I should mention that I’m also an infinite set atheist.
You’ve mentioned this before, and I have always wondered: what does this mean? Does it mean that you don’t believe there are any infinite sets? If so, then you have to believe that a mathematician who claims the contrary (and gives the standard proof) is making a mistake somewhere. What is it?
Frankly, even if you actually are a finitist (which I find hard to imagine), it doesn’t seem relevant to this disucssion: every argument you have presented could equally well have been given by someone who accepts standard mathematics, including the existence of infinite sets.
Eliezer:
I should mention that I’m also an infinite set atheist.
You’ve mentioned this before, and I have always wondered: what does this mean? Does it mean that you don’t believe there are any infinite sets? If so, then you have to believe that a mathematician who claims the contrary (and gives the standard proof) is making a mistake somewhere. What is it?
Frankly, even if you actually are a finitist (which I find hard to imagine), it doesn’t seem relevant to this disucssion: every argument you have presented could equally well have been given by someone who accepts standard mathematics, including the existence of infinite sets.