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The ideas of space and time are therefore no separate or distinct ideas, but merely those of the manner or order, in which objects exist: Or in other words, it is impossible to conceive either a vacuum and extension without matter, or a time, when there was no succession or change in any real existence. | |

The intimate connexion betwixt these parts of our system is the reason why we shall examine together the objections, which have been urged against both of them, beginning with those against the finite divisibility of extension. | |

I.The first of these objections, which I shall take notice of, is more proper to prove this connexion and dependence of the one part upon the other, than to destroy either of them. | |

It has often been maintained in the schools, that extension must be divisible, in infinitum, because the system of mathematical points is absurd; and that system is absurd, because a mathematical point is a non-entity, and consequently can never by its conjunction with others form a real existence. | |

This would be perfectly decisive, were there no medium betwixt the infinite divisibility of matter, and the non-entity of mathematical points. | |

But there is evidently a medium, viz. the bestowing a colour or solidity on these points; and the absurdity of both the extremes is a demonstration of the truth and reality of this medium. | |

The system of physical points, which is another medium, is too absurd to need a refutation. | |

A real extension, such as a physical point is supposed to be, can never exist without parts, different from each other; and wherever objects are different, they are distinguishable and separable by the imagination. | |

II. The second objection is derived from the necessity there would be of PENETRATION, if extension consisted of mathematical points. | |

A simple and indivisible atom, that touches another, must necessarily penetrate it; for it is impossible it can touch it by its external parts, from the very supposition of its perfect simplicity, which excludes all parts. | |

It must therefore touch it intimately, and in its whole essence, SECUNDUM SE, TOTA, ET TOTALITER; 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? |

Gilles Tran © 1993-2009 www.oyonale.com