4 ms·

Godel proved the whole endeavor to be futile. Really no point in reading it beyond curiousness.

• schoen 5y ago
  That's not right! Gödel proved that PM couldn't do what people like Hilbert (or PM's authors) hoped it could do. However, we still have * mathematics * formalized mathematics * mathematical research despite the incompleteness phenomenon. All of them are still making progress, even often using approaches that are no more powerful than PM's approach. There are still interesting and important conjectures that can be resolved by a PM-like system, but haven't been resolved yet. I'm sure lots of mathematicians were deeply disappointed when they understood Gödel's result, but it didn't persuade anyone that mathematics was over or that we should no longer work within formal systems!
  • LudwigNagasena 5y ago
    > However, we still have >* mathematics >* formalized mathematics >* mathematical research Yeah, none of them are based on or rely in any way on PM.
    • echopurity 5y ago
      HN can't handle the truth.
• carnitine 5y ago
  That is not even remotely what Goedel did. He showed some inherent limitations to all mathematical formalisation, not that they were useless.
  • LudwigNagasena 5y ago
    Yeah, that’s true, he also showed that the PM project was futile. That’s why no one uses it nowadays, unlike ZFC.
    • drdeca 5y ago
      What are the goals of the project of Principia Mathematica which you are claiming he showed were futile?
      • LudwigNagasena 5y ago
        They are stated in its introduction.
• amw-zero 5y ago
  You don’t understand the incompleteness theorems, that’s for certain.