Process and Reality — the Gifford Lectures, 1929

Secondly, the primary requisite for a ‘ground’ suitable for statistical probability seems itself to appeal to probability. The members of the class, called the ‘ground,’ must themselves be ‘cases of equal probability,’ some favourable and some unfavourable, with the possibility of the limiting types of ‘ground’ in which all members are favourable, or all members are unfavourable. The proposition in question, whose probability is to be estimated, must be known to be a member of the ‘ground’; but no other evidence, as to which set—favourable or unfavourable—the proposition belongs, enters into consideration. It is evident that, for the ultimate ground, the phrase ‘cases of equal probability’ must be explicable without reference to any notion of probability. The principle of such an explanation is easily found by reference to the six faces of dice. A die is a given fact; and its faces do not differ, qua faces, in any circumstance relative to their fall with one face upwards or another face upwards. Also beyond this given fact, there is ignorance. Thus again we are driven to an ultimate fact: there must be an ultimate species, and the specific character must be irrelevant to the ‘favourableness’ or ‘unfavourableness’ of the members of the species in their capacity of cases. All this must be given in direct knowledge without any appeal to probability. Also there must be equally direct knowledge of the proportion of favourable or unfavourable cases within the species—at least within the limits of precision or vagueness presupposed in the conclusion.

Thirdly, it is another requisite for a ‘ground’ that the number of instances which it includes be finite. The whole theory of the ratios of cardinal numbers, on whichp. 308 statistical probability depends, breaks down when the cardinal numbers are infinite.

Fourthly, the method of ‘sampling’ professes to evade two objections. One of them is the breakdown, mentioned above, when the number of cases in the ‘ground’ is infinite. The other objection, thus evaded, is that in practice the case in question is novel and does not belong to the ‘ground’ which is in fact examined. According to this second objection, unless there is some further evidence, the statistical state of the ‘ground’ is bogus evidence as to the probability of the case in question. To sum up: The method of sampling professes to overcome, (i) the difficulty arising from the infinity of the ground; and (ii) that arising from the novelty of the case in question, whereby it does not belong to the ground examined. In the discussion it must be remembered that we are considering that ultimate ground which must not require any appeal to probability beyond itself. Thus the statistical facts as to the ground, must be ‘given’ and not merely ‘probable.’

(1) When we have infinite ‘ground,’ containing an infinite number of favourable cases and an infinite number of unfavourable cases, ‘random’ sampling can give no help towards the establishment of statistical probability ; for one reason because no such notion of ratios can apply to these infinities; and for another reason, no sample is ‘random’; it has only followed a complex method. <A finite number of samples each following some method of its own, however complex each method may be, will give a statistical result entirely dependent upon those methods. In so far as repetitions of so-called random samplings give concordant results, the only conclusion to be drawn is that there is a relevant, though concealed, analogy between the ‘random’ methods. Thus a finite ‘ground’ is essential for statistical probability. It must be understood that this argument implies no criticism on a properly interpreted method of sampling applied to a finite ‘ground.’

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(11) When the ‘case’ in question does not belong to the ground examined, these can, apart from further information, be no rational inference from the ‘ground’ to the novel case. If probability be in truth purely statistical, and if there be no additional information, there can be no escape from this conclusion. But we certainly do unhesitatingly argue from a ‘ground’ which does not include the case in question, to a probable conclusion concerning the case in question. Thus either such an inference is irrational, futile, useless; or, when there is justification, there is additional information. This is the famous dilemma which perplexes the theories of induction, and of probability.

SECTION VI

It is evident that the ultimate ‘ground’ to which all probable judgments must refer can be nothing else than the actual world as objectified in judging subjects. A judging subject is always passing a judgment upon its own data. Thus, if the statistical theory is to hold, the relations between the judging subject and its data must be such as to evade the difficulties which beset that theory.

Every actual entity is in its nature essentially social; and this in two ways. First, the outlines of its own character are determined by the data which its environment provides for its process of feeling. Secondly, these data are not extrinsic to the entity; they constitute that display of the universe which is inherent in the entity. Thus the data upon which the subject passes judgment are themselves components conditioning the character of the judging subject. It follows that any general presupposition as to the character of the experiencing subject also implies a general presupposition as to the social environment providing the display for that subject. In other words, a species of subject requires a species of data as its preliminary phase of concrescence. But such data are nothing but the social environment under thep. 310 abstraction effected by objectification. Also the character of the abstraction itself depends on the environment. The species of data requisite for the presumed judging subject presupposes an environment of a certain social character.

Thus, according to the philosophy of organism, inductive reasoning gains its validity by reason of a suppressed premise. This tacit presupposition is that the particular future which is the logical subject of the judgment, inductively justified, shall include actualities which have close analogy to some contemporary subject enjoying assigned experience; for example, an analogy to the judging subject in question, or to some sort of actuality presupposed as in the actual world which is the logical subject of the inductive judgment. It is also presumed that this future is derived from the present by a continuity of inheritance in which this condition is maintained. There is thus the presupposition of the maintenance of the general social environment—either by reference to judging subjects, or by more direct reference to the preservation of the general type of material world requisite for the presupposed character of one or more of the logical subjects of the proposition.