godels incompletness theorem - arcturus9/useful-link GitHub Wiki

• godels incompletness theorem

https://www.youtube.com/watch?v=YrKLy4VN-7k
https://www.youtube.com/watch?v=svOTZEbj3ys
https://www.youtube.com/watch?v=7fvkbvWaRPk

https://www.youtube.com/watch?v=O4ndIDcDSGc

• Barriers and bounds to Rationality (2000, Structural Change and Economic Dynamics, site 54) https://pdfs.semanticscholar.org/cc14/3361bf9dfe37e586e2dcb984707fa96f95a0.pdf
  괴델의 불완전성 정리를 찾아보다가 Simon의 paper(2000년)를 만나게 되었다. "Barriers and bounds to Rationality"라는 제목의 그의 글에서 괴델의 정리와 complexity에 대해 논하는 문장들 속에서 마치 2001년 숨을 거두기 전 유언을 paper에 남긴 듯한 느낌을 받았다

• reference book : Barriers and Bounds to Rationality: Essays on Economic Complexity and Dynamics in Interactive Systems(Peter S. Albin)
  https://www.researchgate.net/publication/220327282_Barriers_and_Bounds_to_Rationality_Essays_on_Economic_Complexity_and_Dynamics_in_Interactive_Systems
  --> economics + complexity (using cellular automata)

• 'Consistency and Incompleteness in General Equilibrium Theory(2017 - cob.jmu.edu)
  http://cob.jmu.edu/rosserjb/Paper%20JEEC%20SLMGBR%2011ii17%20Rev2.pdf
  ==> godel theorem이용해서 General Equilibrium Theory 공격 내용

• Computational and dynamic complexity in economics(2006, J. Barkley Rosser, Jr. ,James Madison University , site 57)
  http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.329.8640&rep=rep1&type=pdf
  ==> complexity + economics 여러 공식들 있음

• The incompleteness of theories of games (Journal of Philosophical Logic, 1998, site 37)
  http://angg.twu.net/doria/tsuji98.pdf
  ==> game theroy에 godel theorem을 적용하려 한듯

• Learning rational expectations under computability constraints(SE Spear - Econometrica: 1989)
  http://healy.econ.ohio-state.edu/pubfiles/infomkts/litreview/Spear%20-%20Learning%20RE%20under%20Computability%20Constraints%2089.pdf

• Towards an algorithmic revolution in economic theory (KV Velupillai - Journal of Economic Surveys, 2011, site 12)
  https://pdfs.semanticscholar.org/b1d6/15576b513a88bf1918d74b866ee3e6d67f05.pdf
  ==> 아래 괴델의 말을 인용한것이 인상적임 "인간도 finite machine 이므로, unsolvable problem이 있다"
  [I]f the human mind were equivalent to a finite machine, then objective mathematics not only would be incompleatable in the sense of not being contained in any well-defined axiomatic system, but moreover there would exist absolutely unsolvable diophantine problems... . where the epithet ‘absolutely’ means that they would be undecidable, not just within some particular axiomatic system, but by any mathematical proof the human mind can conceive. So the following disjunctive conclusion is inevitable: Either mathematics is incompleatable in this sense, that its evident axioms can never be compromised in a finite rule, that is to say the human mind (even within the realm of pure mathematics) infinitely surpasses the powers of any finite machine, or else there exist absolutely unsolvable Diophantine problems... (where the case that both terms of the disjunction are true is not excluded, so that there are, strictly speaking, three alternatives). Godel (1951/1995, p. 310; italics in the original)

• Agent‐based computational models and generative social science (JM Epstein - Complexity, 1999, site 1055)
  http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.118.546&rep=rep1&type=pdf
  ==> bounded rationality + godel limit + basic social science ...

• The metalogic of economic predictions, calculations and propositions(Peter S.Albin)
  https://www.sciencedirect.com/science/article/abs/pii/0165489682900166
  ==> godel 이용해서 증명한 내용.
  Indeterminacy is a matter of concern in the analysis of ideal forms and this paper shows that Gödel incompleteness and undecidability directly pertain to the analysis of theoretical economic systems - specifically, that certain solution concepts such as ‘predictions of characteristics of policy outcomes guided by a social welfare function’, ‘the existence of equilibrium’, ‘the existence of welfare optima’ are subject to Gödel undecidability. This consideration brings into question the convention of a finite decision unit or economic actor, and the paper considers more-appropriate (metatheoretic) assumption structures and the implications of specifying richer information structures in microeconomics and choice theory.