PROBABILISM. 420 PROBABILITY. tloctrinc regarding the use of so-called 'probable 0|plnions' in guiding the conscience as to the law- iulncss or unlawlulness of any particular action. The word came prominently into discussion in the seventecntli century and seems now fully accepted as a technical name. As the ground of the doc- trine, it is assumed that, in human actions, abso- lute certainty is not always attainable as to their lawfulness or unlawfulness. Short of this cer- tainty, the intellect passes through the stages of 'doubt' and of 'probability.' In the former, it is swayed Ifctween eonllieting views, so as to be un- able to decide, or even to approach toward de- ciding, what is true. In the latter, although there is a conflict of views, yet the reasons in their favor are not so equal that the intellect can- not see preponderating motives in favor of the truth of one or of the other. Moreover, in the con- flict of views, another element will arise, as to their comparative "safety,' that is, the greater or less danger of moral culpability which they involve; and this greater or less moral 'safety' of a view may or may not coincide with its greater or less 'probability.' The doctrine of probabilism arose in the Mid- dle Ages from the wide play given in penitential books to the idea of the morally indifl'erent, and was further promoted by the discussions of the scholastics upon conflict of autliorities, and thus upon ai)parent or real conflict of duties, in the moral sphere. Vasquez introduced (1598) proba- bilism into the moral theology of the Jesuits, and it soon gained a large place, being developed with great subtlety. In its extremest developments probabilism held that it is lawful to act upon any opinion which has in its favor the authority of any grave and approved doctor, though it may be less probable than its opposite. Escobar taught that a confessor must absolve if a penitent ap- peals to a probable opinion, even if he himself holds another. In the sequel there was a very great relaxation of the whole moral tone, and serious scandals arose, leading to the condemna- tion of probabilism Ijy the Surljonne (1G20). Against this theory, called probabilism simple, Pascal (q.v. ) directed some of his famous ProriH- cial Letters (1656). Discu.ssion upon the subject ■was long continued, and in 1691 Gonzalez, the general of the Jesuits, issued his Elements of Moral Thcolofin, which took the anti-probabilistic side, requiring that an opinion shall be certain before it is acted upon. Later s]irang u]) three schools of probabilism: (1) that of (riiui-proha- hilism, according to which, of two opinions one can be chosen only if it is at least equally proba- ble with the other; (2) prohabiliorisni. according to which there are no cases of exactly equal proba- bility, and the more probable is always to be fol- lowed; (3) tvtiorism. according to which the safer opinion is to be followed, even if less proba- ble. The great modern master on the subject is Saint Alfonso Liguori. whose system may be de- scribed as a kind of practical prohabiliorisni. in which, by the ise of what are called reflex princi- ples, an opinion which nhjcctU-rhi is but probable is made siihjrctiprh/ the basis of a certain and safe practical judgment. There can be no doubt that the system of probabilism has been pushed by some individual divines to scandalous ex- tremes ; but it is only just to add that these ex- tremes have been condemned by authority in the Roman Church ; and that, on the other hand, the in-inciples of the higher Roman schools of proba- bilism are substantially the same as those of all moralists, whether of the old or of the new schools of ethics. Consult: Dollinger-Reusch, Gcschichie der Mo- rals<treitigkeiten in dcr riimischen Kirche seit dein 16. Jahrhundert (Nordlingen, 1889) : Luth- ardt, Oeschichte der christUchcn Ethik (Leipzig, 1892). ' " PROBABILITY (Lat. prohahilitas, from probabilis, ]jrobable). Expressions like the fol- lowing are in common use: "It will probably rain to-day," "The chance of finding the article is very small," "He is more likely to succeed than to fail," "A is almost sure to be elected." These expressions all imply a lack of knowledge, an un- certainty as to the actual condition of affairs. But they signify ditlereut degrees of uncertainty. The first and tliird are indefinite, the second and fourth are quite definite. In order to answer in mathematical terms the question, "^Vliat is the chance of an event happening?" it is neces- sary to have some standard of measure or of com- parison. Suppose we know only one of ten can- didates on examination for a degree, and we hear that one passed. What is the chance or proba- bility that our acquaintance is that one? If, ac- cording to our knowledge of the case, one candi- date is as likely to pass as any other, we may say that the chance of our acquaintance having passed is 1 to 10. If, however, si.x of the candi- dates are men. and our acquaintance is a man, and we hear that it is a man who passed, the chance is now 1 to 6. But if we hear the name of the successful candidate, this name corresponding to that of our acquaintance, and observe that the names on the list are all different, the chance is now 1 to 1, or it is a certainty. Certainty is called the unit of probability. It is the standard which all estimate alike. All other degrees of probability will be expressed as fractions of cer- tainty. E.g., in the above case of the candidate, on the first evidence the chance is 1:10, on the second evidence it is 1:6, on the third 1, or cer- tainty. If an event can occur in only one of a number of dift'erent ways, equally likely to occur, the probability of its happening at all is the sum of the several probabilities of its happening in the several ways. This proposition, the result of common e.xperience, is generally accepted as axio- matic. Thus a coin can fall either head or tail, therefore the chance of its falling head is %, and of its falling tail is 14, the sum of these chances being 1. This is as it should be. for the coin must certainly fall in order to pruduce head" or tail. The probability of an event not happen- ing is found by subtracting from unity the frac- tion representing the probaliility that it will hap- pen. E.g., if the chance of an event happening is 4, the chance of its not happening is 1 — y = f- Or, if A's chance of hitting a target is -'- and B s chance of hitting it is ^l, the chance of both missing it is 1 — (^- -f- J) =r }-. Two probabilities whose sum is unity are called romplcnunlnry probabilities. E.g. the probability of drawing at one trial a white ball from a bag containing 2 Avhite and .S black balls is I. The prol)ability of drawing a black ball is J. Their sum is 1, hence they are complementary probabilities. In gen- eral, if an event can happen in n ways and fail in b ways, all of which are equally likely to oc-
