This astronomical contingency, and the beliefs which cluster round it, have been stated with some detail, because—as thus expressed—they illustrate the problem as it shapes itself in philosophy. Also the example of the railway time-tables illustrates another point. For it is possible momentarily, in Vermont on July 1, 1927, to forget that the unprecedented Mississippi floods hap- pened during that May and June; so that although the estimate as to error in punctuality was justified by the evidence consciously before us, it did not in fact allow for the considerable derangement of the traffic in some states in the Union.* The point of this illustration from railway trains is that there is a conformity to matter of fact which these judgments exhibit, even if the events concerned have not happened, or will not happen. These considerations introduce the fundamental princi- ple concerning ‘judgment.’ It is that all judgment is categorical; it concerns a proposition true or false in its application to the actual occasion which is the subject making the judgment. This doctrine is not so far from Bradley’s doctrine of judgment, as explained in his Logic. According to Bradley, the ultimate subject of every judg- ment is the one ultimate substance, the absolute. Also, according to him, the judging subject is a mode of the absolute, self-contradictory if taken to be independently actual. For Bradley, the judging subject has only a
* Since this sentence was written in July, 1927, a star has unexpectedly split in two, in March, 1928.
“Still less, at the time of writing this sentence, were the Vermont floods of November, 1927, foreseen.
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derivative actuality, which is the expression of its status as an affection of the absolute. Thus in Bradley’s doc- trine, a judgment is an operation by which the absolute, under the limitations of one of its affections, enjoys self- consciousness of its enjoyment of affections. It will be noticed that in this bald summary of Bradley’s position, I am borrowing Spinoza’s phrase, ‘affectiones substantia.’
In the philosophy of organism, an actual occasion—as has been stated above—is the whole universe in process of attainment of a particular satisfaction. Bradley’s doctrine of actuality is simply inverted. The final actu- ality is the particular process with its particular attain- ment of satisfaction. The actuality of the universe is merely derivative from its solidarity in each actual entity. It must be held that judgment concerns the uni- verse as objectified from the standpoint of the judging subject. It concerns the universe through that subject.
With this doctrine in mind, we pass to the discussion of the sense in which probability can be a positive fact in an actual entity; so that a proposition expressing the probability of some other proposition can in this respect agree or disagree with the constitution of the judging entity. The notion of ‘probability,’ in the widest sense of that term, presents a puzzling philosophical problem. The mathematical theory of probability is based upon certain statistical assumptions. When these assumptions hold, the meaning of probability is simple; and the only remaining difficulties are concerned with the technical mathematical development. But it is not easy to under- stand how the statistical theory can apply to all cases to which the notion of more or less probability is habitu- ally applied. For example, when we consider—as we do consider—the probability of some scientific conjecture as to the internal constitution of the stars, or as to the future of human society after some unprecedented con- vulsion, we seem to be influenced by some analogy which it is very difficult to convert into an appeal to any defi- nite statistical fact. We may consider that it is probable
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that the judgment could be justified by some statistical appeal, if we only knew where to look. This is the belief that the statistical probability is itself probable. But here, evidently, there is an appeal to a wider meaning of probability in order to support the statistical proba- bility applicable to the present case. It is arguable that this wider probability is itself another statistical prob- ability as to the existence of the special statistics rele- vant to such types of scientific argument. But in this explanation puzzling questions are accumulating; and it is impossible to avoid the suspicion that we are being put off with one of those make-believe explanations, so useful to reasoners who are wedded to a theory. The philosophy of organism provides two distinct elements in the universe from which an intuition of probability can originate. One of them is statistical. In this and the next section, an attempt will be made to justify the statistical theory. It is therefore the more imperative to survey carefully the difficulties which have to be met.
In the first place, probability is always relevant to evi- dence; so, on the statistical theory, the numerical proba- bility will mean the numerical ratio of favourable to unfavourable cases in the particular class of ‘cases’ selected as the ‘ground’ for statistical comparison. But alternative ‘grounds’ certainly exist. Accordingly we must provide a reason not based upon ‘probability,’ why one ‘ground’ is selected rather than another. We may admit such a chain of vaguer and vaguer probabilities, in which our first ground is selected as statistically prob- able in respect to its superiority to other ‘grounds’ of other types. We are thus driven back to a second-order ‘ground’ of probability. We may logically proceed to third-order ‘grounds,’ and so on. But if the statistical theory is to be substantiated, after a finite number of steps we must reach a ‘ground’ which is not selected for any reason of probability. It must be selected because it is the ‘ground’ presupposed in all our reasonings.
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Apart from some such ultimate ‘ground,’ the statisti- cal theory, viewed as an ultimate explanation for all our uses of the notion of ‘probability,’ must inevitably fail. This failure arises by reason of the complete arbitrari- ness of the ultimate ‘ground’ upon which the whole esti- mate of probability finally rests.
Secondly, the primary requisite for a ‘ground’ suitable for statistical probability seems itself to appeal to prob- ability. 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 esti- mated, 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 con- sideration. 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 ref- erence 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 igno- rance. Thus again we are driven to an ultimate fact: there must be an ultimate species, and the specific char- acter 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 knowl- edge without any appeal to probability. Also there must be equally direct knowledge of the proportion of favour- able 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 which
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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, men- tioned 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 evi- dence, the statistical state of the ‘ground’ is bogus evi- dence 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 exam- ined. 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 infi- nite 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 informa- tion, 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 induc- tion, and of probability.
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 environ- ment 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 pre- supposition as to the character of the experiencing sub- ject 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 the
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abstraction effected by objectification. Also the charac- ter 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, induc- tive 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, induc- tively justified, shall include actualities which have close analogy to some contemporary subject enjoying assigned experience; for example, an analogy to the judging sub- ject 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 gen- eral type of material world requisite for the presupposed character of one or more of the logical subjects of the proposition.