INDUCTION. — In common language (apart from the technical meaning in the physical sciences, e.g., magnetic i.), it signifies a conjecture, a “supposition.” In philosophical language, to which the term primarily refers, i. (Gk. ἐπαγωγή, from ἐπ-ἀγω, I lead, bring) is, in general, the logical-epistemological process by which human thought ascends from particular facts of experience to universal principles or values. In this comprehensive sense, it also includes the formation of concepts from the concrete data of experience. With a more restricted meaning, which has become common in logic, it is the inference of universal propositions (relating to the cause, law, or nature of a phenomenon) from particular cases or instances: for example, the general conclusion about the medicinal properties of a substance from positive experience in some cases. In this latter sense, i. is distinguished, with technical terminology due to the Wolffian school, into complete if it proceeds from the consideration of all possible cases, and incomplete if from a partial consideration of them. It should be noted, however, that by extension the term i. is also used when the phenomenon under examination does not admit a multiplicity of cases, e.g., the rotational motion of the earth: i. is then the determination of the law, cause, or essential nature of the phenomenon through the methods of scientific observation.
Complete i., as a general statement derived from the verification of the predicate in all possible subjects (e.g., the conclusion that every species of biological organism is composed of cells, from its verification in plants, animals, and man), evidently has absolute logical value, inasmuch as it implies a total equivalence between premises and conclusion. Because of this character of logical necessity, complete i. (which, moreover, is very rarely possible in the observation of nature) presents no scientific interest or particular problems: rather than i., it may be called the limiting case of i., in which i. itself assumes substantially the meaning of deduction (q.v.), understood in its most general sense as necessary formal inference. On the contrary, incomplete i., which in itself represents a progress and an extension of knowledge, is of essential importance in the process and method of science and has given rise to significant problems in the history of philosophical thought, touching upon vital points of logic and metaphysics. It expresses, in fact, the movement of thought from the particular to the universal, from the contingency of fact to the absoluteness of principle, and is thus at once the process by which the premises of demonstration (q.v.) are put into effect, and the scattered multiplicity of experience is organized into a scientific-philosophical system of concepts and principles. Through it, therefore, the most essential emergence of human knowledge takes place, and its scope extends as far as experience itself, wherever this is posited in human knowing as the foundation of meaning and value.
I. was already inherent in the essence of the Socratic method (cf. Aristotle, Met., XIII, 4, 1078 b 27 ff.; Xenophon, Memorabilia, IV, 6, §§ 13–15), but as a simple conceptual universalization through a process of comparison between particular sensible representations and common opinions. I. was thus the path to the formation of the concept. This general sense is preserved in Aristotle, who constantly refers the origin of the universal to i.: ἐπαγωγή δὲ ἡ ἀπὸ τῶν καθ' ἕκαστον ἐπὶ τὰ καθόλου ἐφόδος (Top., I, 12, 105 a 13); ἡ μὲν δὲ ἐπαγωγή ἀρχή ἐκτὸς τοῦ καθόλου (Eth. Nic., VI, 3, 1139 b 28). In a general sense, therefore, i. also includes abstraction (ἀφαίρεσις: ibid.). But the universal to which i. leads is not only the concept but also the proposition: in this sense, i. is the inverse argumentative process of deduction and proceeds from particulars: ἐστὶ δὴ μὲν ἀπόδειξις ἐκ τῶν καθόλου, ἡ δὲ ἐπαγωγή ἐκ τῶν καθ' ἕκαστον ἐφόδος (Anal. post., I, 13, 81 a 40; cf. Anal. pr., II, 23, 68 b 13). As such, i. has in human knowledge the essential task of leading to the formulation of the principles of the syllogism (Eth. Nic., loc. cit.); if, therefore, the syllogism, as a process that deduces the particular from the universal, is, in the order of being, prior to i. (in Aristotle the universal is prius τῇ φύσει), in the order of human knowledge it precedes i. as a dialectical and investigative argumentation: δῆλον δὴ ὅτι τὰ πρῶτα ἐπαγωγή γνωρίζειν ἀναγκαῖον (Anal. post., II, 19, 100 b 3–4). A much-debated question is whether Aristotle intends to speak of complete i. or incomplete i. In a well-known passage of Anal. pr. (II, 23) he seems to require for i. a total enumeration of singulars (ἡ γὰρ ἐπαγωγή διὰ πάντα: 69 b 28) and thus to deny argumentative value to incomplete i. Yet both the examples he adduces here and elsewhere (Top., I, 2) and the expressions by which he determines the specific value and meaning of i. seem to leave no doubt that he has clearly in mind incomplete i. (of which, moreover, he made extensive use in his natural history researches). Indeed, i. is the most manifest instrument of proof, most known to sense and common to many (τοῖς πολλοῖς κοινόν), but less urgent and less effective than the syllogism (Top., loc. cit.); it is not an easy operation and requires knowledge of the characters of similarity among singular things (ibid., ch. 16); he who uses i. properly “does not demonstrate, but nevertheless shows something” (Anal. post., II, 5); from the memory of the same fact repeated many times (πολλαχῶς) arises experience (ἐμπειρία), and such experience, in which the universal is contained and made present (“the one beyond the many”), “is the principle of art and science” (ibid., ch. 15 [19]; cf. Anal. post., I, 31). Similar and analogous expressions cannot be understood of complete i., which presupposes knowledge of all particulars and as such has a demonstrative value substantially equal to that of the syllogism (cf. F. A. Trendelenburg, Elementa logicae Aristotelicae, 7th ed., Berlin 1892, pp. 111–12).
If Aristotle was not unaware of incomplete i. and its essential logical-epistemological significance, he did not, however, arrive at a formulation of the conditions for its methodical use in science. And such, it may be said, essentially remains the doctrine of i. up to Bacon. The Aristotelian definition is taken up again in Boethius (De diff.
top., II: PL 64, 1183 a D). ALBERT the Great, following ARISTOTLE, distinguishes the two kinds of syllogism (I Top., tract. 3, cap. 4), though he admits the possibility of a material reduction of one to the other (II Pr. anal., tract. 7, cap. 4). PETER of SPAIN introduces into Aristotle’s definition an element that later becomes common in logic to indicate the fundamental requirement of incomplete induction: “Induction is a process from singulars sufficiently enumerated to a universal” (Sum. logic., 5; but already ARISTOTLE in Anal. pr., I, 30, 46 a 20, had spoken of a “sufficient” observation of phenomena). ST. THOMAS, commenting on ARISTOTLE, states: “It is necessary to suppose that all things contained under some common notion have been taken; otherwise the one inducing could not conclude a universal from the singulars taken” (in Anal. post., II, lect. 4a, n. 4; cf. I, lect. 1a, 3, 8). The text would seem to attribute value only to complete induction; but in reality the term “suppose” allows us to understand that complete enumeration is to be taken in a virtual sense, inasmuch as even a partial consideration, if it refers to an essential and therefore common character of the individual, virtually amounts to a complete enumeration. In ST. THOMAS incomplete induction, even in its broadest sense as a process from the particular to the universal, is still indicated in the exposition and assimilation of Aristotle’s doctrine of induction (ἐμπειρία (experimentum: V. text cited above): “Experimentum enim est ex collatione plurium singularium in memoria receptorum”; “ex multis memoris unius rei accipit homo experimentum de aliquo” (In I Met., lect. 1a; ed. R. Cathala, nn. 15, 17; cf. in Post. anal., II, lect. 20). The legitimacy of a general conclusion in incomplete induction is explicitly affirmed by SCOTUS in a well-known passage: “...even if experience is not had of all singulars, but of many, nor always but frequently, nevertheless the expert infallibly knows that it is so always and in all, and this through that proposition resting in the soul: whatever happens as in most cases from some non-free cause is the natural effect of that cause” (In I Sent., dist. 3, q. 4, n. 9).
The value, not only more epistemological but also scientific (in the modern sense of the term), of induction, together with the fundamental lines of its method, is clearly announced in F. Bacon. For science, “the only hope lies in true induction” (Nov. Org., I, aph. 14). But the induction truly useful to science is not that which proceeds “by simple enumeration,” without taking into account contrary cases and thus “yields precarious conclusions and exposes itself to the danger of contradictory instances” (ibid., aph. 105); scientific induction must proceed “by eliminations and exclusions (per exclusiones ac rejectiones) and thus arrive at affirmative conclusions after as many negative ones as necessary” (ibid.). Bacon reproaches the ancients for having too readily generalized from a few affirmative instances, later forcing the facts to fit into pre-established conclusions (ibid., aph. 125). The true method of induction must unfold in three essential moments: a) tables of positive instances (tabulae praesentiae), which note the various cases in which the fact or phenomenon occurs; b) tables of negative instances (tabulae absentiae), which note similar cases in which the fact does not occur; c) tables of quantitative variations (tabulae graduum), which describe the cases and circumstances in which the fact varies in intensity, both in the same subject and in different subjects (ibid., II, 10 ff.). Through this method (the literate experience, i.e., written, noted: ibid., I, 101-103), and, where possible, by means of “prerogative instances” or privileged cases, in which the phenomenon occurs under entirely new and singular circumstances, or does not present itself under usual circumstances, Baconian induction aimed at the determination of the “form,” i.e., the internal structure of things, from which the various effects proceed (ibid., II, aph. 1). Bacon, however, did not provide a philosophical theory of induction, nor did he discuss the problem of how the general conclusion is justified from an incomplete enumeration. The essential lines of the method of scientific induction (beyond its sagacious application in experimental research) are also indicated by Galileo (cf. Opere, ed. naz., IV, Florence 1865, p. 27): he explicitly affirms that only incomplete induction has value in science: “induction, if it were to pass through all particulars, would be impossible or useless; impossible if the particulars were innumerable; and if they were numerable, considering them all would render the conclusion useless, or, to put it better, nullify the conclusion by induction” (op. cit., VI, p. 701). From Galileo, it can be said that induction, as the handmaid of experiment, becomes the classical instrument of physical research. The definitive theorization of its method is due to J. Stuart Mill. For Mill, induction is “the operation of the mind by which we infer that what we know to be true in one or more particular instances is also true in all cases that resemble it in certain definable respects” (System of Logic, III, ch. 2, p. 333, § 1); it is not properly in “complete” induction, nor in the simple description in terms of a complex fact, as, for example, in the case of someone sailing along a coast and finding himself back at the starting point and “concluding” that it is an island. True induction is an extension, a generalization of experience (ibid., ch. 3, 354, § 1): such a generalization, which is based on the principle of the constancy of the order of nature, or, which is the same, on the law of causality as constant succession, is not legitimated by the mere constatation of many positive cases (such is induction per enumerationem simplicem), which notes the fact but does not proceed to an examination of the fact; it is necessary, in addition, to have the certainty that there are no contrary cases. To this end are ordered the four methods of experimental research that integrate Bacon’s three “tables”: a) method of agreement: if two or more cases of the phenomenon under examination have in common only one among many circumstances, that is the cause of the phenomenon; b) method of difference: if a case in which the phenomenon occurs and a case in which it does not occur differ in only one circumstance, present in one case and absent in the other, that is the cause (or at least part of the cause) of the phenomenon; a variant of these two methods is the joint method of agreement and difference: if two or more cases in which the phenomenon occurs have in common only one circumstance, and two or more cases in which it does not occur have in common only the absence of the same circumstance, this is the cause (or part of the cause) of the phenomenon; c) method of residues: having subtracted from a given phenomenon that part which is already known as the effect of a certain antecedent, what remains of the phenomenon is the effect of the remaining antecedents; a typical example was the discovery of the planet Neptune (1846): certain irregularities observed in the motions of Uranus and not attributable to known causes led Le Verrier to suppose the existence (and also, approximately, the position and mass) of a new planet, later confirmed by direct observation; d) method of concomitant variations: every phenomenon that undergoes variations whenever another phenomenon varies in a certain way is a cause or an effect of that phenomenon, or at least is connected to it by some causal fact: such, for example, is the dilation of bodies always associated with heat and its variations, or the retardation of motion that varies with the variation of friction. Mill’s formulas (which, like Bacon’s “rules,” are in part spontaneously applied even in common experience; and therefore it is a purely polemical attitude to attribute to the ancients only induction “per enumerationem simplicem”) represent the most complete definition of the scientific method of induction (see the detailed exposition, ibid., ch. 8, p. 448 ff.).
But, beyond being a problem of scientific method, induction presented itself, especially with the rise of empiricism, as essentially a philosophical problem, bound up with the general question of the value of human knowledge.
The philosophical problem of induction has a twofold aspect: epistemological and logical, according as induction itself is considered in its general (and fundamental) function as a process of knowledge from concrete-sensible data to universal conceptualization, or instead as the inference of a general proposition from its constatation in some particular cases. Under the first
The problem of induction (ì.) is the same as the problem of the origin of the concept, that is, of the derivation in human knowledge of necessity and universality. A fundamental tenet of empiricism is that such necessity and universality cannot derive from experience. According to Hume, there is no certainty in experience except for what is given at a precise moment in time (Enquiring concerning human underst., sect. 4a, part 2a, Italian trans. by G. Prezzolini, Bari 1927, p. 39; cf. Treatise, I, part 3a, sect. 2 ff.). This assertion is echoed by Kant: “Experience teaches us indeed that a thing is made in this or that way, but not that it could not be otherwise” (Kritik d. r. Vernunft, Intr., § 2; Italian trans. by G. Gentile, Bari 1940, p. 39); the necessity of conceptual knowledge, which is an undisputed presupposition of Christianity, is consequently referred by Kant to the a priori organization of thought. The derivation of the universal from experience (and thus from the ì.: cf. St. Thomas, In Post. anal., I, lect. 30) is, however, in a certain sense, essential to the Aristotelian-Thomistic system: through the repetition of sensory presentations of a given object and their persistence in memory (the experimentum), the singular datum is determined in its ontological unity, and thus, by the intuitive-abstractive power of thought, emerges in the intellectual act as a universal value. This doctrine has a profound correspondence with the actual condition of human knowing. It is further clarified by the virtual objectivity attributed, within the same Thomistic thought, to the agent intellect (cf. Sum. Theol., 1a, q. 84, a. 5; C. Gent., I, III, cap. 47; De ver., q. 11, a. 1, 3).
Indeed, it must be said that while the sensible datum is capable of grounding a general representation, it could not, however, constitute an absolute necessity of value unless the intellect itself were imbued with a relation to a higher objective necessity. It is thought, as a transcendental relation to being—which is in itself positivity and necessity—that contains the roots of absolute universality and necessity: that universality which may be called foundational and which flows back, according to the finite participations and determinations of being, into the concrete data of experience. The ì. thus presents itself as the emergence or ascent of objects and contents of experience to the universality and necessity of being, according to the determinations that such universality assumes in their own ontological concreteness. Consequently—and in this direction lies the overcoming of both empiricism and rationalism—the derivation of the universal is not purely empirical but also transcendental, inasmuch as thought itself, as a relation to being, is already in a metaphysical situation of virtual transcendence in comparison to the individual moments of experience.
The logical problem of the ì. was already clearly formulated by ancient skepticism in the dilemma: either the ì. claims to conclude from all particulars, which is an impossible task since particulars are infinite, or it concludes from only some of them, in which case it is unreliable “since it is possible that some particular omitted in the ì. may contradict the universal” (Pyrrh. hypoth., II, 15). Jevons, Goblot, Bolzano, Hamilton, Windelband, and indeed the entire empiricist school, based on this dilemma, recognize in the ì. only a purely probabilistic value. It must first be affirmed that the ì. is not to be reduced to syllogism (a reduction attempted first by Wolff: Logica, part 1a, sect. 4a, ch. 6, and later accepted by many others), nor is it to be understood as a formal logical process analogous to syllogism. Even as an “argument,” the ì. is an emergence from the particular to the universal. Its logical antinomy lies precisely in the transition from some cases to a universal conclusion: one has not made, nor can one make, experience of all individual bodies that exist, and yet the general formula is accepted: all bodies are heavy. As a purely formal inference, the ì. would not be legitimate. From this difficulty arises the problem of the “foundation” of the ì. Such a foundation cannot be of a logical order but must necessarily be either empirical, metaphysical, or a synthesis of both.
The foundation of the ì. in pure experience is characteristic of empiricism: according to Hume, the extension of experience is based on a psychological habit by which one expects in the future what one has experienced in the past; for Stuart Mill, the principle governing the ì.—“that there is a constant causality in nature”—is itself derived from experience and is thus the product of previous ì.s (op. cit., III, ch. 3, p. 355, § 1). The metaphysical foundation, on the other hand, is characteristic of rationalism and idealism: rationalism transfers the order and necessity of thought into nature, while in idealism the very problem of the ì. is dissolved insofar as nature is posited as a function of spirit and its becoming.
Whereas the empirical foundation ends in the negation of the legitimacy of the inductive process, the metaphysical derivation is a systematic position unsupported by the phenomenology of human knowing. It must be held that the ì. cannot be founded on a pure rational principle, e.g., “the same causes produce the same effects”; for it is indispensable to know that there actually exist identical causes or permanent causes. It is therefore correct that the ì. is based on the principle, derived from experience, that the order of nature (of beings) is constant (already explicit in St. Thomas: Sum. Theol., 1a, q. 19, a. 4, c.; q. 41, a. 2, c.). But the very breadth of experience that attests to the constancy of being and the activity of the world is validated by the metaphysical consideration that recognizes in being (in every being) an essential ontological determination and thus an immanent principle of operative determination: “each thing operates according to the mode in which it is” (Sum. Theol., q. 75, a. 2).
The principle of the uniformity of nature thus admits of a metaphysical justification derived from the principle of the determination of being. And this principle—which ultimately relates to an absolute rational Value, the principle of all being—is the general presupposition of the possibility of knowledge, action, and human history: the metaphysical indeterminacy of reality would dissolve all firmness in being and thus every possibility of truth and action. This does not, however, negate the margin of probability that must accompany the inductive process in the knowledge of nature. Not only in the realm of human reality (history) does the ì. present a radical uncertainty due to the principle of freedom, in which action originates as an undefined possibility, but even in nature the ì. becomes more dialectical insofar as it reaches the more complex and profound phenomena of being. Where, as in the subatomic world, the vast interaction of cosmic causes can at any moment modify the effect, the function of the ì. is reduced to a mere determination of statistical probability, more or less broad. Indeed, since the operative process of beings is in reality bound up with the entire dynamism of the universe, one may generally admit with Broutoux (L’idea di legge naturale, Italian trans. by A. Pass, Verona 1940, pp. 252–53) an inadequacy of physical laws to constrain reality and time within rigid schemes. This is of no importance either for science or for action, to which the inductive process confers a solidity of affirmations and explanations that finds in the grand successes of science itself the clearest and most enduring confirmation.
eliminating every possibility of doctrinal deviation.
The Church’s infallibility differs from that of God, from which it derives by participation; it does not imply either the manifestation of new truths or a supernatural impulse to write, but rather a divine assistance (attributed to the Holy Spirit) that guides all ecclesiastical teaching through both negative and positive interventions, preventing the definitive formulation of false judgments and directing the minds of the teaching body toward the correct understanding and development of revealed truth. Through this assistance, the believer’s infallibility is also guaranteed, as he adheres to the doctrine proposed to his faith by an infallible magisterium. Divine assistance does not exclude human means of investigating revealed truth and its developments, but presupposes them, promotes them, and preserves them from deviations in their final outcome. Infallibility is therefore not the omniscience, impeccability, or habitual thaumaturgy of the Pope, nor the hypostatic union of all bishops with the Holy Spirit, as is not infrequently presented by Protestants.
The Church’s infallibility, in general, has never been formally defined as a dogma, but it must undoubtedly be admitted as a revealed truth proposed by the ordinary and universal magisterium; it is presupposed by the Vatican Council in the definition of the Pope’s infallibility (const. Pastor aeternus, ch. 4; Denz.-U., 1839); it can be established with absolute certainty from an examination of New Testament texts and early tradition.
1) In the New Testament, the Church appears invested with the same mission and power as Christ. Now, Christ’s mission and power had as their object the preaching of the doctrine received from the Father: cf. Mt. 18:18; 28:18-20; Mk. 16:15-16; Lk. 10:16; Rom. 1:5; 1 Cor. 1:17; 2 Cor. 5:20; 10:4; 1 Tim. 1:19; 1 Jn. 2:24; 2 Jn. 1:10.
2) The texts of Christ’s solemn investiture of the Apostles with power (Mt. 28:18-20 and Mk. 16:15-16), beyond the general mission to teach with the command to “make disciples,” promise effective assistance, whose temporal limits are the same as the duration of the present world. “I am with you” is, in biblical usage, a divine assurance of the successful outcome of the mission entrusted by God to His messengers, a mission that, in the cited texts, is the preservation and oral teaching of the Gospel.
3) Jesus Christ threatens eternal damnation to those who do not believe in apostolic preaching (Mk. 16:16); a threat that would be absurd if the Church’s magisterium could be conceived as being in disharmony with the doctrine of the Master.
4) Jesus also indicated the supernatural cause of infallibility, pointing to the Spirit of truth, which, possessed and operative, would assist the Apostles as His witnesses and interpreters of His doctrine, enlightening them, sanctifying them with every truth, making them one with Him and the Father (Lk. 24:48-49; Jn. 14:16 sqq., 26; 15:26; 16:7-14; 17:17; Acts 1:8 and 2:4).
5) The Apostles, moreover, appear fully aware of their infallibility (Acts 5:32; 15:28) and transmit their powers to their successors (1 Tim. 4:11-16; 2 Tim. 2:2; Tit. 1:5) according to a law of succession clearly attested by St. Clement of Rome (Cor. 44:1) and already contemplated in Jesus’ promises.
6) The Fathers closest to the Apostles echo the same teaching. For St. Ignatius of Antioch, the bishops are the very doctrine of Christ, as Christ is the doctrine of the Father; to this doctrine the faithful must adhere (Eph. 3:2; cf. Philad. 3:2). For St. Irenaeus, apostolic doctrine, transmitted through the succession of bishops, is the criterion for discerning truth from heresy (Adv. haer., 1.10.1; 3.3.1; 3.4.1).
Yet the episcopal college, heir to the powers of the apostolic college, is infallible both in solemn conciliar definitions (v.) and in its ordinary and universal magisterium (v. CHIESA), exercising its teaching mission only in subordination to its head, according to the divine institution of the primacy, which thus encompasses, in its very nature, the infallibility attributed inseparably from the universal magisterium. The Pope is, in fact, the sole immediate or direct subject, or the source, with respect to the Church, of infallibility, according to the theological speculation prevalent today, hinted at even in a text of the *Mystici Corporis* (AAS, 35 [1943], p. 216), and already formulated thus by the Passionist theologian Giacomo del S. Curto di Maria: “The Pope is not infallible by himself, but from Him, Jesus; nonetheless, the Pope is infallible in himself, just as Jesus Christ is infallible in Himself. Whereas the Church is not infallible either by herself or in herself, but by Christ through the Pope.” The conclusion follows from the universal scope of papal teaching, for where ecumenical teaching is exercised with its full intensity, there too is the exercise of infallibility. For this reason, the biblical texts that establish the primacy also bear witness to papal infallibility. Thus, in Mt. 16:18-19, the three parallel images of foundation, keys, and binding and loosing, functioning as Christ’s vicar and ratified in his decisions by Heaven, assign to Peter, along with other sovereign powers, that of the supreme magisterium. In Jn. 21:15-17, the charge to “feed my sheep” is even more explicitly indicated. A specific indication of papal infallibility is found in Lk. 22:31-32. Jesus has just responded to the Twelve’s disputes over primacy, inculcating in them the new spirit of authority (24-27), when He entrusts to Peter, repeating earlier designations, the office of confirming all His brethren in the faith. This seems an application of Mt. 16:18-19, a particular instance of the struggle there announced between the Church and the powers of hell. Many Fathers and the Vatican Council have seen in this text a clear affirmation of papal infallibility (const. *Pastor aeternus*, ch. 4; Denz.-U., 1836).
S. Irenaeus in a celebrated passage (Adv. haer., 3, 3, 2) openly affirms the supreme magisterium of the Roman Church, personified in its bishops, as the root of the doctrinal unity of the universal Church. They embody the qualities of witness, guardian, and organ of the apostolic Tradition, serving as the most perfect criterion of truth against all heresies, comparable to the consensus of all the apostolic Churches together (v. C. Mohrmann, A propos de Ireneo, 3, 3, 2, in Vigiliae Christianae, 3 [1949], pp. 57-61: a new interpretation of the passage, which enhances its probative value). Tertullian is compelled, albeit reluctantly, to acknowledge that the Bishop of Rome is recognized as the arbiter of ecumenical communion and orthodoxy (Adv. Prax., 1).
The practice of appealing to Rome at the emergence of any threat to the faith is particularly well attested from the earliest centuries of Christianity. Numerous and decisive are the papal interventions against heresies, such as the cases of St. Dionysius of Alexandria, Pelagianism, Nestorianism, and Monophysitism, with the decisions of the popes St. Innocent I, St. Zosimus, St. Boniface I, St. Celestine I, and St. Leo the Great, as well as the formula of St. Hormisdas, among the most well-known and demonstrative (Denz-U, 100, 109, 110, 112, 149, 171).
After a recognition in the West that can be considered almost uninterrupted, the Second Council of Lyon (1274) proclaims the pope as “the definitive judge of matters concerning the faith” (Denz-U, 466). The conciliarist interlude (v. CONCILIARISM) seemed closed when the Council of Florence (1445) addressed the pope as “the supreme Doctor of all Christians,” endowed with full authority (Denz-U, 694). However, the error spread widely (v. H. Jedin, Geschichte des Konzils von Trient, I, Brescia 1949, pp. 34-53), and Gallicanism (v.) persisted along its perilous path, affirming that the pope is not infallible “nisi Ecclesiae consensus accesserit” (Denz-U, 1325). It fell to the Vatican Council (1870) to solemnly reaffirm Tradition and to clarify the meaning of the term *ex cathedra*, thereby excluding exaggerations and uncertainties among some of the infallibilists (Denz-U, 1832-40).
The *ex cathedra* definition, the only case in which the papal infallibility is strictly speaking exercised, occurs only when the pope pronounces a judgment that is manifestly definitive and intended for the whole Church, exercising his full doctrinal authority.
The pope’s infallibility is a personal prerogative, not because as a private person he is personally preserved from error or heresy—a matter still open to discussion—but in the sense that each successor of Peter is infallible without exception, and not merely the series or the Roman See considered as a moral entity, as certain Gallicans claimed. It might also be described as personal in a more positive sense, to exclude any notion of its being shared: it cannot, in fact, be delegated. It has been and is sometimes still called “absolute” and “separate,” terms rejected by many, which are only admissible in their historical function of excluding the condition of the Church’s consent, under which condition (which would fundamentally diminish it) even the last Gallicans were willing to accept it, though they attempted in vain to introduce at least a hint of it in the Vatican definition.
The Vatican Council, however, did not define the object of papal infallibility, limiting itself to declaring it identical to that of the Church’s infallibility, which some Fathers would have preferred to see defined first. On this subject, however, there are precise indications from the ordinary magisterium and a well-developed doctrine among theologians.
It must be held as a matter of faith that the Church is infallible in teaching what is explicitly or implicitly revealed, according to the most common understanding of “explicit” and “implicit” in contemporary theology. For the custody, explanation, and proclamation of the very doctrine of the Divine Master was entrusted to the apostolic magisterium. The imperfection of this object is clearly indicated in the very terms that guarantee infallibility: within its scope are “all the truths” revealed to the Apostles by the Holy Spirit (Jn. 14:26; 16:13), “all the preaching” of Jesus (Mt. 28:20), “the words of Jesus that came from the Father” (Jn. 17:6-8), and “the Gospel of the Kingdom” (Mt. 24:14; 26:13). Logically included is the Church’s infallibility in condemning heresy (v.), which contradicts revealed Truth. By this prerogative, the Church can also infallibly determine the canon of Sacred Scripture, declare the extent of biblical inspiration, define the sense of a dogmatic biblical text, and select the appropriate dogmatic formula, etc. Most modern theologians refer to this as the object of the *primary* or *proper* infallibility.
The *secondary* object includes those truths that are generally termed “connected truths.” These are not formally contained in Revelation but are so closely linked to it that they can be said to be virtually contained within II. Error regarding these applications of revealed principles would shake the very foundations on which they rest and endanger faith itself. Therefore, connected truths must be considered as present in the mind of the Divine Master at the moment of communicating His Revelation, just as in every intelligent being the immediate consequences of its affirmations are logically present.
The most significant classes of these connected truths are theological conclusions (v.), dogmatic facts (v.), canonizations (v.), and ecclesiastical legislation. The connection of canonization with Revelation is evident from the fact that it is nothing other than the concrete application of two articles of faith: that on the cult of the saints (v.) and that on the communion of saints (v.), as well as the Christian religious custom itself, since the canonized are proposed as models of perfect virtue. Regarding legislation, the link is revealed in its dependence on revealed moral principles, which are here interpreted and applied for the whole Church. A particular case is constituted by the solemn approval of religious orders in the strict sense. Through this, the Church declares that a particular way of life is a sure path to Christian perfection. However, infallibility does not extend to a judgment on the greater or lesser prudence in the promulgation of universal ecclesiastical laws.
The principle of infallibility regarding the secondary object is supported by the unanimous consensus of Catholic theology; indeed, some theologians, inspired by the breadth of Christ’s promises, would elevate its certainty to the level of divine faith (hints of ecclesiastical magisterium on this matter in Denz-U, 1698, 1722, 1817, 2005). The assent owed by the faithful to definitions concerning connected truths is generally called ecclesiastical faith. However, a strong theological current, whose leading representatives include Schifini, Gardell, Tuyaerts, Marin-Sola, Beraza, and Stolz, seeks to abolish, along with the distinction between the primary and secondary objects of infallibility, the very notion of ecclesiastical faith itself. Instead, they propose a single object—the revealed doctrine, however revealed—which, after a definition by the Church, must be held with divine-catholic faith.