Foundations of Geometry and Induction 1st Edition by Jean Nicod ISBN 0415613736 9780415613736

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ISBN 10: 0415613736 
ISBN 13: 9780415613736
Author: Jean Nicod

Foundations of Geometry and Induction 1st Table of contents:

Part I Geometric Order
Chapter I. Pure Geometry is an Exercise in Logic
Chapter II. Formal Relationship of Various Systems of Geometry
Chapter III. Material Consequences of this Relationship
Chapter IV. Points and Volumes

Part II Terms and Relations
Introduction
Chapter I. Spatio-Temporal Relations Independent of the Distinction between Extension and Duration; The Notion of a Sense-Datum
Chapter II. Temporal Relations and the Hypothesis of Durations (Durées)*
Chapter III. Global Resemblance
Chapter IV. Qualitative Similarity and Local Similarity
Chapter V. Relations of the Group of Local Similarities

Part III Some Geometries of Sensation
Introduction
Chapter I. Succession and Global Resemblance (Data of any external sense)
Chapter II. Succession and Global Resemblance (Kinesthetic data and data of any external sense)
Chapter III. Introduction of Local Diversity in Sense Data
Chapter IV. Relations of Position (Visual Data)
Chapter V. Limitations of the Hypothesis of a Natural Spatial Symbolism
Chapter VI. Relations of Position, Simultaneity, Qualitative Similarity, Local Similarity (Visual Data)
Chapter VII. Reflections on the Preceding Universe
Chapter VIII. Elimination of the Relations of Position
Chapter IX. The Geometry of Perspectives
Summary and Conclusion

Contents
Preface
Introduction
Methodology and Logic
Preliminary Notions
Certain and probable inference.—
Certain and probable premises; general definition of Inference.—
Definition of induction.—
Inductions about the relations of characters.—
Inductions about classes of individuals and inductions about classes of classes.—
Inductions from THESE to ALL and from THESE to ANY.—
Primary and secondary inductions.—
Probability and certainty.—
Limitation of this work to inductions from THESE to ALL.—

Hypothesis Concerning the Two Elementary Relations of a Fact to a Law
Confirmation, Invalidation
Theoretical advantage of invalidation over confirmation.—
Induction by invalidation
The mechanism of induction by invalidation: elimination.—
The assumption of determinism for any given character.—
Induction by elimination requires a deterministic assumption.—
Range of this assumption.—
The other conditions of induction by elimination.—

A.—Instances Completely Known
Plurality of causes.—
The possibility of a complex cause renders complete elimination impossible.—
Partial elimination: a principle directed against the complexity of causes.—
Insufficiency of such a principle.—
Another principle directed against the plurality of causes.—
The indefinite increase of probability by multiplying instances.—
Idea of a theory of induction by repetition.—
Summary.—

B.—Instances Incompletely Known
The individual samples of nature are known only incompletely.—
Conditions of primary induction.—
Primary induction by elimination when applied to nature is not satisfactory.—
Recourse to repetition.—
Attempt to found the influence of repetition on a principle of elimination: preliminary assumption.—
Theory of the probability of elimination.—
Development of the theory of determinism.—
Application to induction by elimination.—
M. Lachelier’s ideas.—
Conclusion of the study of induction by invalidation.—

Induction by confirmation
Probability of the conjunction of two propositions.—
Justification of induction by repetition.—
Induction by repetition does not have determinism for a premise.—
The force of induction by repetition does not arise from a probability of elimination.—
A new instance identical with an acquired or known instance may render the law more probable.—
State of the question.—
Two necessary and sufficient conditions for the probability of a law to approach certainty by the multiplication of its instances to infinity.—
Replacing the second condition by a condition that is only sufficient.—
The postulate of the limitation of independent variety.—
It satisfies the first condition.—
But does it also satisify the second condition? Mr. Keynes’ reasoning.—
This reasoning rests on an unacceptable hypothesis.—
Present state of the problem.—

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