TALITER; which is the very definition of penetration.
But penetration is impossible: Mathematical points are of consequence
equally impossible.

I answer this objection by substituting a juster idea of penetration.
Suppose two bodies containing no void within their circumference, to
approach each other, and to unite in such a manner that the body, which
results from their union, is no more extended than either of them; it
is this we must mean when we talk of penetration. But it is evident this
penetration is nothing but the annihilation of one of these bodies, and
the preservation of the other, without our being able to distinguish
particularly which is preserved and which annihilated. Before the
approach we have the idea of two bodies. After it we have the idea
only of one. It is impossible for the mind to preserve any notion of
difference betwixt two bodies of the same nature existing in the same
place at the same time.

Taking then penetration in this sense, for the annihilation of one body
upon its approach to another, I ask any one, if he sees a necessity,
that a coloured or tangible point should be annihilated upon the
approach of another coloured or tangible point? On the contrary, does
he not evidently perceive, that from the union of these points there
results an object, which is compounded and divisible, and may be
distinguished into two parts, of which each preserves its existence
distinct and separate, notwithstanding its contiguity to the other? Let
him aid his fancy by conceiving these points to be of different colours,
the better to prevent their coalition and confusion. A blue and a red
point may surely lie contiguous without any penetration or annihilation.
For if they cannot, what possibly can become of them? Whether shall the
red or the blue be annihilated? Or if these colours unite into one, what
new colour will they produce by their union?

What chiefly gives rise to these objections, and at the same time
renders it so difficult to give a satisfactory answer to them, is the
natural infirmity and unsteadiness both of our imagination and senses,
when employed on such minute objects. Put a spot of ink upon paper, and
retire to such a distance, that the spot becomes altogether invisible;
you will find, that upon your return and nearer approach the spot
first becomes visible by short intervals; and afterwards becomes always
visible; and afterwards acquires only a new force in its colouring
without aug