Theory of Genesis in S[eries]’s philosophy:

This theory is made clear by an analogy with the numbers in an infinite series, in the simple series of arithmetical progression. Thus, O, 1, 2, 3, 4, 5, 6, 7, 8,..., ¥ —. By looking upon this we can assert that the series begins at 1, though we are unable to say where it ends. To us, indeed, it does not end anywhere. But what we cannot explain is how to pass from zero to one.

Consider the problem of the world in time and see how exact is the analogy. Nay, there is more than an analogy; this of number is the basis of the other.

For, of a truth, time is duration, duration is moments and moments are numbers in time; duration is the union of the ideas of number and of time.

If we wish the solution of the problem of the world in time, we have but to consider number in its ideal extension, as it is here done, and to induce the idea of time.

Let us then examine the problem. In the first place it is to be noticed that the passage from zero to 1 is a passing of nothing to something, of a thing to its contrary. (If I may so speak.)

(But zero is not the contrary of anything for a contrary is something and zero is nothing. Moreover, when we say a thing has a contrary, if we assert afterwards that zero is that contrary we unsay our former statement or make it absurd, for to say a thing is contrary to nothing, is to say it has no contrary at all. [...]

The 1 cannot produce the 2, neither if it be taken in the sense of quantity nor in the sense of a unit of order. In the first case the one cannot sum itself to itself and produce 2. In the second, the one being only one by reason of there being other numbers obviously cannot have produced them. (Here is the materialistc difficulty. Thales, etc., in Arist. Met. I.)

The series then proceeds from a so-called nothing and yet has not produced itself. The series has been produced. Produced by what? Not by any number of the series, because, as we have already seen, that is impossible. (Not by some numbers of the series, for then it is required to know how the numbers which compose this sum have come to be. And if an attempt be made to answer this by twisting it in any way, the essay fails, for it can either make the sum a number — a case which we have already discussed — or the whole which we shall now consider).

Not by the series as a whole, for, as I have said, nothing can produce itself.

We must now make a distinction between the total and the series in itself (the whole). The total is produced by the units, consequently by units in a definite number. The whole, on the contrary, produces the numbers; it is not produced by them. [...]

The series (whole) is Quantity, Number (in its most abstract meaning).

A total is any number resulting from a sum, for instance, 1302.

A number, a unit is any member of the series.

Some may yet think that a whole can be empirically obtained. They say, for instance, «the numbers 1, 2, 3 plus an infinity of numbers give us the total series, the whole».

We must consider this argument. It contains an old term, that of infinity.

What is this, what does it mean? It means either of 2 things: or the greatest possible number, that which contains all numbers; or that which transcends all number.

lf it mean the first (as materialists indeed understand it) it is identical to the series, it means «the whole». So that to prove the whole by it is to beg the question and most miserably to fail. Cur opium dormiri facit? Quia est in eo vis dormitiva.

Analogy and consequence of this in the materialist argument for the empirical origin for the idea of infinite.