Space
space
(Latin: spatium)
A notion derived by abstraction from our sense impressions. It is conceived as a medium constituted by extra posed parts in which our perceptions of bodies are localized. In so far as there are really existing bodies possessing quantity and hence extension, space may be regarded as real, but as an abstraction it is ideal, in the mind. Such space is uncurved and tri-dimensional, i.e., Euclidian space. Mathematical space may have more than three dimensions and may be curved, either elliptic or hyperbolic. According to Einstein the real space of the world is curved, and hence the physical universe must be finite.
Fuente: New Catholic Dictionary
Space
(Lat. spatium).
The idea of space is one of the most important in the philosophy of the material world; for centuries it has preoccupied and puzzled philosophers and psychologists, and even today the views as to its nature are far from being harmonious.
It is important first to ascertain the exact meaning of the term. In ordinary language space means empty extension occupied by bodies, and in which local motion takes place. This notion of emptiness is so closely connected with it, that the word is often used to mean the distance between bodies. Space is thus put in contrast with bodies, and we imply, more or less unconsciously, that space by itself contains no body—in a word, that it is empty. Evidently space in this popular sense is the extension of the world. It surpasses in magnitude all that the strongest imagination can picture, and consequently it is assigned no limits. Not indeed that space, in the popular sense, is considered strictly infinite; but rather it is conceived as something “indefinite”. Again, space, in the popular mind, is clearly conceived as being tri-dimensional, that is, we can draw in it three straight lines each of which is perpendicular to both of the others, and which exhaust all its dimensional possibilities.
The concept which mathematicians form of space does not correspond in every respect with the popular notion. The geometrician is concerned only accidentally with the space of the world. From it he derives his idea of mathematical space; but he eliminates from it all predicates which are not absolutely necessary to establish his geometrical relations. Mathematical space therefore abstracts from all existence. It is conceived as an extensive, continuous, abstract quantity, in which geometrical points and places can be determined. Mathematical space is said to be infinite—not a metaphysical infinity, which affirms the positive absence of all limits, and with which the mathematician has no concern, but that mathematical infinity, which signifies that the nature of a reality is such that no limit can be assigned to it. The distinction between mathematical and metaphysical infinity is somewhat subtle, but it is real; it prevents much confusion and facilitates the solution of difficult problems. It may be remarked here that mathematical space is not necessarily tri-dimensional or homogeneous, matters to which we shall refer presently.
Philosophers cannot be satisfied with mathematical space, an abstract construction useful for theoretical purposes, for they wish to arrive at the real space of nature. Nor can they restrict themselves to the popular notion, for their task is precisely to purify the data of common sense from all the extraneous factors modifying them and giving rise to latent contradictions. But in their efforts to discover pure and real space, they have sometimes arrived at the most perplexing results; so that many philosophers, while not subscribing to the doctrines of Kantian criticism, consider the idea of space as hopelessly contradictory, as a purely illusory fancy. To recall all the successive explanations of the nature of real space given by the great philosophers it would be necessary to go through the history of philosophy; but, leaving aside the complete negation of extension, all the doctrines, from Hesiod (cf. Aristotle, IV Phys., vi, 213b) to our day, fluctuate between the idea of absolute space, a real substance independent of the bodies it contains, and purely relative space, a mental fiction based on the real extension of material bodies. The most radical expressions of these two conflicting views are those of Newton and Clarke, on the one hand, who consider space as the sensorium of God, and on the other, of Leibniz, who asserts that there is no space independent of extended bodies, and reduces it to “the order of co-existing things”.
The traditional philosophy of the Catholic schools rejects absolute space. Newton’s idea is incompatible with the concept which the great doctors of the school, following Aristotle, formed of quantity. Suarez declares that space is only “a conceptual entity [ens rationis], not, however, formed at will like chimeras, but extracted form bodies, which by their extension are capable of constituting real spaces” (Met. disp., 51). The expression ens rationis may be equivocal, but it expresses somewhat exaggeratedly the very active part played by the human intellect in the construction of space. Space is not material bodies themselves, since it appears to be rather a receptacle containing them. From this point of view it must be pure extension, an unqualified quantity. In the strict sense of the terms a quantity without quality is contradictory; for quantity is only the multiplicity of the homogeneous parts in the unity of a body; it is the distribution of an essence, simple in its formal determination. Multiplicity implies a thing that is multiplied, and distribution something that is distributed. Every quantity is the quantity of something; all extension is therefore, in itself, the extension of an extended substance. Yet quantity is something more more than a modal accident; it is in truth the absolute accident par excellence (see ACCIDENT); it confers on a substance a perfection such that, granted the existence of a substance, the corporeal body is measured by its quantity. It is none the less true that quantity postulates a quantitative substance; and, in a sense, entirely different however from the fancies of ancient physics, it may always be said that an empty quantity is a contradiction in terms. From this we must conclude that extension is only a derivative of quantity; a non-qualified extension, pure extension, pure space in the reality of the corporeal world is contradictory. We conceive it, however, and what is, properly speaking, contradictory is inconceivable. The contradiction arises when we add the condition of existence to pure space. Space is not contradictory in the mind, though it would be contradictory in the real world, because space is an abstraction. Extension is always the extension of something; but it is not the thing extended. Mentally we can separate extension from the substances from which we distinguish it; and it is extension thus separated, conceived apart, which constitutes the space of the universe. Space is therefore as real, as objective, as the corporeal world itself, but in itself it exists apart only in the human mind, seeing that in the reality of existing things it is only the extension of bodies themselves.
Space thus conceived avoids many of the difficulties raised against its reality. But there still remain questions that have taxed the ingenuity of philosophers. What is to be thought of the infinity of space, which to many philosophers seems to be an indisputable postulate? Here we must carefully distinguish the two ideas to which we alluded above. Mathematicians do not understand infinity in the same sense as philosophers. The latter consider absolute infinity as the plenitude of being, being itself; spatial infinity for them can signify only plenitude of extension. There are no limits to an infinite space, nowhere can there exist a definite relation to its extremities or even to itself. It is impossible to add even mentally anything to such extension, for it would be an absurdity to conceive anything greater than infinite extension. Mathematical infinity is something quite different. It is not considered solely in relation to the being to which it is attributed, but in relation to this being and to the determinations of limits possible to the intellect. Whatever by its nature surpasses all the limits we can assign it, that is mathematically infinite. It must be carefully noted that these two ideas in no way coincide, since it is possible that the intellect may not grasp the nature of a being fully enough to determine its limits: the possibility that its nature may surpass all assignable limits does not involve the conclusion that the being is in itself unlimited. Mathematical infinity introduces into the problem a factor extrinsic to the nature of the being: the relative perfection, or rather the imperfection, of the human idea; and it is noteworthy that in all problems concerning quantity our intellect is, to a very great extent, dependent on our senses and our imagination. This distinction being established, we may remark that real space evidently surpasses all that experience can teach us. We are forced, consequently, to solve the problem by analysis.
Mathematical space is abstract and mathematically infinite; but we are dealing here with the real universe. The notion of mathematical infinity may be applied to it in a secondary sense. The nature of real space is such as not to demand any definite dimensions. No part of space in itself needs be the last. For all we know, or do not know, about it, space may be greater than any limits whatsoever we might assign. But space cannot be metaphysically infinite. It is impossible to have an actual quantitive infinite being composed of finite parts. To infinite extension nothing can be added, and from it nothing can be taken away, even mentally. For if, by hypothesis, infinite extension is divided in two, neither of the parts is infinite since neither by itself contains the plenitude of extension. Both therefore are finite; by their union they would form the original whole, but it is absurd to imagine that an infinite whole is formed by the union of two finite parts. It is clear that we can mentally take way a portion of space. Hence it is clear that space cannot be metaphysically infinite. An actually infinite quantity is a contradiction in terms. Here of course our imagination cannot follow our intellect. We cannot represent exactly to ourselves what may be the limits of the world; and it is clear that in this case certain physical laws, those of motion for instance, cannot be fully applied. It is useless to discuss the subject further because, owing to the limitations of our experience, we are apt to indulge in mere fantastic and arbitrary speculations.
A still more abstruse subject is reached when we come to deal with the number of dimensions of space and its homogeneity. Our imagination always represents real space as having but three dimensions. We reach this intuitive space (see below) spontaneously; it seems to us so natural, so inevitable, that we have great difficulty in freeing ourselves from the domination of this image, and in conceiving (to imagine it is impossible) a space with more than three dimensions. However, the question has been raised; for geometricians reason frequently about a space of four, of five, or of n dimensions. The problem is not of the experimental order. Our sensory experiences and everything in practical life reveal only three dimensions. But does experience exhaust the possibilities of real space? And can this space have no more than three dimensions? Nothing obliges us to believe that such is the case. The material world requires essentially only quantity, and this is not identical with extension. Quantity confers on substance a multiplicity of parts; extension supposes this multiplicity and gives a relative position to the parts. Quantity implies a distinction of parts, extension adds extraposition, i. e. the placing of part outside of part; hence it will be seen that, in a strict sense, material beings do not necessarily postulate extension. It would then be quite arbitrary to declare a priori that they must have extension according to three mutually perpendicular directions, and that they cannot have any more. The word dimensions is here used, of course, only by analogy with the three dimensions perceived by experience; we can get at pure quantity only through extension. But the intellect in its analysis goes beyond the data offered to it by sense, and it is forced to conclude that space of more than three dimensions implies no contradiction.
By a very similar process we can solve the problem, so perplexing for the average mind, of the homogeneity of space. The essential properties of quantity require no definite number of dimensions. The same may be said of the quality, or rather intensity, of extension: the parts may be more or less extraposed. The parts, remaining the same, may give a greater or a less extension in the ordinary sense of the word. There is nothing contradictory, therefore, in all the parts of space being everywhere equally extraposed, in which case space would be homogeneous. But, on the other hand, there is no reason why space should not be differently extraposed in different parts, and if this be so, space would be heterogeneous; and if the variation be simple and constant, we can formulate the laws of these spaces and determine the properties of the figures formed therein. This explains why geometry, so rigorous in its methods and simple in its postulates, is not necessarily one. The ancient geometry of Euclid takes for granted the homogeneity of space; but it is well known that non-Euclidian geometries have been constructed, notably those of Riemann and of Lobatchewski, differing from Euclid’s and yet free form all incoherency.
These speculations on the nature of space cannot, however, do away with the fundamental fact that the human mind is dominated by an image, imposing irresistibly on it a homogeneous tri-dimensional space. One of the central questions of classic psychology concerns the origin of this representation. We dismiss Kant’s well-known view, that space is an a priori form of sensory activity. But psychologists fluctuate between two extremes: on the one hand, nativism, represented by Johann Müller, Fichte, Sigwart, Mach, and many others; and on the other hand, empiricism, followed by Locke, Hume, Condillac, Maine de Biran, John Stuart Mill, Bain, Spencer, and others. The former hold that we obtain the image of space from the primordial subjective dispositions of our mentality; and many of them see therein a condition precedent of all experience. The second class, on the contrary, believe that this image is acquired, that it results from visual and tactile impressions and is only a result of association. Many authorities hesitate and try to discover an intermediate position. From the facts adduced and the analysis to which they have been subjected it seems clear that the image of space is in reality acquired like all other images: in very young children we see it, so to say, in process of formation. It is the result of the spontaneous interpretation of all the extensive sensations; and it is because this interpretation takes place in the simplest manner that our intuitive space is homogeneous and tri-dimensional. Evidently this elaboration supposes a special nature in the subject, the faculty of receiving extensive impressions, and that of combining them by synthesis. But this is natural to man, and there is nothing to justify us in speaking of an innate image of space.
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Every philosopher and psychologist has treated the question of space; here merely a few important works are cited to help towards a deeper study of the question.—FARGES, L’idée du continu dans l’espace et le temps (Paris, 1892); HODGSON, Time and Space (London, 1865); JAMES, Perception of Space in Mind, XII (1887); FULLERTON, The Doctrine of Space and Time in Philos. Rev., X (1901); GUTBERLET, Die neue Raumtheorie (Mainz, 1882); WILLEMS, Institutiones philosophicæ, II (Trier, 1906); NYS, La notion d’sepace au point de vue cosmologique et psychologique (Louvain, 1901); WUNDT, Grundiss der Psychologie (Leipzig, 1907); IDEM, Grundzüge der physiol. Psychologie, II (Leipzig, 1903); HÖFFDING, Esquisse d’une psychologie basée sur l’expérience (Paris, 1906); EBBINGHAUS-DURR, Grundzüge der Psychologie (Leipzig, 1911); ZIEHEN, Physiologische Psychologie (Jena, 1911); EISLER, Wörterbuch der philosophischen Begriffe (Berlin, 1910); BERGSON, Essai sur les données immédiates de la conscience (Paris, 1908).
M. P. DE MUNNYNCK Transcribed by Thomas J. Bress
The Catholic Encyclopedia, Volume XIVCopyright © 1912 by Robert Appleton CompanyOnline Edition Copyright © 2003 by K. KnightNihil Obstat, July 1, 1912. Remy Lafort, S.T.D., CensorImprimatur. +John Cardinal Farley, Archbishop of New York
Fuente: Catholic Encyclopedia
Space
(Lat. spatium) is a term which, taken in it, most general sense, comprehends whatever is extended and may be measured by the three dimensions, length breadth, and depth. In this sense it is the same with extension. Space, in this large significance, is either occupied by body or it is not. If it be not, but is void of all matter and contains nothing, then it is space in the strictest meaning of the word. This is the sense in which it is commonly used in English philosophical language, and is the same with what is called a vacuum.
Very many theories have been held respecting space a few of which are mentioned below. Zelio of Elea argues against the reality of space, and says, If all that exists were in a given space, this space must be in another space, and so on ad infinitum. Melissus of Samo, declares that there exists no empty space, since such a space, if it existed, would be an existing nothing.
The Atomists, on the other hand, held to an empty space, arguing
(1) that motion requires a vacuum;
(2) that rarefaction and condensation are impossible without empty intervals of space; and
(3) that organic growth depends on the penetration of nutriment into the vacant spaces of bodies. Aristotle held that; space is limited; the world possesses only a finite extension; outside of it is no place.
The place of anything, he defines, is the inner surface of the body surrounding it, that surface being conceived as fixed and immovable. As nothing exists outside of the world except God, who is pure thought and not in space, the world naturally cannot be in space, i.e. its place cannot be defined. The Stoics believed that beyond the world exists an unlimited void. According to Epicurus, space exists from eternity, and that in the void spaces between the worlds the gods dwell. Arnobius, the African, asserted that God is the place and space of all things. Space, as containing all things, was by Philo and others identified with the infinite. So the text (Act 17:28) which says that in God we live, and move, and have our being was interpreted to mean that space is an affection or property of the Deity. Eckhart declares that out of God the creature is a pure nothing; time and space, and the plurality which depends on them, are nothing in themselves.
According to Campanella (1568-1639), God produced space (as well as ideas, angels, etc.) by mingling in increasing measures nonbeing with his pure being. Space is animate, for it dreads a vacuum and craves replenishment. Newton regards space as infinite, the sensorium of the Deity. Leibnitz defines space as the order of possible coexisting phenomena. Locke has attempted to show that we acquire the idea of space by sensation, especially by the senses of touch and sight. In the philosophy of Kant, space and time are mere forms of the sensibility, the form of all external phenomena; and as the sensibility is necessarily anterior in the subject to all real intention, it follows that the form of all these phenomena is in the mind a priori. There can, then, be no question about space or extension but in a human or subjective point of view. The idea of space has no objective validity; it is real only relatively to phenomena, to things, in so far as they appear to us; it is purely ideal in so far as things are taken in themselves and considered independently of the forms of sensibility, Herder says that space and time are empirical conceptions. Schopenhauer teaches, with Kant, that space, time, etc., have a purely subjective origin, and are only valid for phenomena, which are merely subjective representations in consciousness. Space and time have the peculiarity that all of their parts stand to each other in a relation, with reference to which each of them is determined and conditioned by another. In space this relation is termed position, in time it is termed sequence.
Herbart holds that extension in space involves a contradiction. Extension implies prolongation through numerous different and distinct parts of space, but by such prolongation the one is broken up into the many, while yet the one is to be considered as identical with the many. Trendelenburg seeks to show that space is a product or phase of motion, its, immediate external manifestation. In the philosophy of Thomas Reid (1785), space and its relations, with the axioms concerning its existence and its relations, are known directly in connection with the senses of touch and sight, but not as objects of these senses. James Mill thus explains infinite space: We, know no infinite line, but we know a longer and a longer …. In the process, then, by which we conceive the increase of a line the idea of one portion more is continually associated with the preceding length, and to what extent soever it is carried the association of one portion more is equally close and irresistible. This is what we call the idea of infinite extension, and what some people call the necessary idea. According to lord Monboddo, place is space occupied by body. It is different from body as that which contains is different from that which is contained. Space, then, is place potentially; and when it is filled with body, then it is place actually. See Krauth’s Fleming, Vocabulary of the Philosophical Sciences, s.v.;. Ueberweg, Hist. of Philosophy (see Index).
Fuente: Cyclopedia of Biblical, Theological and Ecclesiastical Literature
Space
In Aristotle, the container of all objects. In the Cambridge Platonists, the sensorium of God. In Kantthe a priori form of intuition of external phenomena. In modern math., name for certain abstract invariant gioups or set’s. See Space-Time. — P.P.W.
Fuente: The Dictionary of Philosophy
Space
“an interval, space” (akin to B), is used of time in Act 5:7.
“to set apart, separate” (dia, “apart,” histemi, “to cause to stand”), see A, is rendered “after the space of” in Luk 22:59; in Act 27:28, with brachu, “a little,” RV, “after a little space” (AV, “when they had gone a little further”). See PART.
Notes: (1) In Act 15:33; Rev 2:21, AV, chronos, “time” (RV), is translated “space.” (2) In Act 19:8, Act 19:10, epi, “for or during” (of time), is translated “for the space of;” in Act 19:34, “about the space of.” (3) In Act 5:34, AV, brachu (the neuter of brachus, “short”), used adverbially, is translated “a little space” (RV “… while”). (4) In Gal 2:1, dia, “through,” is rendered “after the space of,” RV, stressing the length of the period mentioned (AV, “after,” which would represent the preposition meta). (5) In Jam 5:17 there is no word in the original representing the phrase “by the space of,” AV (RV, “for”). (6) In Rev 14:20, AV, apo, “away from,” is translated “by the space of” (RV, “as far as”). (7) In Rev 17:10, AV, oligon, “a little while” (RV), is rendered “a short space.”