by From Lars Syll Gödel’s incompleteness theorems raise important questions about the foundations of mathematics. The most important concerns the question of how to select the specific systems of axioms that mathematics are supposed to be founded on. Gödel’s theorems irrevocably show that no matter what system is chosen, there will always have to be other axioms to prove previously unproved truths. This, of course, ought to be of paramount interest for those mainstream economists who still adhere to the dream of constructing a deductive-axiomatic economics with analytic truths that do not require empirical verification. Since Gödel showed that any complex axiomatic system is undecidable and incomplete, any such deductive-axiomatic economics will always consist of some undecidable statements. When not even being able to fulfil the dream of a complete and consistent axiomatic foundation for mathematics, it’s totally incomprehensible that some people still think that could be achieved for economics.
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from Lars Syll
Gödel’s incompleteness theorems raise important questions about the foundations of mathematics.
The most important concerns the question of how to select the specific systems of axioms that mathematics are supposed to be founded on. Gödel’s theorems irrevocably show that no matter what system is chosen, there will always have to be other axioms to prove previously unproved truths.
This, of course, ought to be of paramount interest for those mainstream economists who still adhere to the dream of constructing a deductive-axiomatic economics with analytic truths that do not require empirical verification. Since Gödel showed that any complex axiomatic system is undecidable and incomplete, any such deductive-axiomatic economics will always consist of some undecidable statements. When not even being able to fulfil the dream of a complete and consistent axiomatic foundation for mathematics, it’s totally incomprehensible that some people still think that could be achieved for economics.