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Full-Text Articles in History of Philosophy
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Journal of Humanistic Mathematics
Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.
From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger
From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger
Journal of Humanistic Mathematics
The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of solvability is commonly identified with the decision problem. Given this identification, there is not the slightest doubt that Hilbert’s conviction was falsified by Gödel’s proof and by the negative results for the decision problem. On the other hand, Gödel’s theorems do offer a solution, albeit a negative one, in the form of an impossibility proof. In this sense, Hilbert’s optimism may still be justified. Here I argue that …
A Four-Legged Megalosaurus And Swimming Brontosaurs, Jordan C. Oldham
A Four-Legged Megalosaurus And Swimming Brontosaurs, Jordan C. Oldham
Channels: Where Disciplines Meet
Thomas Kuhn in his famous work The Structure of Scientific Revolutions laid out the framework for his theory of how science changes. At the advent of dinosaur paleontology fossil hunters like Gideon Mantell discovered some of the first dinosaurs like Iguanodon and Megalosaurus. Through new disciples like Georges Cuvier’s comparative anatomy lead early dinosaur paleontologist to reconstruct them like giant reptiles of absurd proportions. This lead to the formation of a new paradigm that prehistoric animals like dinosaurs existed and eventually went extinct. The first reconstructions of dinosaur made them to look like giant counterparts of their modern cousins. …