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The phrases in their context!


It is evident, that existence in itself belongs only to unity, and is never applicable to number, but on account of the unites, of which the number is composed.
Twenty men may be said to exist; but it is only because one, two, three, four, &c.
are existent, and if you deny the existence of the latter, that of the former falls of course.
It is therefore utterly absurd to suppose any number to exist, and yet deny the existence of unites; and as extension is always a number, according to the common sentiment of metaphysicians, and never resolves itself into any unite or indivisible quantity, it follows, that extension can never at all exist.
It is in vain to reply, that any determinate quantity of extension is an unite; but such-a-one as admits of an infinite number of fractions, and is inexhaustible in its sub-divisions.
For by the same rule these twenty men may be considered as a unit.
The whole globe of the earth, nay the whole universe, may be considered as a unit.
That term of unity is merely a fictitious denomination, which the mind may apply to any quantity of objects it collects together; nor can such an unity any more exist alone than number can, as being in reality a true number.
But the unity, which can exist alone, and whose existence is necessary to that of all number, is of another kind, and must be perfectly indivisible, and incapable of being resolved into any lesser unity.
All this reasoning takes place with regard to time; along with an additional argument, which it may be proper to take notice of.
It is a property inseparable from time, and which in a manner constitutes its essence, that each of its parts succeeds another, and that none of them, however contiguous, can ever be co-existent.
For the same reason, that the year 1737 cannot concur with the present year 1738 every moment must be distinct from, and posterior or antecedent to another.
It is certain then, that time, as it exists, must be composed of indivisible moments.
For if in time we could never arrive at an end of division, and if each moment, as it succeeds another, were not perfectly single and indivisible, there would be an infinite number of co-existent moments, or parts of time; which I believe will be allowed to be an arrant contradiction.
The infinite divisibility of space implies that of time, as is evident from the nature of motion.
If the latter, therefore, be impossible, the former must be equally so.
I doubt not but, it will readily be allowed by the most obstinate defender of the doctrine of infinite divisibility, that these arguments are difficulties, and that it is impossible to give any answer to them which will be perfectly clear and satisfactory.
But here we may observe, that nothing can be more absurd, than this custom of calling a difficulty what pretends to be a demonstration, and endeavouring by that means to elude its force and evidence.
It is not in demonstrations as in probabilities, that difficulties can take place, and one argument counter-ballance another, and diminish its authority.
A demonstration, if just, admits of no opposite difficulty; and if not just, it is a mere sophism, and consequently can never be a difficulty.
It is either irresistible, or has no manner of force.