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Mathematical Implications of Mach’s Ideas: Positivistic Geometry, the Clarification of Functional Connections

In: Selecta Mathematica

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  • Karl Menger

Abstract

The highest tribute to a scientist on an anniversary of his death is the demonstration that his ideas are still alive. Fifty years after Mach, some thoughts of this great Austrian philosopher-scientist have an unspent vitality. Two ideas of his on which I wish to concentrate lead to implications for mathematics that have not yet been fully explored: Mach’s general philosophical views suggest the development of a positivistic geometry, which has hardly begun; and his maxim that causal explanations should be replaced by functional connections calls for a clarification of the method of applying the function concept and other ideas of mathematical analysis to science — a clarification which is still in its initial stage.

Suggested Citation

  • Karl Menger, 2002. "Mathematical Implications of Mach’s Ideas: Positivistic Geometry, the Clarification of Functional Connections," Springer Books, in: Bert Schweizer & Abe Sklar & Karl Sigmund & Peter Gruber & Edmund Hlawka & Ludwig Reich & Leopold Sc (ed.), Selecta Mathematica, pages 575-593, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7091-6110-4_43
    DOI: 10.1007/978-3-7091-6110-4_43
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