The Logic of Chance, 3rd edition 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

§§ 1, 2. Distinction between the proportional propositions of Probability, and the propositions of Logic. 3, 4. The former are best regarded as presenting a series of individual...

§§ 1, 2. Indication of the nature of a Law of Error or Divergence. 3. Is there necessarily but one such law, 4. Applicable to widely distinct classes of things? 5, 6. This canno...

§ 1. The causes consist of (1) 'objects,' 2, 3. Which may or may not be distinguishable into natural kinds, 4-6. And (2) 'agencies.' 7. Requisites demanded in the above: 8, 9. C...

§ 1. The data of Probability are established by experience; 2. Though in practice most problems are solved deductively. 3-7. Mechanical instance to show the inadequacy of any à...

§ 1. _General Indication._ 2-5. _The postulate of ultimate uniform distribution at one stage or another._ 6. _This area of distribution must be finite:_ 7, 8. _Geometrical illus...

§§ 1, 2. Preliminary remarks. 3, 4. Are we accurately conscious of gradations of belief? 5. Probability only concerned with part of this enquiry. 6. Difficulty of measuring our...

§ 1. Nature of these inferences. 2. Inferences by addition and subtraction. 3. Inferences by multiplication and division. 4-6. Rule for independent events. 7. Other rules someti...

§ 1. Reasons for desiring some such rule: 2. Though it could scarcely belong to Probability. 3. Distinction between Probability and Induction. 4, 5. Impossibility of reducing th...

§§ 1-5. Statement of the Inductive problem, and origin of the Inductive inference. 6. Relation of Probability to Induction. 7-9. The two are sometimes merged into one. 10. Exten...

§ 1. Old Theological objection to Chance. 2-4. Scientific version of the same. 5. Statistics in reference to Free-will. 6-8. Inconclusiveness of the common arguments here. 9, 10...

§§ 1, 2. _Broad distinction between these views;_ 2, 3. _Difficulty of adhering consistently to the objective view;_ 4. _Especially in the case of Hypotheses._ 5. The doubtful s...

§§ 1, 2. Probability has no relation to time. 3, 4. Butler and Mill on Probability before and after the event. 5. Other attempts at explaining the difficulty. 6-8. What is reall...

§ 1. Various senses of Modality; 2. Having mostly some relation to Probability. 3. Modality must be recognized. 4. Sometimes relegated to the predicate, 5, 6. Sometimes incorrec...

§§ 1-3. (I.) Errors in judging of events after they have happened. 4-7. Very various judgments may be thus involved. 8, 9. (II.) _Confusion between random and picked selections....

§§ 1, 2. The certainties and uncertainties of life. 3-5. Insurance a means of diminishing the uncertainties. 6, 7. Gambling a means of increasing them. 8, 9. Various forms of ga...

§§ 1, 2. Doubtful applicability of Probability to testimony. 3. Conditions of such applicability. 4. Reasons for the above conditions. 5, 6. Are these conditions fulfilled in th...

§ 1. Improbability before and after the event. 2, 3. Does the rejection of this lead to the conclusion that the credibility of a story is independent of its nature? 4. General a...

§ 1. _Preliminary rude notion of an average,_ 2. _More precise quantitative notion, yielding_ (1) _the Arithmetical Average,_ 3. (2) _the Geometrical._ 4. _In asymmetrical curve...

6. (i) _The law of dispersion may be determinable _à priori_,_ 7. (ii) _or experimentally, by statistics._ 8, 9. _Thence to determine the modulus of the error curve._ 10-14. _Nu...

1. It is sometimes not easy to give a clear definition of a science at the outset, so as to set its scope and province before the reader in a few words. In the case of those sci...

1. In the course of the last chapter the nature of a particular kind of series, that namely, which must be considered to constitute the basis of the science of Probability, has...

1. In discussing the question whether all the various groups and series with which Probability is concerned are of precisely one and the same type, we made some examination of t...

1. At the point which we have now reached, we are supposed to be in possession of series or groups of a certain kind, lying at the bottom, as one may say, and forming the founda...

2. For the use of those not acquainted with the common notation employed in this subject, it may be remarked that HH is simply an abbreviated way of saying that the two successi...

1. There is a term of frequent occurrence in treatises on Probability, and which we have already had repeated occasion to employ, viz. the designation _random_ applied to an eve...

1. Originally written in somewhat of a spirit of protest against what seemed to me the prevalent disposition to follow De Morgan in taking too subjective a view of the science....

1. In the previous chapter, an investigation was made into what may be called, from the analogy of Logic, Immediate Inferences. Given that nine men out of ten, of any assigned a...

1. A word of apology may be offered here for the introduction of a new name. The only other alternative would have been to entitle the rule one of _Induction_. But such a title...

1. We were occupied, during the last chapter, with the examination of a rule, the object of which was to enable us to make inferences about instances as yet unexamined. It was p...

1. The remarks in the previous chapter will have served to clear the way for an enquiry which probably excites more popular interest than any other within the range of our subje...

1. In the previous edition a large part of this chapter was devoted to the general consideration of the distinction between a Material and a Conceptualist view of Logic. I have...

1. We are now in a position to explain and justify some important conclusions which, if not direct consequences of the distinctions laid down in the last chapter, will at any ra...

1. The reader who knows anything of the scholastic Logic will have perceived before now that we have been touching in a variety of places upon that most thorny and repulsive of...

1. In works on Logic a chapter is generally devoted to the discussion of Fallacies, that is, to the description and classification of the different ways in which the rules of Lo...

1. If the reader will recall to mind the fundamental postulate of the Science of Probability, established and explained in the first few chapters, and so abundantly illustrated...

1. On the principles which have been adopted in this work, it becomes questionable whether several classes of problems which may seem to have acquired a prescriptive right to ad...

1. It is now time to recur for fuller investigation to an enquiry which has been already briefly touched upon more than once; that is, the validity of testimony to establish, as...

1. There is much need of some good account, accessible to the ordinary English reader, of the nature and properties of the principal kinds of Mean. The common text-books of Alge...

1. In the last chapter we were occupied with the Average mainly under its qualitative rather than its quantitative aspect. That is, we discussed its general nature, its principa...