Philosophical Introduction To Probability

by Galavotti, Maria Carla

• ISBN13: 9781575864907
• ISBN10: 1575864908
• Format: Paperback
• Copyright: 2005-02-15
• Publisher: Stanford Univ Center for the Study

Summary

Not limited to merely mathematics, probability has a rich and controversial philosophical aspect.A Philosophical Introduction to Probabilityshowcases lesser-known philosophical notions of probability and explores the debate over their interpretations. Galavotti traces the history of probability and its mathematical properties and then discusses various philosophical positions on probability, from the Pierre Simon de Laplace's "classical" interpretation of probability to the logical interpretation proposed by John Maynard Keynes. This book is a valuable resource for students in philosophy and mathematics and all readers interested in notions of probability.

Table of Contents

Introductory remarks	1	(6)
The notion of probability
A historical sketch	7	(20)
The birth of probability	7	(5)
The dual character of probability	12	(1)
Jakob Bernoulli and direct probability	13	(2)
Nikolaus and Daniel Bernoulli	15	(2)
Thomas Bayes and inverse probability	17	(1)
Probability and social mathematics: Condorcet and Quetelet	18	(3)
The rise of contemporary statistics: Galton, Pearson, Fisher	21	(4)
The advent of probability in physics	25	(2)
Probability and induction	27	(12)
Francis Bacon	28	(1)
Induction as ampliative inference	29	(2)
Hume's problem of induction	31	(3)
Mill, Herschel, Whewell	34	(5)
The laws of probability
The fundamental properties of probability	39	(8)
Bayes' rule	47	(5)
Kolmogorov's axiomatization	52	(5)
The classical interpretation
Laplace and the Principle of insufficient reason	57	(9)
Determinism	57	(3)
The `Principle of insufficient reason'	60	(2)
The `Rule of succession'	62	(2)
Expectation and certainty	64	(2)
Problems of the classical definition	66	(5)
The frequency interpretation
Robert Leslie Ellis	71	(3)
John Venn	74	(7)
Probability as limiting frequency	74	(3)
Criticism of the rule of succession	77	(1)
Probability and belief	78	(3)
Richard von Mises and the theory of `collectives'	81	(10)
Von Mises' approach	81	(2)
Collectives	83	(2)
Randomness	85	(2)
Collective-based probability	87	(2)
Applications to science	89	(2)
Hans Reichenbach's probabilistic epistemology	91	(10)
Reichenbach's frequentism	91	(4)
The theory of posits	95	(3)
The justification of induction	98	(1)
Causality	99	(2)
Ernest Nagel's `truth-frequency' theory	101	(4)
The propensity interpretation
Peirce, the forerunner	105	(1)
Popper's propensity interpretation	106	(8)
Falsificationism	106	(3)
The propensity interpretation of probability	109	(3)
A world of propensities	112	(2)
After Popper	114	(11)
Single-case and long-run propensity theories	114	(4)
Humphrey's paradox	118	(3)
Propensity as an ingredient of the description of chance phenomena	121	(4)
Digression on chance and randomness	125	(10)
Historical remarks	125	(1)
Poincare's views on chance	126	(2)
The riddle of randomness	128	(4)
Is chance objective?	132	(3)
The logical interpretation
Beginnings	135	(1)
The nineteenth century English Logicists: De Morgan, Boole, Jevons	136	(8)
Augustus De Morgan	136	(2)
George Boole	138	(3)
William Stanley Jevons	141	(3)
John Maynard Keynes	144	(9)
Probability as a logical relation	144	(3)
Rationality and the role of intuition	147	(2)
Analogy, relevance and weight	149	(3)
Ramsey's criticism	152	(1)
William Ernest Johnson	153	(5)
Viennese logicism: Wittgenstein and Waismann	158	(6)
Ludwig Wittgenstein	158	(3)
Friedrich Waismann	161	(3)
Rudolf Carnap's inductive logic	164	(14)
Two concepts of probability	164	(5)
The logic of confirmation	169	(5)
The turn of the Sixties	174	(4)
Harold Jeffreys between logicism and subjectivism	178	(11)
Bayesianism	178	(3)
The interpretation of probability	181	(3)
Probabilistic epistemology	184	(5)
The subjective interpretation
The beginnings	189	(5)
William Donkin	189	(2)
Emile Borel	191	(3)
Frank Plumpton Ramsey and the notion of coherence	194	(14)
Degrees of belief and consistency	194	(6)
Ramsey, Keynes and Wittgenstein	200	(2)
Belief, frequency and `probability in physics'	202	(6)
Bruno de Finetti and exchangeability	208	(17)
De Finetti's radical probabilism	208	(7)
Subjective Bayesianism	215	(5)
Criticism of other interpretations of probability	220	(3)
Indeterminism	223	(2)
Some recent trends	225	(10)
Richard Jeffrey's radical probabilism	225	(5)
Patrick Suppes' probabilistic empiricism	230	(5)
Closing remarks	235	(4)
References	239	(22)
Index	261