NEWTON

MATHEMATICAL PRINCIPLES OF NATURAL PHILOSOPHY (Second Edition, 1713)

Translation © George MacDonald Ross, 1999

Book 3: The Rules of Philosophising

Rule 1

No more causes of natural things are to be admitted than such as are true, and sufficient for explaining the phenomena they cause.

[387] Philosophers certainly say that Nature does nothing in vain; and something happens in vain if it comes about by more means, when it could have come about by fewer. For Nature is simple, and does not luxuriate in superfluous causes of things.

Rule 2

Therefore the same causes must be assigned to natural effects of the same kind, as far as is possible.

For example, the cause of respiration in humans and in animals; the cause of the falling of stones in Europe and in America; the cause of light in a cooking fire and in the sun; the cause of the reflection of light on earth and in the planets.

Rule 3

The qualities of bodies which cannot be intensified or diminished, and which belong to all bodies of which observations can be made, must be taken as qualities of all bodies.

The qualities of bodies become known only by observation, and hence whatever qualities square with observation universally must be held to be universal; [388] and those which cannot be diminished, cannot be lost to them. Certainly, fantastic theories must not be arbitrarily invented contrary to the regularity of experience; nor must there be any departure from the harmony of Nature, since she tends to be simple and always consistent with herself.

The extension of bodies is known only by the senses; and although it is not sensed in all of them, it is attributed to all of them, since it belongs to all sensible bodies.

We experience many bodies as being hard. But the hardness of the whole arises from the hardness of the parts; and we rightly conclude from this that the undivided particles of all bodies are hard, and not just those of the bodies we sense.

We infer that all bodies are impenetrable, not by reason, but by sensation. Those which we handle are discovered to be impenetrable, and we conclude from this that impenetrability is a property of all bodies.

We infer that all bodies are capable of motion, and persist in their motion or rest by virtue of certain forces (which we call ‘inertial forces’) from these properties of visible bodies.

The extension, hardness, impenetrability, mobility, and inertial force of the whole arises from the extension, hardness, impenetrability, mobility, and inertial forces of the parts. From this we conclude that all the smallest parts of all bodies are extended, and hard, and impenetrable, and mobile, and endowed with inertial forces. And this is the foundation of the whole of philosophy.

Further, we know from the phenomena that the divided parts of bodies which are in mutual contact can be separated from each other; and from mathematics it is certain that the undivided parts can be distinguished into smaller parts by reason. But it is uncertain whether distinct parts which have not yet been divided can be divided and separated from each other by natural forces. But if a single experiment established that some undivided particle underwent division by breaking a hard and solid body, we would conclude, by means of the present rule, that not only divided parts were separable, but also that undivided parts could be divided to infinity.

Finally, if it is universally established by experience and astronomical observations that all bodies in the earth’s orbit gravitate towards the earth in proportion to the quantity of matter in each; and that the moon gravitates towards the earth in proportion to the quantity of its matter, and that the ocean in turn gravitates towards the moon; and that all the planets gravitate towards each other, and that there is a similar gravitation of the comets towards the sun — then in accordance with the present rule, it must be said that all bodies gravitate towards each other. For the argument from the phenomena about universal gravitation will be even stronger than [389] the argument about the impenetrability of bodies, since we have absolutely no experience or observation in the case of celestial bodies. However, I certainly do not assert that gravity is essential to bodies. The only intrinsic force I recognise is inertial force. It is immutable, whereas gravity is diminished by increasing distance from the earth.

 

Book 3: General Scholium

[527] . . . This most elegant structure of sun, planets, and comets could not have come into being without the wisdom and authority of an intelligent and powerful being. And if the fixed stars are the centres of similar systems, all these systems, constructed with similar wisdom, will be under the dominion of One being, especially since the light of the fixed stars is of the same nature as the light of the sun, and all the systems transmit light to each other. And the systems of the fixed stars would gradually collapse into each other, unless everything was governed by the wisdom of a supreme Being. [n.1]

[528] He rules them all, not as the soul of the world, but as the lord of the universe. Because of his dominion, the Lord God is often called ‘Pantokrator’. [n.2] For ‘God’ is a relative term — relative to his servants. God’s deity consists, not in his domination over his own body, [n.3] but over his servants. God the Highest is an eternal, infinite, and absolutely perfect being; but a being, however perfect, is not the Lord God without dominion. For we say ‘my God,’ ‘your God,’ ‘The God of Israel,’ [n.4] — but we do not say ‘my Eternal,’ ‘your Eternal,’ or ‘the Eternal of Israel;’ nor do we say ‘my Infinite,’ ‘your Infinite,’ or ‘the Infinite of Israel;’ nor do we say ‘my Perfect,’ ‘your Perfect,’ or ‘the Perfect of Israel.’ These expressions are not relative to servants.

The word ‘God’ often means ‘lord’, [n.5] but not every lord is God. If the domination of a spiritual being is genuine, it constitutes a genuine God; if it is supreme, it constitutes a supreme God; and if it is false, it constitutes a false god. And from his genuine domination, it follows that the true God is alive, intelligent, and powerful; and from the rest of his perfections, it follows that he is supreme, or supremely perfect. He is eternal and infinite, omnipotent and omniscient — that is, he lasts from eternity to eternity, and he is present from infinity to infinity. He governs everything, and knows everything which happens or can be known. [n.6] He is not eternity or infinity, but eternal and infinite; he is not duration or space, but he continues to exist and is present. He continues to exist for ever, and is present everywhere; and by existing always and everywhere, he constitutes time and space. Since every smallest part of space always exists, and every indivisible moment of time exists everywhere, it is certain that the creator and lord of all things will not be never or nowhere. [n.7] He is omnipresent, not merely by virtue of his power, but by virtue of his substance, since power cannot subsist without substance. [529]

Everything is contained [n.8] and moves in him, but without any mutual passivity. God is not affected by the motions of bodies, and they do not encounter any resistance from the omnipresence of God. Everyone agrees that God the Highest necessarily exists. and by the same necessity he exists always and everywhere. For the same reason, the whole is of the same nature throughout: all eye, all ear, all brain, all arm, all power of sensing, understanding, and acting — but in a way which is utterly non-human, a way which is utterly non-corporeal, a way which is completely unknown to us. Just as a blind person has no idea of colours, we have no idea of the ways in which the all-wise God senses and understands everything. He is completely devoid of any body or bodily shape, and therefore he cannot be seen, or heard, or touched, and should not be worshipped in the form of any corporeal thing.

We have ideas of his attributes, but we have the barest knowledge of the substance of any thing. We see only the shapes and colours of bodies, we hear only sounds, we touch only external surfaces, we smell only odours, and we taste only flavours. We do not know the inner substances by any sense or by any reflective act; and much less do we have any idea of God. We know him only through his properties and attributes, and through the most wise and perfect structures and final causes of things; [n.9] and we revere and worship him on account of his dominion over us. For we worship him as his servants, and a God without dominion, providence, and final causes is nothing other than Fate and Nature. [n.10]

And this is all I shall say about God — a topic which belongs to experimental [n.11] philosophy, since it is certainly based on the phenomena.

[530] So far I have explained the phenomena of the heavens and of the terrestrial oceans by means of the force of gravity; but I have not yet indicated the cause of gravity. This force certainly arises from some cause or other which penetrates right to the centres of the sun and planets without any diminution of its power. Its action is proportional, not to the quantity of the surfaces of the particles on which it acts (as is the case with mechanical causes), but to the quantity of solid matter. Its action is extended over immense distances in all directions, and it is always inversely proportional to the square of the distance. The gravitational force towards the sun is the sum of the gravitational forces towards the individual particles of the sun, and receding from the sun, it decreases in exact proportion to the square of the distance, as far as the orbit of Saturn (as is obvious from the fact that the maximum distance of each planet from the sun remains constant) — and even as far as the most remote comets (if it is indeed the case that they have a constant maximum distance from the sun).

However, I have not yet been able to deduce the reason for these properties of gravity from the phenomena, and I do not invent hypotheses. For anything which is not deduced from the phenomena must be called a ‘hypothesis’; and hypotheses — whether metaphysical, or physical, or about occult qualities, or mechanical — have no place in experimental philosophy. In this philosophy, propositions are deduced from the phenomena, and made general by induction. This is how we have come to know about impenetrability, mobility, and the impetus of bodies, and the laws of motion and of gravity. It is enough that gravity really exists, and that it acts in accordance with the laws I have expounded, and that it is sufficient for explaining all the motions of heavenly bodies and of the oceans.

I could add a lot about a very tenuous spirit which permeates solid bodies and lies hidden within them. It is by its force and actions that the particles of bodies attract each other over very short distances, and stick together when in contact. It is also how electrified bodies act over longer distances, both repelling and attracting corpuscles which are close to them. It is how light is emitted, reflected, refracted, inflected, and warms bodies. Again, it is how all sensation is stimulated, and how the members of animal bodies are moved by the will — that is, by vibrations of this spirit which are propagated through the solid fibres of the nerves from the external sense organs to the brain, and from the brain to the muscles. But these topics cannot be covered in a few words, and there is insufficient experimental evidence to determine precisely, and to demonstrate, the laws which govern the actions of this spirit.

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