In my last post I gave an argument for (metaphysical) finitism based on the absurdities and logical impossibilities that would result if an actually infinite number of things could exist in reality. I used the Hilbert's Hotel thought experiment. I also pointed out that while there are prohibitions in mathematics on performing operations like subtraction when dealing with actual infinities, those prohibitions would not apply in a real-world scenario. So it would seem that finitism is correct, or at least that it has a great deal of plausibility.
Now I would like to briefly consider some objections to the argument. I know of a number of objections that could be made, but I want to focus on two in particular because they seem to be the most common objections that come up, and other objections often turn out to be variations of these two. Each of the objections we will consider claims that finitism is false because we can point to examples of actual infinities that exist in reality.