We give a brief historical sketch of the clash of dualism vs. naturalism and then analyse the arg... more We give a brief historical sketch of the clash of dualism vs. naturalism and then analyse the argument that Gödel’s incompleteness theorems support dualism by implying human-machine non-equivalence. We prove that this implication is not valid. Instead, we give a correct implication.
Gentzen’s singular sequential system of first-order logic was an alternative notation for his sys... more Gentzen’s singular sequential system of first-order logic was an alternative notation for his system of natural deductions. His multiple sequential system was his symmetric generalization that was more appropriate to classical logic. Beth’s tableaus system was a system that was derived directly from the semantic analysis of connectives and quantifiers. It was soon realized that the Beth’s system and the Gentzen’s multiple system were only notational variants of each other. Kneale’s system of multiple natural deductions was a generalization of Gentzen’s system of natural deductions. We prove that Kneale’s natural deductions are also a notational variant of Beth’s tableaus.
We give a brief historical sketch of the clash of dualism vs. naturalism and then analyse the arg... more We give a brief historical sketch of the clash of dualism vs. naturalism and then analyse the argument that Gödel’s incompleteness theorems support dualism by implying human-machine non-equivalence. We prove that this implication is not valid. Instead, we give a correct implication.
Gentzen’s singular sequential system of first-order logic was an alternative notation for his sys... more Gentzen’s singular sequential system of first-order logic was an alternative notation for his system of natural deductions. His multiple sequential system was his symmetric generalization that was more appropriate to classical logic. Beth’s tableaus system was a system that was derived directly from the semantic analysis of connectives and quantifiers. It was soon realized that the Beth’s system and the Gentzen’s multiple system were only notational variants of each other. Kneale’s system of multiple natural deductions was a generalization of Gentzen’s system of natural deductions. We prove that Kneale’s natural deductions are also a notational variant of Beth’s tableaus.
We compare Epstein’s diagrams [2] (a very simple technique for explaining Einstein’s special theo... more We compare Epstein’s diagrams [2] (a very simple technique for explaining Einstein’s special theory of relativity; STR) with Minkowski’s diagrams [3] (a technique with the same aim but not as simple as Epstein’s).
Epstein used his diagrams to introduce Einstein’s STR [1] with almost no mathematics. We would like to show that his approach is even more powerful with a little bit of mathematics. Especially, we would like to show that both types of diagrams are different projections of a Euclidian higher dimensional representation of STR.
Epstein’s approach makes obvious the fact that the speed of light (supposed to be frame independent in STR) is, in a sense, the speed of everything. This explains the speed of light as a fundamental constant.
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Epstein used his diagrams to introduce Einstein’s STR [1] with almost no mathematics. We would like to show that his approach is even more powerful with a little bit of mathematics. Especially, we would like to show that both types of diagrams are different projections of a Euclidian higher dimensional representation of STR.
Epstein’s approach makes obvious the fact that the speed of light (supposed to be frame independent in STR) is, in a sense, the speed of everything. This explains the speed of light as a fundamental constant.