1.—Quantity
Quantity is the first accident of all to modify a material substance.
Definition.—From the concrete point of view, ‘quantity’ means a thing divisible into parts which are in it and each of which is capable of existing as an individual. This definition of Aristotle’s is worthy of close attention.
Although he assigns divisibility as the chief note, it does not follow that since all quantity is necessarily divisible, therefore wherever there is divisibility there is quantity. Certain conditions must also be verified
1. It is necessary, he says, that quantity formally contain the parts to which division gives rise (insita). Hence the actual and complete reality of the parts obtained must be antecedent to the division. This is a reservation meant to exclude a mode of division quite foreign to quantity, viz., the dissolution of the chemical body into its component elements. Indeed the inorganic compound, which is essentially one, can under the power of dissolving forces be disintegrated and its elements regain their state of liberty, but this dissolution does not imply the existence of a quantitative whole, since the elements do not exist as such in the compound; they are there only in a potential state and are re-instated in their existence only after an essential change.
2. As a second necessary condition Aristotle lays down the aptitude of each of the parts to form, after division, a new individual being (‘unum . . . hoc quid’). If you break up a piece of wood or a bar of iron, you have parts each enjoying its own existence; as the result of division separate complete beings issue from a real quantified whole. This second condition rules out another case of divisibility not indicative of the existence of a quantitative whole, namely the divisibility of a body into its two essential constitutive parts, matter and form. Here, although there is a division inasmuch as the matter can be deprived of its actual form in exchange for another, nevertheless since neither of these principles is capable of existing in isolation, it is not a true sign of a quantitative whole.
On account of this twofold condition limiting divisibility, the Aristotelian definition possesses the great advantage of being applicable to its object and to it alone, whatever may be the various modes of its existence.
Kinds of Quantity.—
Discrete quantity is made up of parts really distinct which have each their own limits. It forms a whole whose unity is purely mental. In reality, since its parts are actually distinct, it is a multitude or number.*
Continuous quantity is made up of parts not distinct which adhere to one another in such a way that the limit of one is identical with that of the next. Independently of any act of the mind it has a true unity. It represents size or amount which has as a property the characteristic of being measurable, either entirely or in part according as it is finite or infinite (Gen. Metaphysics).
According to one view, supported by scientific research, we have no sufficient reason for asserting that elements do not actually remain in an inorganic compound and that when they are liberated an essential change takes place; .cp. SCHAAF, Institutiones Cosmologiae, p. 339 ff. (Privately printed for the Gregorian University, Rome, 1907). There is proof also of the opposite view.
*’Multitude’ signifies that there are distinct units gathered in a single mental concept; nothing more. It is by its definition neither limited nor unlimited. ‘Number’ on the other hand, signifies how many there are of a thing. See Gen. Metaphysics.
Continuous quantity is subdivided into many kinds: —
Successive quantity has its integral parts succeeding one another without interruption according to an order of’ before’ and’ after’. Its principal subdivisions are time and movement.
Permanent quantity has all its parts existing simultaneously and occupying different positions in space. To this kind of quantity belong extension and space. Extension in its three dimensions represents to us a body as it really is and is called volume; considered only under the one aspect of length, it is a line; and under the double aspect of length and breadth, a surface.
The Essence of Quantity.—Many attributes may be predicated of a body in virtue of its quantitative state. It appears to us as a complexus of many integral parts, each of which, if separated from the whole, takes with it a fragment, so to speak, of the matter and form; it is moreover subject to ever further divisions; it is by nature impenetrable; it is extended in space, and forms a measurable amount.
Now of these many properties connected with quantity is there one which may be regarded as the foundation of the others, one that cannot be posited without involving also all the others?
Such a primary property of quantity we think to be its entitative composition. Being essentially composed of integral parts, quantity by its union with substance communicates to it that composition which it possesses within itself and makes it a whole capable of division. This is not to say that quantity gives to the body the reality of the integral elements of which it is constituted, for an accident cannot produce a substance; but, that quantity is the reason on account of which the substantial mass, of itself indivisible, becomes a whole or, rather, a potential multiple which can be broken up into integral parts.
This is the most fundamental of all the attributes of quantity; divisibility, extension in space, measurability and impenetrability all follow naturally from it.
There is a Real Distinction between Quantity and Substance.—
By the ‘essence’ of a body we mean that which constitutes it, that which is its underlying foundation, the principle and support of all its accidental phenomena. On the other hand the idea of ‘quantity’ expresses simply a mode of being, that in virtue of which the body has extended mass in space and is capable of division. These two representations of material being are different.
The question is: Are these two aspects the result of a mental process or are they really distinct in nature?
With Aristotle and many of the Scholastics we think that substance and quantity are two things really distinct.
Argument from Reason.— Substance and quantity appeal to our sense-perception in ways really different: for quantity is directly perceptible by the senses, substance only indirectly. The eye, and even the taste, may indeed mistake for milk chemical substances that are essentially different from it though having certain physical resemblances. But one and the same thing cannot make two mutually exclusive relations with the same term of comparison — our sense-perception. Therefore substance and quantity, which appeal to our cognitive faculty in two different ways are not one and the same thing.
There exists this further ancient proof which may have presented an obstacle to the Protestant attacks upon a central feature of Christian worship pertaining until then — the doctrine that bread and wine during the Mass became the actual body and blood of Jesus Christ. It is no secret that this doctrine, which has remained as the defining feature of Roman Catholicism, caused embarrassment to post Reformation theologians, and ultimately led them to abandon even Scholastic philosophy. As late as the 17th century, Thomas Hobbes rebuked and silenced Cambridge theologians who attempted to refute his atheism through classical arguments. He simply hinted that they could be reported for teaching the Old Religion. However the proposed theological proof is commonly given thus …
Theologico-philosophical Proof .— The proof from reason just given is not without its value. Yet there are many who fail to see in it a convincing proof of the Scholastic theory. However this may be, if reason left to its own natural powers remains in doubt, it can be so no longer when it receives the confirmation afforded by the data of Revelation. The Catholic Faith teaches that by the Consecration at Mass ‘the substance of the bread and wine is changed totally into the substance of the Body and Blood of Christ’. Now to sense-perception the natural properties of the substances that have disappeared remain identically the same: the Consecrated Host keeps the same extension in space as the plain bread and is capable of division; in a word, its quantity persists without any apparent change. But it is impossible that two things really separable — as in this case Christ in the sacramental Real Presence and the quantity of the bread — should not be two realities distinct from one another.
It is true that accidents are intrinsically dependent on their substance, and therefore we may well wonder how realities having such a precarious existence can exist outside their connatural subject. Yet if the reality of quantity is not confounded with that of substance, there appears nothing contradictory in the Almighty supplying the influence of the secondary cause (the substance of the bread) which has temporarily disappeared.
[Council of Trent, sess. XIII, ch. 4 and can. 2. Cp. DENZINGER, Enchiridion Symbolorum, nn. 877 and 884 (Herder, London, etc., 12th edn., 1913).]
We must now examine the properties of extension.
Every Part of an Extended Thing is itself Extended and therefore Indefinitely Divisible.—Are the parts resulting from a division, however far it is carried, themselves always extended? To answer in the affirmative is to say that the continuous whole can be broken up indefinitely, for the reason that extension is essentially capable of division. To answer in the negative is to say that the ultimate results of a process of division, themselves impervious to any further division, must be simple points destitute of real extension. Aristotle, St. Thomas and the majority of the older and modern Scholastics agree in holding the first opinion.
Proof of the Thesis.— It is impossible for an extended thing to be formed of unextended parts. For either the parts are united according to an order of perfect continuity, or following an order of simple contiguity or contact. But, in either case, the opinion that reduces the extended thing to a collection of simple points leads to conclusions manifestly false.
In the first place, the parts cannot be continuous. Indivisible things have no parts. If their boundaries are not separate from each other, the bodies must wholly interpenetrate. To two elements thus interpenetrating add ten, twenty or a hundred others: all of them will interpenetrate alike in a single mathematical point that excludes all real extension.
In the second place, it is equally impossible for simple parts to be contiguous. Objects are contiguous when they touch one another while keeping their respective boundaries. Either, then, a part of one touches a part of the other, or a part of one touches the whole of the other, or they touch one another according to the totality of their being. Now the first two cases are impossible for the reason that an indivisible thing has no parts. And the last case can never result in extension, no matter how many parts be superadded, since it is essential to this quality that its elements occupy different portions of space.
The Parts of a Continuous Whole are not Actual but Potential.—Whilst it is evident that the reality of the parts produced by division must be antecedent to it), it remains a question whether these parts possess their own respective boundaries and are thus really distinct from one another, or whether the elements which constitute extension, instead of being actually distinct parts, form a true unity in which there is no multiplicity until a division, real or ideal, has been made.
Proof of the Thesis.— If each of the elements forming a continuous whole possesses its individual boundaries, we may naturally ask how many parts actually distinct there are in the surface of a square centimetre. We are justified in asking this question, seeing that elements which are distinct are units and therefore capable of being counted. Now there are two alternatives possible: either these elements are finite in number or else there is an infinite multitude of them. If we say they are finite, we are bound to acknowledge limits to the divisibility of a continuous whole and to reduce it to a collection of unextended points: for the only reason why parts become incapable of further division lies in their simplicity or lack of extension. If we say they are infinite, we are thereby granting an actual infinity in a thing of finite dimensions —which is a contradiction, since ‘there is no part. however conceivably small provided it is greater than zero, which repeated an infinite number of times does not make up a quantity greater than any that can be measured’. Hence, as soon as it is admitted that integral parts are really distinct that they are actual parts, be they finite or infinite in number, the idea of a continuum becomes impossible.
Scientific Definition of Mass.— The notion of ‘mass’ is closely allied to that of quantity. It is generally defined in the natural sciences and particularly in mechanics as: The constant relation between force and acceleration.
To determine the acceleration of a body moving under the influence of a moving principle, it is not sufficient to consider only the intensity of the impelling action. Experience establishes the fact that the velocity of the movement imparted during a unit of time depends also on the nature of the moving body to which the force is applied.
If two bodies of unequal weights, for instance, are submitted in the same place to the action of the same mechanical force, the velocity communicated to them will be different in each case, and less in proportion to the greater weight of the body. But in the case of a single body moving in a straight line under the influence of a force which does not vary during the experiment, there exists, between the intensity of the force and the amount of velocity produced by it in a unit of time, a relation which is always and everywhere constant; such that if the force is increased, the acceleration increases in proportion.
By dividing the force applied to a body by the acceleration which it produces we obtain therefore a quotient which is invariable but proper to the particular body in question. This is called mass. Hence the classical definition given above.
Criticism of this Definition.— Although there is nothing to be said against this definition from a scientific point of view, it is nevertheless inadequate for philosophy: it does not help us at all in getting to know the intimate nature of this mysterious factor which plays so important a part in cosmic phenomena. For, inasmuch as mass is a kind of intermediary between force and acceleration, we know it as something purely relative; it is a number, a quotient, the value of which is essentially dependent upon two other numbers. In itself it is neither force nor acceleration but a constant relation between these two factors which are themselves alien to it. Yet this relation only expresses the measure of it, it in no way tells us what it is, what is its nature.
That mass is something absolute is clear from the fact that a body possesses it equally in a state of rest as in a state of motion. And were there but one body in existence, it would still have its own mass.
The cosmologist, then, though he be possessed of this well-known formula, is justified in asking, What is the real entity of mass? Is it an accident or a substance? How does it fulfil the function which the scientist assigns to it?
Philosophical Definition of Mass.— Since the natural sciences stop on the very threshold of these further questions, it remains for us to appeal to metaphysics.
In metaphysics the only definition which seems capable of bearing the test of facts is this: The mass of a body is its dimensive quantity; or, to use a more concrete form: It is by its quantity that a body fulfils the function of mass and possesses the properties belonging to this mechanical factor.
BALFOUR STEWART, The Conservation
ol Energy (London, 1890). Examples of active resistance,
or forces of resistance, are friction and the resistance which a body at
rest makes against one in motion. If all resistance of this kind ceased,
the push given by a fly’s wing would be sufficient to set the heaviest
wagon in motion. This kind of resistance is no measure of mass.
Now dimensive quantity, and that alone, is endowed with this power of reducing the velocity of motion.
Quantity, be it observed, is the receptive subject, the common substratum, of all corporeal properties: it communicates to substance the multiplicity of integral parts of which it is itself made up and sets up an internal arrangement which determines the manner according to which all other qualities are received in it; thus all other properties of necessity partake of its manner of being, they all spread over, so to speak, this common foundation.
ST. THOMAS, Sum. Theol., III, q. 77, a. 2. Colour, e.g., clearly spreads over the extent of surface. Cp. General Metaphysics, 23
Now if this is so, we can understand how a mechanical impulse communicated to a body has to be dispersed throughout the whole mass, and this dispersion of it will be so much the greater as the number of material parts in it is greater; in a word, the dispersion will be proportionate to the quantity. Next consider the truth, which is verified by daily experience, that the more a force is dispersed, the less is its intensity. By the hypothesis, the intensity of the acceleration of the motion resulting from the mechanical impulse will in every case suffer a decrease proportionate to the dispersion of the motion imparted; that is, the velocity will bear an inverse ratio to the greatness of the mass. Lastly, the resistance on the part of the moving body is here purely passive, as the data of mechanics require. It consists in a simple dispersion which destroys none of the quantity of the motion transmitted. The velocity alone of the moving body is affected by it.
Inertia.— Inertia may be taken in different senses. Newton has defined it as the property in virtue of which a body cannot of itself modify its state, whether of rest or of motion. Thus understood, it is rather a negative property of matter. It signifies the absolute indifference of a body in respect of two opposite states, rest and motion. The reason of this indifference lies in the fact that a material part, even in the case of living beings, never acts upon itself, but only upon the parts placed in proximity to it. Since the action of inorganic bodies and that of each of the particles of organic beings is always transitive, it is naturally impossible that matter should modify, on its own initiative, the state in which it has been placed.
From a second point of view, inertia signifies a passive resistance, a power that reduces communicated motion. It is this power of reduction that is proper to each body and absolutely constant which physicists call the ‘quantity of inertia’, ‘quantity of mass’, ‘force of inertia’. Now the concrete reality which has this function is, we have said, none other than dimensive quantity in the strict sense of the word.
The term ‘force’, so often applied by scientists to signify this passive property of matter, is not a felicitous one. For, whilst the ordinary meaning attached to this word is that of an active principle, an efficient cause, all are agreed that the ideas of inertia, of mass, and of quantity would be falsified, if there were introduced into them any notion of a causality which is not entirely passive.
Impenetrability. Scientific Interpretation.—Though subjected to the most violent shocks or the most intense pressure, neither different masses of matter nor the parts of the same body can ever be made to occupy simultaneously one and the same spatial position. Scientists generally make the cause of this impenetrability to consist in the force of resistance. According to them, what keeps two bodies from interpenetrating is simply that energy in virtue of which each resists the entrance of the other into its own spatial position.
Consequences of this Interpretation.—
1. The first and most serious objection to this scientific explanation is that it introduces life into all the beings of the inorganic world.
Let us consider the atom of a simple body, that is, the smallest possible chemical individual being. Like every other extended being, the atom possesses a multiplicity of parts occupying space in such a way that to each there corresponds its own proper spatial position. In a word, all the component elements of the atom are naturally impenetrable among themselves.
Suppose now that the impenetrability arises from the continuous exercise of internal forces of resistance. In this case, the parts of the atomic mass cannot preserve the law of externality to each other that governs them, without acting upon one another, and the atom thus becomes the scene of a multiplicity of actions of which it is at once both the cause and the receptive subject. Yet such activity as has its principle and objective in the same substantial being is none other than immanent or vital activity (Ref; Psychology).
2. Moreover this theory leads to another error, namely the real distinction of parts in a continuous whole. If all the particles of matter contained in an atom exercise contrary activities upon one another, they must necessarily be realities actually and really distinct.
Thomistic Interpretation.—To have recourse to the force of resistance or to any active force is to be faced with the above difficulties. Since then impenetrability demands a cause, it remains to look for the reason of it in some passive aptitude of matter. In what does this aptitude, or rather this exigency consist?
That a thing cannot be something actually except it first be so potentially, that a subject cannot receive a determination except it be fitted by its nature to be so determined, is a truth of Metaphysics: accordingly extension, which is a certain actuality or determination, presupposes a natural adaptation on the part of the subject which is extended, Now whilst the quantified parts of a body have a natural aptitude to be affected by spatial extension, they have yet no such aptitude to occupy positions in space which are already occupied by other parts. Hence the impossibility of two bodies or of two parts of the same body interpenetrating can be accounted for by the complete absence of this requisite receptive power.
However do not let us lose sight of the fact that all matter is seen universally to possess forces of resistance. Such forces we believe even to be indispensable for the maintenance of the cosmic order, for it would be hard to say what would become of the universe if but the least effort sufficed to displace a mountain or to overturn a house. But while we recognize how important their concurrence is for safeguarding the relative stability of bodies and for preventing their too easy displacement, we fail to see here the reason of their natural impenetrability.
Forces or A ctive and Passive Powers of Bodies.
All the multifarious elements of the universe, the smallest not excepted, conspire by their joint action to bring about the welfare of the whole. All are depositories of certain powers of action corresponding to their respective natures. Now of these natural energies the basic or ultimate principle is always the substance. But, since action in any created being is not a substantial perfection, the substance’s energy has to be distributed through as many different accidental powers or faculties as it has different modes of action. These secondary powers that are intimately connected with substance and are derived from it are the immediate causes of a body’s activities. Our present concern is to say what kinds of powers a body has.
First Classification.—From the point of view of their origin material powers may be divided into intrinsic and
extrinsic.
Some powers have their root in the very substance of the body and cannot be separated from it. Such are chemical affinity, electricity, magnetism, the energies of heat and light, forces of resistance, elasticity, repulsion and attraction. These are very properly called intrinsic forces.
Extrinsic forces are those of which a body is not itself the cause, but which are communicated to it in the course of its existence and subsequently lost without any prejudice to it. An example of this kind of power is the force of impulse communicated to a body at rest by one in motion: the motor energy that is communicated is clearly a borrowed energy.
Second Classification.—This comprises active and passive powers.
Active powers are so named because they have of themselves an immediate and complete adaptation to their effect. It may of course happen that certain extrinsic conditions necessary for the development of their energy are lacking; in which case they must necessarily remain inoperative until such time as the realization of these favourable circumstances render their exercise possible. In this sense they are active powers without being always and necessarily in action. Thus when chlorine and antimony are in contact, they exercise a violent action on one another, independently of any outside agency, and discharge an enormous quantity of heat and electricity. It is obvious that these forces existed previously to the contact; they were abiding in the two bodies as active powers, as forces already quite disposed for action; yet they were incapable of exercising their native power as long as the condition of contact was lacking.
Passive Powers are likewise powers of action but such that before they can produce their effect they require to be in some way perfected so as to have their intrinsic indetermination removed. For example, bodies which in perfect darkness have no colour, when exposed to light assume each one its own; each receives in its own way the influence of the luminous ether and immediately exercises its own particular action upon our visual organ: each therefore possesses a passive power, a natural aptitude for making an impression on us, which cannot however develop its energy except in the measure in which it is itself determined by light.
Third Classification.—There is a generic distinction between purely mechanical forces and physical forces properly so called. By the former are here to be understood weight, the forces of repulsion and attraction, resistance, and motor qualities communicated at the moment of collision between masses of matter. These energies constitute quite a distinctive class from those of light, sound, heat, electricity and magnetism, which we denominate as ‘physical forces properly so called’.
Indeed, the only effect which brings before us the activity of mechanical forces is local motion, i.e. simple spatial displacement: weight attracts towards the centre of the earth all bodies in its vicinity; forces of repulsion drive bodies away from one another or keep them at a distance; forces of attraction tend to make them meet; motor qualities arouse bodies from their state of rest. All other effects are manifestations of physical forces. Local motion, it is true, may also appear in the resultant of their action, but it is not the principal and final result, which is rather the appearance of a new state, of a quality sui generis, that is irreducible to terms of simple motion. When our eyes rest on the varied colouring of flowers or we inhale their perfume or taste their fruit, or when we feel the pleasure of warmth stealing over our chilled limbs, it is not the local movement accompanying these phenomena which we first advert to, nor any of the common mechanical principles which cause sensation; but it is some real manner of being which though perhaps difficult to define bears a character distinct from all the ordinary causes of local movement.
Fourth Classification.—Physical forces are themselves specifically distinct from one another.
1 By our external senses we perceive the world around us and amongst other things the physical forces of matter. These senses are to-day universally admitted to differ from one another both anatomically and physiologically. Now how comes it that each of our senses has been provided by the Creator with its own special constitution and activity, if these properties of the material world that they are to make known to us are all of exactly the same nature?
If the objection be raised that our sense-organs are different in constitution and functional activity because the representative movements of these physical agents are different, we may reply in the first place that what we are conscious of perceiving in these agents is not movement but qualities properly so called; and in the second, that diversity of movements does not justify a diversity of sense-organs, since one and the same sense can inform us of movements that are different both in direction and in speed.
2. We know to-day what quantities of heat, electricity and motor force are absolutely equivalent to one another from the mechanical point of view. Yet these quantities, though quantitatively identical, remain just as much qualitatively distinct from one another as a colour, an electric current, a sound and a smell. This is clear proof that under the mechanical equality there lies some real basis of differentiation.
Secondary Aspect of Physical Forces.—Physical forces always have a double efficiency — one, specific and proper to each, such as colour, a thermic state, etc., and another common to all, namely that of imparting a movement to bodies subjected to their influence. Although they are specifically distinct and their primary function is to give bodies diverse qualitative states, they all fulfil, in a secondary way, the role of motor forces. On this account local movement always accompanies the exercise of these forces and is even the measure of their intensity.
Now why this is so is explained by the very manner of being which is proper to physical energies. For since all the qualities of bodies are by their nature extended, as we have already said, any modification produced in a quality or physical energy must accordingly have its corresponding effect in spatial extension. But change in spatial position is nothing else than movement. Therefore the alteration of properties or physical forces naturally involves a local movement of equal intensity.
The chief error of mechanism has been in recognizing only one of the aspects of material phenomena, namely movement, and denying the existence of the other, which is force or quality.