Matter, Philosophy of
MATTER, PHILOSOPHY OF
That of which things are made, an intrinsic determinable principle whose opposite (and correlative) is form. As a type of substance, matter is opposed also to spirit. The term is defined differently in the various philosophical traditions and, even as employed by scholastic philosophers, has acquired a wide range of meanings in logic, epistemology, psychology, and ethics. This article is concerned primarily with the concept of matter as used in natural philosophy and metaphysics, and sketches its historical development from the earliest times to the present.
Greek naturalists. Matter is, in a sense, the oldest of philosophical concepts. When man first began to speculate about the world in which he lived and his own place in it, he tended to use concrete terms and images from everyday experience. His language did not possess the wealth of general terms, such as being and relation, that would later become available. So he spoke in terms of simple myth, of gods (who were like men) and processes of making and molding. As time went on, the characteristically human drive to understand the world took the form of reducing the complexity of human experience to some sort of unity. To understand was to make one of the diverse and dispersed many. If the many could be seen in some way as instances of a one, it would then be sufficient to grasp the one. For example, if a person knows what a horse is, he knows something about all horses, and the multiplicity and diversity of the group has been reduced to unity.
When the entire physical universe, and not a single species, is approached in this spirit, it is not at first sight obvious where the one is to be found. The two simplest kinds of unity (in terms of ordinary experience) are the unity of a common origin (e.g., a craftsman-god who is responsible for the diversity and change of man's world) and that of a common stuff (a single stuff that can take on diverse and changing forms). Stress on the former was characteristic of many early religions; however, it rarely led to any sort of speculative clarification of the notions involved (god, making, etc.). The latter approach was adopted by some speculative-minded thinkers of Ionia in the 6th century b.c., who saw the universe as bound together in some sort of material unity. Thales said that it had originally come from water. This first suggestion was undoubtedly influenced by myths of religious origin; Thales did not (as far as is known) go on to claim that the world is constituted of water in different forms. Anaximander held that the universe came from an "indeterminate" (Gr. [symbol omitted]περου) to which it ultimately returns: this indeterminate is both inexhaustible (to allow for unceasing change) and lacking in any intrinsic properties (so that it can take on all properties freely). Anaximenes was the first to suggest that the universe actually consists of a single stuff that takes on different forms. And this stuff was no other than the familiar air that (he thought) could condense into cloud, then water, then earth, then rock. heraclitus preferred to think of the primary stuff as fire, though he spoke in allegory and it is difficult to be sure of his meaning. (see greek philosophy.)
Several points should be noted at this stage. There was as yet no word for matter; to say that these Ionians had begun to articulate the concept of matter means that they were positing a single stuff (usually under some familiar guise such as that of air) as the answer to the central problem of unity-in-diversity. They were explaining diversity and change in terms of an as-yet-unnamed general category of matter-stuff. Second, this stuff was still vague in character. It was sometimes described as divine, sometimes as living. The later contrast between matter and spirit had not yet appeared; their matter-stuff was much too nondescript to allow one to regard them as materialist in the later, much more precise, sense of that term.
Pythagoras to Democritus. A stuff would provide unity. But what could explain change? Why should there be change in the first place? The first answer to this was expressed in terms of contraries such as full and empty, love and strife: the tension between these somehow provided the spring of action. The Pythagoreans were the first to push this to the limit and to posit a contrary of matter-stuff itself, namely, void. This was a new philosophical category, one whose history would continue to be bound up with that of matter. The void surrounded the world and served to differentiate things from one another. (see pythagoras and pythagoreans.)
parmenides rejected the entire "matter" approach to explanation of the physical world. He preferred to seek cosmic unity at a much more abstract level, that of being, or "what is." Being does not allow of differences of density or of quality, so that diversity and change are alike illusory or at least can be dismissed from serious speculative consideration. But this was much too sweeping a conclusion for Parmenides's successors, even though they were influenced by his ideal of an unchanging Being. empedocles argued for four different types of basic stuff. They could combine in endless ways; but each remained forever the same stuff, and each was structurally simple and homogeneous. Thus, instead of a single matter-stuff, he was holding for four elements, as they later came to be called (see element). anaxagoras suggested a much more sophisticated view: the universe contains an infinity of elements, each element forever itself but all mixed together in ever-varying proportions. The familiar things man perceives consist of a mixture of the elements; even apparently simple substances, such as water, contain small traces (seeds) of other things that can come to be from them. democritus tried perhaps the most interesting variation of all. Being does not change in itself (Parmenides), and yet change does occur. If void be admitted (Pythagoras), it allows one to have a multiplicity of beings or atoms whose movements explain all the changes of everyday experience. These beings must be below the level of perception, since their motions must explain growth, change of color, etc. They are in themselves unchanging and homogeneous. The atoms are thus a special sort of matter-stuff; the void is described as "rarefied" and appears as a diminished sort of reality—a second kind of stuff, it seems. Diversity and change are explained in terms of these two somewhat different sorts of material.
Plato. Matter plays two quite central roles in the complex metaphysics of plato. His analysis of knowledge led him to assert the existence of a realm of Forms on whose stability and immutability science depends. The Forms are imaged in a defective and flickering fashion in a matrix of extendedness or multiplicity. This world of image is the world man perceives. Its intelligibility arises from its relation to Form; the limited character of this intelligibility is traceable to the defective and multiple character of the "space-matter" in which the images occur. What is striking here is that matter, formerly the principle of unity (and therefore of intelligibility) for the Ionians, has become the principle of multiplicity, and thus of nonintelligibility, for Plato. Diversity is not to be understood by a reduction to one or more underlying types of stuff. One facet of diversity, the sheer and indefinite multiplicity of the sensible instances of any Form, is a "given," not something that can be further understood. The other facet, the multiplicity of the Forms themselves, is more mysterious: it is apparently constituted by relations of negation, in which the original unity of the One-Good (the sole locus of true intelligibility) is gradually dissipated.
But there must also be motion. And the principle of this is soul, seen at its purest in man, but working less obviously in all moving things, even those apparently inanimate. The regular motions of the universe, noted in the stars and seasons, the working of all things toward an ordered good, argue to the existence of a world soul animating the matter of the universe, just as the soul of man animates his body. Here matter is contrasted with living soul, not with unchanging Form; it is the passive, the resistant, not the empty space on which instances of a Form can be endlessly projected. Matter in this sense actively opposes soul; it is the source of defect, of breakdown in finality. Clearly the two notions are not the same, though they must be closely related. There is an uneasy tension between Plato's two great dualisms, the dualism of Form and the space-matrix of becoming in the Timaeus and that of soul and body in the Phaedo. There are two doctrines of matter here; or to put this in another way, since Soul and Form are not identical, their contrast-principles are not the same either.
Aristotle. aristotle was the first to coin an explicit term for the general category of material in the domain of scientific explanation. He adapted the common terms for timber, the material on which the carpenter works, [symbol omitted]λη, to his technical usage, although he frequently made use of other terms as well. Though his analysis sounds like that of the Ionians, it is in reality of a significantly different sort. He begins with an analysis of predication itself, of how man talks about the kinds of things there are in the world, and claims to distinguish on the basis of this analysis two levels of reference. There are things to which man refers by names, things that are not predicated of anything else. These are the ultimate subjects of all predication about the natural world—substance is their common English designation, although perhaps entity would be a better translation for Aristotle's term. There are, besides, those second-order things that are predicated of entities and do not stand on their own: attributes of any kind, whether "essential" (pertaining properly, and in all cases, to a particular type of entity) or "accidental" (not necessarily belonging to all instances of a particular type of entity)—both commonly designated by the term accident.
Principles of Change. Now when this simple distinction is applied to the domain of change, an interesting thing happens. In any change, there must be a subject of predication; there obviously must be something that can be said to change. Furthermore, if one is to have a truly "scientific" analysis that will remain true in all instances, it will not do to choose attributes at random, and say, for instance, that the musical entity comes to be from the black entity. Only one way of describing this will be "scientifically" true, and that is to say that the musical entity comes to be from the nonmusical entity. This description holds good for any change terminating in the attainment of the attribute "musical." Three conditions are thus necessary and sufficient for any "scientific" description of change: there must be a subject of the proposition describing the change; this subject must first lack a certain attribute, and then it must come to possess it. Thus, when a nonmusical man becomes musical, the subject of predication is the man. Aristotle calls the man the matter of this change, and the other two conditions he calls privation and form, respectively. The man may be called the "matter-subject" of the change, in order to emphasize the function of the analysis of predication in Aristotle's assertion.
Note what has happened here. It is not that Aristotle has made an empirical inspection of changes, and discovered that in all cases a substratum remains throughout the change. The apparent similarity with the Ionian analysis is misleading. His form and privation are contradictories, not contraries, and thus whereas it would have taken observation to support the Ionian claim that all change involves contraries (e.g., black and white), it is analytic to say that it involves contradictories (white and nonwhite). Aristotle's claim that all change involves a matter-subject, a form, and a privation is, in fact, irrefutable because analytic. An understanding of the concept of change, or more exactly of predication about change, shows this immediately.
But here a major difficulty arises for Aristotle. If the matter-subject above be identified with an entity, or a substance, it seems that entitative change or substantial change is impossible. For in any change there must be a common matter-subject of which the privation can first be predicated, and then subsequently the form. This matter-subject is either an entity, or it is not. If it is, then the change is not entitative, or substantial, since the same entity, or substance, is present throughout the change. If it is not, what can the matter-subject be? There are only two possible kinds of referent: entity and attribute, and the matter-subject of a properly entitative, or substantial, change is obviously neither of these.
To put the quandary in a yet sharper way: If there is a truly entitative, or substantial, change, of what can the privation and form be predicated? Can there be a common subject of predication before and after? How can it be named if it is not an entity? And how can it be a subject of predication if it cannot be named? If an acorn becomes an oak (to take one of Aristotle's examples), is there any way of maintaining the matter-subject type of analysis, which requires one to be able to break down "A becomes B " into "X is non Y and later X is Y "? "That which was acornlike now is oaklike"—but what does the "that" stand for here?
Primary Matter. It was from this quandary that Aristotle's distinctive (and at first sight paradoxical) doctrine of primary matter took its origin. He wished at all costs to maintain as a basic "given" of experience that entitative, or substantial, changes occur, that entities truly come to be and pass away. He was opposing the Parmenidean tradition in all its varied forms (Empedocles, Democritus, Anaxagoras) on this point. The coming-to-be and passing-away that man perceives is not simply a rearrangement of atoms or elements or seeds, themselves unchanging; for if this were the case, the passing unities they form would be merely incidental, and a true science of the middle-sized objects of human perception would be impossible. Aristotle, as biologist, was quite sure that a science of living things was possible, and this proved to him that biological entities are not simply accidental conformations of more fundamental unchanging entities lying below the level of perception. Experience shows that living things have a unitary τέλος, or goal; one cannot dissolve it into incidental relationships without challenging the validity of perception generally, which Aristotle was determined to safeguard at all costs.
This meant that he had also to oppose the entire Ionian approach to physics. If intelligibility were to be sought through a permanent "stuff" that survives all changes, it would once again imply that the entities of everyday experience are simply complex configurations of a single underlying entity such as air or water. The fundamental reality, unity, and intelligibility would lie at the level of the "stuff," and once again no proper science of the complex entities of everyday experience would be possible. Yet on the other hand, the matter-form-privation analysis had been shown to be fundamental to predication about change. There must be a matter-subject of some sort in entitative changes, but it could not be a "stuff" in the Ionian sense, that is, a material entity with definite properties. Thus Aristotle posits an indefinite matter-subject, itself lacking in all properties, even quality and quantity. It is not an entity, and thus it is not a proper subject of predication, nor can it even be named, properly speaking. It provides a sort of limit to predication itself, even apart from analysis of change. If one carries predication to more and more fundamental levels, there must be an ultimate matter-subject of which the basic form of the entity can (in a special terminal sense) be predicated; otherwise there would be an infinite regress.
The doctrine of primary matter thus depends on an analysis of predication, and especially on the notion of entity or substance. It does not depend on detailed observation of actual entitative changes, and is thus what later thinkers would call a typically metaphysical doctrine. To say that "primary matter exists" is simply to say that the notions of predication and of entity put forward by Aristotle are valid and that entitative changes occur. To say that a particular entity is "composed of primary matter and substantial form" (a popular later way of putting Aristotle's thesis) is to say that it is capable of ceasing to be and that it can give rise to other entities. It does not imply that the form is imposed upon the matter as a shape is imposed upon bronze; though Aristotle uses the bronze analogy in his original analysis of change-in-general, it seems fundamental to his entire ontology that primary matter not be regarded as a sort of limit-case of a qualityless "stuff." Such a substratum would not be a "this," could not individuate, would still be quantified, and so would not satisfy two central criteria of Aristotle's primary matter.
Material Causality. There is a second context in which Aristotle introduces the notion of a "material," and this is in his analysis of the different types of explanation of physical change. He claims that there are four and only four of these, and that for a complete explanation all four ought be given, so that they are complementary to one another. One can "explain" a change (i.e., make it more intelligible) by mentioning the material in which it occurs, the intrinsic form involved, the agent responsible for it, or the end toward which it is directed. This division raises many problems, and one of the most difficult is that posed by the "material" mode of explanation (material causality, as it is often called, though the English term causality is more often restricted to the category of agency alone). In what way is a change "explained" by specifying its material? To explain a statue in terms of the bronze that went to its making seems to involve the form of the bronze principally. When a nonmusical man becomes musical, is the material cause the man; i.e., is the material cause identical with the matter-subject of predication about the change? If it is, then what is had is description, not explanation. It seems dubious whether one should regard the man as a causal principle of this change.
One alternative would be to take the material cause of a particular physical explanation to be the material elements that are assumed (without any further enquiry into their nature) in this explanation. It would thus be relative to the particular explanation given and correlative to the level of formal explanation chosen as most appropriate. Clearly, material cause comes much closer to "stuff" than matter-subject does, but even here in most changes (other than elemental or artistic ones) the "material" will be a complex structure; yet the emphasis will not be on the structure as such, but rather on its being the substratum for a further structure of a higher order.
Potency. In discussing change, Aristotle introduced another crucial metaphysical category that was, in his mind, closely linked with matter. This was potency. Besides saying of something that it is X or non X, there is a third choice that the dichotomies of his predecessors had tended to obscure: one could say that though it is non X, it has the capacity to become X. Potency is something more than mere privation, though it is less than actuality, or act. To say that an acorn can become an oak is an important fact about the acorn, one that is not conveyed by saying simply that it is non-oak. Thus a complete analysis of change requires one to introduce potency.
Potency has a dual aspect: it involves both capacity to be acted upon and capacity to act upon another. In both instances, potency is oriented to change; in both instances the complete actuality is lacking, but part of what it takes to bring about the complete actuality is already there. Passive potency can be said to reside in the material cause of the change, in the sense that it is the "material" aspect of the entity that makes it capable of change in the first place, the aspect that makes it part of an order in which outside agencies intervene and the unexpected can happen. Matter is thus in this sense the source of chance and defect, not that there is something within it that (as Plato had suggested) works actively against the agency of form, but rather that it simply renders the entity subject to unpredictable outside interference with its proper intrinsic finality.
Stoics. The Stoic philosophers of the generation after Aristotle were the nearest to being materialist, in the modern sense, of any ancient school. For them, fire is the primary element; life and reason are its highest manifestations. From it issues the more inert elements in an unending cycle of growth and catastrophe. All things are corporeal, i.e., extended and capable of being acted upon by other bodies: this is true of soul and even of the Divinity, which is somehow immanent in the life-tension of the universe itself. Even qualities must somehow be bodies, since only bodies can act. Yet the alleged Stoic materi alism has to be taken cautiously: the Stoics conceded an existence of a nonbodily sort to the void and, interestingly, to propositions; and their fire-stuff is more reminiscent of vitalism than of materialism.
Plotinus to Augustine. The solution to the problem of the one-in-many proposed by plotinus constituted a powerful rethinking of the Neoplatonist themes. The One is beyond Mind and even Being; it is the source of the multiplicity of the world of Form, which is the product of Mind. As the lower contemplates the higher, the movement of contemplation issues in a product; in this way, by a movement of emanation, all multiplicity comes forth from the Mind, faced by One. Below Mind there is a Soul, and over against Mind there is matter, which is the featureless principle not of multiplicity (since each individual entity has its own form, and thus all multiplicity is the result of emanation) but of negation, and ultimately of evil and opposition.
augustine inherited this dualism, but the Christian doctrine of creation forced him to modify it. He could not admit emanation, nor could he allow a matter over against, and thus not existentially dependent upon, God. Formless matter is the first and lowest of God's creatures. It is the condition of time, the principle of mutability of all creatures, whether spiritual or bodily, since all of them can turn away from the unity of God to the dispersion of the self. This matter does not exist by itself before the first forms but is concreated with them and has a reality, even though "next to nothing." Multiplicity comes from God rather than from matter, at least in the case of rational creatures, who in some sense individually preexist in the divine mind. Mutability leads to evil and suffering. In the Augustinian tradition of theology, matter was always to have this overtone: it would be something to be turned away from. But matter is only one aspect of the physical world; the intelligibility of the material creation is a sign for man of God's power and love.
Thomas Aquinas. In the medieval period, the Aristotelian doctrine of matter was deepened in several directions. Because of the problem of universals, the question of what constitutes the principle of individuation of physical beings became a vital one. Aristotle had had very little to say on this point; since individual entities are prior in being, he seems to have held that "thisness" is rooted in form. But in general, it seems clear that individuation must depend on the multiplicity made possible by matter. Yet primary matter itself is not a "this"; and quantity must be conceded some role in individuation too. thomas aquinas gradually worked out a complex theory, in which quantity is the principle of multiplicity, and primary matter is what constitutes the individual existentially as part of the physical order and as a unique object of reference.
Matter and Limitations. To the Greek mind, lack of limit meant imperfection; primary matter was the "unlimited," whereas form and perfection lay on the side of limit. Plotinus and Aquinas together reversed this: God's perfection lies in His infinity, so that it is the principle of limit that is now imperfect, lacking (see infinity; infinity of god). Thus primary matter is now described as a source of limitation, and the limitation is of a sort that escapes formal intelligible expression. What makes the individual unique is also what makes it material. A further development in Aquinas's doctrine comes from his shifting the boundary between Creator and creature from the matter-form distinction to a new essence-existence distinction, and thus implicitly changing the notion of matter itself. What divides the mutable creature from the Creator, according to St. Thomas, is finite essence, not matter, as Augustine had held. Angels are no longer regarded as "spiritual-material." They can change, but they cannot cease to be. Primary matter is what situates certain creatures in an order in which they can cease to be. It is in no way a stuff (a stuff could never be a principle of uniqueness); it is not an entity at all, but rather the aspect of certain entities that marks them off as corruptible.
What, then, of the notion of a matter-substrate that guarantees permanence throughout change and that serves as a material cause of the change? It seems clear that even in entitative, or substantial, changes there are some continuities, of quantity, of location, etc. When a dog dies, most of the chemical substructures appear to remain. How can one speak here of a featureless substratum? Two answers were given to this question in the 13th century. Aquinas argued that there can be only a single substantial form in any being and that if one such form is succeeded by another, no determination can be properly said to persevere in the substratum. For if one does, the substratum itself is a substance, and one does not have substantial change. But he conceded that various subsidiary forms could be "virtually" present, though subordinated to the principal form, and that these could somehow persevere. Others preferred to say that an organized and unified plurality of forms is "actually" present in the composite and that the subsidiary ones could therefore "actually" persevere in entitative change. (see forms, unicity and plurality of.)
No matter which of these views one follows, it is clear that the substratum of entitative, or substantial, change cannot be regarded as altogether indeterminate, since even the "virtual" form is still a determination. When a dog dies, the substratum of the change must carry certain quantitative and qualitative factors; it is obvious that a dog cannot change into just anything and that this limitation of potency must somehow be borne by the matter-substrate. What Aquinas insists on is the Aristotelian dichotomy between entity (substance) and attribute (accident). The substrate of substantial change cannot be fully qualified by any attribute, or it would have to be itself an entity; no third ontological possibility, he claims, is open. The problem is again one of predication: Can any attribute (e.g., "weighing 20 lbs.") be predicated throughout the change from dog to corpse? Aquinas answers: strictly speaking, no; different substantial forms are involved, and the perseverance of the accidental form of weight is "virtual," not actual.
Matter and Knowledge. One final medieval theme was that of matter as the barrier to knowledge. Some scattered clues in Aristotle were woven into an elaborate theory of abstraction. Physics became the study of "sensible matter," abstracting only from individual differences but still conceived as mutable and qualitatively defined. Mathematics studies "intelligible matter," when one abstracts from all but the quantitative aspects of physical beings. Materiality here connotes both uniqueness and mutability; the more material an object is, the less knowable, on both scores. The Thomistic doctrine of the "three degrees of abstraction" (physics, mathematics, metaphysics) has an unmistakable Platonic overtone, insofar as it is based on degrees of relative distance from matter. (see sciences, classification of.)
Giles of Rome to Newton. The Aristotelian primary matter that was somehow "conserved" in change was not quantified. So how did the notion of a "quantity of matter" conserved through all change arise, the notion that was to give rise in a very complicated way to the concept of mass? The metaphor of materia (stuff) exercised a constant pressure in this direction. Discussions of rarefaction indicated that when bodies expanded and contracted, a factor (often called "quantity of matter") remained the same. giles of rome argued that quantity of matter was the most plausible subject for the accidents that remained in the miracle of transubstantiation. John Buridan suggested that the impetus given a body by its moving cause is proportional to the "quantity of matter" it contains; here matter is not only conserved precisely in its quantity but it also becomes the source of resistance to change of state. This view of matter as working against impressed force was central to J. Kepler's first formulation of the notion of inertia; the Neoplatonic influence on him is clear. I. newton drew together the threads. The concept of mass was the key to his entire dynamics: it is a measure of the response of a given body to impressed force, and is different from weight. Newton speaks of it as "quantity of matter," but nowhere defines what he means by "matter." He appears to have some intuitive "stuff" view in mind; in practice he defines mass in terms of volume and density, thus risking circularity. Matter in his Principia is simply "that of which mass is the quantity." In actual calculations in mechanics, the notion of mass suffices; matter need never be introduced explicitly. Thus does the notion of matter begin to vanish from natural science, as the latter becomes more and more operational.
Descartes to Bergson. But matter continued to be a central category for most metaphysicians. R. descartes went further than Plato had and equated matter with extension, thus making it entirely subject to geometrical thought and reducing physics to geometry. For the rationalistic tradition that followed (N. malebranche, B. spinoza, G. W. leibniz), the problem of matter was the problem of individuation: how could the individual be secured in a world of purely intelligible relations? In the materialist tradition, on the other hand (T. hobbes, J. O. de la Mettrie, etc.), the stress was on matter as opposed to spirit. It was identified with extended body operating under purely mechanical laws, and the existence of spirit was denied. J. locke presented matter as a featureless inert substrate of extension.
G. berkeley launched the phenomenalist attack on this approach to matter by arguing that all man knows is ideas. These are necessarily mind-dependent, so that there is no reason to postulate an independent substratum over against mind, one in which the qualities of perceived objects are supposed to inhere. I. kant in turn criticized Berkeley's view, holding that there must be a principle of "appearance," i.e. matter, that furnishes the object for outer sense and that makes physics irreducible to mathematics. Matter is the barrier to the a priori; it is the source of that which cannot be anticipated. Thus, to assert the "materiality" of the world was, for Kant, a compact way of rejecting both rationalism and phenomenalism.
G. W. F. hegel opposed this view of matter as the ground of appearance and returned to the Plotinian theme of matter as negation, as the product of spirit positing body and exteriority by way of negation. The tension between the materialist and the Hegelian philosophies is sharpest in their notions of matter, and it is thus no wonder that the dialectical materialism of marx was unable to provide a satisfactory treatment of the category of matter, and especially of its relation to mind (see materialism, dialectical and historical). Evolutionary philosophers have seen in matter both the repository of the manifold potentiality of the evolutionary process and a barrier to that process. H. bergson, for instance, builds a basic dualism between life and matter; the impetus of life carries the universe on, but it tends to be "congealed" by the drag of matter.
It will be noted that the notion of matter differs greatly from one to the other of these philosophers, but that in all cases it is one of the central defining concepts of their entire philosophy. It may be noted also that the themes they introduce are recapitulations, often at a more sophisticated level, of the basic matter-themes of Greek philosophy.
See Also: matter, theology of; matter and form.
Bibliography: e. mcmullin, ed., The Concept of Matter (Notre Dame, Ind. 1963). m. jammer, The Concepts of Mass in Classical and in Modern Physics (Cambridge, Mass. 1961). r. eisler, Wörterbuch der philosophischen Begriffe, (4th ed. Berlin 1927–30) 2:80–94. f. c. copleston, History of Philosophy, v.1–7 (Westminster, Md.). g. dinapoli and v. mathieu, Enciclopedia filosofica 3:376–382. h. dolch and m. moser, Lexikon für Theologie und Kirche, 7:163–165. a. michel, Dictionnaire de théologie catholique, ed. a. vacant et al. (Paris 1903–50) 10:335–355.
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