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A philosophical term used to designate, first, a property of things; secondly, a process of reasoning. We have here to consider its meaning and use:

I. In physical and natural sciences;
II. In metaphysics and scholastic philosophy;
III. In theodicy;
IV. In relation to the mysteries of faith.

Analogy in physical and natural sciences

As a property, analogy means a certain similarity mixed with difference. This similarity may be founded entirely or chiefly upon a conception of the mind; in this sense we say that there is analogy between the light of the sun and the light of the mind, between a lion and a courageous man, between an organism and society. This kind of analogy is the source of metaphor. The similarity may be founded on the real existence of similar properties in objects of different species, genera, or classes; those organs, for instance, are analogous, which, belonging to beings of different species or genera, and differing in structure, fulfil the same physiological functions or have the same connections. As a process of reasoning, analogy consists in concluding from some analogical properties or similarity under certain aspects to other analogical properties or similarity under other aspects. It was by such a process that Franklin passed from the analogy between the effects of lightning and the effects of electricity to the identity of their cause; Cuvier, from the analogy between certain organs of fossils and these organs in actual species to the analogy of the whole organism; that we infer from the analogy between the organs and external actions of animals and our own, the existence of consciousness in them. Analogical reasoning is a combination of inductive and deductive reasoning based on the principle that "analogical properties considered as similar involve similar consequences". It is evident that analogical reasoning, as to its value, depends on the value of the analogical property on which it rests. Based on a mere conception of the mind, it may suggest, but it does not prove; it cannot give conclusions, but only comparisons. Based on real properties, it is more or less conclusive according to the number and significance of the similar properties and according to the fewness and insignificance of the dissimilar properties. From a strictly logical point of view, analogical reasoning can furnish only probable conclusions and hypotheses. Such is the case for most of the theories in physical and natural sciences, which remain hypothetical so long as they are merely the result of analogy and have not been verified directly or indirectly.

Analogy in metaphysics and Scholastic philosophy

Analogy in metaphysics and Scholastic philosophy was carefully studied by the Schoolmen, especially by the Pseudo-Dionysius, Albertus Magnus, and St. Thomas. It also may be considered either as a property or as a process of reasoning. As a metaphysical property, analogy is not a mere likeness between diverse objects, but a proportion or relation of object to object. It is, therefore, neither a merely equivocal or verbal coincidence, nor a fully univocal participation in a common concept; but it partakes of the one and the other. (Cf. St. Thomas, Summa Theol., I, Q. xiii, a. 5, 10; also, Q. vii, De potentiâ, a. 7.) We may distinguish two kinds of analogy:

• Two objects can be said to be analogous on account of a relation which they have not to each other, but to a third object: e.g., there is analogy between a remedy and the appearance of a person, in virtue of which these two objects are said to be healthy. This is based upon the relation which each of them has to the person's health, the former as a cause, the latter as a sign. This may be called indirect analogy.
• Two objects again are analogous on account of a relation which they have not to a third object, but to each other. Remedy, nourishment, and external appearance are termed healthy on account of the direct relation they bear to the health of the person. Here health is the basis of the analogy, and is an example of what the Schoolmen call summum analogatum (Cf. St. Thomas, ib.)

This second sort of analogy is twofold. Two things are related by a direct proportion of degree, distance, or measure: e.g., 6 is in direct proportion to 3, of which it is the double; or the healthiness of a remedy is directly related to, and directly measured by, the health which it produces. This analogy is called analogy of proportion. Or, the two objects are related one to the other not by a direct proportion, but by means of another and intermediary relation: for instance, 6 and 4 are analogous in this sense that 6 is the double of 3 as 4 is of 2, or 6:4::3:2. The analogy between corporal and intellectual vision is of this sort, because intelligence is to the mind what the eye is to the body. This kind of analogy is based on the proportion of proportion; it is called analogy of proportionality. (Cf. St. Thomas, Q. ii, De verit., a. 11; Q. xxiii, De verit., a. 7, ad 9^am).

Analogy as a method in theodicy

As human knowledge proceeds from the data of the senses directed and interpreted by reason, it is evident that man cannot arrive at a perfect knowledge of the nature of God which is essentially spiritual and infinite. Yet the various elements of perfection, dependence, limitation, etc., which exist in all finite beings, while they enable us to prove the existence of God, furnish us also with a certain knowledge of His nature. For dependent beings must ultimately rest on something non-dependent, relative beings on that which is non-relative, and, even if this non-dependent and non-relative Being cannot be conceived directly in itself, it is necessarily conceived to some extent through the beings which depend on it and are related to it. It is not an Unknown or Unknowable. It can be known in different ways. We remark in finite things a manifold dependence. These things are produced; they are produced according to a certain plan and in view of a certain end. We must conclude that they have a cause which possesses in itself a power of efficiency, exemplarity, and finality, with all the elements which such a power requires: intelligence, will, personality, etc. This way of reasoning is called by the Schoolmen "the way of causality" (via causalitatis). (Cf. Pseudo-Dionysius, De Div. Nom., c. i, sect. 6, in P.G., III, 595; also, St. Thomas, Summa Theol., I, Q. iii, a. 3; Q. xiii, a. 12.) When we reason from the effects to the First, or Ultimate, Cause, we eliminate from it all the defects, imperfections, and limitations which are in its effects just because they are effects, as change, limitation, time, and space. This way of reasoning is "the way of negation or remotion" (via negationis, remotionis). (Cf. Pseudo-Dionysius, ibid.; also, St. Thomas, Summa Theol., I, QQ. iii-xiii, a. 1; C. Gent., lib. I, c. xiv.) Finally, it is easily understood that the perfections affirmed, in these two ways, of God, as First and Perfect Cause, cannot be attributed to Him in the same sense that they have in finite beings, but only in an absolutely excellent or supereminent way (via eminentiae, excellentiae). (Cf. Pseudo-Dionysius, Div. Nom., c. i, sect. 41, in P.G., III, 516, 590; c. ii, sect. 3, 8, in P.G., III, 646, 689; St. Thomas, ibid.)

What is the value of our knowledge of God acquired by such reasoning? According to Agnosticism this attribution of perfections to God is simply impossible, since we know them only as essentially limited and imperfect, necessarily relative to a certain species or genus, while God is the essentially Perfect, the infinitely Absolute. Therefore all that we say of God is false or at least meaningless. He is the Unknowable; He is infinitely above all our conceptions and terms. Agnosticism admits that these conceptions and names are a satisfaction and help to the imagination in thinking of the Unthinkable; but on condition that we remember that they are purely arbitrary; that they are practical symbols with no objective value. According to Agnosticism, to think or say anything of God is necessarily to fall into Anthropomorphism. St. Thomas and the Schoolmen ignore neither Agnosticism nor Anthropomorphism, but declare both of them false. God is not absolutely unknowable, and yet it is true that we cannot define Him adequately. But we can conceive and name Him in an "analogical way". The perfections manifested by creatures are in God, not merely nominally (equivoce) but really and positively, since He is their source. Yet, they are not in Him as they are in the creature, with a mere difference of degree, nor even with a mere specific or generic difference (univoce), for there is no common concept including the finite and the Infinite. They are really in Him in a supereminent manner (eminenter) which is wholly incommensurable with their mode of being in creatures. (Cf. St. Thomas, Summa Theologiæ I.13.5-6; C. Gent., lib. I, c. xxii-xxxv; in I Sent. Dist., xiii, Q. i, a. 1, ad 4^am.) We can conceive and express these perfections only by an analogy; not by an analogy of proportion, for this analogy rests on a participation in a common concept, and, as already said, there is no element common to the finite and the Infinite; but by an analogy of proportionality. These perfections are really in God, and they are in Him in the same relation to His infinite essence that they are in creatures in relation to their finite nature. (Cf. St. Thomas, Summa Theol I.4.3; I.13.5; Q. ii, De verit., a. 11, in corp. ad 2^am; ibid., xxiii, a. 7, ad 9^supam.) We must affirm, therefore, that all perfections are really in God, infinitely. This infinitely we cannot define or express; we can say only that it is the absolutely perfect way, which does not admit any of the limitations which are found in creatures. Hence our conception of God, though very positive in its objective content, is, as represented in our mind and expressed in our words, more negative than positive. We know what God is not, rather than what He is. (Cf. St. Thomas, Summa Theologicæ I.3, the whole question; I.13.2, 3, 5, 12; Q. ii, De veritate, a. 1, ad 9^am, ad 10^am.) Such a conception is evidently neither false nor meaningless; it is clearly inadequate. In a word, our conception of God is a human conception and it cannot be other. But if we necessarily represent God in a human way, if even if it is from our human nature that we take most of the properties and perfections which we predicate of Him, we do not conceive Him as a man, not even as a perfected man, since we eliminate from those properties, as attributes of God, all limits and imperfections which in man and other creatures are a very part of their essence.

Analogy in the knowledge of the mysteries of faith

The Fathers of the Church always emphasized the inability of the human reason to discover or even to represent adequately the mysteries of faith, and insisted on the necessity of analogical conceptions in their representations and expressions. St. Thomas, after the Pseudo-Dionysius and Albertus Magnus, has given the theory of analogy so applied to the mysteries of faith. (Cf. St. Thomas, Summa, Theol., I, Q. i, a. 9; Q. xxii, a. 1; In Librum Boëthii De Trinitate Expositio.) The Vatican Council set forth the Catholic doctrine on the point. (Cf. Const., Dei Filius, cap. iv; cf. also Conc. Coloniense, 1860.) (1) Before Revelation, analogy is unable to discover the mysteries, since reason can know of God only what is manifested of Him and is in necessary causal relation with Him in created things. (2) In Revelation, analogy is necessary, since God cannot reveal the mysteries to men except through conceptions intelligible to the human mind, and therefore analogical. (3) After Revelation, analogy is useful to give us certain knowledge of the mysteries, either by comparison with natural things and truths, or by consideration of the mysteries in relation with one another and with the destiny of man.