The ultimate substantive legacy of Principia Mathematica is mixed. It is generally accepted that Kurt Gödel's incompleteness theorem of 1931 definitively demonstrated that for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced from them, and hence that Principia Mathematica could never achieve its aims. However, Gödel could not have come to this conclusion without Whitehead and Russell's book. In this way, Principia Mathematica's legacy might be described as its key role in disproving the possibility of achieving its own stated goals. But beyond this somewhat ironic legacy, the book popularized modern mathematical logic and drew important connections between logic, epistemology, and metaphysics. COUNT 9
QSN1 Despite its imperfection, what are now considered valuable achievements of Principia Mathematica? ANS1 the book popularized modern mathematical logic and drew important connections between logic, epistemology, and metaphysics QSN2 What is the general consensus of the axioms and inference rules declared in Principia Mathematica?  ANS2 mixed QSN3 Who discovered the incompleteness theorem of 1931? ANS3 Kurt Gödel QSN4 What did the incompleteness theorem of 1931 indicate regarding Principia Mathematica? ANS4 for any set of axioms and inference rules proposed to encapsulate mathematics, there would in fact be some truths of mathematics which could not be deduced QSN5 Why was Gödels finding ironic? ANS5 Gödel could not have come to this conclusion without Whitehead and Russell's book QSN6 When was Kurt Godel's incompleteness theorem? ANS6 1931 QSN7 What did Kurt Godel's theorem demonstrate about axioms and the inference rules? ANS7 some truths of mathematics which could not be deduced from them QSN8 Godel couldn't have come to his conclusion without what book? ANS8 Principia Mathematica QSN9 Besides logic and epistemology, what else did Principia Mathematica connect? ANS9 metaphysics