89 research outputs found

    Herbert Alexander Simon: 15th June, 1916–9th February, 2001 A Life

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    We present a concise summary of the personal and professional life of Herbert Alexander Simon

    Frank Plumpton Ramsey

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    This is a short biographical note about Frank Ramsey and his place in the history of economic thought

    A Primer on the Tools and Concepts of Comutable Economics.?

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    Computability theory came into being as a result of Hilbert s attempts to meet Brouwer s challenges, from an intuitionistc and constructive standpoint, to formalism as a foundation for mathematical practice. Viewed this way, con- structive mathematics should be one vision of computability theory. However, there are fundamental di¤erences between computability theory and construc- tive mathematics: the Church-Turing thesis is a disciplining criterion in the former and not in the latter; and classical logic - particularly, the law of the excluded middle - is not accepted in the latter but freely invoked in the former, especially in proving universal negative propositions. In Computable Economics an eclectic approach is adopted where the main criterion is numerical content for economic entities. In this sense both the computable and the constructive traditions are freely and indiscriminately invoked and utilised in the formaliza- tion of economic entities. Some of the mathematical methods and concepts of computable economics are surveyed in a pedagogical mode. A digital economy is considered embedded in an information society and speculative methodolog- ical, epistemological and ontological notes suggest a theory of the information society

    A Stochastic Complexity Perspective of Induction in Economics and Inference in Dynamics

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    Rissanen\u27s fertile and pioneering minimum description length principle (MDL) has been viewed from the point of view of statistical estimation theory, information theory, as stochastic complexity theory - i.e., a computable approximation of Kolomogorov Complexity - or Solomonoff\u27s recursion theoretic induction principle or as analogous to Kolmogorov\u27s sufficient statistics. All these - and many more - interpretations are valid, interesting and fertile. In this paper I view it from two points of view: those of an algorithmic economist and a dynamical system theorist. From these points of view I suggest, first, a recasting of Jevon\u27s sceptical vision of induction in the light of MDL; and a complexity interpretation of an undecidable question in dynamics

    The Unreasonable Ineffectiveness of Mathematics in Economics.

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    In this paper I attempt to show that mathematical economics is unreasonably ineffective. Unreasonable, because the mathematical assumptions are economically unwarranted; ineffective because the mathematical formalizations imply nonconstructive and uncomputable structures. A reasonable and effective mathematization of economics entails Diophantine formalisms. These come with natural undecidabilities and uncomputabilites. In the face of this, I conjecture that an economics for the future will be freer to explore experimental methodologies underpinned by alternative mathematical structures. The whole discussion is framed within the context of the celebrated Wignerian theme: The Unreasonable Effectiveness of Mathematics in the Natural Sciences

    Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics

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    It is natural to claim, as I do in this paper, that the emergence of non-constructivities in economics is entirely due to the formalizations of economics by means of \u27classical\u27 mathematics. I have made similar claims for the emergence of uncomputabilities and undecidabilities in economics in earlier writings. Here, on the other hand, I want to suggest a way of confronting uncomputabilities, and remedying non-constructivities, in economics, and turning them into a positive force for modelling, for example, endogenous growth, as suggested by Stefano Zambelli. In between, a case is made for economics to take seriously the kind of mathematical modelling fostered by Feynman and Dirac, in particular the way they developed the path integral and the ?- function, respectively. A sketch of a \u27research program\u27 in mathematical economics, analogous to the way Gödel thought incompleteness and its perplexities should be interpreted and resolved, is also outlined in the concluding section

    Production of Commodities by Means of Commodities in a Mathematical Mode

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    The claim in this paper is that Sraffa employed a rigorous logic of mathematical reasoning in his book, Production of Commodities by Means of Commodities (PCC), in such a mode that all existence proofs were constructive. This is the kind of mathematics that was prevalent at the beginning of the 19th century, which was dominated by the concrete, the constructive and the algorithmic. It is, therefore, completely consistent with the economics of the 19th century, which was the fulcrum around which the economics of PCC is centred