HYPOTHESIS. – A logical term indicating a proposition posited as the foundation of reasoning in the search for an explanation of a fact, or also as a doubtful but plausible conjecture regarding an unknown cause or reality, i.e., as an anticipation of the truth that must be further verified or refuted. The use of hypothesis is part of ordinary life and common reasoning and has assumed great importance in the modern scientific method.
I. HISTORY
Aristotle repeatedly discusses the logical use of hypothesis: ὑπόθεσις (Lat. *suppositio*), as distinct from axioms (v.), definitions (v.), and postulates (v.), is a proposition assumed as the principle of demonstration, affirming or denying something without being itself demonstrated or imposed on the mind by immediate and necessary evidence, though appearing plausible or probable (Anal. Post., I, 2, 72 a 14–24; 10, 76 b 23–29). Hypothesis can give rise to true demonstration and proper science only if it is demonstrated in a higher science or appears immediately true as a result of the formulation proposed by the teacher (ibid., 2, 71 b 19–25; Top., I, 1, 100 a 27–29). Yet even in the contrary case, it is indirectly useful to science insofar as it forms the premises of a “dialectical” reasoning, which, by unfolding the premises of opposing probable or plausible propositions, constitutes an effective instrument in the search for truth and falsehood and often the only path to establishing the certain premises of individual sciences (ibid., 2, 101 a 34–35). Aristotle’s use of dialectical argumentation is by no means rare; the most well-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, though not necessary (Met., XII, 8, 1074 a 14–17).In post-Aristotelian philosophical thought, and particularly in Scholasticism, attention is directed predominantly toward apodictic demonstration and the conditions of its premises; yet the scientific utility of conjecturing probable explanations in the search for the explanation of a fact is still recognized. St. Thomas, speaking of Aristotelian hypotheses, approvingly notes that “although such hypotheses seem to provide a solution to the problem, it is not necessary to say that these hypotheses are true, for perhaps astronomical phenomena can be explained in another way as well, according to human understanding. Aristotle, however, makes use of such hypotheses as if they were true” (II *De caelo*, lect. 17). He adds that arguments based on probable hypotheses can also be employed in sacred science to show the congruity of the mysteries of faith (Sum. Theol., Iª, q. 32, a. 1, ad 2).
The conscious use of hypotheses and their organic integration into the scientific method dates to Galileo, who may be considered the creator of the hypothetical-deductive experimental method, consisting of four distinct phases: observation of facts, formulation of hypotheses expressible in mathematical formulas or realizable in mechanical models, deduction of consequences, experimental verification of these, and thus indirect confirmation of the hypotheses (cf. A. Pastore, *Il problema della causalità con particolare riguardo alla teoria del metodo sperimentale*, I, Torino 1921, cap. 7, pp. 119–140). The hypothesis of floating bodies thus had characteristics quite distinct from the hypotheses of the declining Scholastic naturalists, which consisted in affirmations of occult qualities—mere nominalistic palliatives devoid of scientific utility. When Newton spoke of “hypotheses non fingo,” his words must be understood as directed not against hypotheses in general but against “metaphysical” hypotheses in a pejorative sense, and not against all scientific hypotheses: “Whatever is not deduced from the phenomena is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy” (*Philosophiae naturalis principia mathematica*, General Scholium, Amsterdam 1713, p. 487; cf. E. Meyerson, *Identité et réalité*, Paris 1912, pp. 46 and 510–15).
The positivist movement sought to oppose the ever-wider employment in science of the hypothesis in the Galilean sense. Comte already maintained that many scientific hypotheses of his time reintroduced chimerical entities into science by seeking occult causes of phenomena and universal agents; for Comte, hypothesis should be reduced to the simple probable anticipation of a fact or a universal law (*Cours de philosophie positive*, II, Paris 1835, pp. 335–354). Opposition intensified toward the end of the last century, giving rise to the well-known controversy between mechanists and energetists. On one side, the empiriocritical and conventionalist school, led by E. Mach, H. Poincaré, and H. Leroy, rejected Aristotle’s distinction between axioms and postulates and the absolute logical value of the principles of science and fundamental inductive laws, placing hypothesis as a free convention at the foundation of all experimental and rational science, physical and mathematical, regarding economy, convenience, and practical utility as the sole criteria of choice. On the other side, even more moderate authors such as P. Duhem and W. Ostwald denied any ontological or causal value to hypotheses as anticipations of truth and reality, attributing to them at most a heuristic value as symbolic models, mental schemas, or logical syntheses of experimental laws.
Even today, epistemological currents remain divided on this subject; yet an intermediate theory is increasingly gaining ground. Many hypotheses that positivism considered methodologically unacceptable have definitively established themselves in science, while others, especially those of a rigidly mechanistic nature, have proved incompatible with further scientific progress and can only be regarded as symbolic models and mental schemas. In this regard, the method of operational definition, introduced into modern physics, is of great importance, as it restricts scientific hypotheses to the introduction of only those entities that are definable by experience at least conceptually possible, rejecting as meaningless all unobservables.
II. LOGICAL JUSTIFICATION OF THE HYPOTHESIS
The methodical use of hypothesis is a necessity for the natural sciences. For man does not possess intuitive knowledge of material reality and the physical qualities that immediately reach its essence; nor does knowledge of one or more facts, or even of true universal laws, ordinarily suffice to identify the causes and structure of reality, which can generally be explained by different and partially opposing causes. It is therefore indispensable to resort, as an instrument of research, to hypotheses that allow the construction of theoretical and mathematical reasoning and the advancement of experimental investigations. Hypothesis thus completes the method of science, belonging to the phase of research into the premises of the syllogism (v.) and the preparation of induction (v.).The formulation of a hypothesis, though formally a free convention arising from the researcher’s ingenuity, is not arbitrary but subject, to a greater or lesser degree, to certain logical requirements: 1) freedom from internal contradiction; 2) compatibility with rationally and experimentally established truths; 3) plausibility and capacity to explain known physical phenomena; 4) fruitfulness, in that it permits the prediction of new phenomena that experience must then verify; 5) simplicity, in that it allows the explanation of a greater number of phenomena with a smaller number of hypothetical elements. The last two conditions, less emphasized by the ancients but not unknown to them (Aristotle: “the best demonstration is that which makes use of the fewest postulates, i.e., suppositions” (*Anal. Post.*, I, 25, 86 a 33–35), carry the greatest weight in the transformation of hypotheses into established knowledge.
Such a transformation, which is the ultimate goal of science in general, is not achieved merely by verifying consequences—even numerous ones—though this does increase the probability of the hypothesis. In this case, a critical analysis of the hypothesis is also required, along with the application of the logical principle of eliminating superfluous elements—those elements that, while historically connected to the hypothesis, are logically separable from it and whose removal has no bearing on the theoretical and mathematical deduction of consequences confirmed by experience. An example of such an element is the mechanical nature of light vibrations in Fresnel’s wave theory, later eliminated by the electromagnetic theory of Maxwell and Lorentz. In particular cases, however, it is possible to progress from a hypothesis to certain knowledge. Indeed, in some instances, the formulation of a hypothesis may enable observations or experiments that lead to its direct confirmation; in others, a crucial experiment may be devised, allowing one to infer with certainty the falsity of the hypothesis from the verification of a contradictory consequence; or, finally, it may be possible to establish such a convergence of probability and evidence that, taken together, no other explanation is possible than the truth of a specific hypothesis. An example of the first case is the discovery of the planet Neptune, first posited as a hypothetical cause of the observed perturbations in Uranus’s orbit and later directly observed in the predicted position; an example of the second case is radioactivity, which compelled chemists to reject the hypothesis of the indivisibility of the atom; and an example of the third is the body of experiments and verifications derived from the kinetic-molecular hypothesis of gases, which led even Poincaré to affirm: *“les atomes ne sont plus une fiction commode... L'atome du chimiste est maintenant une réalité”* (Dernières pensées, Paris 1913, pp. 196–99).
The use of hypotheses in science is therefore logically justified, not only as working tools or mental frameworks destined to remain mere hypotheses but also as anticipations of truth that may be transformed into certainties through inductive and deductive reasoning.
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### III. THE SCIENTIFIC HYPOTHESIS AND THE TEACHING AUTHORITY OF THE CHURCH
The relationship between scientific hypotheses and the truths of faith is a particular instance of the broader relationship between science and faith (see FAITH, III, f. and reason), though it presents a special difficulty: while one may be certain *a priori* that no truly demonstrated fact can oppose revealed truths, the same cannot be said of mere hypotheses, even when they are scientifically grounded. Three possibilities may arise in this regard: either the hypotheses bear no relation to truths of faith, in which case the scientist enjoys full religious freedom; or they “directly or indirectly contradict revealed doctrine” and “cannot in any way be admitted” (Pius XII, encyclical *Humani generis*; see); this follows logically from the second logical requirement of hypotheses, in accordance with the definition of the Fifth Lateran Council: *“Cumque verum vero minime contradicat, omnem assertionem veritati illuminatae fidei contrariam omnino falsam esse definimus”* (Denz.-U., 738; cf. Vatican Council, Denz.-U., 1797); or, finally, the hypotheses may “touch upon doctrine contained in Holy Scripture or tradition” and appear to conflict with it, without it being possible, “given the present state of science and theology,” to provide a certain solution. In such circumstances, the Church’s teaching authority rightly demands of its faithful “the greatest moderation and caution,” so that opposing opinions “be weighed and judged with the necessary seriousness, moderation, and measure (by competent authorities in both fields) and that all be ready to submit to the judgment of the Church” (Pius XII, *ibid.*). This norm of respect and caution does not, however, restrict the freedom of research in doubtful matters, nor does it impede the progress of science; for even when a hypothesis contradicts a given doctrine, such as the hypothesis of creation *ab aeterno*, scientific examination of it remains free, and it may even be employed as a mere working hypothesis—provided that in such a case its reality is in no way affirmed, not even as probable.
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### IV. BIBL.:
E. Naville, *La logique de l'hypothèse*, Paris 1880;
H. Poincaré, *La science et l'hypothèse*, ibid. 1902;
E. Mach, *Erkenntnis und Irrtum*, Leipzig 1905, cap. 14;
P. Duhem, *La théorie physique*, Paris 1906;
F. Enriques, *Problemi della scienza*, Bologna 1906, cap. 11;
E. Meyerson, *Identité et réalité*, Paris 1907;
id., *De l'explication dans la science*, ibid. 1921;
J. Stuart Mill, *Système de logique*, II, French trans. by L. Peisse, Paris 1909, pp. 1–27;
E. Goblot, *Traité de logique*, ibid. 1918, pp. 204–312;
A. Pastore, *Il problema della causalità*, II, Turin 1921, sect. I;
J. L. Destouches, *Principes fondamentaux de physique théorique*, Paris 1942;
F. Selvaggi, *Il neopositivismo e il metodo della nuova scienza*, in *Civ. Catt.*, 1947, II, pp. 501–513;
F. Amerio, *Epistemologia*, Brescia 1948 (for the historical section);
P. Hoenen, *Filosofia della natura inorganica*, Italian trans. by M. Cavajoni-Bologna, Brescia 1949, pp. 168–76.
Filippo Selvaggi.