Epistemology and Psychology of Functions

Years ago, prompted by Grize, Apostel and Papert, we undertook the study of functions, but until now we did not properly understand the relations between functions and operations, and their increasing interactions at the level of 'constituted functions'. By contrast, certain recent studies...

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Bibliographic Details
Main Authors: Piaget, J., Grize, J.B. (Author), Szeminska, A. (Author), Bang, V. (Author)
Format: eBook
Published: Dordrecht Springer Netherlands 1977, 1977
Edition:1st ed. 1977
Series:Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science
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Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • I/From Constitutive Functions to Constituted Functions
  • 1. The Coordination of Pairs
  • 2. From Constitutive Functions to Equivalence Classes
  • 3. From Regularities to Proportionalities
  • 4. An Example of Causal and Spatial Functions
  • 5. From Coproperties to Covariations: The Equalization and Estimation of Inequalities
  • 6. The Composition of Differences: Unequal Partitions
  • 7. An Example of the Composition of the Variations of Variations
  • II/The Quantification of Constituted Functions
  • 8. The Functional Relation between the Increase and the Decrease of Both Sides of a Rectangle Having a Constant Perimeter — The Transformations of the Perimeter of a Square
  • 9. Serial Regularities and Proportions
  • 10. The Relation between the Size of a Wheel and the Distance Travelled
  • 11. The Establishment of a Functional Relation among Several Variables: Distance Travelled, Wheel Size and Rotational Frequency
  • 12. The Inverse Proportional Relationship between Weight W and Distance D (Arm of a Lever) in the Equilibrium of a Balance
  • 13. Conclusion of Chapters 8 to 12: The General Evolution of Behaviors
  • III/Theoretical Problems
  • 14. Analyses to Aid in the Epistemological Study of the Notion of Function
  • 15. General Conclusions