1: Rules of Reasoning

Book 1 laid down the principles of mathematical philosophy. This will be the basis of our reasonings on philosophical inquiries.

These mathematical principles are the laws and conditions of certain motions and forces. I use them to build a system of the universe.

To prevent them from being dry and barren, I have illustrated them here with some philosophical scholiums, such as:

• the density and the resistance of bodies
• spaces void of all bodies and
• the motion of light and sounds.

I explain the principles as propositions. Readers should go through Books 1 and 2 first, specifically:

• the definitions
• laws of motion
• sections 1-3 of Book 1

Rules Of Reasoning

Rule 1: We only need to look for the causes of natural phenomena that are enough to explain their appearances.

Nature is pleased with simpicity.

Rule 2: The same natural effects come from the same natural causes

• Respiration is the same for humans and animals
• The light of our stove fire is the same as the light of the sun

Rule 3(!*): Universal qualities are those which are common to all the bodies which we experiment with

The qualities of bodies are only known to us by experiments. We deem universal all those qualities that universally agree with experiments.

We will not relinquish the evidence of experiments for the sake of vain fictions.

We can only know bodies by our senses.

We perceive extension [space] in all that are sensible.

Therefore, we ascribe it universally to all others also.

Many bodies are hard from our experience.

• The hardness of the whole arises from the hardness of the parts.

We therefore infer the hardness of the undivided particles not only of the bodies we feel but of all others.

We know from sensation that all [material] bodies are impenetrable.

We thence conclude impenetrability as a universal property of all [material] bodies.

All bodies:

• can move
• have vires inertiæ powers
  • This perseveres their motion or rest

The extension, hardness, impenetrability, mobility, and vis inertiæ of the whole, result from the extension, hardness, impenetrability, mobility, and vires inertiæ of the parts.

Thence, we conclude the smallest particles of all bodies to be also all extended, and hard and impenetrable, and moveable, and endowed with their proper vires inertia.

This is the foundation of all [my] philosophy.

The divided but contiguous particles of bodies may be separated from one another, is matter of observation.

But I do not know whether the parts can be actually divided by the powers of Nature.

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 around the earth gravitate towards the earth according to the the quantity of matter they contain
• the moon likewise, according to the quantity of its matter, gravitates towards the earth
• our sea gravitates towards the moon
• all the planets mutually one towards another
• the comets in like manner towards the sun

in consequence of this rule, it meants that all bodies are have a principle of mutual gravitation universally.

Rule 4*: Induction from Phenomena over Imaginary Hypothesis

Our experiments, must be based on propositions collected by general induction from phenomena as accurately or very nearly true, despite any contrary imaginary hypotheses, until these are corrected by other phenomena. The argument of induction cannot evaded by hypotheses.