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This volume brings together those papers of mine which may be of interest not only to various specialists but also to philosophers. Many of 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 occasioned by personal relations with economists. Hence a wide range of subjects will be discussed: epistemology, logic, basic concepts of pure and applied mathematics, philosophical ideas resulting from geometric studies, mathematical didactics and, finally, economics. The papers also span a period of more than fifty years. What unifies the various parts of the book is the spirit of searching for the elarification of basic concepts and methods and of articulating hidden ideas and tacit procedures. Part 1 ineludes papers published about 1930 which expound an idea that Carnap, after a short period of opposition in the Cirele, fully adopted ; and, under the name "Princip/e of To/erance", he eloquently formulated it in great generality in his book, Logica/ Syntax of Language (1934), through which it was widely disseminated. "The New Logic" in Chapter 1 furthermore ineludes the first report (I932) to a larger public of Godel's epochal discovery presented among the great logic results of ali time. Chapter 2 is a translation of an often quoted 1930 paper presenting a detailed exposition and critique of intuitionism.
Sommario
I. Papers Introducing Logical Tolerance.- Logical Tolerance in the Vienna Circle.- 1 The New Logic (1933).- 2 On Intuitionism (1930).- II. Opuscula logica.- 3 Meaningfulness and Structure (1930).- 4 A New Point of View on the Logical Connectives (1978).- 5 An Intuitionistic-Formalistic Dictionary of Set Theory (1928).- 6 Ultrasets and the Paradoxes of Set Theory (1928).- 7 A Logic of the Doubtful. On Optative and Imperative Logic (1939).- III. Fundamental Concepts in Pure and Applied Mathematics.- 8 A Counterpart of Occam's Razor (1960, 1961).- 9 A Theory of the Application of the Function Concept to Science (1970).- 10 Variables, Constants, Fluents (1961).- 11 Wittgenstein on Formulae and Variables (1978).- IV. Didactics of Mathematics.- 12 A New Approach to Teaching Intermediate Mathematics (1958).- 13 Why Johnny Hates Math (1956).- 14 On the Formulation of Certain Questions in Arithmetic (1956).- 15 On the Design of Grouping Problems and Related Intelligence Tests (1953).- 16 The Geometry Relevant to Modern Education (1971).- V. Philosophical Ramifications of some Geometric Ideas.- 17 On Definition, Especially of Dimension (1921-1923, 1928).- 18 Square Circles (The Taxicab Geometry) (1952, 1978).- 19 The Algebra of Geometry (1978).- 20 Geometry and Positivism. A Probabilistic Microgeometry (1970).- VI..- 21 My Memories of L. E. J. Brouwer (1978).- VII. Economics. Meta-Economics.- 22 The Role of Uncertainty in Economics (1934).- 23 Remarks on the Law of Diminishing Returns. A Study in Meta-Economics (1936).- VIII. Gulliver's Interest in Mathematics.- 24 Gulliver in the Land without One, Two, Three (1959).- 25 Gulliver's Return to the Land without One, Two, Three (1960).- 26 Gulliver in Applyland (1960).- Bibliography of Works by Karl Menger.- Index of Names.
