The man who crushed the mathematical dream

21 March, 2017 at 16:17 | Posted in Economics | 1 Comment

b00dshx3_640_360Gödel’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.


1 Comment

  1. This is not just a problem for the egos of theoreticians, it has real-world consequences. The same diagonalization argument that Godel used to prove incompleteness of axiomatic systems can be used to show that financial systems that allow higher-order derivative instruments are fundamentally unregulatable into stability. And it follows from that that economic systems that have a financial component cannot be stabilized by any finite, predefined set of policies. Maybe that’s one of the reasons that DSGE models are not allowed to incorporate finance — equilibrium becomes impossible to obtain, even under the most tortured definitions of the word “equilibrium”.

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