On our view of Probability, therefore, its ‘relativeness’ in any given case is a misleading expression, and it will be found much preferable to speak of the effect produced by variations in the nature and amount of the data which we have before us. Now it must be admitted that there are frequently cases in our science in which such variations are peculiarly likely to be found. For instance, I am expecting a friend who is a passenger in an ocean steamer. There are a hundred passengers on board, and the crew also numbers a hundred. I read in the papers that one person was lost by falling overboard; my anticipation that it was my friend who
was lost is but small, of course. On turning to another paper, I see that the man who was lost was a passenger, not one of the crew; my slight anxiety is at once doubled. But another account adds that it was an Englishman, and on that line at that season the English passengers are known to be few; I at once begin to entertain decided fears. And so on, every trifling bit of information instantly affecting my expectations.
§ 15. Now since it is peculiarly characteristic of Probability, as distinguished from Induction, to be thus at the mercy, so to say, of every little fact that may be floating about when we are in the act of forming our opinion, what can be the harm (it may be urged) of expressing this state of things by terming our state of expectation relative?
There seem to me to be two objections. In the first place, as just mentioned, we are induced to reject such an expression on grounds of consistency. It is inconsistent with the general spirit and treatment of the subject hitherto adopted, and tends to divorce Probability from Inductive logic instead of regarding them as cognate sciences. We are aiming at truth, as far as that goal can be reached by our road, and therefore we dislike to regard our conclusions as relative in any other sense than that in which truth itself may be said to be relative.
In the second place, this condition of unstable assent, this constant liability to have our judgment affected, to any degree and at any moment, by the accession of new knowledge, though doubtless characteristic of Probability, does not seem to me characteristic of it in its sounder and more legitimate applications. It seems rather appropriate to a precipitate judgment formed in accordance with the rules, than a strict example of their natural employment. Such precipitate judgments may occur in the case of ordinary deductive
conclusions. In the practical exigencies of life we are constantly in the habit of forming a hasty opinion with nearly full confidence, at any rate temporarily, upon the strength of evidence which we must well know at the time cannot be final. We wait a short time, and something else turns up which induces us to alter our opinion, perhaps to reverse it. Here our conclusions may have been perfectly sound under the given circumstances, that is, they may be such as every one else would have drawn who was bound to make up his mind upon the data before us, and they are unquestionably ‘relative’ judgments in the sense now under discussion. And yet, I think, every one would shrink from so terming them who wished systematically to carry out the view that Logic was to be regarded as an organon of truth.
§ 16. In the examples of Probability which we have hitherto employed, we have for the most part assumed that there was a certain body of statistics set before us on which our conclusion was to rest. It was assumed, on the one hand, that no direct specific evidence could be got, so that the judgment was really to be one of Probability, and to rest on these statistics; in other words, that nothing better than them was available for us. But it was equally assumed, on the other hand, that these statistics were open to the observation of every one, so that we need not have to put up with anything inferior to them in forming our opinion. In other words, we have been assuming that here, as in the case of most other sciences, those who have to draw a conclusion start from the same footing of opportunity and information. This, for instance, clearly is or ought to be the