BOOK THREE
THE SYSTEM OF THE WORLD
(IN MATHEMATICAL TREATMENT)
IN the preceding books I have laid down the principles
of philosophy; principles not philosophical but mathematical: such, namely,
as we may build our reasonings upon in philosophical inquiries. These
principles are the laws and conditions of certain motions, and powers or
forces, which chiefly have respect to philosophy; but, lest they should
have appeared of themselves dry and barren, I have illustrated them here
and there with some philosophical scholiums, giving an account of such
things as are of more general nature, and which philosophy seems chiefly
to be founded on; such as the density and the resistance of bodies, spaces
void of all bodies, and the motion of light and sounds. It remains that,
from the same principles, I now demonstrate the frame of the System of
the World. Upon this subject I had, indeed, composed the third book
in a popular method, that it might be read by many; but afterwards, considering
that such as had not sufficiently entered into the principles could not
easily discern the strength of the consequences, nor lay aside the prejudices
to which they had been many years accustomed, therefore, to prevent the
disputes which might be raised upon such accounts, I chose to reduce the
substance of this book into the form of Propositions (in the mathematical
way), which should be read by those only who had first made themselves
masters of the principles established in the preceding books: not that
I would advise anyone to the previous study of every Proposition of those
books; for they abound with such as might cost too much time, even to readers
of good mathematical learning. It is enough if one carefully reads the
Definitions, the Laws of Motion, and the first three sections of the first
book. He may then pass on to this book, and consult such of the remaining
Propositions of the first two books, as the references in this, and his
occasions, shall require.
RULES OF REASONING IN PHILOSOPHY
RULE I
We are to admit no more causes of natural things than such as are both
true and sufficient to explain their appearances.
To this purpose the philosophers say that Nature does nothing in vain,
and more is in vain when less will serve; for Nature is pleased with simplicity
and affects not the pomp of superfluous causes.
RULE II
Therefore to the same natural effects we must, as far as possible, assign
the same causes.
As to respiration in a man and in a beast, the descent of stones in
Europe and in America, the light of our culinary fire and of the sun, the
reflection of light in the earth and in the planets.
RULE III
The qualities of bodies, which admit neither intensification nor remission
of degrees, and which are found to belong to all bodies within the reach
of our experiments, are to be esteemed the universal qualities of all bodies
whatsoever.
For since the qualities of bodies are only known to us by experiments,
we are to hold for universal all such as universally agree with experiments;
and such as are not liable to diminution can never be quite taken away.
We are certainly not to relinquish the evidence of experiments for the
sake of dreams and vain fictions of our own devising; nor are we to recede
from the analogy of Nature, which is wont to be simple and always consonant
to itself. We in no other way know the extension of bodies than by our
senses, nor do these reach it in all bodies; but because we perceive extension
in all that are sensible, therefore we ascribe it universally to all others
also. That abundance of bodies are hard we learn by experience; and
because the hardness of the whole arises from the hardness of the parts,
we therefore justly infer the hardness of the undivided particles, not
only of the bodies we feel, but of all others. That all bodies are impenetrable,
we gather not from reason, but from sensation. The bodies which we handle
we find impenetrable, and thence conclude impenetrability to be a universal
property of all bodies whatsoever. That all bodies are movable and endowed
with certain powers (which we call the inertia) of persevering in their
motion, or in their rest, we only infer from the like properties observed
in the bodies which we have seen. The extension, hardness, impenetrability,
mobility, and inertia of the whole result from the extension, hardness,
impenetrability, mobility, and inertia of the parts; and hence we conclude
the least particles of all bodies to be also all extended, and hard and
impenetrable, and movable, and endowed with their proper inertia. And
this is the foundation of all philosophy. Moreover, that the divided
but contiguous particles of bodies may be separated from one another is
a matter of observation; and, in the particles that remain undivided, our
minds are able to distinguish yet lesser parts, as is mathematically demonstrated.
But whether the parts so distinguished and not yet divided may, by the
powers of Nature, be actually divided and separated from one another we
cannot certainly determine. Yet had we the proof of but one experiment
that any undivided particle, in breaking a hard and solid body, suffered
a division, we might by virtue of this rule conclude that the undivided
as well as the divided particles may be divided and actually separated
to infinity.
Lastly, if it universally appears, by experiments and astronomical
observations, that all bodies about the earth gravitate toward the earth,
and that in proportion to the quantity of matter which they severally contain;
that the moon likewise, according to the quantity of its matter, gravitates
toward the earth; that, on the other hand, our sea gravitates toward the
moon; and all the planets one toward another; and the comets in like manner
toward the sun: we must, in consequence of this rule, universally allow
that all bodies whatsoever are endowed with a principle of mutual gravitation.
For the argument from the appearances concludes with more force for the
universal gravitation of all bodies than for their impenetrability, of
which, among those in the celestial regions, we have no experiments nor
any manner of observation. Not that I affirm gravity to be essential
to bodies; by their vis insita I mean nothing but their inertia.
This is immutable. Their gravity is diminished as they recede from the
earth.
RULE IV
In experimental philosophy we are to look upon propositions inferred
by general induction from phenomena as accurately or very nearly true,
notwithstanding any contrary hypotheses that may be imagined, till such
time as other phenomena occur by which they may either be made more accurate
or liable to exceptions.
This rule we must follow, that the argument of induction may not be
evaded by hypotheses.
[End of Book 3. Rules of Reasoning in Philosophy]

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