PROBABILITY. - In the sense now common, a fact is probable which, while not presenting itself as absolutely certain, is nevertheless presumable to have happened or to be going to happen; and a proposition is probable which is not fully evident but which presents good reasons for being admitted. Probability is therefore the admissibility of a fact or of a proposition not entirely certain, and at the same time the objective reasons that ground it.
I. TERMINOLOGY
P. (Gr. πιθανότης) derives from probatio, which means proof, experiment, and also approval, demonstration. Probable is therefore in ancient usage: a) that which can be held, accepted, since it usually happens or is generally admitted ("Probabile est id quod fere fieri solet, aut quod in opinione positum est": Cic., Invent., I, 29, 46); b) that which is reasonable, just, to be approved ("probabilis orator, cuius ingenium et eloquentia probari ac placere debet": id., Brut., 76, 263 c); c) finally, that which is "verisimilar" (cf. German Wahrscheinlichkeit), with or without objective foundation ("multa quae nos fallunt probabilitate magna": id., Acad., 4, 25, 75; "ne cui falso assentiamus neve nunquam captiosa probabilitate fallamur": De fin., 21, 72).
II. HISTORICAL NOTES
In Aristotle, probable things (ἐνδόξα, πιθανά, ὅμοια τῷ ἀληθῷ) are those things "quae videntur omnibus aut pluribus aut sapientibus; et his vel omnibus vel plurimis vel maxime nobilibus et probatis" (Top., I, ch. 1, 100 b 21 ff.; cf. ch. 10 [8] 104 a 6 ff.). "What is probable is either probable and credible in itself (for intrinsic reasons) or is shown to be such for other reasons" (Rhet., I, ch. 2, 1356 b 26 ff.). But "not everything that seems probable is also probable" (Top., I, ch. 1, 100 b 26). Probability generates opinion (δόξα), which "concerns the true and the false (that is, it is an affirmation), but of a thing that can also be - and is admitted to be able to be - otherwise" (Anal. post., I, ch. 33, 89 a 2-3). Consequently, it is not possible to have at the same time, of one and the same object, both "science" and "opinion": "simul enim haberet quis notitiam quod aliter et non aliter sese habere contingat unum et idem" (ibid., 38 ff.). St. Thomas opposes "probabilitas" to "probatio demonstrativa" (Sum. Theol., 1a-2a, q. 105, a. 2 ad 8). Probability is a degree of human knowledge, inferior to certainty: it entails "opinion," that is, true adherence and assent to a determinate proposition, but with fear that the opposite proposition may be true: "Per huiusmodi processum (rationis) quandoque... fit fides vel opinio vel probabilitas, propter probabilitatem propositionum ex quibus proceditur, quia ratio totaliter [this last term is explicitly abandoned by St. Thomas in other texts: cf. De verit., q. 14, a. 1, c.] inclinat in unam partem propositionis, licet cum formidine alterius" (In Post. anal., I, lect. 1a). In opinion, therefore, although assent is given, it is not definitive: "non terminatur intellectus ad unum, quia semper remanet metus in contrarium" (In III Sent., dist. 23, q. 2, a. 2, sol. 1; cf. Sum. Theol., 1a, q. 79, a. 9 ad 4; 1a-2a, q. 67, a. 3, c.). Locke (v.) defines probability as "the appearance of a concordance or discordance between two ideas," founded on proofs "whose connection is not constant and immutable, or at least is not perceived to be such, but is or appears such for the most part, and is sufficient to induce the mind to judge the proposition to be true or false, rather than the contrary" (Essay, IV, ch. 15, § 1). A similar definition is found in Leibniz: "If demonstration shows the connection of ideas, probability is nothing other than the appearance of this connection, founded on proofs in which no immutable connection is seen" (Nouv. ess., IV, ch. 15 § 1). In Hume probability has a purely empirical value: it arises from the greater number of cases that experience presents (or allows one to expect) for one event rather than for another; and this superiority of cases is also the measure of our persuasion or opinion (belief and opinion): where it is a question of an entirely constant cause (entirely uniform and constant in producing a particular effect), our persuasion reaches the greatest assurance (the greatest assurance): it excludes doubt of the opposite, but since it derives solely from experience it is not apodictic or "demonstrated" certainty (Enquiries concerning hum. underst., sec. 6; ed. Selby-Bigge, p. 56 ff.). For Kant "opinion is a belief insufficient both subjectively and objectively." While "in judgments deriving from pure reason - for example, in mathematics - it is not permitted to opine..., in the transcendental use of reason, opinion is too little, science is too much": of God and of the future life one possesses instead a "moral faith," that is, a persuasion that is not "logical certainty" but "moral certainty," insofar as it rests on "subjective grounds," that is, on moral feeling (Kritik d. rein. Vernunft. Transcendental Doctrine of Method, ch. 2, sec. 3; Ital. trans., II, Bari 1941, p. 611 ff.). Kantian fideism has nourished in later thought not a few currents which, tracing propositions of a metaphysical-religious order back to "feeling" or "faith," must logically recognize in them a purely probabilistic value. Outside its philosophical meaning, probability was carefully studied from the mathematical-scientific point of view with the works of Laplace (Théorie analytique des probabilités, Paris 1812; Essai philosophique sur les probabilités, ibid. 1814), of Cournot (Exposition de la théorie des chances et des probabilités, ibid. 1843), of Poincaré (La science et l'hypothèse, ibid. 1902), and of numerous others (Milhaud, von Mises, Keynes, Reichenbach). Recent scientific theories (indeterminism, relativity: Boutroux, Einstein, neopositivism; v. these entries), starting from various orders of considerations and from the fact that in a series of scientific measurements carried out several times each result presents itself slightly different from the other, hold that scientific propositions, because of the diversity of circumstances and of observation in which they are formulated, have only a greater or lesser probabilistic value; of which the "true" and the "false," in the scientific field, represent only the limiting cases. Such conclusions are made to hold particularly for the phenomena of the subatomic world, whose laws are held to have a purely statistical value.
III. DISTINCTIONS AND DEGREES OF PROBABILITY
a) First of all, mathematical p. must be distinguished from philosophical p.: the former is founded solely on the numerical relation of statistically probable cases (e.g., if 50 white balls and 50 black balls are mixed in an urn, the mathematical p. that a white ball will be drawn is exactly 50%; v. PROBABILITÀ, calcolo delle). Philosophical p., on the other hand, is founded on positive reasons - of an order not only numerical-statistical but also qualitative - that validate a fact or a proposition. Such reasons are not absent in mathematical p. (that a white ball is drawn in 50% of cases depends on a multiplicity of objective causes), but in evaluating it they are not taken into account, also because they are difficult to analyze. b) Empirical p. and rational p.: the former is founded on facts of experience and on their frequency ("frequency theory"), the latter concerns the admissibility of theoretical propositions (metaphysical-moral, etc.) that are not evident and yet are validated by solid arguments permitting a prudent assent. d) In relation to the motives, p. is intrinsic if it is founded on reasons inherent in the object itself - a probable fact or proposition -; extrinsic, if founded solely on authority (e.g., the p. inherent in a doctrine because it is defended by competent authors - cf. the already cited Aristotelian definition). It is clear that extrinsic p. implies intrinsic p., since one does not believe authority except insofar as one supposes that the authority itself is founded on positive-intrinsic reasons (hence the norm that authority must not be evaluated quantitatively but qualitatively, in relation to its proven competence). e) P. is objective or subjective according as the motives on which it is founded are considered in their real-objective value or in that which they assume in the subject, in relation to the individual conditions of knowledge. But it must be noted that to some extent the subjective element always enters into the evaluation of p. f) P. is absolute or relative according as it concerns the admissibility of a fact or proposition considered in themselves, or in relation to opposing facts and propositions, which are also probable.
The degrees of p. are measured by the solidity of the motives that found it and are referred both to intrinsic p. and to extrinsic p. Moral doctrine has classified these degrees into divisions of easy intuition: a proposition can be vix probabilis, tenuiter (leviter) probabilis (in these cases, strictly speaking, it would not seem that one should speak of a true and proper "p."), minus probabilis, probabilis, valde probabilis, probabilior (simpliciter, notabiliter, valde), probabilissima; and again: certe, dubie probabilis (probabilior). In relation to moral action, the distinction of p. into speculative (theoretical) and practical must be noted: the latter concerns the validity of an opinion to be assumed as the norm of action: practical p. does not always follow from speculative p., inasmuch as opinions that are theoretically probable cannot sometimes, for contingent reasons, be followed in practice. Moral doctrine further distinguishes the probable opinion into minus tuta, tuta, tutior: this distinction concerns the security of an opinion in relation to the safeguarding of a law or to the exclusion of a danger whether material or moral. It is clear that the "tutior" opinion can be, theoretically, less probable than the "minus tuta."
IV. THEORETICAL-PRACTICAL MEANING OF PROBABILITY
P. plays a significant part in human knowledge. Its broad domain in philosophy, in the natural sciences and in the moral sciences is due, on the one hand, to the multiform contingency of nature and of becoming, and on the other to the imperfection of human thought. Nevertheless, p. is opinion, while they represent the limits of certainty; in the general dialectic of knowledge they often also mark the way to attain it (cf. the "hypotheses" in the scientific field). From the psychological-gnoseological point of view, the at once objective-subjective character of p. must be noted. That is, p., while it is founded on the conditions and reasons inherent in the objects of knowledge, that is, is a function of the ontological-operative constitution of being, at the same time expresses the inadequacy of human knowing. This holds first of all in the theoretical order, where "opinion" or "probable judgment" indicate nothing but the imperfect degree of knowledge of a problem; but also in the empirical order, where many "probable" events are in themselves necessary and determined in their causes, and therefore are called "probable" only in relation to the uncertainty of our knowledge. Therefore Bradley's statement may be accepted: p. is neither simply subjective nor simply objective: "neither simply subjective, nor yet simply subjective" (The principles of logic, I, ch. 7, repr., Oxford 1950, p. 221).
As for the psychological nature of opinion, as was indicated above, it involves true assent, but not definitive assent because it is united with the awareness of the possibility of error (the "formido alterius" of the traditional formulas). The opinative assent, therefore, although it is rightly contrasted with doubt (v.), understood as suspension of adherence and of assent, nevertheless on the other hand implies in itself an element of doubt, insofar as it is a consciously non-definitive and non-absolute assent. Where the awareness of the possibility of error were lacking, there would be no opinion but psychologically certain assent, even if objectively unfounded.
As regards the mutual relationship of two opposed probable opinions, the general principle must be kept in mind that p.s of themselves do not cancel one another out, particularly when they are founded on motives and reasons of a heterogeneous order. The greater p. of one opinion therefore does not of itself destroy the p. of the opposite opinion, when this is founded on solid motives; and, conversely, the sure p. of one opinion precludes the certainty of the contrary opinion. The principle, applied to a probable opinion opposed to the law, is upheld particularly by the moral system of probabilism (v.).
As a norm of action, given the sociality of human knowledge, for those who are not capable of a valid judgment of their own on moral problems, extrinsic p. is sufficient. Common doctrine recognizes the practical normative value of an opinion when it is held by "serious" and truly competent authors, and is not contradicted by others of equal worth; or also, sometimes, when it is defended by a single author of exceptional significance, provided that no decisive reasons to the contrary intervene.
St. Thomas observes: "in negotia humanis non potest haberi demonstrativa probatio et infallibilis, sed sufficit coniecturalis probabilitas" (Sum. Theol., 1a-2a, q. 105, a. 2, ad 8). In effect, because of the many contingent circumstances in which human activity unfolds, a theoretical certainty regulating our acts is often impossible, and it is therefore in the practical-moral field that p. reveals its irreplaceable function as a directive of knowledge and of action.