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The Open World

Journal of Philosophy 29 (26):720 (1932)

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  1. A Philosophical Path from Königsberg to Kyoto: The Science of the Infinite and the Philosophy of Nothingness.Rossella Lupacchini - 2020 - Sophia 60 (4):851-868.
    ‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a valuable dialectical opposition. Struggling to spell (...)
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  • Objectivity and its relation to physical science.I. I. Polonoff - unknown
    On all sides, one hears appeals to objectivity and exhortations to be objective. These admonitions are usually made by scientifically-minded people. Laudable as these appeals may be, they are sometimes so framed as to give the impression that objectivity is a quality or property of events that is immediately recognizable. It is thus, a finality, an ultimate for knowledge, which, when recognized, is taken as given. Ulterior questions, as to what constitutes the objective character of fact, are considered spurious meanderings (...)
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  • Causal Reasoning in Physics.Mathias Frisch - 2014 - Cambridge, United Kingdom: Cambridge University Press.
    Much has been written on the role of causal notions and causal reasoning in the so-called 'special sciences' and in common sense. But does causal reasoning also play a role in physics? Mathias Frisch argues that, contrary to what influential philosophical arguments purport to show, the answer is yes. Time-asymmetric causal structures are as integral a part of the representational toolkit of physics as a theory's dynamical equations. Frisch develops his argument partly through a critique of anti-causal arguments and partly (...)
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  • Leibniz Equivalence. On Leibniz's Influence on the Logical Empiricist Interpretation of General Relativity.Marco Giovanelli - unknown
    Einstein’s “point-coincidence argument'” as a response to the “hole argument” is usually considered as an expression of “Leibniz equivalence,” a restatement of indiscernibility in the sense of Leibniz. Through a historical-critical analysis of Logical Empiricists' interpretation of General Relativity, the paper attempts to show that this labeling is misleading. Logical Empiricists tried explicitly to understand the point-coincidence argument as an indiscernibility argument of the Leibnizian kind, such as those formulated in the 19th century debate about geometry, by authors such as (...)
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  • Weyl’s Appropriation of Husserl’s and Poincar“s Thought.Richard Feist - 2002 - Synthese 132 (3):273 - 301.
    This article locates Weyl''s philosophy of mathematics and its relationship to his philosophy of science within the epistemological and ontological framework of Husserl''s phenomenology as expressed in the Logical Investigations and Ideas. This interpretation permits a unified reading of Weyl''s scattered philosophical comments in The Continuum and Space-Time-Matter. But the article also indicates that Weyl employed Poincaré''s predicativist concerns to modify Husserl''s semantics and trim Husserl''s ontology. Using Poincaré''s razor to shave Husserl''s beard leads to limitations on the least upper (...)
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  • Reliability and Interpretability in Science and Deep Learning.Luigi Scorzato - 2024 - Minds and Machines 34 (3):1-31.
    In recent years, the question of the reliability of Machine Learning (ML) methods has acquired significant importance, and the analysis of the associated uncertainties has motivated a growing amount of research. However, most of these studies have applied standard error analysis to ML models—and in particular Deep Neural Network (DNN) models—which represent a rather significant departure from standard scientific modelling. It is therefore necessary to integrate the standard error analysis with a deeper epistemological analysis of the possible differences between DNN (...)
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  • Integral analysis and the phenomena of lifeDie Integralanalyse und die LebenserscheinungenL'Analyse intégrale et les phénomènes de la vie.F. G. Donnan - 1936 - Acta Biotheoretica 2 (1):1-11.
    Der Beschreibung der zeitlichen Entwicklung lebender Systeme kann eine reine Differentialanalyse nicht genügen. In solchen Fällen muss man sich an Stelle der gewöhnlichen Differentialgleichungen der integraldifferentiellen, bezw. der Integralgleichungen bedienen. Zur leichteren Veranschaulichung der mathematischen Darstellung betrachtet Verfasser zuerst diejenigen Systeme, deren innerer Zustand sich durch ein einziges Parameterc bestimmen lässt. Die zeitliche Entwicklung eines leblosen Systems dieser Klasse werde durch die Differentialgleichung $$\frac{{dc}}{{dt}} = kf...$$ dargestellt, wot=Zeit, undk eine Funktion der äusseren Parameterα, Β, γ. ist. Im Falle eines jeden (...)
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  • Divergent conceptions of the continuum in 19th and early 20th century mathematics and philosophy.John L. Bell - 2005 - Axiomathes 15 (1):63-84.
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