Ebook: Selected Papers in Logic and Foundations, Didactics, Economics

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.

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Content:
Front Matter....Pages i-xii
Introduction....Pages 1-7
Front Matter....Pages 9-9
Logical Tolerance in the Vienna Circle....Pages 11-16
The New Logic....Pages 17-45
On Intuitionism....Pages 46-58
Front Matter....Pages 59-59
Meaningfulness and Structure....Pages 61-67
A New Point of View on the Logical Connectives....Pages 68-78
An Intuitionistic-Formalistic Dictionary of Set Theory....Pages 79-87
Ultrasets and the Paradoxes of Set Theory....Pages 88-90
A Logic of the Doubtful on Optative and Imperative Logic....Pages 91-102
Front Matter....Pages 103-103
A Counterpart of Occam’s Razor....Pages 105-135
A Theory of the Application of the Function Concept to Science....Pages 136-143
Variables, Constants, Fluents....Pages 144-152
Wittgenstein on Formulae and Variables....Pages 153-158
Front Matter....Pages 159-159
Introduction....Pages 161-162
A New Approach to Teaching Intermediate Mathematics....Pages 163-173
Why Johnny Hates Math....Pages 174-184
On the Formulation of Certain Questions in Arithmetic....Pages 185-188
On the Design of Grouping Problems and Related Intelligence Tests....Pages 189-198
The Geometry Relevant to Modern Education....Pages 199-204
Front Matter....Pages 205-205
On Definitions, Especially of Dimension....Pages 207-216
Front Matter....Pages 205-205
Square Circles (The Taxicab Geometry)....Pages 217-219
The Algebra of Geometry....Pages 220-224
Geometry and Positivism a Probabilistic Microgeometry....Pages 225-234
Front Matter....Pages 235-235
My Memories of L. E. J. Brouwer....Pages 237-255
Front Matter....Pages 257-257
The Role of Uncertainty in Economics....Pages 259-278
Remarks on the Law of Diminishing Returns a Study in Meta-Economics....Pages 279-302
Front Matter....Pages 303-303
Gulliver in the Land without One, Two, Three....Pages 305-314
Gulliver’s Return to the Land without One, Two, Three....Pages 315-319
Gulliver in Applyland....Pages 320-323
Back Matter....Pages 324-344

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Content:
Front Matter....Pages i-xii
Introduction....Pages 1-7
Front Matter....Pages 9-9
Logical Tolerance in the Vienna Circle....Pages 11-16
The New Logic....Pages 17-45
On Intuitionism....Pages 46-58
Front Matter....Pages 59-59
Meaningfulness and Structure....Pages 61-67
A New Point of View on the Logical Connectives....Pages 68-78
An Intuitionistic-Formalistic Dictionary of Set Theory....Pages 79-87
Ultrasets and the Paradoxes of Set Theory....Pages 88-90
A Logic of the Doubtful on Optative and Imperative Logic....Pages 91-102
Front Matter....Pages 103-103
A Counterpart of Occam’s Razor....Pages 105-135
A Theory of the Application of the Function Concept to Science....Pages 136-143
Variables, Constants, Fluents....Pages 144-152
Wittgenstein on Formulae and Variables....Pages 153-158
Front Matter....Pages 159-159
Introduction....Pages 161-162
A New Approach to Teaching Intermediate Mathematics....Pages 163-173
Why Johnny Hates Math....Pages 174-184
On the Formulation of Certain Questions in Arithmetic....Pages 185-188
On the Design of Grouping Problems and Related Intelligence Tests....Pages 189-198
The Geometry Relevant to Modern Education....Pages 199-204
Front Matter....Pages 205-205
On Definitions, Especially of Dimension....Pages 207-216
Front Matter....Pages 205-205
Square Circles (The Taxicab Geometry)....Pages 217-219
The Algebra of Geometry....Pages 220-224
Geometry and Positivism a Probabilistic Microgeometry....Pages 225-234
Front Matter....Pages 235-235
My Memories of L. E. J. Brouwer....Pages 237-255
Front Matter....Pages 257-257
The Role of Uncertainty in Economics....Pages 259-278
Remarks on the Law of Diminishing Returns a Study in Meta-Economics....Pages 279-302
Front Matter....Pages 303-303
Gulliver in the Land without One, Two, Three....Pages 305-314
Gulliver’s Return to the Land without One, Two, Three....Pages 315-319
Gulliver in Applyland....Pages 320-323
Back Matter....Pages 324-344
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