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Gödel's Incompleteness Theorem essentially thwarted Principia Mathematica by proving that mathematics itself is either consistent or complete (read: either usef
by jchook 6y ago
Gödel's Incompleteness Theorem essentially thwarted Principia Mathematica by proving that mathematics itself is either consistent or complete (read: either useful or definable), but not both.
The best definition I've heard calls math "the science of pattern". However, proving itself undefinable seems fundamentally better.
- LudwigNagasena 6y agoJust because you can’t assign a truth-value to “this sentence is false” doesn’t mean that language is “undefinable”, the same with math.
- mathgenius 6y agoIt is such a mystery, how consciousness can perceive pattern.
- ethn 6y agoNote this is Whitehead's and Russell's Principia. Although provably a failed project, I've found tremendous value in the texts.
- proc0 6y agoIMHO Gödel's Incompleteness is also evidence that what is colloquially referred to as math is just a part of something much larger that we cannot yet grasp.