Chapter VIII: A Startling Disclosure (4)

“Yes,” she said fervently. “To be punished, and yet the very punishment to contain the power to pray on still--to speak to God--to plead with him for souls, the souls he died for on the cross. What though one were shut for all time in Friar’s Rock, if one trusted that at the end the Vision of God would be his for ever, and till then could and must ask him continually to have mercy on immortal souls? Or who would not live that living death in _Dol des Fées_ to live it in prayer at the altar, and to die a martyr’s death?

“Joanne, my darling, what, after all, are sorrow and death and separation and loneliness to us who can speak to God? In him we are all brought near. His blood makes each of his children dear to those who love him. Day by day to forget self in them, in him; day by day to let grief or pleasure grow less and less in one absorbing prayer that his kingdom come; day by day to lose one’s self in him--_that_ is living, and _that_ is loving. I cannot mourn much for my precious ones that are only absent from my sight, but safe and present with him; my tears are for souls that are _not_ safe, the wide world over; and I cannot miss much what I have never really lost. A thousand times Friar’s Rock speaks to me, and this is what it says:

“‘If thou, Lord, wilt mark iniquities, Lord, who shall stand it?

“‘For with thee there is merciful forgiveness; and by reason of thy law I have waited--_for thee_, O Lord.

“‘From the morning watch even until night, let Israel hope in the Lord.

“‘Because with the Lord there is mercy, and with him plentiful redemption.

“‘And he shall redeem Israel from all his iniquities.’”

It was years ago, as I have said, that Anne d’Estaing told me this legend. Since then, her parents have died, the château has passed into other hands, she is head of a convent in Bretagne, and I--I lie here, the last of my name, a hopeless invalid, with not a penny to call my own. Rich once, and young, and fair, and proud; sad once, and doubting how to bear a lonely future, I know the meaning of Anne’s story now. “I have waited _for thee_, O Lord! And he shall redeem Israel from all his iniquities.”

While I wait for him, I pray. It does not grieve me that I do not hear from Anne. La Mère Angélique is more to me, and nearer to me, than when, in days long past, we spoke face to face. For I _know_ we meet in the sure refuge of the Sacred Heart of Jesus, and that, with saints on earth and saints in glory, and the souls beneath the altar, we pray together the same prayer--“Thy kingdom come.”

DUNLUCE CASTLE.

(COUNTY ANTRIM.)

Oh! of the fallen most fallen, yet of the proud
Proudest; sole-seated on thy tower-girt rock;
Breasting for ever circling ocean’s shock;
With blind sea-caves for ever dinned and loud;
Now sunset-gilt; now wrapt in vapor-shroud;
Till distant ships--so well thy bastions mock
Primeval nature’s work in joint and block--
Misdeem _her_ ramparts, round thee bent and bowed,
For thine, and on _her_ walls, men say, have hurled
The red artillery store designed for thee:--
Thy wars are done! Henceforth perpetually
Thou restest, like some judged, impassive world
Whose sons, their probatory period past,
Have left that planet, void amid the vast.

AUBREY DE VERE.

SPACE.

III.

Bodies have bulk or volume, whereby they are said to occupy a certain place, and to fill it with their dimensions. Hence, to complete our task, we have now to consider space in relation with the volumes and places of bodies. To proceed orderly, we must first determine the proper definition of “place,” and its division; then we shall examine a few questions concerning the relation of each body to its place, and particularly the difficult and interesting one whether bodies can be really bilocated and multilocated.

_Place._--Aristotle, in the fourth book of his _Physics_, defines the place of a body as “the surface by which the body is immediately surrounded and enveloped”--“_Locus est extrema superficies corporis continentis immobilis._” This definition was accepted by nearly all the ancients. The best of their representatives, S. Thomas, says: “_Locus est terminus corporis continentis_”--viz., The place of a body is the surface of the body which contains it; and the Schoolmen very generally define place to be “the concave surface of the surrounding body: _Superficies concava corporis ambientis._” Thus, according to the followers of Aristotle, no body can have place unless it is surrounded by some other body. Immobility was also believed to be necessarily included in the notion of place: _Superficies immobilis._ Cardinal de Lugo says: “the word _place_ seems to be understood as meaning the real surface of a surrounding body, not, however, as simply having its extension all around, but as immovable--that is, as attached to a determinate imaginary space.”[179] We do not see what can be the meaning of this last phrase. For De Lugo holds that “real space” is the equivalent of “place,” and that space, as distinguished from place, is nothing real: _Non est aliquid reale._[180] His imaginary space is, therefore, a mere nothing. How are we, then, to understand that a real surface can be “attached to a determinate imaginary space”? Can a real being be attached to a determinate nothing? Are there many nothings? or nothings possessing distinct determinations? We think that these questions must all be answered in the negative, and that neither Cardinal de Lugo, nor any one else who considers imaginary space as a mere nothing, can account for the immobility thus attributed to place.

The reason why Aristotle’s definition of place came to be generally adopted by the old Schoolmen is very plain. For, in the place occupied by any given body, two things can be considered, viz., the limiting surface, and the dimensive quantity which extends within the limiting surface. Now, as the ancients believed the matter of which bodies are composed to be endowed with continuity, it was natural that they should look upon the dimensive quantity included within the limiting surface as an appurtenance of the matter itself, and that they should consider it, not as an intrinsic constituent of the place occupied, but as a distinct reality through which the body could occupy a certain place. According to this notion of dimensive quantity, the limiting surface was retained as the sole constituent of the place occupied; and the dimensions within the surface being thus excluded from the notion of place, were attached to the matter of the body itself, as a special accident inhering in it.

This manner of conceiving things is still looked upon as unobjectionable by those philosophers who think that the old metaphysics has been carried to such a degree of perfection by the peripatetics as to have nothing or little to learn from the modern positive sciences. But whoever has once realized the fact that the dimensions of bodies are not continuous lines of matter, but intervals, or relations, in space, will agree that such dimensions do not _inhere_ in the matter, but are extrinsic relations between material terms distinctly ubicated. What is called the volume of a body is nothing but the resultant of a system of relations in space. The matter of the body supplies nothing to its constitution except the extrinsic terms of the relations. The foundation of those relations is not to be found in the body, but in space alone, as we have proved in our last article; and the relations themselves do not _inhere_ in the terms, but only _intervene_ between them. Hence the dimensive quantity of the volume is intrinsically connected with the place it occupies, and must enter into the definition of place as its material constituent, as we are going to show.

As to the Aristotelic definition of place, we have the following objections: First, a good definition always consists of two notions, the one generic and determinable, as its material element, the other differential and determinant, as its formal element. Now, Aristotle’s definition of place exhibits at best only the formal or determinant, and omits entirely the material or determinable. It is evident, in fact, that the surface of any given body determines the limits and the figure of something involved in the notion of place. But what is this something? It cannot be a mere nothing; for nothing does not receive limits and figure, as real limits and real figure must be settled upon something real. This something must therefore be either the quantity of the matter, or the quantity of the volume enclosed within the limiting surface. And as we cannot admit that the quantity of the place occupied by a body is the quantity of matter contained in the body (because bodies which have different quantities of matter can occupy equal places), we are bound to conclude that the quantity of the place occupied by a body is the quantity of the volume comprised within the limiting surface. This is the determinable or material constituent of place; for this, and this alone, is determined by the concave surface of the surrounding body. In the same manner as a cubic body contains dimensions within its cubic form, so also a cubic place contains dimensions under its cubic surface; hence the place of a body has volume, the same volume as the body; and therefore it cannot be defined as a mere limiting surface.

Secondly, the definition of a thing should express what every one understands the thing to be. But no one understands the word “place” as meaning the exterior limit of the body which occupies it, therefore the exterior limit of the body is not the true definition of place. The minor of this syllogism is manifest. For we predicate of place many things which cannot be predicated of the exterior limit of the body. We say, for instance, that a place is full, half-full, or empty; that it is capable of so many objects, persons, etc.; and it is plain that these predicates cannot appertain to the exterior limit of the body, but they exclusively belong to the capacity within the limiting boundary. Hence a definition of place which overlooks such a capacity is defective.

Thirdly, to equal quantities of limiting surfaces do not necessarily correspond equal quantities of place. Therefore, the limiting surface is not synonymous with place, and cannot be its definition. The antecedent is well known. Take two cylinders having equal surfaces, but whose bases and altitudes are to one another in different ratios. It is evident by geometry that such cylinders will have different capacities--that is, there will be more occupable or occupied room in the one than in the other. The consequence, too, is plain; for, if the room, or place, can be greater or less while the limiting surface does not become greater or less, it is clear that the place is not the limiting surface.

Fourthly, what Aristotle and his school called “the surface of the surrounding body,” is now admitted to be formed by an assemblage of unextended material points, perfectly isolated; and therefore such a surface does not constitute a continuous material envelope, as it was believed in earlier times. Now, since those isolated points have no dimensions, but are simply terms of the dimensions in space, the so-called “surface” owes its own dimensions to the free intervals between those points, just as the dimensions also of the volume enclosed owe their existence to similar intervals between the same points. Therefore the same terms which mark in space the limit of place, mark also its volume; and thus the volume under the surface belongs to the place itself no less than does the limiting surface.

Fifthly, a body in vacuum would have its absolute place; and yet in vacuum there is no surface of surrounding bodies. Therefore an exterior surrounding body is not needed to constitute place. In fact, the body itself determines its own place by the extreme terms of its own bodily dimensions. This the philosophers of the peripatetic school could not admit, because they thought that the place of the body could not move with the body, but ought to remain “attached to a determinate imaginary space.” But, in so reasoning, they confounded the absolute place with the relative, as will be shown hereafter. Yet they conceded that a body in vacuum would have its place; and, when asked to point out there the surface of a surrounding body, they could not answer, except by abandoning the Aristotelic definition and by resorting to the centre and the poles of the world, thus exchanging the absolute place (_locus_) for the relative (_situs_), without reflecting that they had no right to admit a relative place where, according to their definition, the absolute was wanting.

Sixthly, the true definition of place must be so general as to be applicable to all possible places. But the Aristotelic definition does not apply to all places. Therefore such a definition is not true. The major of our argument needs no proof. The minor is proved thus: There are places not only within surfaces, but also within lines, and on the lines themselves; for, if on the surface of a body we describe a circle or a triangle, it is evident that a place will be marked and determined on that surface. Its limiting boundary, however, will be, not the surface of a surrounding body, but simply the circumference of the circle, or the perimeter of the triangle.

For these reasons we maintain that place cannot properly be defined as “the surface of the surrounding body.” As to the additional limitation, that such a surface should be considered as “immovable”--that is, affixed to a determinate space (imaginary, of course, according to the peripatetic theory, and therefore wholly fictitious)--we need only say that even if it were possible to attach the surface of a body to a determinate space, which is not the case, yet this condition could not be admitted in the definition of place, because the _absolute_ place of a body is invariably the same, wherever it be, in absolute space, and does not change except as compared with other places. Absolute place, just as absolute ubication, has but one manner of existing in absolute space; for all places, considered in themselves, are extrinsic terminations of the _same_ infinite virtuality, and are all _equally_ in the centre, so to say, of its infinite expanse, whatever be their mutual relations.

_True Notion of Place._--What is, then, the true definition of place? Webster describes it in his _Dictionary_ as “a particular portion of space of indefinite extent, occupied, or intended to be occupied, by any person or thing, and considered as the space where a person or thing does or may rest, or has rested, as distinct from space in general.” This is in fact the meaning of the word “place” in the popular language. The philosophical definition of place, as gathered from this description, would be: “Place is a particular portion of space.” This is the very definition which all philosophers, before Aristotle, admitted, and which Aristotle endeavored to refute, on the ground that, when a body moves through space, its place remains intrinsically the same.

We have shown in our last article that space considered in itself has no parts; but those who admit portion of space, consider space as a reality dependent on the dimensions of the bodies by which it is occupied--that is, they call “space” those resultant relative intervals which have their foundation in space itself. If we were to take the word “space” in this popular sense, we might well say that “place is a portion of space,” because any given place is but one out of the many places determined by the presence of bodies in the whole world. On the other hand, since space, properly so called, is itself _virtually_ extended--that is, equivalent in its absolute simplicity to infinite extension, and since _virtual_ extension suggests the thought of _virtual_ parts, we might admit that there are _virtual_ portions of space in this sense, that space as the foundation of all local relations corresponds by its virtuality to all the dimensions and intervals mensurable between all terms ubicated, and receives from them distinct extrinsic denominations. Thus, space as occupied by the sun is virtually distinguished from itself as occupied by the moon, not because it has a distinct entity in the sun and another in the moon, but because it has two distinct extrinsic terminations. We might therefore admit that place is “a virtual portion of space determined by material limits”; and we might even omit the epithet “virtual” if it were understood that the word “space” was taken as synonymous with the dimensions of bodies, as is taken by those who deny the reality of vacuum. But, though this manner of speaking is and will always remain popular, owing to its agreement with our imagination and to its conciseness, which makes it preferable for our ordinary intercourse, we think that the place of a body, in proper philosophical language, should be defined as “a system of correlations between the terms which mark out the limits of the body in space”; and therefore place in general, whether really occupied or not, should be defined as “a system of correlations between ubications marking out the limits of dimensive quantity.”

This definition expresses all that we imply and that Webster includes in the description of place; but it changes the somewhat objectionable phrase “portion of space” into what people mean by it, viz., “a system of correlations between distinct ubications,” thereby showing that it is not the absolute entity of fundamental space, but only the resultant relations in space, that enter into the intrinsic constitution of place.

By “a system of correlations” we mean the adequate result of the combination of all the intervals from every single term to every other within the limits assumed, in every direction. Such a result will therefore represent either a volume, or a surface, or a line, according as the terms considered within the given limits are differently disposed in space. Thus a spherical place results from the mutual relations intervening between all the terms of its geometric surface; and therefore it implies all the intervals which can be measured, and all the lines that can be traced, in all directions, from any of those terms to any other within the given limits. In like manner, a triangular place results from the mutual relations intervening between all the terms forming its perimeter; and therefore it implies all the intervals and lines of movement which can be traced, in all directions, from any of those terms to any other within the given limits.

In the definition we have given, the material or determinable element is the system of correlations or intervals which are mensurable within the limiting terms; the formal or determinant is the disposition of the limiting terms themselves--that is, the definite boundary which determines the extent of those intervals, and gives to the place a definite shape.

Thus it appears that, although there is no place without space, nevertheless the entity of space does not enter into the constitution of place as an intrinsic constituent, but only as the extrinsic foundation. This is what we have endeavored to express as clearly as we could in our definition of place. As, however, in our ordinary intercourse we cannot well speak of place with such nice circumlocutions as are needed in philosophical treatises, we do not much object to the common notion that place is “space intercepted by a limiting boundary,” and we ourselves have no difficulty in using this expression, out of philosophy, owing to the loose meaning attached to the word “space” in common language; for all distances and intervals in space are called “spaces,” even in mechanics; and thus, when we hear of “space intercepted,” we know that the speakers do not refer to the absolute entity of space (which they have been taught to identify with nothingness), but merely to the intervals resulting from the extrinsic terminations of that entity.

Most of the Schoolmen (viz., all those who considered void space as imaginary and unreal) agreed, as we have intimated, with Aristotle, that the notion of place involves nothing but the surface of a surrounding body, and contended that within the limits of that surface there was no such chimerical thing as mere space, but only the quantity of the body itself. Suarez, in his _Metaphysics_ (Disp. 51, sect. 1, n. 9), mentions the opinion of those who maintained that place is the space occupied by a body, and argues against it on the ground that no one can say what kind of being such a space is. Some have affirmed, says he, that such a space is a body indivisible and immaterial--which leads to an open contradiction--though they perhaps considered this body to be “indivisible,” not because it had no parts, but because its parts could not be separated. They also called it “immaterial,” on account of its permeability to all bodies. But this opinion, he justly adds, is against reason and even against faith; for, on the one hand this space should be eternal, uncreated, and infinite, whilst on the other no body can be admitted to have these attributes.

Others, Suarez continues, thought that the space which can be occupied by bodies is mere quantity extending all around without end. This opinion was refuted by Aristotle, and is inadmissible, because there cannot be quantitative dimensions without a substance, and because the bodies which would occupy such a space have already their own dimensions, which cannot be compenetrated with the dimensions of space. And moreover, such a quantity would be either eternal and uncreated--which is against faith--or created with all other things, and therefore created in space; which shows that space itself is not such a quantity.

Others finally opine, with greater probability, says he, that space, as distinct from the bodies that fill it, is nothing real and positive, but a mere emptiness, implying both the absence of bodies and the aptitude to be filled by bodies. Of this opinion Toletus says (4 _Phys._ q. 3) that it is probable, and that it cannot be demonstratively refuted. Yet, adds Suarez, it can be shown that such a space, as distinct from bodies, is in fact nothing; for it is neither a substance nor an accident, nor anything created or temporal, but eternal.

Such is the substance of the reasons adduced by Suarez to prove that the space occupied by bodies is nothing real. Had he, like Lessius, turned his thought to the extrinsic terminability of God’s immensity, he would have easily discovered that, to establish the reality of space, none of those old hypotheses which he refuted were needed. As we have already settled this point in a preceding article, we will not return to it. It may, however, be remarked that what Suarez says regarding the incompenetrability of the quantity of space with the quantity of the body is based entirely on the assumption that bodies have their own volume independently of space--an assumption which, though plausibly maintained by the ancients, can by no means be reconciled with the true notion of the volume of bodies as now established by physical science and accepted by all philosophers. As all dimensive quantity arises from relations in space, so it is owing to space itself that bodies have volume; and therefore there are not, as the ancients imagined, two volumes compenetrated, the one of space, and the other of matter; but there is one volume alone determined by the material terms related through space. And thus there is no ground left for the compenetration of two quantities.

S. Thomas also, in his Commentary to the _Physics_ of Aristotle (4 _Phys._ lect. 6), and in the opuscule, _De Natura Loci_, argues that there is no space within the limiting surface of the body, for two reasons. The first is, that such a quantity of space would be an accident without a subject: _Sequitur quod esset aliquod accidens absque subjecto; quod est impossibile_. The second is, that if there is space within the surface of the body, as all the parts of the body are in the volume of the same, so will the places of all the parts be in the place of the whole; and consequently, there will be as many places compenetrated with one another as there can be divisions in the dimensions of the body. But these dimensions admit of an infinite division. Therefore, infinite places will be compenetrated together: _Sequitur quod sint infinita loca simul; quod est impossibile_.

These two reasons could not but have considerable weight in a time when material continuity formed the base of the physical theory of quantity, and when space without matter was considered a chimera; but in our time the case is quite different. To the first reason we answer, that the space within the surface of the body will not be “an accident without a subject.” In fact, such a space can be understood in two manners, viz., either as the foundation of the intervals, or as the intervals themselves; and in neither case will there be an accident without a subject. For, the space which is the foundation of the intervals is no accident; it is the virtuality of God’s immensity, as we have proved; and, therefore, there can be no question about its subject. Moreover, such a space is indeed within the limits of the body, but it is also without, as it is not limited by them. These limits, as compared with space, are extrinsic terms; and therefore they do not belong to space, but to the body alone. Lastly, although without space there can be no place, yet space is neither the material nor the formal constituent of place, but only the extrinsic ground of local relations, just as eternity is not an intrinsic constituent of time, but only the extrinsic ground of successive duration. Whence it is manifest that the entity of space is not the dimensive quantity of the body, but the eminent reason of its dimensions.

If, on the other hand, space is understood in the popular sense as meaning the accidental intervals between the limits of the body, then it is evident that such intervals will not be without their proportionate subject. Relations have a subject of predication, not of inhesion; for relation is a thing whose entity, according to the scholastic definition, consists entirely of a mere connotation; _cuius totum esse est ad aliud se habere_. Hence all relation is merely _ad aliud_, and cannot be _in alio_. Accordingly, the intervals between the terms of the body are _between_ them, but do not inhere in them; and they have a sufficient subject--the only subject, indeed, which they require, for the very reason that they exist _between_ real terms, with a real foundation. Thus the first reason objected is radically solved.

To the second reason we answer, that it is impossible to conceive an infinite multitude of places in one total place, unless we admit the existence of an infinite multitude of limiting terms--that is, unless we assume that matter is mathematically continuous. But, since material continuity is now justly considered as a baseless and irrational hypothesis, as our readers know, the compenetration of _infinite_ places with one another becomes an impossibility.

Yet, as all bodies contain a very great number of material terms, it may be asked: Would the existence of space within the limits of place prove the compenetration of a _finite_ number of places? Would it prove, for instance, that the places of different bodies existing in a given room compenetrate the place of the room? The answer depends wholly on the meaning attached to the word “space.” If we take “space” as the foundation of the relations between the terms of a place, then different places will certainly be compenetrated, inasmuch as the entity of space is the same, though differently terminated, in every one of them. But, if we take “space” as meaning the system of relative intervals between the terms of a body, then the place of a room will not be compenetrated with the places of the bodies it contains; because neither the intervals nor the terms of one place are the intervals or the terms of another, nor have they anything common except the absolute entity of their extrinsic foundation. Now, since place is not space properly, but only a system of correlations between ubications marking out the limits of the body in space, it follows that no compenetration of one place with another is possible so long as the terms of the one do not coincide with the terms of the other.

S. Thomas remarks also, in the same place, that if a recipient full of water contains space, then, besides the dimensions of the water, there would be in the same recipient the dimensions of space, and these latter would therefore be compenetrated with the former. _Quum aqua est in vase, præter dimensiones aquæ sunt ibi aliæ dimensiones spatii penetrantes dimensiones aquæ._ This would certainly be the case were it true that the dimensions of the body are materially continuous, as S. Thomas with all his contemporaries believed. But the truth is that the dimensions of bodies do not consist in the extension of continuous matter, but in the extension of the intervals between the limits of the bodies, which is greater or less according as it requires a greater or less extension of movement to be measured. The volume of a body--that is, the quantity of the place it occupies--is exactly the same whether it be full or empty, provided the limiting terms remain the same and in the same relation to one another. It is not the matter, therefore, that constitutes its dimensions. And then there are, and can be, no distinct dimensions of matter compenetrating the dimensions of place. But enough about the nature of place. Let us proceed to its division.

_Division of Place._--Place in general may be divided into _real_ and _imaginary_, according as its limiting terms exist in nature or are only imagined by us. This division is so clear that it needs no explanation. It might be asked whether there are not also _ideal_ places. We answer, that strictly ideal places there are none; for the ideal is the object of our intellect, whilst place is the object of our senses and imagination. Hence the so-called “ideal” places are nothing but “imaginary” places.

Place, whether real or imaginary, is again divided by geometers into _linear_, _superficial_, and _cubic_ or solid, according to the nature of their limiting boundaries. A place limited by surfaces is the place of a volume or geometric solid. A place limited by lines is the place of a surface. A place limited by mere points is the place of a line.

The ancients, when defining place as “the surface of the surrounding body,” connected the notion of place with the quantity of volume, without taking notice of the other two kinds just mentioned. This, too, was a necessary consequence of their assumption of continuous matter. For, if matter is intrinsically extended in length, breadth, and depth, all places must be extended in a similar manner. But it is a known fact that the word “place” (_locus_) is used now, and was used in all times, in connection not only with geometric volumes, but also with geometric surfaces and with geometric lines; and as the geometric quantities have their counterpart in the physical order, it is manifest that such geometric places cannot be excluded from the division of place. Can we not on any surface draw a line circumscribing a circle or any other close figure? And can we not point out the “place” where the circle or figure is marked out? There are therefore places of which the boundaries are lines, not surfaces. And again, can we not fix two points on a given line, and consider the interval between them as one of the many places which can be designated along the line? The word “place” in its generality applies to any kind of dimensive quantity in space. Those who pretend to limit it to “the surface of a volume” should tell us what other term is to be used when we have to mention the place of a plane figure on a wall, or of a linear length on the intersection of two surfaces. It will be said that the ancients in this case used the word _Ubi_. But we reply that _Ubi_ and _Locus_ were taken by them as synonymous. The quantities bounded by lines, or terminated by points, were therefore equivalently admitted to have their own “places”; which proves that the definition of place which philosophers left us in their books, did not express all that they themselves meant when using the word, and therefore it was not practically insisted upon. With us the case is different. The _Ubi_, as defined by us, designates a single point in space, and is distinct from _locus_; hence we do not admit that our _ubi_ is a place; for there is no place within a point. But the philosophers of the old school could not limit the real ubication of matter to a mere point, owing to their opinion that matter was continuous.

Thus we have three supreme kinds of place--the linear, with one dimension, length; the superficial, with two dimensions, length and breadth; the cubic or solid, with three dimensions, length, breadth, and depth. The true characteristic difference between these kinds of place is drawn from their _formal_ constituents, viz., from their boundaries. The cubic place is a place terminated by surfaces. The superficial place is a place terminated by lines. The linear place is a place terminated by two points.

These supreme species admit of further subdivision, owing to the different geometrical figures affected by their respective boundaries. Thus the place of a body may be tetrahedric, hexahedric, spherical, etc., and the place of a surface may be triangular, polygonal, circular, etc.

Place is also divided into _absolute_ and _relative_. It is called absolute when it is considered _secundum se_--that is, as to its entity, or as consisting of a system of correlation within a definite limit. It is called relative when it is considered in connection with some other place or places, as more or less distant from them, or as having with respect to them this or that position or situation.

The absolute place of a body, whatever our imagination may suggest to the contrary, is always the same as long as the body remains under the same dimensions, be it at rest or in movement. In fact, whenever we speak of a change of place, we mean that the place of a body acquires a new relation to the place of some other body--that is, we mean the mere change of its relativity. When the world was believed to be a sphere of continuous matter with no real space outside of it, the absolute place of a body could be considered as corresponding to one or another definite portion of that sphere, and therefore as changeable; but since the reality of infinite space independent of matter has been established, it is manifest that absolute place has no relation to the limits of the material world, but only to the infinity of space, with respect to which bodies cannot change their place any more than a point can change its ubication. Hence, when a body moves, its relative place, or, better, the relativity of its place to the places of other bodies, is changed; but its absolute place remains the same. Thus the earth, in describing its orbit, takes different positions round the sun, and, while preserving its absolute place unchanged, it undergoes a continuous change of its relativity.

Lastly, place is also divided into _intrinsic_ and _extrinsic_. Omitting the old explanations of this division, we may briefly state that the intrinsic place is that which is determined by the dimensions and boundary of the body, and therefore is coextensive with it. The extrinsic place of a body is a place greater than the body which is placed in it. Thus Rome is the extrinsic place of the Vatican Palace, and the Vatican Palace is the extrinsic place of the Pope; because the Vatican Palace is in Rome, and the Pope in the Vatican Palace.

_Occupation of Place._--We have now to answer a few questions about the occupation of place. The first is, whether bodies fill the space they occupy. The second is, whether the same place can be simultaneously occupied by two bodies. The third is, whether the place limits and conserves the body it contains. The fourth is, whether the same body can be miraculously in two places or more at the same time.

That bodies fill place is a very common notion, because people do not make any marked distinction between filling and occupying. But to fill and to occupy are not synonymous. To fill a place is to leave no vacuum within it; and this is evidently impossible without continuous matter. As we have proved that continuous matter does not exist, we cannot admit that any part of place, however small, can be _filled_. Place, however, is _occupied_. In fact, the material elements of which bodies are ultimately composed, by their presence in space occupy distinct points in space--that is, take possession of them, maintain themselves in them, and from them direct their action all around, by which they manifest to us their existence, ubication, and other properties. This is the meaning of _occupation_. Hence the formal reason of occupation is the presence of material elements in space. Therefore, the place of a body is occupied by the presence in it of discrete material points, none of which fill space--that is to say, the place is occupied, not filled. The common expression, “a place filled with matter,” may, however, be admitted in this sense, that when the place is occupied by a body, it does not naturally allow the intrusion of another body. This amounts to saying, not that the place is really filled, but that the resistance offered by the body to the intrusion of another body prevents its passage as effectually as if there were left no occupable room. So much for the first question.

The second question may be answered thus: Since space is not filled by the occupying bodies, the reason why bodies exclude one another from their respective places must be traced not to a want of room in them, but only to their mutual opposite actions. These actions God can neutralize and overcome by an action of His own; and if this be done, nothing will remain that can prevent the compenetration of two bodies and of their respective places. It is therefore possible, at least supernaturally, for two bodies to occupy the same place. Nevertheless, we must bear in mind that, as the elements of the one body are not the elements of the other, so the ubications of the first set of elements are not the ubications of the second, and consequently the correlations of the first set are not identically the correlations of the second. Hence, if one body penetrates into the place of another body, their places will be intertwined, but distinct from each other.

The third question must be answered in the negative, notwithstanding the contrary opinion of all the Peripatetics. The place does not limit and conserve the body by which it is occupied; it is the body itself that limits and conserves its own place. For what is it that gives to a place its formal determination, and its specific and numeric distinction from all other places, but its extreme boundary? Now, this boundary is marked out by the very elements which constitute the limits of the body. It is, therefore, the body itself that by its own limits defines the limits of its own place, and constitutes the place formally such or such. There is the same connection between a body and its place as between movement and its duration. There is no movement without time, nor time without movement; but movement does not result from time, for it is time itself that results from movement. Hence, the duration of the movement is limited by the movement itself. In like manner, there is no body without place, and no place without a body; but the body does not result from the place, for it is the place itself that results from the presence of the body in space. Hence, the place of the body is formally determined by the body itself. Therefore, it is the body that limits and conserves its place, not the place that limits and conserves the body.

This conclusion is confirmed by the manner in which our knowledge of place is acquired. Our perception of the place of a body is caused, not by the place, but by the body, which acts upon our senses from different points of its surface, and depicts in our organs the figure of its limits. This figure, therefore, is the figure of the place only inasmuch as it is the figure of the body; or, in other terms, it is the body itself that by its limits determines the limits of its place.

From this it follows that, when a body is said to be in a place _circumscriptively_, we ought to interpret the phrase, not in the sense that the body is circumscribed by its place, as Aristotle and his followers believed, but in this sense, that the body circumscribes its place by its own limits. And for the same reason, those beings which do not exist _circumscriptively_ in place (and which are said to be in place only _definitively_, as is the case with created spirits) are substances which do not circumscribe any place, because they have no material terms by which to mark dimensions in space.

The fourth and last question is a very difficult one. A great number of eminent authors maintain with S. Thomas that real bilocation is intrinsically impossible; others, on the contrary, hold, with Suarez and Bellarmine, that it is possible. Without pretending to decide the question, we will simply offer to our reader a few remarks on the arguments adduced against the possibility of real bilocation.

The strongest of those arguments is, in our opinion, the following. The real bilocation of a body requires the real bilocation of all its parts, and therefore is impossible unless each primitive element of the body can have two distinct, real ubications at the same time the one natural and the other supernatural. But it is impossible for a simple and primitive element to have two distinct, real ubications at the same time, for two distinct, real ubications presuppose two distinct, real terminations of the virtuality of God’s immensity, and two distinct, real terminations are intrinsically impossible without two distinct, real terms. It is therefore evident that one point of matter cannot mark out two points in space, and that real bilocation is impossible.

To evade this argument, it might be said that it is not evident, after all, that the same real term cannot correspond to two terminations. For to duplicate the ubication of an element of matter means to cause the same element, which is _here_ present to God, to be _there_ also present to God. Now this requires only the correspondence of the material point to two distinct virtualities of divine immensity. Is this a contradiction? The correspondence to one virtuality is certainly not the negation of the correspondence to another; hence it is not necessary to concede that there is a contradiction between the two. It may be added that the supernatural possibility of bilocation seems to be established by many facts we read in ecclesiastical history and the lives of saints, as also by the dogma of the Real Presence of Our Lord’s Body in so many different places in the Sacrament of the Eucharist. Lastly, although real bilocation is open to many objections on account of its supernatural character, yet these objections can be sufficiently answered, as may be seen in Suarez, in part. 3, disp. 48, sec. 4.

These reasons may have a certain degree of probability; nevertheless, before admitting that a point of matter can mark two points in space at the same time, it is necessary to ascertain whether a single real term can terminate two virtualities of God’s immensity. This is a thing which can scarcely be conceived; for two distinct ubications result from two distinct terminations; and it is quite evident, as we have already intimated, that there cannot be two distinct terminations if there be not two distinct terms. For the virtualities of divine immensity are not distinct from one another in their entity, but only by extrinsic denomination, inasmuch as they are distinctly terminated by distinct extrinsic terms. Therefore, a single extrinsic term cannot correspond to two distinct virtualities of divine immensity; whence it follows that a single material point cannot have two distinct ubications.

As to the facts of ecclesiastical history above alluded to, it might be answered that their nature is not sufficiently known to base an argument upon them. Did any saints ever _really_ exist in two places? For aught we know, they may have existed really in one place, and only phenomenically in another. Angels occupy no place, and have no bodies; and yet they appeared in place, and showed themselves in bodily forms, which need not have been more than phenomenal. Disembodied souls have sometimes appeared with phenomenal bodies. Why should we be bound to admit that when saints showed themselves in two places, their body was not phenomenal in one and real only in the other?

The fact of the Real Presence of Christ’s body in the Blessed Sacrament, though much insisted upon by some authors, seems to have no bearing on the present question. For, our Lord’s body in the Eucharist has no immediate connection with place, but is simply denominated by the place of the sacramental species, as S. Thomas proves; for it is there _ad modum substantiæ_, as the holy doctor incessantly repeats, and not _ad modum corporis locati_.[181] Hence, S. Thomas himself, notwithstanding the real presence of Christ’s body on our altars, denies without fear the possibility of real bilocation properly so called.

Though not all the arguments brought against real bilocation are equally conclusive, some of them are very strong, and seem unanswerable. Suarez, who tried to answer them, did not directly solve them, but only showed that they would prove too much if they were applied to the mystery of the Real Presence. The inference is true; but S. Thomas and his followers would answer that their arguments do not apply to the Eucharistic mystery.

One of those arguments is the following: If a man were simultaneously in two places, say, in Rome and in London, his quantity would be separated from itself; for it would be really distant from itself, and relatively opposed to itself. But this is impossible. For how can there be real opposition without two real terms?

Some might answer, that a man bilocated is one term _substantially_, but equivalent to two _locally_, and that it is not his substance nor his quantity that is distant from itself, but only one of his locations as compared with the other. But we do not think that this answer is satisfactory. For, although distance requires only two _local_ terms, we do not see how there can be _local_ terms without two distinct beings. One and the same being cannot be actually in two places without having two contrary modes: and this is impossible; for two contraries cannot coexist in the same subject, as S. Thomas observes.[182]

Another of those arguments is based on the nature of quantity. One and the same quantity cannot occupy two distinct places. For quantity is the formal cause of the occupation of place, and no formal cause can have two adequate formal effects. Hence, as one body has but one quantity, so it can occupy but one place.

This argument cannot be evaded by saying that the quantity which is the formal cause of occupation is not the quantity of the mass, but the quantity of the volume. In fact, the duplication of the volume would duplicate the place; but the volume cannot be duplicated unless each material term at the surface of the body can acquire two ubications. Now, this is impossible, as a single term cannot correspond to two extrinsic terminations of divine immensity, as already remarked. Hence, the quantity of volume cannot be duplicated in distinct places without duplicating also the mass of the body--that is, there cannot be two places without two bodies.

A third argument is as follows: If a body were bilocated, it would be circumscribed and not circumscribed. Circumscribed, as is admitted, because its dimensions would coextend with its place; not circumscribed, because it would also exist entirely outside of its place.

This argument, in our opinion, is not valid; because it is not the place that circumscribes the body, but the body that circumscribes its own place. Hence, if a body were bilocated, it would circumscribe two places, and would be within both alike. It will be said that this, too, is impossible. We incline very strongly to the same opinion, but not on the strength of the present argument.

A fourth argument is, that if a thing can be bilocated, there is no reason why it could not be trilocated and multilocated. But, if so, then one man could be so replicated as to form by himself alone two battalions fighting together; and consequently such a man might in one battalion be victorious, and in the other cut to pieces; in one place suffer intense cold, and in another excessive heat; in one pray, and in another swear. The absurdity of these conclusions shows the absurdity of the assumption from which they follow.

This argument is by no means formidable. Bilocation and multilocation are a duplication and multiplication of the place, not of the substance. Now, the principle of operation in man is his substance, whilst his place is only a condition of the existence and of the movements of his body. Accordingly, those passions of heat and cold, and such like, which depend on local movement, can be multiplied and varied with the multiplication of the places, but the actions which proceed from the intrinsic faculties of man can not be thus varied and multiplied. Hence, from the multilocation of a man, it would not follow that he, as existing in one place, could slay himself as existing in another place, nor that he could pray in one and swear in another. After all, bilocation and multilocation would, by the hypothesis, be the effect of supernatural intervention, and, as such, they would be governed by divine wisdom. Hence it is unreasonable to assume the possibility of such ludicrous contingencies as are mentioned in the argument; for God does not lend his supernatural assistance to foster what is incongruous or absurd.

To conclude. It seems to us that those among the preceding arguments which have a decided weight against the possibility of real bilocation, are all radically contained in this, that one and the same element of matter cannot have at the same time two modes of being, of which the one entails the exclusion of the other. Now, the mode of being by which an element is constituted in a point, _A_, excludes the mode of being by which it would be constituted in another point, _B_. For, since the ubication in _A_ is distant from the ubication in _B_, the two ubications are not only distinct, but relatively opposed, as S. Thomas has remarked: _Distinguuntur ad invicem secundum aliquam loci contrarietatem_; and therefore they cannot belong both together to the same subject. On the other hand, we have also proved that a single element cannot terminate two distinct virtualities of God’s immensity, because no distinct virtualities can be conceived except with reference to distinct extrinsic terms. Hence, while the element in question has its ubication in _A_, it is utterly incapable of any other ubication. To admit that one and the same material point can terminate two virtualities of divine immensity, seems to us as absurd as to admit that one and the same created being is the term of two distinct creations. For this reason we think, with S. Thomas, that bilocation, properly so called, is an impossibility.

AN EPISODE.

The caption “episode” is advisedly adopted, inasmuch as we are going to transcribe only one short chapter from a large manuscript of several hundred pages containing “The Life of Sixtus V.”

However, it is to be regretted that such a life is not published. For it would reveal unto us the _man_, whereas Ranke and Hübner describe only the _prince_.