82. ANALYSIS OF THE CONCEPT OF QUANTITY.—A detailed study of Quantity,
including Space and Time, and the Aristotelian categories _Ubi_, _Quando_
and _Situs_, belongs to Cosmology. Here we shall confine ourselves mainly
to the exposition of certain elementary notions preparatory to such
detailed study; and we shall assume the validity of the Scholastic Theory
of Knowledge: that a real, material world exists independently of our
minds; that it consists of material substances or bodies, animate and
inanimate, endowed with the fundamental accident of quantity or extension;
that these bodies possess, moreover, many other real accidents such as
qualities and energies, chemical, physical and mechanical; that they are
subject to real change, local, quantitative, qualitative and substantial;
that our concepts of space and time, derived from those of extension and
change, are not purely subjective or mental forms of cognition, but are
objectively valid notions grounded in the reality of the corporeal
universe and giving us a genuine, if inadequate, insight into the nature
of this reality.
Among the characteristics recognized by physicists in all perceptible
matter—divisibility, commensurability, impenetrability, passivity or
inertia, subjection to external forces or energies, external extension or
volume, internal quantity or mass—there are none more fundamental than
those of volume and mass, or extension and quantity.(354) Nowhere,
however, do we find a better illustration of the fact that it is
impossible to give a definition proper of any supreme category, or even a
description of it by the aid of any more elementary notions, than in the
attempts of philosophers to describe _Quantity_. When, for instance, we
describe _external_, _actual_, _local_, or _spatial extension_ as _that
accident of a corporeal substance or body in virtue of which the latter so
exists that it has parts outside parts in space_, we have to admit at once
that the notions expressed by the terms “parts,” “outside” and “space” are
no simpler than the notion of extension itself: in fact our notions of
“place” (_locus_) and “space” (_spatium_) are derived from, and
presuppose, that of extension. This, however, is no serious disadvantage;
for the description, such as it is, indicates what we mean by the terms
“local, spatial, external, actual extension,” and declares this latter to
be an accident of corporeal substances.
Extension, as it is actually in the concrete body, affected by a variety
of sensible qualities, is called _physical_ extension; regarded in the
abstract, apart from these qualities, it is called _geometrical_ or
_mathematical_ extension: _trina dimensio_, or extension in three
dimensions, length, breadth and depth. If we abstract from one of these we
have extension in _two_ dimensions, _superficial_ extension; if we
abstract from _two_, we have extension in _one_ dimension, _linear_
extension; and if we abstract from all three we have the extreme _limiting
concept_ of the _mathematical point_. Of these four abstract mathematical
concepts, “point,” “line,” “surface,” and “volume,” each expresses the
_mathematical limitation_ of the succeeding one.
We cannot conceive a body existing by having parts outside parts in space,
each part occupying exclusively a place appropriated to itself, unless we
conceive the body, the corporeal _substance_, as having already a
plurality of _really distinct_ or _distinguishable_ parts _in itself_, and
abstracting from all relation to space. The _substance_ must be conceived
as having a plurality of really distinct or distinguishable _integral_
parts of itself, before these parts can be conceived as existing _outside_
one another, each in its own place. And the property in virtue of which
the corporeal substance has in itself this plurality of distinct integral
parts, whereby it is _capable_ of occupying space, and of being
impenetrable, divisible, measurable, etc., is called _internal_,
_radical_, _potential quantity_ or _extension_.(355)
The corporeal substance itself is, of course, _essentially_ composite,
essentially divisible into two _essential_ constitutive principles, the
passive, determinable, or material principle (_materia prima_), and the
specifying, determining, formative principle (_forma substantialis_). Then
we conceive this essentially composite substance as necessarily endowed
with the _property_ of _internal quantity_ whereby it is composite in
another order: composed of, and divisible into, really distinct _integral_
parts, each of which is, of course, essentially composite like the whole
itself.(356) Finally we conceive that the corporeal substance, endowed
with this property, has also, as a connatural but really distinct and
absolutely separable effect of the latter, the accidental mode of being,
called external or local extension, in virtue of which it actually
occupies space, and thus becomes the subject of all those qualities
whereby it is perceptible to our senses.
We have next to inquire into the relations between these three distinct
objective concepts, corporeal substance, internal quantity, and local or
external extension.
83. CORPOREAL SUBSTANCE, QUANTITY AND EXTENSION.—The corporeal substance
is an essentially composite substance, resulting from the union of two
distinct essential constitutive principles. It exists in itself and is the
ultimate subject of all the determinations whereby it reveals itself to
our senses. Its actual extension in space is a fundamental mode or
determination of its reality, but it is a mode which is distinct from the
reality itself of the corporeal substance. Aristotle regarded the
distinction as real. In his _Metaphysics_ he declares that the three
dimensions of bodies are quantities, not substances, that quantity is not
a substance, whereas that in which it ultimately inheres is a
substance;(357) in his _Physics_ he says that substance is of itself
indivisible and is made divisible by its quantity or extension;(358) in
his _De Anima_(359) he observes that [external] quantity is directly
perceptible by the senses (_sensibile_ per se) while substance is only
indirectly perceptible (_sensibile_ per accidens):(360) from which it is
inferred that substance and extension cannot be really identical. Again,
St. Thomas argues that a corporeal substance as such, and so far as its
essence is concerned, is indifferent to greater or less extension in
space, that the whole nature or substance of a man, for instance, is
indifferent to, and independent of, his particular size at any point of
time, that while he grows from childhood to manhood it is his external
quantity that changes, but not his humanity, his human essence, nature, or
substance.(361)
Considerations such as these, though they do not indeed amount to cogent
proofs of a real distinction between spatial extension and corporeal
substance, should make any serious philosopher hesitate to identify these
absolutely, as Descartes and his followers did when they declared the
essence of corporeal substance to consist in three dimensions of spatial
extension. Even looking at the matter from the point of view of natural
reason alone, and apart altogether from any light that may be thrown upon
it for the Christian philosopher by Divine Revelation, it is only the
superficial thinker who will conclude that because extension—which reveals
to his intellect through the medium of external sense perception the
presence of a corporeal substance—is naturally inseparable from the
latter, therefore it is really and absolutely identical with this latter.
The philosopher who remembers how little is known for certain about the
ultimate, essential constitution of bodies or corporeal substances, will
be slow to conclude that the spatially extended mode of their being enters
into the constitution of their essence, and is not rather an accidental
determination whereby these substances have their integral parts dispersed
or extended in space and thus revealed to the human intellect through
sense perception.
And if he be a Christian philosopher he will naturally inquire
whether any truth of the Christian Revelation will help indirectly
to determine the question. Descartes and his followers were
Christian philosophers; and hence it was all the more rash and
imprudent of them, in spite of what they knew concerning the
Blessed Eucharist, to identify the corporeal substance with its
spatial extension. They knew that by transubstantiation the bread
and wine are changed _substantially_ into the Body and Blood of
Christ. But all the _appearances_ or _phenomena_ of bread and wine
remain after transubstantiation, the Eucharistic _species_ as they
are called, the taste, colour, form, etc., in a word, all the
sensible qualities of these substances, including the _extension_
in which they immediately inhere. From the revealed truth that the
_substances_ disappear, and from the manifest fact that all their
_accidents_ remain, Christian philosophers and theologians have
rightly drawn the sufficiently obvious inference that the
spatially extended quantity, which immediately supports all the
other sensible qualities, must be itself an _absolute_ accident
not only _really distinct_, but by the absolute power of God
_really separable_, from its _connatural substance_, the bread and
the wine respectively; and that this extended quantity remains in
this state of actual separation miraculously supported by the
direct influence of the Divine Omnipotence. And while Christian
philosophers who hold this view can defend it from all charges of
inconsistency, unreasonableness and impossibility, Descartes and
his followers can defend their particular view only by the
admission that in the case of the consecrated Eucharist our senses
are deceived. In this view, while no accidents of the bread and
wine remain objectively, God Himself produces directly in our
minds the subjective, mental states which the bread and wine
produced before consecration.(362) This gratuitous aspersion is
cast on the trustworthiness of sense perception, simply on account
of the preconceived theory identifying the corporeal substance
with its extension. According to the common view, on the other
hand, the senses are not really deceived. That to which they
testify is really there, _viz._ the whole collection of natural
accidents of bread and wine. It is not the function of the senses,
but of the intellect, to testify to the presence of the substance.
Of course the unbeliever looking at the consecrated species, or
the believer who looks at them not knowing that they have been
consecrated, thinks that the substance of bread and the substance
of wine are there. Each is deceived intellectually, the one by his
unbelief of a truth, the other by his ignorance of a fact. If both
knew of the fact of consecration, and if the former believed in
the effect of it, neither would be deceived.(363)
While the Cartesian view is thus open to such serious objections,
the only plausible difficulty against the traditional view is that
of conceiving how the reality of a merely accidental mode of
being, such as extension, can be sustained in the actual order of
things apart from its connatural substance, and yet not become
itself _eo ipso_ a substance. Needless to say we have no
_positive_ conception of the manner in which the Divine
Omnipotence thus sustains extension; but since this latter, being
an absolute accident, and not a mere modal determination of the
substance, has a reality of its own, the miraculous persistence of
this reality cannot be shown to be impossible. Nor is it, in this
separated condition, itself a substance, for it still retains its
natural aptitude for inherence in its connatural substance; and
this _aptitude_ alone, not _actual_ inherence, is of its essence
as an accident (65): retaining this natural aptitude it cannot
possibly become a substance, it cannot be identified with the
_substantial_ mode of being which has essentially the very
opposite aptitude, that of _existing in itself_.
External extension, then, is an absolute accident, really distinct from
the corporeal substance, and naturally though not absolutely inseparable
from the latter. It is the natural concomitant or consequence of the
_internal quantity_ whereby the corporeal substance has in itself a
plurality of distinct integral parts. This _internal quantity_ itself is
either an aspect of the corporeal substance itself, only virtually
distinct from the latter, or else in the strict sense a _property_,
absolutely inseparable, if really distinct, from the substance. Natural
experience furnishes no example of a corporeal substance actually existing
devoid of internal quantity or internal distinction of integral
parts.(364) But scholastic philosophers are not agreed as to whether the
corporeal substance is itself and by its own essence a manifold of really
distinct integral parts (in which case internal quantity would be merely
the aspect under which the essence is thus regarded as an integral whole
constituted by a plurality of distinct integral parts; while, looked at as
an essence, it would be an essential whole constituted by the union of two
essential parts or principles)—or whether it is formally constituted an
integral whole, not by its essence (which makes it only an essential
whole, an essentially composite substance), but by a property really
distinct, though necessarily flowing, from this essence, _viz._ internal
quantity. According to the former view the material principle (_materia
prima_) of the composite corporeal substance is such that the essence
resulting from its union with the formative principle (_forma
substantialis_) is necessarily an integral whole with distinguishable
integral parts, each of which naturally demands the spatially extended
mode of being which external extension _de facto_ confers upon it.
According to the latter view, which is that of St. Thomas and his
followers generally, the corporeal substance as such has no mode of
composition other than _essential_ composition: it is not of itself an
_integral_ whole, compounded of distinct or distinguishable integral parts
(each of which would be, like the whole, essentially composite): of itself
it is _indivisible_ into integral parts: it is, therefore, in this order
of being, simple and not composite. It has, no doubt, by reason of its
material principle, an absolutely necessary exigence for divisibility into
distinct integral parts, for integral composition in other words. But this
actual integral composition, this actual divisibility, is the formal
effect of a property really distinct from the substantial essence itself;
and this property is internal quantity: the connatural, but absolutely
separable, complement of this internal quantity being, as in the other
view, local or spatial extension.
In both views external extension is an absolute accident of the corporeal
substance; and in the Thomist view internal quantity would also appear to
be an absolute accident, and not a mere mode.
It is instructive to reflect how far this scholastic doctrine
removes us from the Cartesian view which sets up an absolute
antithesis between mind or spirit, and matter or body, placing the
essence of the former in _thought_ and that of the latter in
_extension_. According to the scholastic view the spiritual
substance is an immaterial “actuality” or “form”; it is
_essentially simple_, and not like a corporeal substance an
_essentially composite_ substance resulting from the union of a
formative principle or “form” with a passive, determinable,
material principle. And since it is the material principle that
demands the property of internal quantity and the accident of
external extension, whereby the corporeal substance becomes an
integral whole with its parts extended in space, it follows that
the spiritual substance, having no material principle in its
constitution, is not only _essentially_ simple—to the exclusion of
distinct principles of its essence,—but is also and as a
consequence _integrally_ simple, to the exclusion of distinct
integral parts, and of the extended or characteristically
corporeal mode of occupying space. So far there is contrast
between the two great substantial modes of finite being, matter
and spirit; but the contrast is by no means an absolute
antithesis. For if we look at the essence alone of the corporeal
substance it is not _of itself_ actually extended in space: in the
Thomist view it is not even of itself divisible into distinct
integral parts. It differs from spirit in this that while the
latter is essentially simple the former is essentially composite
and has by reason of this compositeness a natural aptitude for
divisibility into parts and for the extension of these parts in
space, an aptitude which spirit does not possess. But the
corporeal substance _may_ exist without actual extension, and
consequently without any of those other attributes such as
impenetrability, solidity, colour, etc., through which it is
perceptible to our senses. In this condition, how does it differ
from spirit? In being essentially composite, and in being perhaps
endowed with distinguishable integral parts.(365) But in this
condition the essential mode of its being has a relation to space
which closely resembles the mode in which spirit exists in space:
it is related to space somewhat in the manner in which the soul is
in the space occupied by the body—whole in the whole of this space
and whole in every assignable portion of this space. So that after
all, different as matter and spirit undoubtedly are, the
difference between them is by no means that sort of Cartesian
chasm which human thought must for ever fail to bridge.
By virtue of its external extension the corporeal substance exists by
having distinguishable parts outside parts in space. We can conceive any
perceptible volume of matter as being _perfectly continuous_, if it has no
_actual_ limits or _actual_ distinction of parts within itself, but is
_one_ individual being _completely filling_ the whole space within its
outer surface; or _imperfectly continuous_, if while being one and
undivided it has within its volume pores or interstices, whether these be
empty or filled with some other sort of matter; or as made up of
_contiguous_ integral parts if each or these is really distinct and
actually divided from every other, while each actually touches with its
outer limits the adjacent limits of the parts lying next to it, so that
all the internal parts or limits are co-terminous; or as made up of
separate, _discrete_ or distant parts no one of which actually touches any
other.
It is clear that there must be, in any actually extended volume of matter,
_ultimate_ parts which are really _continuous_—unless we are to hold, with
dynamists, that our perception of extension is produced in our minds by
the action of extramental points or centres of force which are themselves
_simple_ or _unextended_. But the physical phenomena of contraction,
expansion, absorption, undulatory and vibratory motions accompanying our
sensations of light, heat and sound, as well as many other physical
phenomena, all point to the fact that volumes of matter which are
_apparently_ continuous are really porous: the molecular structure of
perceptible matter is an accepted physical theory; and scientists also
universally accept as a working hypothesis the existence of an
imperceptible material medium pervading and filling all real space, though
there is no agreement as to the properties with which they suppose this
hypothetical medium, the “ether,” to be endowed.
Again, as regards the _divisibility_ of extended matter, it is obvious
that if we conceive extension in three dimensions _geometrically_,
_mathematically_ or _in the abstract_, any such volume or extension is
_indefinitely divisible_ in thought. But if we inquire how far any
concrete, actually existing volume of matter is divisible, we know in the
first place that we cannot divide the body of any actual organic living
thing indefinitely without destroying its life, and so its specific
character. Nor can we carry on the division of inorganic matter
indefinitely for want of sufficiently delicate dividing instruments. But
apart from this the science of chemistry points to the fact that every
inorganic chemical compound has an ultimate individual unit, the chemical
molecule, which we cannot sub-divide without destroying the specific
nature of the compound by resolving it into its elements or into less
complex compounds. Furthermore, each “elementary” or “chemically simple”
body—such as gold, oxygen, carbon, etc.—seems resolvable into units called
“atoms,” which appear to be ultimate _individual_ units in the sense that
if their mass _can_ be subdivided (as appears possible from researches
that have originated in the discovery of radium) the subdivisions are
specifically different kinds of matter from that of the atom so divided.
In the inorganic world the perceptible mass of matter is certainly not an
_individual_ being, a _unum per se_, but only a collection of individual
atoms or molecules, a _unum per accidens_. Whether the molecule or the
atom of the chemically elementary body is the “individual,” cannot be
determined with any degree of certitude. It would appear, however, that
every specifically distinct type of inorganic matter, whether compound or
elementary, requires for its existence a certain minimal volume, by the
sub-division of which the type is substantially changed; and this is
manifestly true of organic or living matter: so that matter _as it
naturally exists_ would appear not to be indefinitely divisible.
If in a chemically homogeneous mass of _inorganic_ matter (such as
carbon or water) the chemical molecule be regarded as the
“individual,” this cannot be the case in any _organic_, _living
thing_, for whatever matter is assimilated into the living
substance of such a being _eo ipso_ undergoes substantial change
whereby it loses the nature it had and becomes a constituent of
the living individual. The _substantial_, “_individual_” unity of
the organic living being seems to be compatible not merely with
qualitative (structural and functional) heterogeneity of parts,
but also with (perhaps even _complete_) spatial separateness of
these parts. If the structure of the living body is really
“molecular,” _i.e._ if it has _distances_ between its ultimate
integral units, so that these are not in spatial contact, then the
fact that the formative, vital principle (_forma substantialis_,
_anima_) unifies this material manifold, and constitutes it an
“individual” by actualizing and vitalizing each and all of the
material units, spatially separate as they are,—this fact will
help us to realize that the _formative principle_ of the composite
corporeal substance has not _of itself_ the _spatial_, _extended_
mode of being, but that the substance derives the latter from its
material principle (_materia prima_).
84. PLACE AND SPACE.—From the concept of the volume or actual extension of
a body we pass immediately to that of the “place” (_locus_) which it
occupies. We may distinguish between the _internal_ and the _external_
place of a body. By the former we understand _the outer (convex) surface
of the body itself, regarded as a receptacle containing the volume of the
body_. If, therefore, there were only one body in existence it would have
its own internal place: this is independent of other bodies. Not so,
however, the external place; for by the external place of a body we mean
_the immediately surrounding (concave) surface_, formed by the bodies
which circumscribe the body in question, and _considered formally as an
immovable container of this body_. This is a free rendering of Aristotle’s
definition: _Place is the first (or immediate) immovable surface (or
limit) of that which contains a body_: _prima immobilis superficies ejus
quod continet_.(366) If a hollow sphere were filled with water, the inner
or concave surface of the sphere would be the “external place” of the
water. Not, however, this surface considered materially, but _formally as
a surface_, so that if the sphere could be removed, and another
instantaneously substituted for it, the water would still be contained
within the same _formal_ surface; its _locus externus_ would remain the
same. And, again, it is the containing surface considered as _immovable_
or as circumscribing that definite portion of space, that constitutes the
_locus externus_ or “external place” of the located body: so that if the
sphere with the water were moved the latter would thereby obtain a new
external location, for though the containing surface be still materially
and formally the same, it is no longer the same _as a locating_ surface,
seeing that it now marks off a portion of space different from that marked
off by it before it was moved.
Aristotle’s definition defines what is known as the _proper_ external
place of a body. From this we distinguish the _common_ external place or
location of a body: understanding by the latter, or “locus _communis_,”
the whole collection of spatial relations of the body in question to all
the bodies in its immediate neighbourhood. It is by indicating these
relations, or some of them, that we assign the Aristotelian category, or
extrinsic denomination, _Ubi_.(367)
Regarded ontologically, the internal place of a body is an absolute
accident: it is the accident which gives the latter concrete volume or
external extension, and it is not really distinct from the latter. The
external place of a body includes in addition the spatial relations of the
latter to other bodies, relations grounded in the volumes of those bodies.
It is by reason of these spatial relations with certain bodies,
that a being is said to be “present” in a certain place. A
corporeal extended substance is said to occupy space
_circumscriptivé_, or by having parts outside parts in the place
it occupies. A finite or created spiritual substance is said to
occupy space _definitivé_ inasmuch as it can naturally exercise
its influence only within certain more or less extended spatial
limits: as the human soul does within the confines of the
body.(368) The Infinite Being is said to occupy space _repletivé_.
The actual presence of God in all real space, conserving in its
existence all created, contingent reality, is called the Divine
_Ubiquity_. The perfection whereby God can be present in other
worlds and other spaces which He may actualize is called the
Divine _Immensity_.
The local presence of a finite being to other finite beings is
itself a positive perfection—based on its actual extension if it
be an extended corporeal substance, or on its power of operating
within a certain space if it be a spiritual substance. The fact
that in the case of a finite being this local presence is itself
limited, is at once a corollary and an index of the finiteness of
the being in question. Only the Infinite Being is omnipresent or
ubiquitous. But every finite being, whether corporeal or
spiritual, from the very fact that it exists at all, must exist
somewhere or have some _locus internus_, and it must have some
local presence if there are other corporeal, extended beings in
existence. Thus the _local presence_ of a being is a (finite)
perfection which seems to be grounded in the very nature itself of
the creature.(369)
From the concept of _place_ we pass naturally to the more complex and
abstract notion of _space_. It is, of course, by cognitive processes, both
sentient and intellectual, that we come into possession of the abstract
concept of space. These processes are subjective in the sense that they
are processes of the individual’s mental faculties. Distinguishing between
the processes and the object or content which is brought into
consciousness, or put in presence of the mind, by means of them; and
assuming that this object or content is not a _mere_ form or groove of our
cognitive activity, not a _mere_ antecedent condition requisite on the
mental side for the conscious exercise of this activity on its data, but
that on the contrary it is, or involves, an objective, extramental reality
apprehended by the mind,—we go on to inquire in what this objective
reality consists. In approaching the question we must first note that what
is true of every abstract and universal concept is true of the concept of
space, _viz._ that the _abstractness_ and _universality_ (“_intentio
universalitatis_”) of real being, as apprehended by the intellect, are
modes or forms of thought, _entia rationis_, logical conditions and
relations which are created by thought, and which exist only in and for
thought; while the reality itself is the object apprehended in these modes
and under these conditions: _Universale est formaliter in mente et
fundamentaliter in re_. Now through the concept of space we apprehend a
reality. Our concept of real space has for its object an actual reality.
What is this reality? If space is real, in what does its reality consist?
We answer that the reality which we apprehend through this concept is _the
total amount of the actual extension or magnitude of all created and
coexisting bodies_; not, however, this total magnitude considered
absolutely and in itself, but _as endowed with real and mutual relations
of all its parts to one another_,(370) relations which are apprehended by
us as distances, linear, superficial, and voluminal.
Such, then, is the reality corresponding to our concept of real and actual
space. But no sooner have we reached this concept than we may look at its
object in the abstract, remove mentally all limits from it, and conceive
all extended bodies as actually non-existent. What is the result? The
result is that we have now present to our minds the _possibility_ of the
existence of extended bodies, and a concomitant imagination image (which
memory will not allow us to banish from consciousness) of a vast and
boundless emptiness, an indefinite and unmeasurable vacuum in which bodies
were or may be. The intellectual concept is now not a concept of any
_actual_ object, but of a mere _possibility_: the possibility of a
corporeal, extended universe. This is the concept of what we call _ideal_
or _possible space_; and like the concept of any other possible reality it
is derived by us from our experience of actual reality,—in this case from
our experience of extended bodies as actually existing. The corporeal
universe has not existed from all eternity, but it was possible from all
eternity. When we think of that possibility as antecedent to all creation,
we are thinking of bodies, and of their extension, as possible; and the
concept of their total extension as possible is the concept of ideal or
possible space. This concept is, through a psychological necessity,
accompanied by an imagination image of what we call _imaginary space_: the
unlimited vacuity which preceded corporeal creation, which would still
persist were the latter totally annihilated, which reaches out
indefinitely beyond its actual limits, which imagination pictures for us
as a receptacle in which bodies may exist but which all the time our
reason assures us is actually nothing, being really only the known
possibility of corporeal creatures. This familiar notion of an empty
receptacle for bodies is what we have in mind when we think of bodies as
existing “_in_ space”. Hence we say that space, as conceived by the human
mind, is not a mere subjective form of cognition, a mere _ens rationis_,
inasmuch as our concept has a foundation in reality, _viz._ the actual
extension of all existing bodies; nor is it on the other hand simply a
real entity, because this actual extension of bodies does not really exist
in the manner in which we apprehend it under the abstract concept of
space, as a mere possibility, or empty receptacle, of bodies. Space is
therefore an _ens rationis cum fundamento in re_.
A great variety of interesting but abstruse questions arise from
the consideration of space; but they belong properly to Cosmology
and Natural Theology. For example: Is real space actually infinite
in magnitude, or finite? In other words, besides the whole solar
system—which is in reality merely one star _plus_ its planets and
their satellites,—is there in existence an actually infinite
multitude of such stellar worlds? It is not likely that this can
ever be determined empirically. Many philosophers maintain that
the question must be answered in the negative, inasmuch as an
actually infinite multitude is _impossible_. Others, however, deny
that the impossibility of an actually infinite multitude can be
proved.(371) Again, within the limits of the actual corporeal
universe, are there really _vacant_ spaces, or is all space within
these limits actually (or even necessarily) filled with an
all-pervading ether or corporeal medium of some sort? How would
local motion be possible if all space were full of impenetrable
matter? How would the real interaction of distant bodies on one
another be possible if there were only vacant space between them?
Is the _real_ volume or extension of a corporeal substance (as
distinct from its _apparent_ volume, which is supposed to include
interstices, or spaces not filled with that body) actually or
necessarily unchangeable? Or is the internal quantity of a body
actually or necessarily unchangeable? Can more than one individual
corporeal substance simultaneously occupy exactly the same space?
(This is not possible naturally, for impenetrability is a natural
consequence of local extension; but it is possible miraculously—if
all the bodies, or all except one, be miraculously deprived of
local or spatial extension.) Can the same individual body be
present at the same time in totally different and distant places?
(Not naturally, of course; but how it can happen even miraculously
is a more difficult question than the preceding one. It is in
virtue of its actual or local extension that a body is present
sensibly in a definite place. Deprived miraculously of this
extension it can be simultaneously in several places, as our
Blessed Lord’s Body is in the Eucharist. But if a body has its
natural local extension at one definite place, does this extension
so confine its presence to this place that it cannot be
simultaneously present—miraculously, and without its local
extension—at other places? The most we can say is that the
absolute impossibility of this is neither self-evident nor capable
of cogent proof. The Body of our Lord has its natural local
extension in heaven—for heaven, which will be the abode of the
glorified bodies of the blessed after the general resurrection,
must be not merely a state or condition, but a place—and at the
same time it is sacramentally present in many places on earth.)
85. TIME: ITS APPREHENSION AND MEASUREMENT.—If the concept of space is
difficult to analyse, and gives rise to some practically insoluble
problems, this is still more true of the concept of time. “What, then, is
time?” exclaims St. Augustine in his _Confessions_.(372) “If no one asks
me, I know; but if I am asked to explain it, then I do not know!” We reach
the notion of space through our external perception of _extension_ by the
senses of sight and touch. So also we derive the notion of time from our
perception of _motion_ or _change_, and mainly from our consciousness of
change and succession in our own conscious states. The concept of time
involves immediately two other concepts, that of _duration_, and that of
_succession_. Duration, or continuance in existence, is of two kinds,
_permanent_ and _successive_. Permanent duration is the duration of an
_immutable_ being, formally and in so far as it is immutable. Successive
duration is the continued existence or duration of a being that is
_subject_ to change, formally and in so far as it is mutable. Now real
change involves a continuous _succession_ of real states, it is a
continuous _process_ or _fieri_; and it is the duration of a being subject
to such change that we call _time_ or _temporal duration_. Had we no
consciousness of change, or succession of states, we could have no notion
of time; though we might have a notion of unchanging duration if _per
impossibile_ our cognitive activity were itself devoid of any succession
of conscious states and had for its object only unchanging reality. But
since our cognitive activity is _de facto_ successive we can apprehend
permanent or unchanging duration, not as it is in itself, but only after
the analogy of successive or temporal duration (86). The continuous series
of _successive states involved in change_ is, therefore, the real and
objective content of our notion of time; just as the _co-existing_ total
of _extension_ forms the content of our notion of space. The concept of
space is the concept of something static; that of time is the concept of
something kinetic. Time is the continuity of change: where there is change
there is time; without change time would be inconceivable. Change involves
succession, and succession involves the temporal elements of “before” and
“after,” separated by the indivisible limiting factor called the “now” or
“present instant”. The “past” and the “future” are the two _parts_ of
time, while the “present instant” is not a part of time, but a _point of
demarcation_ at which the future flows into the past. Change is a reality;
it is a real mode of the existence of mutable things; but neither the
immediately past state, nor the immediately future state of a changing
reality, are actual at the present instant: it is only to the permanent,
abiding mind, apprehending real change, and endowed with memory and
expectation, that the past and the future are actually (and, of course,
only _ideally_, not _really_) present. And it is only by holding past and
future in present consciousness, by distinguishing mentally between them,
by counting or measuring the continuous flow of successive states from
future to past, through the present instant, that the mind comes into
possession of the concept of time.(373) The mind thus apprehends time as
the measure of the continuous flow of successive states in things subject
to change. As thus apprehended, time is not merely the reality of change:
it is the successive continuity or duration of change considered as a
measure of change. It is that within which all changes are conceived to
happen: just as space is conceived as that within which all extended
things are conceived to exist. We have said that without real change or
motion there could be no time. We can now add that without a mind to
apprehend and measure this motion there could be no time. As St. Thomas
declares, following Aristotle: _Si non esset anima non esset tempus_.(374)
For time, as apprehended by means of our abstract and universal concept,
is not simply a reality, but a reality endowed with logical relations, or,
in other words, a logical entity grounded in reality, an _ens rationis cum
fundamento in re_.
This brings us to Aristotle’s classic definition,(375) which is at once
pithy and pregnant: Τοῦτο γάρ ἐστιν ὁ χρόνος, ἀριθμὸς κινήσεως κατὰ τὸ
πρότερον καὶ ὓστερον: _Tempus est numerus motus secundum prius et
posterius_: Time is the measure of motion or change by what we conceive as
_before_ and _after_, or _future_ and _past_, in its process. Every change
involves its own intrinsic flow of states from future to past. It is by
mentally distinguishing these states, and by thus computing, counting,
numbering, the continuous flow or change, that we derive from the latter
the notion of time.(376) If, then, we consider all created things, all
things subject to change, we shall realize that real time commenced with
the creation of the first of them and will continue as long as they (or
any of them) continue to exist. We thus arrive at a conception of time in
general, analogous to that of space: _the whole continuous series of
successions, in changing things, from future to past, regarded as that in
which these changes occur, and which is the measure of them_.
Here, too, as in the case of space, we can distinguish _real time_, which
is the total duration of actual changes, from _ideal or imaginary time_
which is the conceived and imagined duration of merely possible changes.
But a more important distinction is that between _intrinsic_ or _internal
time_, or the duration of any concrete mutable reality considered in
itself, and _extrinsic_ or _external time_, which is some other extrinsic
temporal duration with which we compare, and by which we may measure, the
former duration. Every change or motion has its own internal time; and
this is what we have been so far endeavouring to analyse. If two men start
at the same instant to walk in the same direction, and if one walk three
miles and the other four, while the hands of a watch mark the lapse of an
hour, the _external time_ of each walk will be the same, will coincide
with one and the same motion of the hands of the watch used as a measure.
But the internal time of the four-mile walk will be greater than that of
the three-mile walk. The former will be a greater amount of change than
the latter; and therefore its internal time, estimated by this amount
absolutely, will be greater than that of the latter estimated by its
amount absolutely.(377) The greater the amount of a change the greater the
internal time-duration or series of successive states which measures this
change absolutely.(378)
Just as the category _Where_ is indicated by the spatial relations of a
body to other bodies, so the category _When_ is indicated, in regard to
any event or process, by its commensuration or comparison with other
events or processes.
This brings us to the notion of measurement. To measure anything
quantitatively is to apply to it successively some quantitative unit taken
as a standard and to count the number of times it contains this unit. This
is a process of mentally breaking up continuous quantity or
_magnitude_—whether permanent or successive, _i.e._ whether extension or
motion—into discontinuous quantity or _multitude_. If the measurement of
permanent quantity by spatial units, and the choosing of such units, are
difficult processes,(379) those of measuring successive quantity and
fixing on temporal units are more difficult still. Is there any natural
motion or change of a general character, whereby we can measure
(externally) the time-duration of all other changes? The motions of the
earth itself—on its axis and around the sun—at once suggest themselves.
And these motions form in fact the _natural_ general standard for
measuring the time of all other events in the universe. All _artificial_
or mechanical devices, such as hour-glasses, watches, clocks,
chronometers, etc., are simply contrivances for the more convenient
application of that general and natural standard to all particular events.
It requires a little reflection to realize that all our means of measuring
time-duration can only attain to _approximate_ accuracy, inasmuch as our
faculties of sense perception, no matter by what devices they are aided,
are so limited in range and penetration that fluctuations which fall below
the _minima sensibilia_ cannot be detected. It is a necessary condition of
any motion used as a standard for time-measurement that it be _regular_.
That the standard motions we actually employ are _absolutely_ regular we
have no guarantee. We can test their regularity only up to the point at
which our power of detecting irregularity fails.
Reflection will also show that our appreciation of time-duration is also
_relative_, not absolute. It is always a comparison of one flow or current
of conscious experiences with another. It is the greater regularity of
astronomical motions, as compared with changes or processes experienced as
taking place within ourselves, that causes us to fix on the former as the
more suitable standard for the measurement of time. “There is indeed,”
writes Father Maher,(380) “a certain rhythm in many of the processes of
our organic life, such as respiration, circulation, and the recurrent
needs of food and sleep, which probably contribute much to our power of
estimating duration.... The irregular character and varying duration of
conscious states, however, soon bring home to us the unfitness of these
subjective phenomena to serve as a standard measure of time.” Moreover,
our estimate of duration is largely dependent on the nature of the
estimated experiences and of our mental attitude towards them: “A period
with plenty of varied incident, such as a fortnight’s travel, passes
rapidly _at the time_. Whilst we are interested in each successive
experience we have little spare attention to notice the duration of the
experience. There is almost complete lapse of the ‘enumerating’ activity.
But _in retrospect_ such a period expands, because it is estimated by the
number and variety of the impressions which it presents to recollection.
On the other hand a dull, monotonous, or unattractive occupation, which
leaves much of our mental energy free to advert to its duration, is
over-estimated whilst taking place. A couple of hours spent impatiently
waiting for a train, a few days in idleness on board ship, a week confined
to one’s room, are often declared to constitute an ‘age’. But when they
are past such periods, being empty of incident, shrink up into very small
dimensions.... Similarly, recent intervals are exaggerated compared with
equal periods more remote. Whilst as we grow older and new experiences
become fewer and less impressive, each year at its close seems shorter
than its predecessor.”(381)
From those facts it would seem perfectly legitimate to draw this
rather surprising inference: that if the rate of _all_ the changes
taking place in the universe were to be suddenly and
simultaneously altered in the same direction—all increased or all
diminished in the same degree—and _if our powers of perception
were simultaneously_ so altered as to be _readjusted to this new
rate_ of change, _we could not become aware of the
alteration_.(382) Supposing, for instance, that the rate of motion
were doubled, the same amount of change would take place in the
new day as actually took place in the old. The _external or
comparative_ time of all movements—that is to say, the time of
which alone we can have any appreciation—would be the same as of
old. The new day would, of course, appear only half as long as the
old to a mind not readjusted to the new conditions; but this would
still be external time. But would the _internal_, _intrinsic_ time
of each movement be unaltered? It would be the same for the
readjusted mind as it was previously for the mind adjusted to
these previous conditions. By an unaltered mind, however, by the
Divine Mind, for instance, the same amount of motion would be seen
to constitute the same movement under both conditions, but to take
place twice as quickly under the new conditions as it did under
the old. This again, however, involves a comparison, and thus
informs us merely of external or relative time. If we identify
intrinsic time with _amount of change_, making the latter the
measure of the former, we must conclude that alteration in the
_rate_ of a motion does not alter its absolute time: and this is
evident when we reflect that the very notion of a _rate_ of motion
involves the comparison of the latter with some other motion.(383)
Finally, we have no positive conception of the manner in which
time duration is related to, or known by, the Divine Eternal Mind,
which is present to all time—past, present and future.
Besides the question of the relativity of time, there are many
other curious and difficult questions which arise from a
consideration of time-duration, but a detailed consideration of
them belongs to Cosmology. We will merely indicate a few of them.
How far is time _reversible_, at least in the case of purely
mechanical movements?(384) Had time a beginning? We know from
Revelation that _de facto_ it had. But can we determine by the
light of reason alone whether or not it _must_ have had a
beginning? The greatest philosophers are divided as to possibility
or impossibility of _created_ reality existing _from all
eternity_. St. Thomas has stated, as his considered opinion, that
the impossibility of _creatio ab aeterno_ cannot be proved. If a
series of creatures could have existed successively from all
eternity, and therefore without any _first_ term of the series,
this would involve the possibility of an _actually infinite
multitude_ of creatures; but an actually infinite multitude of
creatures, whether existing simultaneously or successively, is
regarded by most philosophers as being self-contradictory and
intrinsically impossible. And this although the Divine Essence,
being infinitely imitable _ad extra_, and being clearly
comprehended as such by the Divine Mind, contains virtually the
Divine exemplars of an infinite multitude of possible creatures.
Those who defend the possibility of an actually infinite multitude
of creatures consider this fact of the infinite imitability of the
Divine Essence as the ground of this possibility. On the other
hand, those who hold that an actually infinite multitude is
self-contradictory deny the validity of this argument from
possibility to actuality; and they bring forward such serious
considerations and arguments in favour of their own view that this
latter has been at all times much more commonly advocated than the
former one.(385) Will time have an end? All the evidence of the
physical sciences confirms the truth of the Christian faith that
external time, as measured by the motions of the heavens, will
have an end. But the internal or intrinsic time which will be the
measure of the activities of immortal creatures will have no
end.(386)
86. DURATION OF IMMUTABLE BEING: ETERNITY.—We have seen that _duration_ is
the perseverance or continuance of a being in its existence. The duration
of the Absolutely Immutable Being is a positive perfection identical with
the essence itself of this Being. It is a duration without beginning,
without end, without change or succession, a _permanent_ as distinct from
a _successive_ duration, for it is the duration of the Necessary Being,
whose essence is Pure Actuality. This duration is eternity: _an
interminable duration existing all together_. _Aeternitas est
interminabilis duratio tota simul existens._ This is the common definition
of eternity in the proper sense of the term—absolute or necessary
eternity. The word “_interminabilis_” connotes a _positive_ perfection:
the exclusion of beginning and end. The word “_tota_” does not imply that
the eternity has parts. The expression “_tota simul_” excludes the
imperfection which is characteristic of time duration, _viz._ the
_succession_ of “before” and “after”. The definition given by Boëtius(387)
emphasizes these points, as also the indefectible character of immutable
life in the Eternal Being: _Aeternitas est interminabilis vitae tota simul
et prefecta possessio_.
There is, in the next place, a kind of duration which has been called
_hypothetical_, _relative_, or _borrowed_ eternity: _aeternitas
hypothetica_, _relativa_, _participata_, also called by scholastics
“_aeviternitas_”. It is the duration in existence of a being that is
contingent, but _of its nature incorruptible, immortal_, such as the human
soul or a pure spirit. Even if such a being existed from all eternity its
existence would be contingent, dependent on a real principle distinct from
itself: its duration, therefore, would not be eternity in the strict
sense. On the other hand, once created by God, its nature would demand
conservation without end; nor could it naturally cease to exist, though
absolutely speaking it could cease to exist were God to withdraw from it
His conserving power. Its duration, therefore, differs from the duration
of corporeal creatures which are by nature subject to change, decay, and
cessation of their being. A contingent spiritual substance has by nature a
beginning to its duration, or at least a duration which is not essential
to it but dependent on the Necessary Being, a duration, however, which is
naturally without end; whereas the duration of the corporeal being has by
nature both a beginning and an end.
But philosophers are not agreed as to the nature and ground of the
distinction between these two kinds of duration in contingent
beings. No contingent being is self-existent, neither has any
contingent being the principle of its own duration in its own
essence. Just as it cannot begin to exist of itself, so neither
can it continue to exist of itself. At the same time, granted that
it has obtained from God actual existence, some kind or degree of
duration, of continuance in that existence, seems to be naturally
due to its essence. Otherwise conservation would be not only
really but formally a continued creation. It is such indeed on the
part of God: in God there is no variety of activity. But on the
part of the creature, the preservation of the latter in existence,
and therefore some degree of duration, seems to be due to it on
the hypothesis that it has been brought into existence at all. The
_conserving_ influence of God is to its duration in existence what
the _concurring_ influence of God is to the exercise of its
activities.(388) In this sense the duration of a finite being in
existence is a positive perfection which we may regard as a
property of its nature. But is this perfection or property of the
creature which we call _duration_, (_a_) essentially _successive_
in all creatures, spiritual as well as corporeal? And (_b_) is it
really identical with their actual existence (or with the reality
of whatever change or actualization occurs to their existence), or
it is a _mode_ of this existence or change, really distinct from
the latter and conferring upon the latter the perfection of
continuity or persistence?
This, at all events, is universally admitted: that _we_ cannot
become aware of any duration otherwise than through our
apprehension of _change_; that we have direct knowledge only of
_successive_ duration; that we can conceive the _permanent_
duration of immutable reality only after the analogy of successive
duration, or as the co-existence of immutable reality with the
successive duration of mutable things.
Now some philosophers identify successive duration with change,
and hold that successive duration is formally the duration of
things subject to change; that in so far as a being is subject to
change its duration is successive, and in so far as it is free
from change its duration approaches the essentially permanent
duration of the Eternal, Immutable Being; that therefore the
duration of corporeal, corruptible, mortal beings is _par
excellence_ successive or temporal duration (_tempus_); that
spiritual beings, which are substantially immutable, but
nevertheless have a successive series of spiritual activities,
have a sort of duration more perfect, because more permanent, than
mere temporal duration, but less perfect, because less permanent,
than eternal duration (_aevum_, _aeviternitas_); while the
Absolutely Immutable Being alone has perfect permanent duration
(_aeternitas_).(389) It is not clear whether according to this
view we should distinguish between the duration of spiritual
_substances_ as permanent, and that of their _acts_ as successive;
or why we should not attribute _permanent_ duration to corporeal
_substances_ and their _permanent accidents_, confining successive
duration formally to motion or change itself. It is, moreover,
implied in this view that duration is not any really distinct
perfection or mode superadded to the actuality of the being that
endures.
Other philosophers hold that _all_ duration of _creatures_ is
_successive_; that no individual creature has a mixture of
permanent and successive duration; that this successive duration
is really distinct from that which endures by means of it; that it
is really distinct even from the reality of change or motion
itself; that it is a _real mode_ the formal function of which is
to confer on the enduring reality a series of _actualities in the
order of_ “_succession of posterior to prior_,” a series of
intrinsic _quandocationes_ (analagous to the intrinsic locations
which their extension confers upon bodies in space). These
philosophers distinguish between _continuous_ or (indefinitely)
_divisible_ successive duration, the (indefinitely divisible)
parts of which are “past” and “future,” and the present not a
“part” but only an “indivisible limit” between the two parts; and
_discontinuous_ or _indivisible_ successive duration, whose parts
are separate and indivisible units of duration succeeding one
another discontinuously: each part being a real but indivisible
duration, so that besides the parts that are _past_ and _future_,
the _present_ is also a _part_, which is—like an instant of
time—indivisible, but which is also—unlike an instant of time—a
real duration. The former kind of successive duration they ascribe
to corporeal, corruptible creatures; the latter to spiritual,
incorruptible creatures. This view is defended with much force and
ingenuity by De San in his _Cosmologia_;(390) where also a full
discussion of most of the other questions we have touched upon
will be found.