Final Reflections on Alexander Pruss's Discussion of Finitism

In a recent series of posts, I have been talking about Alexander Pruss's discussion of finitism in his book Infinity, Causation, & Paradox (Oxford: Oxford University Press, 2018). Pruss maintains that it is impossible for an infinite series of causes to precede an event, so he embraces a sort of finitism called causal finitism. Most of his book is aimed at showing how causal finitism is capable of resolving numerous paradoxes related to infinity.

As part of his discussion, Pruss devotes a small section to arguing against a more general finitism, which holds that it is impossible for an actually infinite number of things to exist. He presents six arguments against finitism, which I have discussed in the previous three posts. Perhaps the main failing of Pruss's discussion is that he does not differentiate between mathematical finitism and metaphysical finitism. My preferred position is metaphysical finitism. As for mathematical finitism, I have no position to stake out. In that sense I am agnostic toward it, but I am inclined to be skeptical of it because it seems unnecessarily radical.

Alexander Pruss's Arguments Against Finitism, Part 3

In this series of posts I am looking at a number of arguments against finitism given by Alexander Pruss in his book Infinity, Causation, & Paradox (Oxford: Oxford University Press, 2018). So far I have looked at four arguments (although it's technically five, since one of them involved two different versions). In this post, I will look at the final two.

Alexander Pruss's Arguments Against Finitism, Part 2

I'm continuing my discussion of Alexander Pruss's Infinity, Causation, & Paradox (Oxford: Oxford University Press, 2018). Specifically, I am looking at his arguments against finitism.

Alexander Pruss's Arguments Against Finitism, Part 1

I have been slowly making my way through Alexander Pruss's Infinity, Causation, & Paradox (Oxford: Oxford University Press, 2018). This book is interesting and at times very technical, so it is often difficult for me to understand, but paradoxes related to infinity are one of my favorite topics, so I find myself going back to this book every so often and giving it another try.