Here, I answer when infinities are possible, and when they’re impossible.* [ *Based on: “Virtue and Vice Among the Infinite,” pp. 87-104 in Ad Infinitum: New Essays on Epistemological Infinitism, ed. John Turri and Peter Klein (Oxford University Press, 2014). Later elaborated in
My meta-principle on infinity: Talk about infinities is a shorthand way of talking about limits. If your talk about infinity produces a paradox, you are making a mistake in the way you take the limit. This was worked out the late 19th century for Zeno and similar paradoxes, but it is always and everywhere true.
My meta-principle on infinity: Talk about infinities is a shorthand way of talking about limits. If your talk about infinity produces a paradox, you are making a mistake in the way you take the limit. This was worked out the late 19th century for Zeno and similar paradoxes, but it is always and everywhere true.