(in Chapter VII.)[ TN: space] that corresponding to syllogistic inferences. Our present position therefore is that in which we may consider ourselves in possession of any number of generalizations, but wish to employ them so as to make inferences about a given individual; just as in one department of common logic we are engaged in finding middle terms to establish the desired conclusion. In this latter case the process is found to be extremely simple, no accumulation of different middle terms being able to lead to any real ambiguity or contradiction. In Probability, however, the case is different. Here, if we attempt to draw inferences about the individual case before us, as often is attempted—in the Rule of Succession for example—we shall encounter the full force of this ambiguity and contradiction. Treat the question, however, fairly, and all difficulty disappears. Our inference really is not about the individuals as individuals, but about series or successions of them. We wished to know whether John Smith will die within the year; this, however, cannot be known. But John Smith, by the possession of many attributes, belongs to many different series. The multiplicity of middle terms, therefore, is what ought to be expected. We can know whether a succession of men, residents in India, consumptives, &c.[ TN: space] die within a year. We may make our selection, therefore, amongst these, and in the long run the belief and consequent conduct of ourselves and other persons (as described in Chapter VI.)[** TN: space] will become capable of justification. With regard to choosing one of these series rather than another, we have two opposing principles of guidance. On the one hand, the more special the series the better; for, though not more right in the end, we shall thus be more nearly right all along. But, on the other hand, if we try to make the series too special, we shall generally meet the practical objection
1 Some of my readers may be familiar with a very striking digression in Buffon's Natural History (Natural Hist.[ TN: space] of Man, § VIII.), in which he supposes the first man in full possession of his faculties, but with all his experience to gain, and speculates on the gradual acquisition of his knowledge. Whatever may be thought of his particular conclusions the passage is very interesting and suggestive to any student of Psychology.
2 See also Dugald Stewart (Ed.[ TN: space] by Hamilton; VII.[ TN: space] pp. 115–119).
3 Required that is for purposes of logical inference within the limits of Probability; it is not intended to imply any doubts as to its actual universal prevalence, or its all-importance for scientific purposes. The subject is more fully discussed in a future chapter.
4 As particular propositions they are both of course identical in form. The fact that the ‘some’ in the former corresponds to a larger proportion than in the latter, is a distinction alien to pure Logic.
5 The reason is obvious. The healthiest English lives in Madeira (viz.[ TN: space] the consumptive ones) have now ceased to be reckoned as English; whereas the worst consumptive lives there (viz.[ TN: space] the English) are now increased in relative numbers.