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The beginning of the proof starts with "Suppose to obtain a contradiction, that mathematics is inconsistent". From that assumption, they derived a contradictio
by cobbal 13y ago
The beginning of the proof starts with "Suppose to obtain a contradiction, that mathematics is inconsistent".
From that assumption, they derived a contradiction, therefore the assumption can't be true, and math must be consistent.
- gphilip 13y ago> From that assumption, they derived a contradiction This is what I don't see. To have derived a contradiction, they should have shown: "mathematics is consistent". Instead they ended up showing (because Φ and ¬Φ): "mathematics is inconsistent". Which is what they started out with. Where is the contradiction? Hmm.. while writing this out, I think I am starting to get the source of the confusion. "Mathematics is inconsistent" is a meta statement about mathematics, and "Φ and ¬Φ" is a "plain" statement within the said mathematics. My intuitive feeling is that the latter contradiction does not "affect" the meta statement. I need to think further to make this more rigorous. OT: Why the downvote(s)? Does my comment take away from the discussion?
- acchow 13y agoYeah, you nailed it. He's in metamathematics and doesn't realize it. I elucidate it in another comment: https://news.ycombinator.com/item?id=6119587 https://news.ycombinator.com/item?id=6119587