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  • Articles  (49,349)
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  • Articles  (49,349)
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  • 2010-2014  (28,265)
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  • 1
    Electronic Resource
    Electronic Resource
    Instead of an Editorial Note (1997)
    Springer
    Foundations of science 2 (1997), S. 5-10 
    Details
    ISSN: 1572-8471
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009685021757
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Taming the Infinite (1997)
    Springer
    Foundations of science 2 (1997), S. 53-56 
    Details
    ISSN: 1572-8471
    Keywords: Infinity ; Paradoxes ; Set theory ; Aristotle ; Cantor
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract For over two thousand years thought about the infinite was dominated by Aristotelian hostility to the idea that the infinite could be a legitimate object of mathematical study. Then Cantor's work late in the nineteenth century seemed to overturn this orthodoxy. However, by highlighting ways in which infinitude still could not be brought under the control of mathematicians, Cantor's work may in fact have reinforced the orthodoxy.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009666925392
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  • 3
    Electronic Resource
    Electronic Resource
    Mathematics: Essential Tensions (1997)
    Springer
    Foundations of science 2 (1997), S. 11-19 
    Details
    ISSN: 1572-8471
    Keywords: Polarity ; Platonism ; Infinity ; Continuity ; Complexity ; Unity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract The vivacity of mathematics results (partly) from the fact that mathematics is stretched between several poles, not being committed to any one. The paper presents the following polarities: realism - idealism, the finite - the infinite, the discrete - the continuous, the approximate - the exact, certitute - probability, simplicity - complexity, unity - multiplicity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009654622666
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  • 4
    Electronic Resource
    Electronic Resource
    What is Applied Mathematics? (1997)
    Springer
    Foundations of science 2 (1997), S. 21-37 
    Details
    ISSN: 1572-8471
    Keywords: Applied mathematics ; Representation ; Platonism ; Structuralism ; Measurement
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract A number of issues connected with the nature of applied mathematics are discussed. Among the claims are these: mathematics "hooks onto" the world by providing models or representations, not by describing the world; classic platonism is to be preferred to structuralism; and several issues in the philosophy of science (reality of spacetime, the quantum state) are intimately connected to the nature of applied mathematics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009658723574
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  • 5
    Electronic Resource
    Electronic Resource
    Essential Tension: Mathematics - Physics - Philosophy (1997)
    Springer
    Foundations of science 2 (1997), S. 39-52 
    Details
    ISSN: 1572-8471
    Keywords: Ontology ; Physical theory ; Duhem-Quine thesis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract The author focuses on the tension "realism - idealism" in the philosophy of mathematics, but he does that from the perspective of a theoretical physicist. It is not only that one's standpoint in the philosophy of mathematics determines our understanding of the effectiveness of mathematics in physics, but also the fact that mathematics is so effective in physical sciences tells us something about the nature of mathematics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009662824483
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  • 6
    Electronic Resource
    Electronic Resource
    Inessential Tensions (1997)
    Springer
    Foundations of science 2 (1997), S. 57-60 
    Details
    ISSN: 1572-8471
    Keywords: Mathematics ; Practical considerations ; Politics
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract Some factors which are of great importance in most human affairs seem to play relatively little role in mathematics. We give some examples and suggest reasons why this might be expected to be the case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009671009462
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  • 7
    Electronic Resource
    Electronic Resource
    The Beauty of General Relativity (1997)
    Springer
    Foundations of science 2 (1997), S. 61-64 
    Details
    ISSN: 1572-8471
    Keywords: General Relativity ; Cosmology ; Black holes ; Nonlinearity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract The author proposes to add another dichotomy to the list of essential tensions proposed by Professor Duda, namely beauty and ugliness. Physicists believe that only beautiful theories describe the world correctly, and that General Relativity is one of the most beautiful physical theories. The author explains why physicists regard this theory as beautiful.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009623126300
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  • 8
    Electronic Resource
    Electronic Resource
    Reply to Comments (1997)
    Springer
    Foundations of science 2 (1997), S. 65-66 
    Details
    ISSN: 1572-8471
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009675127209
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  • 9
    Electronic Resource
    Electronic Resource
    Determinism, Indeterminism and Mathematics (1997)
    Springer
    Foundations of science 2 (1997), S. 73-75 
    Details
    ISSN: 1572-8471
    Keywords: Determinism ; Dynamical systems ; Random processes
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract The aim of this paper is to argue that very often one is not able to distinguish between deterministic processes governed by some dynamical systems and stochastic processes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009631428118
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  • 10
    Electronic Resource
    Electronic Resource
    Evolution of Mathematical Proof (1997)
    Springer
    Foundations of science 2 (1997), S. 77-85 
    Details
    ISSN: 1572-8471
    Keywords: Computer-assisted proofs ; Chaos ; Lorenz equations ; Round-off errors ; Interval arithmetic
    Source: Springer Online Journal Archives 1860-2000
    Topics: Natural Sciences in General
    Notes: Abstract The authors present the main ideas of the computer-assisted proof of Mischaikow and Mrozek that chaos is really present in the Lorenz equations. Methodological consequences of this proof are examined. It is shown that numerical calculations can constitute an essential part of mathematical proof not only in the discrete mathematics but also in the mathematics of continua.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1009683412188
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