Granted that the world has no beginning in time; up to every given moment of time, an eternity must have elapsed, and therewith passed away an infinite series of successive conditions or states of things in the world.
There is, consequently, an infinite series of degrees of consciousness down to its entire disappearance.
But this degree of reality can become less and less through an infinite series of smaller degrees.
For that it should all be given is absolutely contradictory of the conception of an infinite series.
But against the real, true argument of the antithesis, that the changes of the world necessarily presuppose an infinite series of changes backwards, absolutely nothing is advanced.
That there must be some such propositions all are agreed, since there can not be an infinite series of proof, a chain suspended from nothing.
Before proceeding to the consideration of the special class of series to be discussed, it is necessary to define with some precision what is to be understood by the representation of an arbitrary function by an infinite series.
The expression, always possible, of integrals in infinite series, may at first be viewed as a happy general means of compensating for the extreme imperfection of the integral calculus.
In like manner there may perhaps be one or more middle terms between A and B, and between B and C; but it is impossible that there can be an infinite series of such intervening middle terms.
So also there may be one or more subjects lower than C, and of which C will be the predicate; but it is impossible that there can be an infinite series of such lower subjects.
Now it is possible that there may be some one or more predicates higher than A, but it is impossible that there can be an infinite series of such higher predicates.
We have here then an infinite series of causative acts--an absurdity of the same kind, with an infinite series of volitions.
Therefore in efficient causes there could be an infinite series, which is disproved (Metaph.
Therefore one man was begotten of another in an infinite series.
Matter, then, may be eternal, and an infinite series of events existing in a state of order is conceivable and possible.
An "infinite series" is therefore a contradiction in adjecto.
Let me not be thought to be an advocate in any sense for the unsupported notion of an infinite series of organic beings.
That the mathematician cannot actually present before us the whole of an infinite series, is indeed most certain; for such, power belongs only to an Infinite Being.
But what analogy suggests, or what law of reason requires, an infinite series of such causes?
Zeno's logical dilemma as to how Achilles could ever catch up with the tortoise provided the tortoise was given a start, however small, may be countered by the ingenuity of the mathematicians' infinite series.
What he maintains is that the description of change in terms of an infinite series of stages leaves out the change altogether.
If Edwards makes mind the efficient cause of volition, what becomes of his famous argument against the self-determining power, by which he reduces it to the absurdity of an infinite series of volitions?
If we rise from this platform, we cannot possibly ascend in any direction, without entering upon an infinite series of causes.
Thus, the two cases are rendered perfectly parallel; and afford the same foundation on which to erect an infinite series of causes.
It is in this assumption, that Edwards lays the foundation of the logic, by which he reduces the self-determining power of the mind to the absurdity of an infinite series of volitions.
The above list will hopefully provide you with a few useful examples demonstrating the appropriate usage of "infinite series" in a variety of sentences. We hope that you will now be able to make sentences using this group of words.
