every impulse without resistance and retains the record of no
impression.

Intelligence is accordingly conditioned by a modification of both
structure and consciousness by dint of past events. To be aware that a
second stroke is not itself the first, I must retain something of the
old sensation. The first must reverberate still in my ears when the
second arrives, so that this second, coming into a consciousness still
filled by the first, is a different experience from the first, which
fell into a mind perfectly empty and unprepared. Now the newcomer finds
in the subsisting One a sponsor to christen it by the name of Two. The
first stroke was a simple 1. The second is not simply another 1, a mere
iteration of the first. It is 1^{1}, where the coefficient represents
the reverberating first stroke, still persisting in the mind, and
forming a background and perspective against which the new stroke may be
distinguished. The meaning of "two," then, is "this after that" or "this
again," where we have a simultaneous sense of two things which have been
separately perceived but are identified as similar in their nature.
Repetition must cease to be pure repetition and become cumulative before
it can give rise to the consciousness of repetition.

The first condition of counting, then, is that the sensorium should
retain something of the first impression while it receives the second,
or (to state the corresponding mental fact) that the second sensation
should be felt together with a survival of the first from which it is
distinguished in point of existence and with which it is identified in
point of character.

[Sidenote: No identical agent needed.]