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Kenneth Manders [14]Kenneth L. Manders [10]
  1. The Euclidean Diagram.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 80--133.
    This chapter gives a detailed study of diagram-based reasoning in Euclidean plane geometry (Books I, III), as well as an exploration how to characterise a geometric practice. First, an account is given of diagram attribution: basic geometrical claims are classified as exact (equalities, proportionalities) or co-exact (containments, contiguities); exact claims may only be inferred from prior entries in the demonstration text, but co-exact claims may be asserted based on what is seen in the diagram. Diagram control by constructions is necessary (...)
     
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  2. Domain Extension and the Philosophy of Mathematics.Kenneth Manders - 1989 - Journal of Philosophy 86 (10):553-562.
  3. Diagram-Based Geometric Practice.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press. pp. 65--79.
    This chapter provides a survey of issues about diagrams in traditional geometrical reasoning. After briefly refuting several common philosophical objections, and giving a sketch of diagram-based reasoning practice in Euclidean plane geometry, discussion focuses first on problems of diagram sensitivity, and then on the relationship between uniform treatment and geometrical generality. Here, one finds a balance between representationally enforced unresponsiveness (to differences among diagrams) and the intellectual agent's contribution to such unresponsiveness that is somewhat different from what one has come (...)
     
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  4.  32
    On the Space-Time Ontology of Physical Theories.Kenneth L. Manders - 1982 - Philosophy of Science 49 (4):575-590.
    In the correspondence with Clarke, Leibniz proposes to construe physical theory in terms of physical (spatio-temporal) relations between physical objects, thus avoiding incorporation of infinite totalities of abstract entities (such as Newtonian space) in physical ontology. It has generally been felt that this proposal cannot be carried out. I demonstrate an equivalence between formulations postulating space-time as an infinite totality and formulations allowing only possible spatio-temporal relations of physical (point-) objects. The resulting rigorous formulations of physical theory may be seen (...)
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  5.  19
    Theories With the Existential Substructure Property.Kenneth L. Manders - 1980 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 26 (1-6):89-92.
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  6. Diagrammatic Reasoning and Representational Systems.Kenneth Manders - 2008 - In Paolo Mancosu (ed.), The Philosophy of Mathematical Practice. Oxford University Press.
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  7.  15
    On Algebraic Geometry Over Rings with Exponentiation.Kenneth Manders - 1987 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (4):289-292.
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  8.  15
    Review: Hartry H. Field, Science Without Numbers. A Defence of Nominalism. [REVIEW]Kenneth L. Manders - 1984 - Journal of Symbolic Logic 49 (1):303-306.
  9. Diagram Contents and Representational Granularity.Kenneth Manders - 1996 - In Jerry Seligman & Dag Westerståhl (eds.), Logic, Language and Computation. Csli Publications, Stanford. pp. 1.
  10.  22
    What Numbers Are Real?Kenneth L. Manders - 1986 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1986:253 - 269.
    We suggest that there can be epistemologically significant reasons why certain mathematical structures - such as the Real numbers - are more important than others. We explore several contexts in which considerations bearing on the choice of a fundamental numerical domain might arise. 1) Set theory. 2) Historical cases of extension of mathematical domains - why were negative numbers resisted, and why should we accept them as part of our fundamental numerical domain? 3) Using fewer reals in physics, without really (...)
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  11.  23
    The Theory of All Substructures of a Structure: Characterisation and Decision Problems.Kenneth L. Manders - 1979 - Journal of Symbolic Logic 44 (4):583-598.
    An infinitary characterisation of the first-order sentences true in all substructures of a structure M is used to obtain partial reduction of the decision problem for such sentences to that for Th(M). For the relational structure $\langle\mathbf{R}, \leq, +\rangle$ this gives a decision procedure for the ∃ x∀ y-part of the theory of all substructures, yet we show that the ∃ x 1x 2 ∀ y-part, and the entire theory, is Π 1 1 -complete. The theory of all ordered subsemigroups (...)
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  12.  22
    Friedman's Criterion for Simplicity.Kenneth L. Manders - 1976 - British Journal for the Philosophy of Science 27 (4):395-397.
  13.  7
    The Marriott Hotel Philadelphia, Pennsylvania December 27–30, 2008.Janet Folina, Douglas Jesseph, Dirk Schlimm, Emily Grosholz, Kenneth Manders, Sun-Joo Shin, Saul Kripke & William Ewald - 2009 - Bulletin of Symbolic Logic 15 (2).
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  14.  14
    Book Review:The Magic of Numbers and Motion: The Scientific Career of Rene Descartes William S. Shea. [REVIEW]Kenneth L. Manders - 1995 - Philosophy of Science 62 (1):162-.
  15.  1
    Review of The Magic of Numbers and Motion: The Scientific Career of Rene Descartes by William S. Shea. [REVIEW]Kenneth Manders - 1995 - Philosophy of Science 62 (1):162-164.
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  16.  2
    Theories With the Existential Substructure Property.Kenneth L. Manders - 1980 - Mathematical Logic Quarterly 26 (1‐6):89-92.
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  17.  2
    Meeting of the Association for Symbolic Logic, Chicago, 1989.Kenneth Manders - 1990 - Journal of Symbolic Logic 55 (1):436-445.
  18.  2
    On Algebraic Geometry Over Rings with Exponentiation.Kenneth Manders - 1987 - Mathematical Logic Quarterly 33 (4):289-292.
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  19. Of the Association for Symbolic Logic.Janet Folina, Douglas Jesseph, Dirk Schlimm, Emily Grosholz, Kenneth Manders, Sun-Joo Shin, Saul Kripke & William Ewald - 2009 - Bulletin of Symbolic Logic 15 (2):229.
  20. Descartes et Faulhaber.Kenneth Manders - 1995 - Archives de Philosophie 58:1-12.
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  21. Field Hartry H.. Science Without Numbers. A Defence of Nominalism. Princeton University Press, Princeton 1980, Xiii + 130 Pp. [REVIEW]Kenneth L. Manders - 1984 - Journal of Symbolic Logic 49 (1):303-306.
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  22. Johann Faulhaber, 1580-1635: Eine Blutezeit der Mathematischen Wissenschaften in Ulm by Kurt Hawlitschek. [REVIEW]Kenneth Manders - 1999 - Isis: A Journal of the History of Science 90:361-362.
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  23. Johann Faulhaber, 1580-1635: Eine Blutezeit der mathematischen Wissenschaften in Ulm. Kurt Hawlitschek.Kenneth Manders - 1999 - Isis 90 (2):361-362.
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  24. The Magic of Numbers and Motion: The Scientific Career of Rene Descartes.William S. Shea & Kenneth L. Manders - 1995 - Philosophy of Science 62 (1):161.