conformable to the definition: They never can exist; for we may produce demonstrations from these very ideas to prove that they are impossible.
But can any thing be imagin'd more absurd and contradictory than this reasoning? Whatever can he conceiv'd by a clear and distinct idea necessarily implies the possibility of existence; and he who pretends to prove the impossibility of its existence by any argument deriv'd from the clear idea, in reality asserts, that we have no clear idea of it, because we have a clear idea. 'Tis in vain to search for a contradiction in any thing that is distinctly conceiv'd by the mind. Did it imply any contradiction, 'tis impossible it cou'd ever be conceiv'd.
There is therefore no medium betwixt allowing at least the possibility of indivisible points, and denying their idea; and 'tis on this latter principle, that the second answer to the foregoing argument is founded. It has been [1]pretended, that tho' it be impossible to conceive a length without any breadth, yet by an abstraction without a separation, we can consider the one without regarding the other; in the same manner as we may think of the length of the way betwixt two towns, and overlook its breadth. The length is inseparable from the breadth both in nature and in our minds; but this excludes not a partial consideration, and a distinction of reason, after the manner above explain'd.
In refuting this answer I shall not insist on the argument, which I have already sufficiently explain'd, that if it be impossible for the mind to arrive at a minimum in its ideas, its capacity must be infinite, in order to comprehend the infinite number of parts, of which its idea of any extension wou'd be compos'd. I shall here endeavour to find some new absurdities in this reasoning.
A surface terminates a solid; a line terminates a surface; a point terminates a line; but I assert, that if the ideas of a point, line or surface were not indivisible, 'tis impossible we
- ↑ L'Art de penser.
