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Goedel's Way
Kurt Gödel (1906-1978) was an Austrian-American mathematician, who is best known for his incompleteness theorems. He was the greatest mathematical logician of the 20th century, with his contributions extending to Einstein’s general relativity, as he proved that Einstein’s theory allows for time machines. The Gödel incompleteness theorem - the usual formal mathematical systems cannot prove nor disprove all true mathematical sentences - is frequently presented in textbooks as something that happens in the rarefied realms of mathematical logic, and that has nothing to do with the real world. Practice shows the contrary though; one can demonstrate the validity of the phenomenon in various ...
A Computable Universe
This volume discusses the foundations of computation in relation to nature. It focuses on two main questions: What is computation? and How does nature compute?
The Map and the Territory
This volume presents essays by pioneering thinkers including Tyler Burge, Gregory Chaitin, Daniel Dennett, Barry Mazur, Nicholas Humphrey, John Searle and Ian Stewart. Together they illuminate the Map/Territory Distinction that underlies at the foundation of the scientific method, thought and the very reality itself. It is imperative to distinguish Map from the Territory while analyzing any subject but we often mistake map for the territory. Meaning for the Reference. Computational tool for what it computes. Representations are handy and tempting that we often end up committing the category error of over-marrying the representation with what is represented, so much so that the distinction be...
Computable Foundations for Economics
Computable Foundations for Economics is a unified collection of essays, some of which are published here for the first time and all of which have been updated for this book, on an approach to economic theory from the point of view of algorithmic mathematics. By algorithmic mathematics the author means computability theory and constructive mathematics. This is in contrast to orthodox mathematical economics and game theory, which are formalised with the mathematics of real analysis, underpinned by what is called the ZFC formalism, i.e., set theory with the axiom of choice. This reliance on ordinary real analysis and the ZFC system makes economic theory in its current mathematical mode complete...
Entangled Political Economy
Volume 18 Entangled Political Economy of the Book Series Advances in Austrian Economics examines the concept 'entangled political economy' from several distinct but complementary points of view. The volume is proof that Wagner's notion of entanglement opens new vistas for political economy in all its dimensions.
Functional Analysis, Holomorphy and Approximation Theory II
Functional Analysis, Holomorphy and Approximation Theory II
Metaphors and Analogies in Sciences and Humanities
In this highly-interdisciplinary volume, we systematically study the role of metaphors and analogies in (mis)shaping our understanding of the world. Metaphors and Analogies occupy a prominent place in scientific discourses, as they do in literature, humanities and at the very level of our thinking itself. But when misused they can lead us astray, blinding our understanding inexorably. How can metaphors aid us in our understanding of the world? What role do they play in our scientific discourses and in humanities? How do they help us understand and skillfully deal with our complex socio-political scenarios? Where is the dividing line between their use and abuse? Join us as we explore some of these questions in this volume.
