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according actual addition alternatives analogy application argue argument arise assert assume assumption balls belief Calcul cause certain certainty chance Chapter characteristic common conclusion connection consider deal defined definition depends determine difficulty direct discussed distinct equal error event evidence example existence experience expression fact favour finite follows frequency fundamental further generalisation give given greater ground hypothesis important increases independent Indifference inductive inference instances irrelevant judgments kind knowledge known lead less limits logical mathematical matter mean measure method nature necessary object observed obtained occur particular positive possible practical precise premisses present Principle priori probability problem proportion proposition quantity question random rational reason reference relation relative relevant respect result rule seems sense statistical suppose Theorem theory tion true valid weight write
286. lappuse - 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.
81. lappuse - 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.
42. lappuse - 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.
5. lappuse - 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.
222. lappuse - 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.
81. lappuse - 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.
172. lappuse - 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).
8. lappuse - a definition of probability is not possible, unless it contents us to define degrees of the probability relation by reference to degrees of rational...
306. lappuse - 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...