PROBABILITY. – In the sense commonly attributed to it today, a fact is probable when, although it does not present itself as absolutely certain, it may nevertheless be presumed to have occurred or to be about to occur; and a proposition is probable when it is not fully evident but presents good reasons for being accepted. P. is therefore the admissibility of a fact or proposition that is not entirely certain, together with the objective reasons on which it is founded.
I. TERMINOLOGY
P. (Greek πιθανότης) derives from probatio, meaning proof, experiment, and also approval, demonstration. In ancient usage, therefore, probable means: a) that which may be held or accepted, because it ordinarily happens or is generally admitted (“Probabile est id quod fere fieri sole, aut quod in opinione positum est”: Cic., Invent., I, 29, 46); b) that which is reasonable, right, worthy of approval (“probabilis orator, cuius ingenium et eloquentia probari ac placere debet”: id., Brut., 76, 263 c); c) finally, that which is “verisimile” (cf. red. Wahrscheinlichheit), with or without an 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, chap. 1, 100 b 21 ff.; cf. chap. 10 [8] 104 a 6 ff.). «What is probable is either probable and credible in itself (for intrinsic reasons), or it is shown to be such by other reasons» (Rhet., I, chap. 2, 1356 b 26 ff.). But «not everything that seems probable is also probable» (Top., I, chap. 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 may also be—and is admitted to be able to be—otherwise» (Anal. post., I, chap. 33, 89 a 2–3). Consequently, it is not possible to have simultaneously of one and the same object «science» and «opinion»: «simul enim haberet quis notitiam quod aliter et non aliter sese habere contingat unum et idem» (ibid., 38 ff.). St. Thomas contrasts «probabilitas» with «probatio demonstrativa» (Sum. Theol., 1a-2a, q. 105, s. 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 might be true: «Per huiusmodi processum (rationis) quandoque... fit fides vel opinio vel probabilitas, propter probabilitatem propositionum ex quibus proceditur, quia ratio totaliter [the latter 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, JOHN (v.) defines probability as «the appearance of an agreement or disagreement between two ideas», founded on proofs «whose connection is not constant and immutable, or, at least, is not perceived as such, but is or appears to be so for the most part, and is sufficient to induce the mind to judge that the proposition is true or false, rather than the contrary» (Essay, IV, chap. 15, § 1). An analogous definition is found in Leibniz: «If demonstration makes the connection of ideas visible, probability is nothing other than the appearance of this connection, founded on proofs in which no immutable connection is seen» (Nanc. ess., IV, chap. 15 § 1). In Hume, probability has a purely empirical value: it arises from the greater number of cases that experience presents (or enables one to expect) for one event rather than another; and this superiority in the number of cases is also the measure of our persuasion or opinion (belief and opinion): when it concerns a cause that is entirely constant (entirely uniform and constant in producing a particular effect), our persuasion reaches the greatest assurance (the greatest assurance): it excludes doubt of the contrary, but since it derives solely from experience, it is not apodictic or «demonstrated» certainty (Enquiries concerning hum. underst., sect. 6a; ed. Selby-Bigge, p. 56 ff.). For Kant, «opinion is a belief insufficient both subjectively and objectively». Whereas «in judgments deriving from pure reason—for example, in mathematics—it is not permissible to opine..., in the transcendental use of reason, opinion is too little, science is too much»: of God and of the future life, on the other hand, one possesses a «moral faith», that is, a conviction which 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, chap. 2, sect. 3a; Italian trans., II, Bari 1941, p. 611 ff.). Kantian fideism nourished in later thought not a few currents which, by referring propositions of a metaphysical-religious order to «feeling» or to «faith», must logically recognize in them a purely probabilistic value. Apart from its philosophical meaning, probability was carefully studied from the mathematical-scientific point of view in the works of Laplace (Théorie analytique des probabilités, Paris 1812; Essai philosophique sur les probabilités, there 1814), Cournot (Exposition de la théorie des chances et des probabilités, there 1843), Poincaré (La science et l'hypothèse, there 1902), and numerous others (Milhaud, von Mises, Keynes, Reichenbach). Recent scientific theories (indeterminism, relativity: Boutroux, Einstein, neopositivism; V. these entries), proceeding from various considerations and from the fact that in a series of scientific measurements repeatedly carried out every result appears slightly different from the others, hold that scientific propositions, because of the diversity of circumstances and observations in which they are formulated, have only a greater or lesser degree of probability; in the scientific field, «true» and «false» represent only its limiting cases. These conclusions are applied particularly to the phenomena of the infratomic world, whose laws are held to possess a purely statistical value.III. DISTINCTIONS AND DEGREES OF P
a) First of all, mathematical probability must be distinguished from philosophical probability: the former is based solely on the numerical ratio of statistically probable cases (e.g., if 50 white balls and 50 black balls are mixed in an urn, the mathematical probability that a white ball will be drawn is exactly 50%; V. PROBABILITÀ, calcolo delle). Philosophical probability, on the other hand, is founded on the positive reasons—of not only a numerical-statistical but also a qualitative order—that validate a fact or proposition. Such reasons are not absent from mathematical probability (the fact that a white ball will be drawn in 50% of cases depends on a multiplicity of objective causes), but they are not taken into account in evaluating it, also because they are difficult to analyze. b) Empirical probability and rational probability: the former is based on facts of experience and on their frequency (“theory of frequency”), while the latter concerns the admissibility of non-evident theoretical propositions (metaphysical-moral, etc.) that are nevertheless validated by sound arguments permitting prudent assent. d) In relation to its grounds, probability is intrinsic when it is based on reasons inherent in the object itself—whether a probable fact or proposition; it is extrinsic when based solely on authority (e.g., the probability inherent in a doctrine because it is defended by competent authors—cf. the already cited Aristotelian definition). It is clear that extrinsic probability implies intrinsic probability, since one believes an authority only insofar as one supposes that the authority itself is founded on positive intrinsic reasons (hence the principle that authority should not be evaluated quantitatively but qualitatively, in relation to its demonstrated competence). e) Probability is objective or subjective according as the grounds on which it is based are considered in their real-objective value or in the value they assume in the subject, in relation to the individual conditions of knowledge. It must be noted, however, that to some extent the subjective element always enters into the evaluation of probability. f) Probability is absolute or relative according as it concerns the admissibility of a fact or proposition considered in itself, or in relation to opposing facts and propositions, which are themselves probable.The degrees of probability are measured by the solidity of the grounds on which it rests and refer equally to intrinsic and extrinsic probability. Moral doctrine has classified these degrees into divisions that are easy to understand: a proposition may be vix probabilis, tenuiter (leviter) probabilis (in these cases, strictly speaking, it would not seem appropriate to speak of genuine “probability”), minus probabilis, probabilis, valde probabilis, probabilior (simpliciter, notabiliter, valde), probabilissima; and also: certe, dubie probabilis (probabilior). In relation to moral action, the distinction between speculative (theoretical) and practical probability should be noted: the latter concerns the validity of an opinion for adoption as a norm of action. Practical probability does not always follow upon speculative probability, since theoretically probable opinions cannot at times, for contingent reasons, be followed in practice. Moral doctrine further distinguishes the probable opinion as minus tuta, tuta, tutior: this distinction concerns the safety of an opinion in relation to safeguarding a law or excluding a danger, whether material or moral. It is clear that the “tutor” opinion may, theoretically, be less probable than the “minus tuta” opinion.
IV. THEORETICAL-PRACTICAL SIGNIFICANCE OF P
P. plays a significant role in human knowledge. Its broad domain in philosophy, the natural sciences, and the moral sciences is due, on the one hand, to the manifold contingency of nature and becoming, and, on the other, to the imperfection of human thought. Nevertheless, p. is opinion, while representing the limits of certainty; in the general dialectic of knowledge, they at the same time often mark the path toward attaining it (cf. the “hypotheses” in the scientific field). From the psychological-gnoseological point of view, the simultaneously objective-subjective character of p. should be noted. That is, while p. is founded on the conditions and reasons inherent in objects of knowledge, and is therefore a function of the ontological-operative constitution of being, it at the same time expresses the inadequacy of human knowing. This applies first of all in the theoretical order, where “opinion” or “probable judgment” indicates only 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 are therefore called “probable” only in relation to the uncertainty of our knowledge. Bradley’s assertion may therefore be accepted: p. is neither simply subjective nor simply objective: “neither simply subjective, nor yet simply subjective” (The principles of logic, I, chap. 7, repr., Oxford 1950, p. 221).As for the psychological nature of opinion, as indicated above, it entails true assent, but not definitive assent, because it is joined to awareness of the possibility of error (the “formido alterius” of the traditional formulas). Opinionative assent, therefore, although doubt (v.), understood as the suspension of adherence and assent, nevertheless on the other hand implies within itself an element of doubt, insofar as it is consciously non-definitive and non-absolute assent. If awareness of the possibility of error were absent, there would be not opinion but psychologically certain assent, even if objectively unfounded.
With regard to the mutual relationship between two opposed probable opinions, the general principle should be kept in mind that p. do not in themselves cancel one another out, particularly when they are founded on motives and reasons of heterogeneous kinds. The greater p. of an opinion does not, therefore, in itself destroy the p. of the opposed opinion when the latter is founded on solid motives; and, conversely, the assured p. of an opinion precludes the certainty of the contrary opinion. The principle, applied to a probable opinion opposed to the law, is asserted particularly probabilism (v.).
As a norm of action, given the social nature of human knowledge, for those who are not capable of forming a valid judgment of their own on moral questions, extrinsic p. is sufficient. The common doctrine recognizes the practical normative value of an opinion when it is held by “grave” authors who are truly competent, and is not contradicted by others of equal standing; or also, at times, when it is defended by a single author of exceptional authority, provided that no decisive reasons to the contrary intervene.
s. Tommaso 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 fact, owing to the many contingent circumstances in which human activity unfolds, a theoretical certainty regulating our acts is often impossible; it is therefore in the practical-moral sphere that p. reveals its irreplaceable function as a guide to knowledge and action.