## A Treatise on Probability |

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ab/h actual alternatives application argue argument arise arithmetic mean assert assume assumption axioms Bernoulli's Theorem binary stars calculation cause certainty Chapter characteristic conclusion correlation Czuber Daniel Bernoulli defined definition degree of probability depends determine discussed event evidence example existence experience fact favour finite probability follows formula frequency theory fundamental generalisation given hypothesis independent inference inverse inverse probability irrelevant judgments knowledge known Laplace law of error Laws of Thought Leibniz less limits logical magnitude mathematical mean method Multiplication Theorem negative analogy number of instances numerical measurement objective chance observed occur particular possible precise premisses Principle of Indifference priori probability prob probabilité probable value problem proportion propositions h pure induction quantity question random rational belief reason reference relations of probability relative relevant result rule sense statistical frequency suppose Theory of Probabilities tion true valid weight white balls

### Popular passages

Page 286 - But it is not always so; it may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible, and we have the fortuitous phenomenon.

Page 81 - Tis not solely in poetry and music, we must follow our taste and sentiment, but likewise in philosophy. When I am convinc'd of any principle, 'tis only an idea, which strikes more strongly upon me. When I give the preference to one set of arguments above another, I do nothing but decide from my feeling concerning the superiority of their influence.

Page 42 - For this theory employs a famous criterion called the principle of insufficient reason or the principle of indifference. According to this principle: // there is no known reason for predicating of our subject one rather than another of several alternatives, then relatively to such knowledge the assertions of each of these alternatives have an equal probability.

Page 5 - We are claiming, in fact, to cognise correctly a logical connection between one set of propositions which we call our evidence and which we suppose ourselves to know, and another set which we call our conclusions, and to which we attach more or less weight according to the grounds supplied by the first.

Page 222 - According to the hypothesis above explain'd all kinds of reasoning from causes or effects are founded on two particulars, viz., the constant conjunction of any two objects in all past experience, and the resemblance of a present object to any one of them.

Page 81 - I think, in every point unquestionable, probability is founded on the presumption of a resemblance betwixt those objects, of which we have had experience, and those, of which we have had none; and therefore 'tis impossible this presumption can arise from probability.

Page 172 - They say that Understanding ought to work by the rules of right reason. These rules are, or ought to be, contained in Logic ; but the actual science of Logic is conversant at present only with things either certain, impossible, or entirely doubtful, none of which (fortunately) we have to reason on. Therefore the true Logic for this world is the Calculus of Probabilities, which takes account of the magnitude of the probability (which is, or which ought to be in a reasonable man's mind).

Page 8 - a definition of probability is not possible, unless it contents us to define degrees of the probability relation by reference to degrees of rational...

Page 308 - Scripture, tradition, councils, and fathers, are the evidence in a question, but reason is the judge, that is, we being the persons that are to be persuaded, we must see that we be persuaded reasonably, and it is unreasonable to assent to a lesser evidence, when a greater and clearer is propounded...

Page 108 - In fact the belief in natural selection must at present be grounded entirely on general considerations...