Titlebook: Selected Papers in Logic and Foundations, Didactics, Economics; Karl Menger Book 1979 Springer Science+Business Media Dordrecht 1979 Ludwi

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A Counterpart of Occam’s RazorThis chapter combines two papers on a counterpart of the famous methodological tool developed by Occam in the 14th century: [1960, 6], on the use of the counterpart in ontology, and [1961, 1], on its semantical applications. By combining the two papers repetitions have been avoided and the introductions merged. Other changes are minor.

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A Theory of the Application of the Function Concept to ScienceThis chapter contains the second half of [1970, 2] — a paper presented at a symposium that the American Association for the Advancement of Science arranged in 1966 on the occasion of the fiftieth anniversary of the death of Ernst Mach. It is here reprinted with a few minor revisions. (For the first half, See Chapter 20.)

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Wittgenstein on Formulae and VariablesThis chapter contains a discussion, announced in [1961, 1] p. 349, of the single reference to mathematical variables that I found in Wittgenstein’s writings published by 1961. The chapter begins with a full description of the context in which the remark occurs.

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IntroductionIn every field, deepening of insight into the basic concepts eventually is bound to affect its presentation to beginners; and without contemplation and clarification of the fundamental ideas, didactics is threatened by stagnation.

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A New Approach to Teaching Intermediate MathematicsA reprint of [1958, 4] with minor omissions and amendments. The writing of this paper was part of the work made possible by a grant from the Carnegie Corporation in New York for the development of a new approach to the teaching of mathematics.

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my writings in mathematics were motivated by epistemological considerations; some papers originated in the critique of certain views that at one time dominated the discussions of the Vienna Cirele; others grew out of problems in teaching fundamental ideas of mathematics; sti II others were occasione

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Ultrasets and the Paradoxes of Set Theoryeries [1928, 1]. I here include a (condensed) translation of the note because it demonstrates in an utterly elementary fashion the need for the distinction between two kinds of totalities (here called . and .) now generally made in the axiomatics of set theory between . and ..