Hypothesis

HYPOTHESIS. - A logical term indicating a proposition laid down as the foundation of a reasoning in the search for the explanation of a fact, or also as a doubtful but probable conjecture of an unknown cause or reality, that is, as an anticipation of the truth, which must be further confirmed or disproved. The use of h. is part of ordinary life and of common reasoning and has assumed great importance in the modern scientific method.

I. HISTORY

Aristotle speaks repeatedly of the logical use of the hypothesis: the ἀνδῶσας (Lat. suppositio), as distinct from axioms (v.), definitions (v.) and postulates (v.), is a proposition assumed as a principle of demonstration, which affirms or denies something, without its being demonstrated or imposing itself on the mind by immediate and necessary evidence, even though it appears plausible or verisimilar (Anal. Post., I, 2, 72 a 14-24; 10, 76 b 23-29). The hypothesis can give rise to true demonstration and to science properly so called only if it is demonstrated in a higher science or if it appears immediately true, following the formulation proposed by the teacher (ibid., 2, 71 b 19-25; Top., I, 1, 100 a 27-29). However, even in the opposite case it is indirectly useful to science in that it forms the premises of a "dialectical" reasoning, which, by developing the premises of opposite probable or verisimilar propositions, constitutes an effective instrument in the search for the true and the false and often the only way to arrive at establishing the certain premises of the individual sciences (ibid., 2, 101 a 34-b 4). The use of dialectical argumentation in Aristotle is anything but rare; the best-known example is that of the celestial spheres, accepted by Aristotle on the authority of Eudoxus and Callippus, as a reasonable explanation of the apparent motions of the stars, but not a necessary one (Met., XII, 8, 1074 a 14-17).

In post-Aristotelian philosophical thought, and particularly in Scholasticism, attention is directed predominantly to apodictic demonstration and to the conditions of its premises; nevertheless the scientific usefulness of the hypothesis as a probable conjecture in the search for the explanation of a fact is recognized. St. Thomas, speaking of the aforementioned Aristotelian hypotheses, affirms that "although, these hypotheses being posited, a solution of the problem seems to be had, nevertheless it is not necessary to say that these hypotheses are true, since perhaps the astronomical phenomena can be explained in another way still unknown to humanity. Aristotle, however, makes use of such hypotheses as if they were true" (II De caelo, lect. 17). He adds that such arguments founded on probable hypotheses may also be used in sacred science to show the congruity of the mysteries of the faith (Sum. Theol., 1ª, q. 32, a. 1, ad 2).

The conscious use of hypotheses and its organic insertion into the scientific method goes back to Galileo, who must be considered the creator of the hypothetical-deductive experimental method, consisting of four distinct phases: observation of the facts, formulation of the hypotheses expressible in mathematical formulas or realizable in mechanical models, deduction of the consequences, experimental verification of these and therefore indirect confirmation of those (cf. A. Pastore, Il problema della causalità con particolare riguardo alla teoria del metodo sperimentale, I, Turin 1921, ch. 7, pp. 119-140). Galileo's hypothesis therefore had characteristics quite distinct from the hypotheses of the naturalists of decadent Scholasticism, which consisted in the affirmation of occult qualities, simple nominalistic palliatives devoid of scientific usefulness. It is against such hypotheses, called "metaphysical" in a disparaging sense, and not against all scientific hypotheses, that Newton's famous phrases must be understood: "Hypotheses non fingo. Quidquid enim ex phaenomenis non deducitur, hypothesis vocanda est, et hypotheses seu metaphysicae, seu physicae, seu qualitatum occultarum seu mechanicae, in philosophia experimentali locum non habent" (Philosophiae naturalis principia mathematica, Scholium generale, Amsterdam 1713, p. 487; cf. E. Meyerson, Identité et réalité, Paris 1912, pp. 46 and 510-15).

Positivism attempted to oppose the ever vaster employment, in science, of the hypothesis in the Galilean sense. Comte already affirmed that many scientific hypotheses of his time reintroduced into science chemical entities, with the search for occult causes of phenomena and for universal agents; for Comte the hypothesis must be reduced to the simple probable anticipation of a fact or of a universal law (Cours de philosophie positive, II, Paris 1835, pp. 335-354). The opposition became more pronounced toward the end of the last century, giving rise to the well-known polemic between mechanists and energetists. On the one hand the empiricocriticist and conventionalist school, headed by E. Mach, H. Poincaré, H. Leroy, having rejected the Aristotelian distinction of axioms and postulates, and the absolute logical value of the principles of science and of the fundamental inductive laws, places the hypothesis as a free convention at the basis of all experimental and rational science, physics and mathematics, holding as the only criteria of choice economy, convenience, practical utility. On the other hand, even more moderate authors, such as P. Duhem, W. Ostwald, deny all ontological and causal value to hypotheses as anticipations of truth and reality, attributing to them at most a purely heuristic value as symbolic models, mental schemas or logical syntheses of experimental laws.

Even today epistemological currents are divided on this subject; nevertheless a middle theory increasingly prevails. Many hypotheses, which positivism considered methodologically unacceptable, have definitively established themselves in science, while other hypotheses, especially those of a rigidly mechanical nature, have appeared incompatible with further scientific progress and can be regarded only as symbolic models and mental schemas. In this regard, of great importance is the method of operational definition, introduced into modern physics, which limits scientific hypotheses to the introduction of those entities alone which are definable by means of experiences at least conceptually possible, rejecting the unobservable as devoid of sense.

II. LOGICAL JUSTIFICATION OF THE HYPOTHESIS

The methodical use of the h. is a necessity for the natural sciences. Indeed, an intuitive knowledge of material reality and of the physical qualities that immediately reaches its essence is not possible for man; nor does the knowledge of one or more facts, and even of true universal laws, ordinarily suffice to identify the causes and the structure of the real, since this can generally be explained by different and partially opposed causes. It is therefore indispensable to resort as an instrument of research to h., which allow the construction of theoretical and mathematical reasonings and the progress of experimental investigations. The h. thus completes the method of science, belonging to the phase of research into the premises of the syllogism (v.) and of preparation of induction (v.).

The formulation of the h., although formally a free convention, the fruit of the researcher's genius, is not arbitrary, but subject, in a more or less rigorous measure, to certain logical requirements: 1) freedom from internal contradiction; 2) compatibility with rational and experimental truths already certainly acquired; 3) verisimilitude and aptitude for the explanation of already known physical phenomena; 4) fecundity, inasmuch as it permits the prediction of new phenomena, which experience must then check; 5) simplicity, inasmuch as it allows the explanation of a greater number of phenomena with a smaller number of hypothetical elements. The last two conditions, less exploited by the ancients but not unknown to them (Aristotle: « the best demonstration is that which makes use of a smaller number of postulates, i.e. propositions »; Anal. Post., I, 25, 86 a 33-35), carry the greatest weight in the transformation of h. into ascertained knowledge.

Such a transformation, which is the final aim of science, in general does not come about through the mere verification of consequences, even if numerous, although the h. thereby acquires a greater probability. In this case, moreover, a critical analysis of the h. is required, along with the application of the logical principle of elimination of superfluous elements, that is, of those elements which, although historically connected with the h., are logically separable from it and whose suppression has no influence on the theoretical and mathematical deduction of the consequences confirmed by experience; an element of this kind is the mechanical nature of light vibrations in Fresnel's wave theory, later eliminated by the Maxwell-Lorentz electromagnetic theory. In particular cases, however, it is possible to pass from the h. to certain knowledge. Indeed, in some cases the formulation of an h. can permit the carrying out of observations or experiments that lead to the direct ascertainment of the h.; in other cases it is possible to establish an experimentum crucis, which, from the verification of the contradictory of the consequence, allows one to ascend with certainty to the contradictory of the h.; or finally one can arrive at establishing such a convergence of probabilities and indications that, taken as a whole, it cannot have any other explanation than the truth of a determinate h. An example of the first case is the discovery of the planet Neptune, first supposed as the hypothetical cause of the perturbations observed in the orbit of Uranus, then directly observed in the predicted position; an example of the second case is radioactivity, which forced chemists to reject the h. of the indivisibility of the atom; an example of the third is the complex of experiments and verifications deduced from the molecular-kinetic h. of gases, which led Poincaré himself to affirm « les atomes ne sont plus une fiction commode... L'atome du chimiste est maintenant une réalité » (Dernières pensées, Paris 1913, pp. 190-99).

The use of h. in science, therefore, is logically justified, not only as instruments of work or mental schemas destined to remain forever mere h., but also as anticipations of truth, which can be transformed into certainties through inductive and deductive reasoning.

III. THE SCIENTIFIC AND THE MAGISTERIUM OF THE CHURCH

The relationship between scientific hypotheses and the truths of faith is a particular case of the relations between science and faith (v. FAITH, III, faith and reason), which however presents a special difficulty: for while one can be certain a priori that no genuinely demonstrated fact can be opposed to the revealed truths, the same cannot be said of mere hypotheses, even though they be scientifically grounded. With regard to these, three possibilities can occur: either the hypotheses have no relation whatever to truths of faith, and then the scientist enjoys full freedom from the religious point of view; or « they go directly or indirectly against the revealed doctrine (and) then they cannot be admitted in any way » (Pius XII, encyclical, Humani generis; v.): this follows logically from the second logical requirement of hypotheses, in accordance with the definition of the Fifth Lateran Council: « Cumque verum vero minime contradictat, omnem assertionem veritati illuminatae fidei contrariam omnino falsam esse definimus » (Denz-U, 738; cf. Vatican Council, Denz-U, 1797); finally, the hypotheses can « touch the doctrine contained in Sacred Scripture or in tradition » and even appear in contrast with it, without its being possible, « in the present state of science and theology », to give a certain solution; in such conditions the magisterium of the Church rightly « demands of its faithful the greatest moderation and caution », in such a way that the opposing opinions « be weighed and judged with the necessary seriousness, moderation and measure (on the part of those competent in both fields) and provided that all be ready to submit to the judgment of the Church » (Pius XII, ibid.). This norm of respect and caution therefore does not take away freedom of research in all doubtful questions, nor does it hinder the progress of science; for even when the hypothesis is contrary to a revealed datum, such as the hypothesis of creation ab aeterno, the scientific examination of it remains free, and so does its use as a mere working hypothesis, provided that in such a case its reality is not affirmed in any way, not even as probable.

Filippo Selvaggi