query: Why aren't vacuous truths just undefined?
positive_passages.docid: 578
positive_passages.text: In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False?
negative_passages.docid: 59757
negative_passages.text: Is a world with constant/decreasing entropy theoretically impossible?
negative_passages.docid: 58256
negative_passages.text: If "clearly evident" is redundant, what word or phrase suggests being indisputable but not readily apparent?
negative_passages.docid: 21670
negative_passages.text: Why does an infinite limit not exist?
negative_passages.docid: 52827
negative_passages.text: Could negative dimension ever make sense?
negative_passages.docid: 93724
negative_passages.text: How to substantiate the claim that something is not known?
negative_passages.docid: 13374
negative_passages.text: Why is "the set of all sets" a paradox, in Layman's terms?
negative_passages.docid: 126713
negative_passages.text: Strong induction and vacuous truth
negative_passages.docid: 147874
negative_passages.text: Why does the existence of independent statements not prove consistency?
negative_passages.docid: 122324
negative_passages.text: Is there a proof of Gödel's Incompleteness Theorem without self-referential statements?
negative_passages.docid: 87992
negative_passages.text: A proposition is non-falsifiable. So what?
negative_passages.docid: 126739
negative_passages.text: Is everything greater than None?
negative_passages.docid: 35370
negative_passages.text: Why is this proposition provable and its converse not?
negative_passages.docid: 61438
negative_passages.text: A question regarding existence and uniqueness in IVP
negative_passages.docid: 5274
negative_passages.text: Are omniscience and omnipotence mutually inconsistent?
negative_passages.docid: 135957
negative_passages.text: Why in an inconsistent axiom system every statement is true? (For Dummies)
negative_passages.docid: 78009
negative_passages.text: Why can't we use implication for the existential quantifier?