Modern History Sourcebook:
The Mathematical Principles of Natural Philosophy
[The Rules of Reasoning in Philosophy]
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
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
The qualities of bodies, which admit neither intension nor
remission of degrees, and which are found to belong to all bodies
within 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
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 impenetrables and thence conclude impenetrability to be a
universal property of all bodies whatsoever. That all bodies are
moveable, and endowed with certain powers (which we call the forces
of inertia) or 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 force of inertia of the whole result from the extension, hardness,
impenetrability, mobility, and forces of inertia of the parts:
and thence we conclude that the least particles of all bodies
to be also all extended, and hard, and impenetrable, and moveable,
and endowed with their proper forces of 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 into 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
mutually one toward another; and the comets in like manner towards
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 all bodies. By their inherent
force I mean nothing but their force of` inertia. This is immutable.
Their gravity is diminished as they recede from the earth.
In experimental philosophy we are to look upon propositions
collected 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.
Isaac Newton, The Mathematical Principles of Natural Philosophy, trans. A. Motte (London, 1729). [Capitalization and spelling
have been modernized.]
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(c)Paul Halsall Aug 1997