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Abstraction, Idealization and Approximation

A Reflection on the Nature of Scientific Concepts

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Abstract

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.

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Notes and Literature

  1. M. Dummett (1980), “Common Sense and Physics” ind ‘Perception and Identity’ — Essays presented to A. Ayer, ed. G.F. Mac Donald, Oxford 1980.

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  2. G. Frege (1879), “Begriffsschrift” — ‘eine der arithmetischen nachgebildete Formelsprache des reinen Denkens’.

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  4. G. Frege (1891) “Funktion und Begriff”.

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  5. G. Frege (1892) “Über Sinn und Bedeutung”.

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  16. 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.

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  22. 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.

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  27. Here I depart from the editor’s recommendation to translate ‘Abbildungsaxiome’ by ‘observational report’ and ‘Bildmengen/relationen’ by ‘interpreted sets/relations’.

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  29. 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.

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© 1981 Plenum Press, New York

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Majer, U. (1981). Abstraction, Idealization and Approximation. In: Hartkämper, A., Schmidt, HJ. (eds) Structure and Approximation in Physical Theories. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-4109-3_8

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  • DOI: https://doi.org/10.1007/978-1-4684-4109-3_8

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