[5] According to Dante, something resembling this prevailed amongst the occupants of the Inferno. The cardinals and others whom he there meets are able to give information about many events which were yet to happen upon earth, but they had to ask it for many events which actually had happened.
CHAPTER XIII.
ON THE CONCEPTION AND TREATMENT OF MODALITY.
§ 1. The reader who knows anything of the scholastic Logic will have perceived before now that we have been touching in a variety of places upon that most thorny and repulsive of districts in the logical territory;—modality. It will be advisable, however, to put together, somewhat more definitely, what has to be said upon the subject. I propose, therefore, to devote this chapter to a brief account of the principal varieties of treatment which the modals have received at the hands of professed logicians.
It must be remarked at the outset that the sense in which modality and modal propositions have been at various times understood, is by no means fixed and invariably the same. This diversity of view has arisen partly from corresponding differences in the view taken of the province and nature of logic, and partly from differences in the philosophical and scientific opinions entertained as to the constitution and order of nature. In later times, moreover, another very powerful agent in bringing about a change in the treatment of the subject must be recognized in the gradual and steady growth of the theory of Probability, as worked out by the mathematicians from their own point of view.
§ 2. In spite, however, of these differences of treatment, there has always been some community of subject-matter in the discussions upon this topic. There has almost always been some reference to quantity of belief; enough perhaps to justify De Morgan's[1] remark, that Probability was “the unknown God whom the schoolmen ignorantly worshipped when they so dealt with this species of enunciation, that it was said to be beyond human determination whether they most tortured the modals, or the modals them.” But this reference to quantity of belief has sometimes been direct and immediate, sometimes indirect and arising out of the nature of the subject-matter of the proposition. The fact is, that that distinction between the purely subjective and purely objective views of logic, which I have endeavoured to bring out into prominence in the eleventh chapter, was not by any means clearly recognized in early times, nor indeed before the time of Kant, and the view to be taken of modality naturally shared in the consequent confusion. This will, I hope, be made clear in the course of the following chapter, which is intended to give a brief sketch of the principal different ways in which the modality of propositions has been treated in logic. As it is not proposed to give anything like a regular history of the subject, there will be no necessity to adhere to any strict sequence of time, or to discuss the opinions of any writers, except those who may be taken as representative of tolerably distinct views. The outcome of such investigation will be, I hope, to convince the reader (if, indeed, he had not come to that conviction before), that the logicians, after having had a long and fair trial, have failed to make anything satisfactory out of this subject of the modals by their methods of enquiry and treatment; and that it ought, therefore, to be banished entirely from that science, and relegated to Probability.
§ 3. From the earliest study of the syllogistic process it was seen that, complete as that process is within its own domain, the domain, at any rate under its simplest treatment, is a very limited one. Propositions of the pure form,—All (or some) A is (or is not) B,—are found in practice to form but a small portion even of our categorical statements. We are perpetually meeting with others which express the relation of B to A with various degrees of necessity or probability; e.g.
A must be B, A may be B; or the effect of such facts upon our judgment, e.g.
I am perfectly certain that A is B, I think that A may be B; with many others of a more or less similar type. The question at once arises, How are such propositions to be treated? It does not seem to have occurred to the old logicians, as to some of their successors in modern times, simply to reject all consideration of this topic. Their faith in the truth and completeness of their system of inference was far too firm for them to suppose it possible that forms of proposition universally recognized as significant in popular speech, and forms of inference universally recognized there as valid, were to be omitted because they were inconvenient or complicated.
§ 4. One very simple plan suggests itself, and has indeed been repeatedly advocated, viz.