query: Is the Russell paradox the only possible contradiction to the axiom schema of comprehension due to Frege (1893)? $\{x:P(x)\}$
positive_passages.docid: 151215
positive_passages.text: Paradox of General Comprehension in Set Theory, other than Russell's Paradox
negative_passages.docid: 104771
negative_passages.text: Dedekind's cut and axioms
negative_passages.docid: 155679
negative_passages.text: If union of two theories is not consistent one of them implies a sentence which the other implies opposite of it
negative_passages.docid: 70166
negative_passages.text: Why is the universal quantifier $\forall x \in A : P(x)$ defined as $\forall x (x \in A \implies P(x))$ using an implication?
negative_passages.docid: 56191
negative_passages.text: How to demystify the axioms of propositional logic?
negative_passages.docid: 118813
negative_passages.text: How can Zeno's dichotomy paradox be disproved using mathematics?
negative_passages.docid: 6535
negative_passages.text: Proof of for-all / there-exists "negation"?
negative_passages.docid: 113640
negative_passages.text: Why is there this strange contradiction between the language of logic and that of set theory?
negative_passages.docid: 106092
negative_passages.text: Can mathematical definitions of the form "P if Q" be interpreted as "P if and only if Q"?
negative_passages.docid: 88566
negative_passages.text: Is denying "Paradoxical Partitioning" equivalent to accepting the Axiom of Choice?
negative_passages.docid: 95851
negative_passages.text: Validity of an argument with a contradictory conclusion
negative_passages.docid: 58631
negative_passages.text: Continuity and the Axiom of Choice
negative_passages.docid: 128843
negative_passages.text: Rolle's Theorem Contradiction
negative_passages.docid: 103154
negative_passages.text: Is there a *simple* example of how the axiom of choice can lead to a counterintuitive result?
negative_passages.docid: 121847
negative_passages.text: Don't we need the axiom of choice to choose from a non-empty set?
negative_passages.docid: 73231
negative_passages.text: Why in implication, if premise is false then implication is true?
negative_passages.docid: 102202
negative_passages.text: The smallest infinity and the axiom of choice