He has, however, fallen into some conceptualistic errors of his own; and these are specially manifest in his “applications to moral and social science.” The most important of these is contained in the chapter “On the Credibility of Extraordinary Stories”; but it is defended with so much ingenuity as almost to give it the value of a real contribution to science. It is maintained that the credibility of an extraordinary story depends either entirely upon the veracity of the witness, or, in more extraordinary cases, entirely upon the a priori credibility of the story; but that these considerations cannot, under any circumstances, be combined, unless arbitrarily. In order to support this opinion, the author invents an illustration. He supposes that statistics were to have shown that nine out of ten consumptives who go to the island of Madeira live through the first year, and that nine out of ten Englishmen who go to the same island die the first year; what, then, would be the just rate of insurance for the first year of a consumptive Englishman who is about to go to that island? There are no certain data for the least approximation to the proportion of consumptive Englishmen who die in Madeira during the first year. But it is certain that an insurance company which insured only Englishmen in Madeira during the first year, or only consumptives under the same circumstances, would be warranted (a certain moral fact being neglected) in taking the consumptive Englishman at its ordinary rate. Hence, Mr. Venn thinks that an insurance company which insured all sorts of men could with safety and fairness insure the consumptive Englishman either as Englishman or as consumptive.1 Now, the case of an extraordinary story is parallel to this: for such a story is, 1st, told by a certain person, who tells a known proportion of true stories,—say nine out of ten; and, 2d, is of a certain sort (as a fish story), of which a known proportion are true,—say one in ten. Then, as much as before, we come out right, in the long run, by considering such a story under either of the two classes to which it belongs. Hence, says Mr. Venn, we must repose such belief in the story as the veracity of the witness alone, or the antecedent probability alone, requires, or else arbitrarily modify one or other of these degrees of credence. In examining this theory, let us first remark, that there are two principal phrases in which the word probability occurs: for, first, we may speak of the probability of an event or proposition, and then we express ourselves incompletely, in as much as we refer to the frequency of true conclusions in the genus of arguments by which the event or proposition in question may have been inferred, without indicating what genus of argument that is; and, secondly, we may speak of the probability that any individual of a certain class has a certain character, when we mean the ratio of the number of those of that class that have that character to the total number in the class. Now it is this latter phrase which we use when we speak of the probability that a story of a certain sort, told by a certain man, is true. And since there is nothing in the data to show what this ratio is, the probability in question is unknown. But a “degree of credence” or “credibility,” to be logically determined, must, as we have seen, be an expression of probability in the nominalistic sense; and therefore this “degree of credence” (supposing it to exist) is unknown. “We know not what to believe,” is the ordinary and logically correct expression in such cases of perplexity.
Credence and expectation cannot be represented by single numbers. Probability is not always known; and then the probability of each degree of probability must enter into the credence. Perhaps this again is not known; then there will be a probability of each degree of probability of each degree of probability; and so on. In the same way, when a risk is run, the expectation is composed of the probabilities of each possible issue, but is not a single number, as the Petersburg problem shows. Suppose the capitalists of the world were to owe me a hundred dollars, and were to offer to pay in either of the following ways: 1st, a coin should be pitched up until it turned up heads (or else a hundred times, if it did not come up heads sooner), and I should be paid two dollars if the head came up the first time, four if the second time, eight if the third time, &c; or, 2d, a coin should be turned up a hundred times, and I should receive two dollars for every head. Each of these offers would be worth a hundred dollars, in the long run; that is to say, if repeated often enough, I should receive on the average a hundred dollars at each trial. But if the trial were to be made but once, I should infinitely prefer the second alternative, on account of its greater security. Mere certainty is worth a great deal. We wish to know our fate. How much it is worth is a question of political economy. It must go into the market, where its worth is what it will fetch. And since security may be of many kinds (according to the distribution of the probabilities of each sum of money and of each loss, in prospect), the value of the various kinds will fluctuate among one another with the ratio of demand and supply,—the demand varying with the moral and intellectual state of the community,—and thus no single and constant number can represent the value of any kind.
1. This is an error. For supposing every man to be insured for the same amount, which we may take as our unit of value, and adopting the notation,
x = unknown ratio of consumptive English who do not die in the first year. The amount paid out yearly by the company would be, in the long run,
and x is unknown. This objection to Venn’s theory may, however, be waived.
Chapter I. One, Two, and Three
MS 144: Summer-Fall 1867
Logic must begin with analyzing the meanings of certain words, which we shall take up in due order.
The first of these is the word ‘is’, as when we say, Julius Caesar is dead, a griffin is a fabulous animal, a four-sided triangle is an absurdity, height is the distance from the ground, nothing is that which does not exist. These examples suffice to show that we apply this word to whatever we give a name, whether it really exists or not, or whether we consider it as existing or not.
The word is is called by logicians the copula because it joins subject and predicate. That which is, in the sense of the copula, was termed ens (pl: entia) by the schoolmen, and the corresponding abstract noun used was entitas. In this as in many other cases, we have taken in English, the abstract noun in a concrete sense, and we can consequently speak of entities. At the same time we have forgotten the very general meaning attached to the word in the middle ages, as denoting whatever can be named, and employ it for what would then have been termed ens reale. Thus, we often hear the schoolmen reviled because they considered abstractions to be “entities,” but in their sense of the term it admits of no dispute that an abstraction is ens. It is true that they frequently use the word ens simply when they mean ens reale, but only in cases in which there can be no doubt of their meaning; and it was universal to consider entia as embracing not only entia realia but also entia rationis. I propose to restore the term ens or entity to its original meaning of whatever can be named or talked about. I shall also endeavor as much as possible to reserve the word being and other derivatives of is, to express this same conception; but these words must be somewhat ambiguous.
It may be observed that entity is so extremely general a name that it has no negative over against it. We may talk of a nonentity, but then as we have given it a name it is also an entity.
In contrast with this general being which is conferred by our mere thought of an object, is the being of real things which is quite independent of what we think.
We shall designate this by ‘reality’, and its cognates; and shall employ ‘figment’ and ‘fiction’ to denote that which is non-existent without meaning to imply that the conception has been a deliberate invention.