HYPOTHESIS. – A logical term denoting a proposition placed at the foundation of a line of reasoning in the search for an explanation of a fact, or also a doubtful but plausible conjecture concerning an unknown cause or reality, that is, an anticipation of the truth, which must subsequently be confirmed or disproved. The use of h. is part of ordinary life and everyday reasoning, and has assumed great importance in the modern scientific method.
I. HISTORY
Aristotle repeatedly discusses 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 the principle of a demonstration, which affirms or denies something without being demonstrated or imposing itself upon the mind through immediate and necessary evidence, although appearing plausible or probable (Anal. Post., I, 2, 72 a 14–24; 10, 76 b 23–29). A hypothesis can give rise to true demonstration and to science properly so called 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 supplies the premises of a “dialectical” argument which, by developing the premises of opposing probable or plausible propositions, constitutes an effective instrument in the search for truth and falsehood, and often the only way of establishing the certain premises of individual sciences (ibid., 2, 101 a 34–b 4). The use of dialectical argument in Aristotle is by no means rare; the best-known example is that of the celestial spheres, which Aristotle accepted on the authority of Eudoxus and Callippus as a reasonable, though not necessary, explanation of the apparent movements of the stars (Met., XII, 8, 1074 a 14–17).In post-Aristotelian philosophical thought, and particularly in scholasticism, attention is directed chiefly toward apodictic demonstration and the conditions of its premises; nevertheless, the scientific usefulness of the hypothesis as a probable conjecture in the search for an explanation of a fact is recognized. St. Thomas, speaking of the Aristotelian hypotheses mentioned above, states that “although, once such hypotheses have been posited, one might seem to have a solution to the problem, nevertheless it is not necessary to say that these hypotheses are true, since perhaps the astronomical phenomena can be explained in yet another way unknown to humanity. Aristotle, however, makes use of such hypotheses as though 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 demonstrate the congruence of the mysteries of faith (Sum. Theol., 1ª, q. 32, a. 1, ad 2).
The conscious use of hypotheses and their organic incorporation into the scientific method date back to Galileo, who must be regarded as the creator of the hypothetical-deductive experimental method. This consists of four distinct stages: observation of the facts; formulation of hypotheses expressible in mathematical formulas or realizable in mechanical models; deduction of the consequences; and experimental verification of these, followed by the indirect confirmation of the hypotheses (cf. A. Pastore, Il problema della causalità con particolare riguardo alla teoria del metodo sperimentale, I, Torino 1921, chap. 7, pp. 119–140). The Galilean hypothesis thus possessed characteristics quite distinct from those of the hypotheses of the natural philosophers of decadent scholasticism, which consisted in affirming occult qualities, mere nominalist palliatives devoid of scientific utility. It is these hypotheses, called “metaphysical” in a disparaging sense, and not all scientific hypotheses, that are targeted by Newton’s famous words: “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, Parigi 1912, pp. 46 and 510–15).
Positivism attempted to resist the increasingly extensive use of the hypothesis, in the Galilean sense, in science. Comte already maintained that many scientific hypotheses of his time were reintroducing chemical entities into science, through the search for occult causes of phenomena and universal agents; for Comte, the hypothesis should be reduced to the mere probable anticipation of a fact or a universal law (Cours de philosophie positive, II, Parigi 1835, pp. 335–354). This opposition intensified toward the end of the last century, giving rise to the well-known controversy between mechanists and energetists. On the one hand, the empiricist and conventionalist school, headed by E. Mach, H. Poincaré, and H. Leroy, having rejected the Aristotelian distinction between axioms and postulates, as well as the absolute logical value of the principles of science and of fundamental inductive laws, places the hypothesis, as a free convention, at the foundation of all experimental and rational science, both physical and mathematical, regarding economy, convenience, and practical utility as the sole criteria of choice. On the other hand, even more moderate authors, such as P. Duhem and W. Ostwald, deny hypotheses any ontological or causal value as anticipations of truth and reality, attributing to them at most a purely heuristic value as symbolic models, mental schemata, or logical syntheses of experimental laws.
Even today, epistemological currents remain divided on this subject; nevertheless, an intermediate theory is increasingly asserting itself. Many hypotheses that positivism regarded as methodologically unacceptable have become definitively established in science, whereas other hypotheses, especially those of a strictly mechanical nature, have proved incompatible with subsequent scientific advances and can be regarded only as symbolic models and mental schemata. In this regard, the method of operational definition, introduced into modern physics, is of great importance: it limits scientific hypotheses to the introduction of those entities alone that can be defined by means of experiences that are at least conceptually possible, rejecting as meaningless whatever is unobservable.
II. LOGICAL JUSTIFICATION OF THE HYPOTHESIS
The methodical use of the hypothesis is a necessity for the natural sciences. An intuitive knowledge of material reality and of physical qualities that reaches their essence immediately is in fact impossible for man; nor is knowledge of one or more facts, or even of true universal laws, ordinarily sufficient to identify the causes and structure of reality, since the latter can generally be explained by different and partially opposed causes. It is therefore indispensable to resort, as an instrument of research, to hypotheses that make possible the construction of theoretical and mathematical reasoning and the advancement of experimental investigations. The hypothesis thus completes the method of science, belonging to the phase of syllogism (v.) induction (v.).The formulation of the hypothesis, although formally a free convention and the product of the researcher’s genius, is not arbitrary but subject, to a greater or lesser degree of rigor, to certain logical requirements: 1) freedom from internal contradiction; 2) compatibility with rational and experimental truths already certainly acquired; 3) plausibility and aptitude for explaining physical phenomena already known; 4) fruitfulness, insofar as it permits the prediction of new phenomena, which experience must subsequently verify; 5) simplicity, insofar as it allows a greater number of phenomena to be explained 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 the smallest number of postulates, i.e. propositions”; Anal. Post., I, 25, 86 a 33-35), carry the greatest weight in the transformation of hypotheses into established knowledge.
This transformation, which is the ultimate aim of science, is not generally achieved through the verification of the consequences alone, even when they are numerous, although the hypothesis thereby acquires greater probability. In this case, moreover, a critical analysis of the hypothesis is required, together with the application of the logical principle of eliminating superfluous elements—that is, those elements which, although historically connected with the hypothesis, are logically separable from it, and whose removal 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, subsequently eliminated by the electromagnetic theory of Maxwell-Lorentz. In particular cases, however, it is possible to pass from the hypothesis to certain knowledge. Indeed, in some cases the formulation of a hypothesis may make possible observations or experiments leading to its direct verification; in other cases it is possible to establish an experimentum cruciale which, by verifying the contradictory of the consequence, makes it possible to infer with certainty the contradictory of the hypothesis; or, finally, one may arrive at establishing such a convergence of probabilities and indications that, taken as a whole, it can have no explanation other than the truth of a given hypothesis. An example of the first case is the discovery of the planet Nettuno, first supposed to be the hypothetical cause of the perturbations observed in the orbit of Urano and later directly observed in the predicted position; an example of the second case is radioactivity, which forced chemists to reject the hypothesis of the indivisibility of the atom; an example of the third is the complex of experiments and verifications derived from the molecular-kinetic hypothesis of gases, which led Poincaré himself to assert: « les atomes ne sont plus une fiction commode... L'atome du chimiste est maintenant une réalité » (Dernières pensées, Parigi 1913, pp. 190-99).
The use of hypotheses in science, therefore, is logically justified, not only as working instruments or mental schemes destined always to remain mere hypotheses, but also as anticipations of the truth, which may be transformed into certainties through inductive and deductive reasoning.