Abstraction, Idealization and Approximation

A Reflection on the Nature of Scientific Concepts
  • U. Majer


It has recently been claimed by M. Dummett1) and other that to be a realist implies the acceptance of Aristotle’s principle of the excluded middle that every proposition has one of two truth-values, either true or false. Hence, if there are propositions the truth-values of which are not decidable in principle, anti-realism perhaps in the form of intuitionism or verificationism is epistemologically a more reasonable position than unrestricted realism presupposing verification-transcendent truthconditions.


Physical Theory Real Object Physical Concept Logical Concept Basic Proposition 
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Notes and Literature

  1. (1).
    M. Dummett (1980), “Common Sense and Physics” ind ‘Perception and Identity’ — Essays presented to A. Ayer, ed. G.F. Mac Donald, Oxford 1980.Google Scholar
  2. (2).
    G. Frege (1879), “Begriffsschrift” — ‘eine der arithmetischen nachgebildete Formelsprache des reinen Denkens’.Google Scholar
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  4. G. Frege (1891) “Funktion und Begriff”.Google Scholar
  5. G. Frege (1892) “Über Sinn und Bedeutung”.Google Scholar
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  10. (3).
    H. Hertz (1894) “Die Prinzipien der Mechanik”, Wiss. Buchg. — Darmstadt, 1963.Google Scholar
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    E. Mach (1883) “Die Mechanik” — ‘historisch-kritisch dargestellt’ reprint of 9th edition, Leipzig 1933.Google Scholar
  12. E. Mach (1905) “Erkenntnis und Irrtum”, 3th edition, Ambrosius Barth-Leipzig 1917.Google Scholar
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    G. Ludwig (1970) “Deutung des Begriffs ‘physikalische Theorie’ und axiomatische Grundlegung der Hilbert-Raumstruktur der Quantenmechanik durch Hauptsätze des Messens”, Springer-Lecture Notes in Physics 4, Berlin, Heidelberg, N.Y.Google Scholar
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  16. (6).
    In this chapter, I give a short summary of “my” understanding of Frege’s conception of concepts. My presentation is insofar “dogmatic”, as I neither give an explicit philological documentation of my view by Frege’s writings, nor I try to defend my view against deviating interpretations. Both is the task of another paper, nevertheless, I hope, my view is correct. My understanding of Frege has most profited from the following three philosophers and their works.Google Scholar
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    A. Trendelenburg (1840) “Logische Untersuchungen” S. Hirzel, Leipzig, 3. Edition (1870).Google Scholar
  21. (8).
    H. Lotze (1874) “Logik — drei Bücher vom Denken, vom Untersuchen und vom Erkennen” ed. G. Misch, Felix-Meiner-Hamburg (1912).Google Scholar
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    Moreover, we have here the rare but interesting case, that the formulation of a theory contains — beside mentioning of the universal ‘Kepler-constant’ — a proper name, that of the sun, and hence refers in its first law to a contingent object, called’ sun’. Insofar is the concept of Kepler’s theory not of the most general form, possible. For an interesting kinematic theory and Newton’s dynamic theory with gravitional forces, see.Google Scholar
  23. E. Scheibe (1973) “Die Erklärung der Keplerschen Gesetze durch Newtons Gravitationsgesetz” in ‘Einheit und Vielheit’ Festschrift für C.F. von Weizsäcker, Vandenhoeck & Ruprecht, Göttingen.Google Scholar
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    Evans & Mc Dowell (1976) “Truth and Meaning” Oxford-Univ. Press.Google Scholar
  25. (11).
    M. Hesse (1961) “Forces and Fields” — ‘The concept of action at a distance in the history of physics’, Nelson and Sons, London.Google Scholar
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    L. Boltzmann (1892) “On the methods of Theoretical Physics” in L. Boltzmann, ‘Theoretical Physics and Philosophical Problems’, ed. B. McGuiness, Vienna circle collection Vol. 5, Reidel, Dordrecht-Holland, (1974).Google Scholar
  27. (13).
    Here I depart from the editor’s recommendation to translate ‘Abbildungsaxiome’ by ‘observational report’ and ‘Bildmengen/relationen’ by ‘interpreted sets/relations’.Google Scholar
  28. (14).
    D. Gallin (1975) “Intensional and Higher-Order Modal-Logic”, North-Holland Publ. Comp., Amsterdam, Oxford, New York.MATHGoogle Scholar
  29. (15).
    What the method of such learning is, how we proceed rationally in fitting our physical theories to experiments, ‘et vice versa’, I have already explained some years ago in: U. Majer (1975) “Paradigmatische Erklärungen und die Kontinuität der Wissenschaften” in ‘Logik, Ethik, Theorie der Geisteswissenschaften’, XI. Deutscher Kongreß für Philosophie, Felix Meiner Hamburg 1977.Google Scholar

Copyright information

© Plenum Press, New York 1981

Authors and Affiliations

  • U. Majer
    • 1
  1. 1.Philosophisches SeminarUniversität Nicolausberger Weg 9cGöttingenFederal Republic of Germany

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