query: Was Russell's purpose in Principia Mathematica to formalize all the possible constructions of logic?
positive_passages.docid: 147760
positive_passages.text: What did Whitehead and Russell's "Principia Mathematica" achieve?
negative_passages.docid: 42517
negative_passages.text: Is formal truth in mathematical logic a generalization of everyday, intuitive truth?
negative_passages.docid: 12569
negative_passages.text: Using the terms 'theorem 'and 'tautology'
negative_passages.docid: 79389
negative_passages.text: Is there an intuitionist (i.e., constructive) proof of the infinitude of primes?
negative_passages.docid: 21479
negative_passages.text: Why cofinality is a cardinal.
negative_passages.docid: 47871
negative_passages.text: Why did mathematician construct extended real number systems, $\mathbb R \cup\{+\infty,-\infty\}$?
negative_passages.docid: 101741
negative_passages.text: Selection of logical connectives {¬,∨,∧,⇒,⇔} in set theory?
negative_passages.docid: 97187
negative_passages.text: In what formal system is Godel's Incompleteness Theorem (or similar statements of undecidability) proven?
negative_passages.docid: 72034
negative_passages.text: Truth table and the meaning of $\oplus$ in propositional logic
negative_passages.docid: 111797
negative_passages.text: Without computers, how can you conjecture the (in)validity of a long convoluted argument in Predicate Logic?
negative_passages.docid: 84378
negative_passages.text: Does axiom of foundation/regularity protect against Russell-like paradoxes?
negative_passages.docid: 84485
negative_passages.text: What is the purpose of the Axiom of regularity/foundation?
negative_passages.docid: 32027
negative_passages.text: Given (p ∧ q), use the Fitch system to prove (q ∨ r)
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: 102899
negative_passages.text: Category theory with objects as logical expressions over $\{\vee,\wedge,\neg\}$ and morphisms as?
negative_passages.docid: 105185
negative_passages.text: What can suffice as a scientific proof for God? to what domain can such a proof belong to?