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Hilbert's axiomatic method and Carnap's general axiomatics
Studies in History and Philosophy of Science Part A, 2015This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed.
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*ZFC: An axiomatic * approach to nonstandard methods
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 1997The author establishes a new foundation of nonstandard analysis in which it is possible to deal with external sets. To do so, a function * defined on the class \(S\) of all standard sets is introduced, namely \[ \biggl\{ \forall x,y,z\;\bigl[^* x=y\wedge {^*x}= z\to(y=z \wedge x\in S)\bigr] \biggr\} \wedge [\forall x\in S\;\exists y\;({}^*x =y ...
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Synthese, 2009
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1965
If the object of which knowledge is acquired is not given directly it has to be known through some other object, i.e. indirectly. Since the object is a state of affairs, and this itself is expressed in a sentence, every indirect acquisition of knowledge proceeds by inference from one sentence to another or by the derivation of the second sentence from ...
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If the object of which knowledge is acquired is not given directly it has to be known through some other object, i.e. indirectly. Since the object is a state of affairs, and this itself is expressed in a sentence, every indirect acquisition of knowledge proceeds by inference from one sentence to another or by the derivation of the second sentence from ...
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1992
Philosophical analysis of axiomatic methods goes back at least to Aristotle. In the large literature of many centuries a great variety of issues have been raised by those holding viewpoints that range from that of Proclus to that of Hilbert. Here I try to consider in detail only a highly selected set of ideas, but they are ones I judge important.
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Philosophical analysis of axiomatic methods goes back at least to Aristotle. In the large literature of many centuries a great variety of issues have been raised by those holding viewpoints that range from that of Proclus to that of Hilbert. Here I try to consider in detail only a highly selected set of ideas, but they are ones I judge important.
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Axiomatic methods, dopamine and reward prediction error
Current Opinion in Neurobiology, 2008The phasic firing rate of midbrain dopamine neurons has been shown to respond both to the receipt of rewarding stimuli, and the degree to which such stimuli are anticipated by the recipient. This has led to the hypothesis that these neurons encode reward prediction error (RPE)-the difference between how rewarding an event is, and how rewarding it was ...
Andrew, Caplin, Mark, Dean
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Axiomatic method in quantum electrodynamics
Theoretical and Mathematical Physics, 1974>A method in the theory of electromagnetic interactions is suggested, which is free from the infrared divergences. The method is based on the equations of the Bogolubov axiomatic approach in quantim fieid theory, from which the infrared divergences are removed.
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Intuition and the Axiomatic Method
2006Preface Part I Mathematical Aspects Locke and Kant on Mathematical Knowledge : Emily Carson The View from 1763: Kant on the Arithmetical Method before Intuition : Ofra Rechter The Relation of Logic and Intuition in Kant's Philosophy of Science, Particularly Geometry : Ulrich Majer Edmund Husserl on the Applicability of Formal Geometry : Rene Jagnow The
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Euclid's Elements and the Axiomatic Method
The British Journal for the Philosophy of Science, 1969algebra, analytic geometry, real number theory, and mathematical logic. It is not possible to describe here the evolution of the idea of structure in the modern era. An important step in it is the realisation that Euclidean geometry has an interpretation in the universe of the real numbers-a realisation made possible by the existence of analytic ...
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The Axiomatic Usability Evaluation Method
2014This chapter introduces a new usability evaluation method, the axiomatic evaluation method, which is developed based on the axiomatic design theory – a formalized design methodology that can be used to solve a variety of design problems. This new evaluation method examines three domains of a product: customer domain, functional domain, and control ...
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