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On some Fundamental Principles in the Theory of Probability1

Published online by Cambridge University Press:  22 April 2013

George Chrystal
George Chrystal
Affiliation:
University of Edinburgh
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Extract

In the Introduction to his famous Théorie Analytique des Probabilités, Laplace, after an eloquent summary of the progress of Astronomy from the days when every rare celestial phenomenon was regarded as a portent of human misery, to the verification in April 1759 of the perihelion passage of Halley's Comet, proceeds to say :—

“The regularity which Astronomy shows us in the movement of Comets exists, beyond doubt, in every phenomenon of nature. The curve described by a simple molecule of air or of vapour is regulated in a manner as certain as the planetary orbits: there is no difference between the two cases save our ignorance.

Type
Articles
Information
Transactions of the Actuarial Society of Edinburgh , Volume 2 , 1891 , pp. 420 - 439
Copyright
Copyright © Institute and Faculty of Actuaries 1891

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References

page 423 note 1 See De Morgan, 's Formal Logic, pp. 182, 180.Google Scholar

page 424 note 1 Notwithstanding that we find in this passage, laid down with admirable clearness, the fundamental principles on which Venn builds his Logic of Chance, Boole did not cast himself loose from the traditional view of the foundations of the mathematical theory of probability. This is clear from the passages that immediately precede nud follow. Still, the fact that he wrote the above, and that he questioned the general applicability of the rules of Inverse Probability, entitles him to rank among those who prepared the way to the sounder views that now seem destined to prevail.

page 426 1 From my Algebra, Part II. p. 538. The reader who wishes to have a fuller discussion of the fundamental principles should consult Venn's Logic of Chance.

page 428 note 1 Ency. Brit., vol. xix. p. 774 (1885).

page 434 note 1 Observe that the “series” includes in the one case merely all the men that die in Edinburgh in 1890, in the other all the men who lived in Edinburgh in 1890 whether they died in that year or not.

page 436 note 1 This for clearness; there is of course, according to our view, no such thing as “indirect” probability

page 437 note 1 Whitworth, , Choice and Chance (1878), p. 151.Google Scholar

page 438 note 1 The reader should refer to the passages in Boole, 's Laws of Thought (especially pp. 250, 356, 370)Google Scholar, where that able writer indicates his views regarding the Inverse Rules.