In the year 1920 there was a famous debate between astronomers Harlow Shapley and Heber Curtis on the interpretation of spiral nebulae that could be seen in the sky with the aid of telescopes. The question was whether these extended, non-stellar objects were part of the Milky Way galaxy, or whether they were in fact other galaxies separate from the Milky Way.
In the year 2015 we define a galaxy to be an object with typically 10-100 billion stars moving in directions and at speeds that are not well understood. The reason the stellar motions are not so well known has to do with the gravitational influence of what we call dark matter. At the time of the debate 95 years ago, there was no notion of dark matter. In fact it was not even known whether the entire universe was larger than the Milky Way galaxy.
Shapley argued that the spiral nebulae were rather close to us on the grounds that some were found to be rotating like pinwheels. If the nebulae were far away, he maintained, then we would not be able to see this rotation (note this result was later retracted through no fault of Shapley).
On the other side of the debate, Curtis forwarded the idea first brought up by philosopher Immanuel Kant in the 18th century that the spiral nebulae were ‘island universes,’ and that there were many other galaxies apart from just the Milky Way. Each astronomer presented his well-researched take on the problem in the Smithsonian Museum in Washington D. C.
Importantly, the answer to this question can be quantified. What we need to do is to find out the distance to one of the spiral nebulae. Astronomer Edwin Hubble measured the distance to a spiral nebulae we now call the Andromeda galaxy. He measured Andromeda to be 2.2 million light years away, or twenty times more distant than the Milky Way.
Curtis won, and Kant before him. Today we know there to be about 100 billion galaxies in the universe, each with 10-100 billion stars.