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Varieties of Mathematics in Economics
(National University of Ireland, Galway, 2007)
Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this ...
A Stochastic Complexity Perspective of Induction in Economics and Inference in Dynamics
(National University of Ireland, Galway, 2007)
Rissanen's 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 ...
Taming the Incomputable, Reconstructing the Nonconstructive and Deciding the Undecidable in Mathematical Economics
(National University of Ireland, Galway, 2007)
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 'classical' mathematics. I have made similar claims for ...
Advanced Computational Complexity Theory from an Elementary Standpoint
(National University of Ireland, Galway, 2007)
A computable economist's view of the world of computational complexity theory is described. This means the model of computation underpinning theories of computational complexity plays a central role. The emergence of ...
Re-reading Jevons's Principles of Science-Induction Redux
(National University of Ireland, Galway, 2007)
In this paper I try to substantiate the thesis that Jevons may have been too harsh on the vices of induction and generously optimistic about the virtues of deduction, as discussed, primarily, in his magnum opus, The ...