The Catholic World, Vol. 20, October 1874‐March 1875Various
Religion
The Catholic World, Vol. 20, October 1874‐March 1875
Various
Catholic Church -- Periodicals
To this we reply that the mathematical expression of the intensity of the
action, in the case of infinitesimal distances, does not become infinite,
except when the action is supposed to last for a finite unit of time. But
the action continued for a finite unit of time is not the _actual_ action
of an element; it is the integral of all the actions exerted in the
infinite series of infinitesimal instants which makes up the finite unit
of time. To judge of the true intensity of the actual exertion, it is
necessary to exclude from the calculation the whole of the past or future
actions, and to take into account the only action which corresponds to the
infinitesimal present. In other terms, the actual action is expressed, not
by an integral, but by a differential. In fact, the elements act when they
are, not when they have been, or when they will be; they act in their
present, not in their future or in their past; and the present, the _now_,
is only an instant, which, though connecting the past with the future, has
in itself neither past nor future, and therefore has a rigorously
infinitesimal duration. It is this instant, and not the finite unit of
time, that measures the actual effort of the elements. Accordingly, the
action as actually proceeding from the elements, when at infinitesimal
distance, is infinitely less than the integral calculated for a finite
unit of time; which shows that the argument proposed has no foundation.
This answer serves also to complete our solution of the preceding
objection. It was there objected that the active power of an element can
be applied to the production of an infinite multitude of _finite_ effects;
to which we answered that a finite power was competent to do this by being
applied simultaneously to an infinite multitude of terms. But now we add
that none of those effects acquire a _finite_ intensity, except by the
continuation of the action during a finite unit of time, and therefore
that the true effect produced in every instant of time is infinitesimal.
Hence the infinite multitude of such effects, as related to the instant of
their actual production, is an infinite multitude of infinitesimals, and
the total effort of a primitive element in every instant of time is
therefore finite, not infinite.
_A sixth objection._—If we admit that a material element has an indefinite
sphere of power, we must also admit that the element has a kind of
immensity. For the active power must evidently be present entitatively in
all the parts of space where it is ready to act. Accordingly, as by the
hypothesis it is ready to act everywhere, its sphere being unlimited, it
must be present everywhere and extend without limit. In other words, the
elementary power would share with God the attribute of immensity—which is
impossible.
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