The Logic of Chance: An Essay on the Foundations and Province of the Theory of Probability, with Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science, and to Statistics"Any work on Probability by a Cambridge man will be so likely to have its scope and its general treatment of the subject prejudged, that it may be well to state at the outset that the following Essay is in no sense mathematical. Not only, to quote a common but often delusive assurance, will 'no knowledge of mathematics beyond the simple rules of Arithmetic' be required to understand these pages, but it is not intended that any such knowledge should be acquired by the process of reading them. Of the two or three occasions on which algebraical formulae occur they will not be found to form any essential part of the text. The science of Probability occupies at present a somewhat anomalous position. It is impossible, I think, not to observe in it some of the marks and consequent disadvantages of a sectional study. By a small body of ardent students it has been cultivated with great assiduity, and the results they have obtained will always be reckoned among the most extraordinary products of mathematical genius"--Preface. (PsycINFO Database Record (c) 2012 APA, all rights reserved). |
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actual admitted agencies amongst amount appeal appeal to Probability apply arithmetical arithmetical mean arrangement assigned assume assumption average bability belief calculation causes certainty chance chapter characteristics circumstances conclusion consider consideration course curve degree determine direct discussion distinction enquiry equally event example experience fact Formal Logic former frequency games of chance given ground happen height individual Induction Inductive Logic inference instance Inverse Probability irregularity justify kind large number Law of Error limit Logic logicians long run magnitude mathematical matter mean measure merely mind modality nature objects observed obtained occur ordinary particular possible practical precisely present problem proportion proposition question random reason reference regarded remarked rule rules of inference seems simple statistics succession supposed supposition syllogisms tails theory of Probability things throws tion tossing true ultimate uniformity universal propositions white ball words
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Page 329 - Conclusive, or, as they are elsewhere termed, imperative or absolute, presumptions of law, are rules determining the quantity of evidence requisite for the support of any particular averment, which is not permitted to be overcome by any proof that the fact is otherwise.
Page 112 - Required less approximate values for the ratio of the circumference to the diameter of a circle, one approximate ratio being f JJol?
Page iii - Are God and Nature then at strife, That Nature lends such evil dreams So careful of the type she seems, So careless of the single life...
Page 236 - Though there be no such thing as chance in the world, our ignorance of the real cause of any event has the same influence on the understanding and begets a like species of belief or opinion.
Page 209 - Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge — knowledge mingled with ignorance, producing doubt.
Page 34 - Fechner's law, in its approximative and simplest form of sensation = log stimulus, tells us that a series of tints, in which the quantities of white scattered on a black ground are as 1, 2, 4, 8, 16, 32, &c., will appear to the eye to be separated by equal intervals of tint. Therefore, in matching a grey that contains 8 portions of white, we are just as likely to err by selecting one that has 16 portions as one that has 4 portions. In the first case there would be an error in excess, of 8 ; in the...
Page 179 - In the preceding chapter we have calculated the chances of an event, knowing the circumstances under which it is to happen or fail. We are now to place ourselves in an inverted position : we know the event, and ask what is the probability which results from the event in favour of any set of circumstances under which the same might have happened1.
Page 123 - Logic — which investigates the rules according to which one proposition can be necessarily inferred from another; hi close correspondence with this there is a science which investigates the rules according to which the amount of our belief of one proposition varies with the amount of our belief of other propositions with which it is connected. The same view is also supported by another high authority, the late Prof. Donkin, who says (Phil. Mag. May, 1851), "It will, I suppose, be generally admitted,...
Page 127 - Tucker, the superstructure of our convictions is not so much to be compared to the solid foundations of an ordinary building, as to the piles of the houses of Rotterdam which rest somehow in a deep bed of soft mud. They bear their weight securely enough, but it would not be easy to point out accurately the dependence of the different parts upon one another. Directly we begin to think of the amount of our belief, we have to think of the arguments by which it is produced — in fact, these arguments...
Page 481 - Find the locus of a point such that the sum of the squares of its distances from two fixed points shall be equivalent to the square of the distance between the fixed points.