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＜電子ブック＞
Philosophy of Mathematics Today / edited by E. Agazzi, György Darvas
(Episteme, A Series in the Foundational, Methodological, Philosophical, Psychological, Sociological, and Political Aspects of the Sciences, Pure and Applied ; 22)

版	1st ed. 1997.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	1997
本文言語	英語
大きさ	XXIX, 361 p : online resource
著者標目	Agazzi, E editor Darvas, György editor SpringerLink (Online service)
件　名	LCSH:Mathematical logic LCSH:Logic LCSH:Science -- Philosophy  全ての件名で検索 LCSH:Knowledge, Theory of FREE:Mathematical Logic and Foundations FREE:Logic FREE:Philosophy of Science FREE:Epistemology
一般注記	General Philosophical Perspectives -- Logic, Mathematics, Ontology -- From Certainty to Fallibility in Mathematics? -- Moderate Mathematical Fictionism -- Language and Coding-Dependency of Results in Logic and Mathematics -- What is a Profound Result in Mathematics? -- The Hylemorphic Schema in Mathematics -- Foundational Approaches -- Categorical Foundations of the Protean Character of Mathematics -- Category Theory and Structuralism in Mathematics: Syntactical Considerations -- Reflection in Set Theory. The Bernays-Levy Axiom System -- Structuralism and the Concept of Set -- Aspects of Mathematical Experience -- Logicism Revisited in the Propositional Fragment of Le?niewski’s Ontology -- The Applicability of Mathematics -- The Relation of Mathematics to the Other Sciences -- Mathematics and Physics -- The Mathematical Overdetermination of Physics -- Gödel’s Incompleteness Theorem and Quantum Thermodynamic Limits -- Mathematical Models in Biology -- The Natural Numbers as a Universal Library -- Mathematical Symmetry Principles in the Scientific World View -- Historical Considerations -- Mathematics and Logics. Hungarian Traditions and the Philosophy of Non-Classical Logic -- Umfangslogik, Inhaltslogik, Theorematic Reasoning Mathematics is often considered as a body of knowledge that is essen­ tially independent of linguistic formulations, in the sense that, once the content of this knowledge has been grasped, there remains only the problem of professional ability, that of clearly formulating and correctly proving it. However, the question is not so simple, and P. Weingartner's paper (Language and Coding-Dependency of Results in Logic and Mathe­ matics) deals with some results in logic and mathematics which reveal that certain notions are in general not invariant with respect to different choices of language and of coding processes. Five example are given: 1) The validity of axioms and rules of classical propositional logic depend on the interpretation of sentential variables; 2) The language­ dependency of verisimilitude; 3) The proof of the weak and strong anti­ inductivist theorems in Popper's theory of inductive support is not invariant with respect to limitative criteria put on classical logic; 4) The language-dependency of the concept of provability; 5) The language­ dependency of the existence of ungrounded and paradoxical sentences (in the sense of Kripke). The requirements of logical rigour and consistency are not the only criteria for the acceptance and appreciation of mathematical proposi­ tions and theories HTTP:URL=https://doi.org/10.1007/978-94-011-5690-5

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