INTRODUCTION

TWENTY-FIVE of the propositions which are employed in the proof for the existence of God, or in the arguments demonstrating that God is neither corporeal nor a force connected with a material being, or that He is One, have been fully established, and their correctness is beyond doubt. Aristotle and the Peripatetics who followed him have proved each of these propositions. There is, however, one proposition which we do not accept — namely, the proposition which affirms the Eternity of the Universe, but we will admit it for the present, because by doing so we shall be enabled clearly to demonstrate our own theory.

PROPOSITION I.

The existence of an infinite magnitude is impossible.

PROPOSITION II.

The co-existence of an infinite number of finite magnitudes is impossible.

PROPOSITION III.

The existence of an infinite number of causes and effects is impossible, even if these were not magnitudes: if, e.g., one Intelligence were the cause of a second, the second the cause of a third, the third the cause of a fourth, and so on, the series could not be continued ad infinitum.

PROPOSITION IV.

Four categories are subject to change: —

(a.) Substance. — Changes which affect the substance of a thing are called genesis and destruction.

(b.) Quantity. — Changes in reference to quantity are increase and decrease.

(c.) Quality. — Changes in the qualities of things are transformations.

(d.) Place. — Change of place is called motion.

The term “motion” is properly applied to change of place, but is also used in a general sense of all kinds of changes.

PROPOSITION V.

Motion implies change and transition from potentiality to actuality.

PROPOSITION VI.

The motion of a thing is either essential or accidental; or it is due to an external force, or to the participation of the thing in the motion of another thing. This latter kind of motion is similar to the accidental one. An instance of essential motion may be found in the translation of a thing from one place to another. The accident of a thing, as, e.g., its black colour, is said to move when the thing itself changes its place. The upward motion of a stone, owing to a force applied to it in that direction, is an instance of a motion due to an external force. The motion of a nail in a boat may serve to illustrate motion due to the participation of a thing in the motion of another thing; for when the boat moves, the nail is said to move likewise. The same is the case with everything composed of several parts: when the thing itself moves, every part of it is likewise said to move.

PROPOSITION VII.

Things which are changeable are, at the same time, divisible. Hence everything that moves is divisible, and consequently corporeal; but that which is indivisible cannot move, and cannot therefore be corporeal.

PROPOSITION VIII.

A thing that moves accidentally must come to rest, because it does not move of its own accord; hence accidental motion cannot continue for ever.

PROPOSITION IX.

A corporeal thing that sets another corporeal thing in motion can only effect this by setting itself in motion at the time it causes the other thing to move.

PROPOSITION X.

A thing which is said to be contained in a corporeal object must satisfy either of the two following conditions: it either exists through that object, as is the case with accidents, or it is the cause of the existence of that object; such is, e.g., its essential property. In both cases it is a force existing in a corporeal object.

PROPOSITION XI.

Among the things which exist through a material object, there are some which participate in the division of that object, and are therefore accidentally divisible, as, e.g., its colour, and all other qualities that spread throughout its parts. On the other hand, among the things which form the essential elements of an object, there are some which cannot be divided in any way, as, e.g., the soul and the intellect.

PROPOSITION XII.

A force which occupies all parts of a corporeal object is finite, that object itself being finite.

PROPOSITION XIII.

None of the several kinds of change can be continuous, except motion from place to place, provided it be circular.

PROPOSITION XIV.

Locomotion is in the natural order of the several kinds of motion the first and foremost. For genesis and corruption are preceded by transformation, which, in its turn, is preceded by the approach of the transforming agent to the object which is to be transformed. Also, increase and decrease are impossible without previous genesis and corruption.

PROPOSITION XV.

Time is an accident that is related and joined to motion in such a manner that the one is never found without the other. Motion is only possible in time, and the idea of time cannot be conceived otherwise than in connexion with motion; things which do not move have no relation to time.

PROPOSITION XVI.

Incorporeal bodies can only be numbered when they are forces situated in a body; the several forces must then be counted together with substances or objects in which they exist. Hence purely spiritual beings, which are neither corporeal nor forces situated in corporeal objects, cannot be counted, except when considered as causes and effects.

PROPOSITION XVII.

When an object moves, there must be some agent that moves it, from without, as, e.g., in the case of a stone set in motion by the hand; or from within, e.g., when the body of a living being moves. Living beings include in themselves, at the same time, the moving agent and the thing moved; when, therefore, a living being dies, and the moving agent, the soul, has left the body, i.e., the thing moved, the body remains for some time in the same condition as before, and yet cannot move in the manner it has moved previously. The moving agent, when included in the thing moved, is hidden from, and imperceptible to, the senses. This circumstance gave rise to the belief that the body of an animal moves without the aid of a moving agent. When we therefore affirm, concerning a thing in motion, that it is its own moving agent, or, as is generally said, that it moves of its own accord, we mean to say that the force which really sets the body in motion exists in that body itself.

PROPOSITION XVIII.

Everything that passes over from a state of potentiality to that of actuality, is caused to do so by some external agent: because if that agent existed in the thing itself, and no obstacle prevented the transition, the thing would never be in a state of potentiality, but always in that of actuality. If, on the other hand, while the thing itself contained that agent, some obstacle existed, and at a certain time that obstacle was removed, the same cause which removed the obstacle would undoubtedly be described as the cause of the transition from potentiality to actuality, [and not the force situated within the body]. Note this.

PROPOSITION XIX.

A thing which owes its existence to certain causes has in itself merely the possibility of existence; for only if these causes exist, the thing likewise exists. It does not exist if the causes do not exist at all, or if they have ceased to exist, or if there has been a change in the relation which implies the existence of that thing as a necessary consequence of those causes.

PROPOSITION XX.

A thing which has in itself the necessity of existence cannot have for its existence any cause whatever.

PROPOSITION XXI.

A thing composed of two elements has necessarily their composition as the cause of its present existence. Its existence is therefore not necessitated by its own essence; it depends on the existence of its two component parts and their combination.

PROPOSITION XXII.

Material objects are always composed of two elements [at least], and are without exception subject to accidents. The two component elements of all bodies are substance and form. The accidents attributed to material objects are quantity, geometrical form, and position.

PROPOSITION XXIII.

Everything that exists potentially and whose essence includes a certain state of possibility, may at some time be without actual existence.

PROPOSITION XXIV.

That which is potentially a certain thing is necessarily material, for the state of possibility is always connected with matter.

PROPOSITION XXV.

Each compound substance consists of matter and form, and requires an agent for its existence, viz., a force which sets the substance in motion, and thereby enables it to receive a certain form. The force which thus prepares the substance of a certain individual being, is called the immediate motor.

Here the necessity arises of investigating into the properties of motion, the moving agent and the thing moved. But this has already been explained sufficiently; and the opinion of Aristotle may be expressed in the following proposition: Matter does not move of its own accord — an important proposition that led to the investigation of the Prime Motor (the first moving agent).

Of these foregoing twenty-five propositions some may be verified by means of a little reflection and the application of a few propositions capable of proof, or of axioms or theorems of almost the same force, such as have been explained by me. Others require many arguments and propositions, all of which, however, have been established by conclusive proofs partly in the Physics and its commentaries, and partly in the Metaphysics and its commentary. I have already stated that in this work it is not my intention to copy the books of the philosophers or to explain difficult problems, but simply to mention those propositions which are closely connected with our subject, and which we want for our purpose.

To the above propositions one must be added which enunciates that the universe is eternal, and which is held by Aristotle to be true, and even more acceptable than any other theory. For the present we admit it, as a hypothesis, only for the purpose of demonstrating our theory. It is the following proposition: —

PROPOSITION XXVI

Time and motion are eternal, constant, and in actual existence.

In accordance with this proposition, Aristotle is compelled to assume that there exists actually a body with constant motion, viz., the fifth element. He therefore says that the heavens are not subject to genesis or destruction, because motion cannot be generated nor destroyed. He also holds that every motion must necessarily be preceded by another motion, either of the same or of a different kind. The belief that the locomotion of an animal is not preceded by another motion, is not true; for the animal is caused to move, after it had been in rest, by the intention to obtain those very things which bring about that locomotion. A change in its state of health, or some image, or some new idea can produce a desire to seek that which is conducive to its welfare and to avoid that which is contrary. Each of these three causes sets the living being in motion, and each of them is produced by various kinds of motion. Aristotle likewise asserts that everything which is created must, before its actual creation, have existed in potentiâ. By inferences drawn from this assertion he seeks to establish his proposition, viz., The thing that moves is finite, and its path finite; but it repeats the motion in its path an infinite number of times. This can only take place when the motion is circular, as has been stated in Proposition XIII. Hence follows also the existence of an infinite number of things which do not co-exist but follow one after the other.

Aristotle frequently attempts to establish this proposition; but I believe that he did not consider his proofs to be conclusive. It appeared to him to be the most probable and acceptable proposition. His followers, however, and the commentators of his books, contend that it contains not only a probable but a demonstrative proof, and that it has, in fact, been fully established. On the other hand, the Mutakallemim try to prove that the proposition cannot be true, as, according to their opinion, it is impossible to conceive how an infinite number of things could even come into existence successively. They assume this impossibility as an axiom. I, however, think that this proposition is admissible, but neither demonstrative, as the commentators of Aristotle assert, nor, on the other hand, impossible, as the Mutakallemim say. We have no intention to explain here the proofs given by Aristotle, or to show our doubts concerning them, or to set forth our opinions on the creation of the universe. I here simply desire to mention those propositions which we shall require for the proof of the three principles stated above. Having thus quoted and admitted these propositions, I will now proceed to explain what may be inferred from them.