22b..999df5d 100644 --- a/content/entry/thoughts-on-logic.md +++ b/content/entry/thoughts-on-logic.md @@ -78,6 +78,6 @@ I've said that for an argument to be valid, the premises must be true. But how d In the early 1920's, famous German mathematician [David Hilbert](https://en.wikipedia.org/wiki/David_Hilbert) put forward a proposal calling for the axiomatization of mathematics. He wanted to make all mathematical truths reducible to an agreed upon set of axioms such that all true statements could be proved, but no false statements could be proved. In 1931, one of the most significant logicians in history, [Kurt Gödel](https://en.wikipedia.org/wiki/Kurt_G%C3%B6del), showed that no set of axioms is capable of proving all truths about the arithmetic of natural numbers. See [Gödel's Incompleteness Theorems](https://stopa.io/post/269). Gödel used mathematical logic to show that there are some places mathematical logic cannot go. Boiled down, he proved that logic cannot prove everything. This is also true in computing. See [The Halting Problem](https://en.wikipedia.org/wiki/Halting_problem). The essence of the trick seems to be, no matter which logic you're talking about, to find a way to encode [the liar paradox](https://rationalwiki.org/wiki/Liar_paradox) in the system. A prerequisite for that is somehow getting the logical system to talk about itself. Gödel found a very fascinating theorem and I would recommend for anyone interested to look more in depth at it. # Conclusion -That's all I've got for this post. I think I've packed in a lot of information and good examples to research. Even if you never learn logic, I believe by reading this post you get a sense of what logic is all about and how to at least recognize some common informal fallacies and misunderstandings. I tried to include plenty of useful external links. This post is barely scratching the surface though. For some readers, just scratching the surface is good enough. But for all I know, the next Gödel might be reading this. In 2011, [a 25-year old math problem about superpermutations was solved by an anonymous 4chan user](https://yewtu.be/embed/OZzIvl1tbPo?local=true). If that doesn't show that cleverness can come from anywhere, I don't what does. +That's all I've got for this post. I think I've packed in a lot of information and good examples to research. Even if you never learn logic, I believe by reading this post you get a sense of what logic is all about and how to at least recognize some common informal fallacies and misunderstandings. I tried to include plenty of useful external links. This post is barely scratching the surface though. For some readers, just scratching the surface is good enough. But for all I know, the next Gödel might be reading this. In 2011, [a 25-year-old math problem about superpermutations was solved by an anonymous 4chan user](https://yewtu.be/embed/OZzIvl1tbPo?local=true). If that doesn't show that cleverness can come from anywhere, I don't what does. I hope you enjoyed the post. If there's anything that you think I should have covered in this post or that I should talk in the future, [let me know about it](mailto:nick@nicholasjohnson.ch). |