Welcome to these Lectures on Infinity, my series of lectures exploring all my favorite paradoxes and conundrums, based on my book, The Book of Infinity.
In this instance, we shall consider the classical dispute between two conceptions of infinity—potential infinity versus actual infinity.
A transcript of this lecture is available.
Find the lectures here on Infinitely More in the lectures-on-infinity tag.
The lectures are appearing on YouTube.
The whole lecture course is hosted at Ergo: Lectures on Infinity.
This lecture is based on my essay Potential versus Actual Infinity.
The essay appears in my new book, The Book of Infinity.
I have been trying to self teach myself set theoretic forcing for quite some time, and your potentialist vs actualist view felt very much related. Low and behold, searching your past posts on this substack, you talk about this relationship in your talk "Forcing is simply the iterative conception undertaken within multi-valued logic", and in your paper "The modal logic of forcing"
I am still working through your slides and this paper, whilst simultaneously trying to compare your view of forcing with the more detailed exposition in various other books I have ( Fitting/Smullyan, Kunen, and Jech) so that I can apply this view to specific examples (such as the continuum hypothesis). I think Fitting/Smullyan is closest to your view of forcing, but I still find it lacking in philosophical intuition.
I am wondering if you have ever considered writing a more technical textbook on set theory that incorporates some of this philosophical intuition?
I think several of your intuitions and examples would be extremely helpful in a more technical book for graduate students or undergrads. E.g. in addition to this potentialist view of forcing, I feel as though if I had been initially introduced to set theory with the 'multiverse' view of things I would have been far less confused.
In general, I would also like to thank you for your lectures: as an undergrad in this time of turbulence due to AI, it is a breath of fresh air and is a much needed reminder of the fun and the 'warmth' that still exists in the practice of mathematics.