Comment Comment by tz18 1. it is not true that (for all hats h in {liar's hats}, h is green)2. by the negation rule, there exists a hat h in {liar's hats}, such that it is not true that h is green.3. there exists a hat in {liar's hats}This is really basic first order logic guys."For all x in {}, P(x)" is always trivially true without regard for P.Similarly, "there exists an x in {}, P(x)" is always trivially false.https://en.wikipedia.org/wiki/Vacuous_truth parent tz18 1 year ago
2. by the negation rule, there exists a hat h in {liar's hats}, such that it is not true that h is green.
3. there exists a hat in {liar's hats}
This is really basic first order logic guys.
"For all x in {}, P(x)" is always trivially true without regard for P.
Similarly, "there exists an x in {}, P(x)" is always trivially false.
https://en.wikipedia.org/wiki/Vacuous_truth