Well, QM didn't exist yet. Instead, you had competing concepts of light as a wave and light as a particle. As a wave, it would seem perfectly reasonable that you could keep dividing and that it was a continuous function. We have the benefit of QM in hindsight.
However, think of it another way ... if the stars had infinite time to pump out these "photon" particles you speak of (harmph! highly dubious), then there ought to be an infinite number of them in any given space, as they have had an infinity of time to reach you.
However, think of it another way ... if the stars had infinite time to pump out these "photon" particles you speak of (harmph! highly dubious), then there ought to be an infinite number of them in any given space, as they have had an infinity of time to reach you.