

Hilbert's Hotel: A Comprehensive Response | (MoR No. 94)
5 snips Sep 28, 2022
Dive into the intriguing world of Hilbert's Hotel and discover why it's time to stop using this paradox. Explore the distinctions between actual and potential infinities and their implications in philosophy and mathematics. The discussion tackles the Kalam cosmological argument, questioning our intuition about infinities. With deeper insights into set theory, the validity of mathematical induction, and the philosophical challenges surrounding infinite causal regressions, this episode offers a thought-provoking critique of familiar notions on infinity.
Chapters
Transcript
Episode notes
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Intro
00:00 • 1min
Exploring the Kalam Cosmological Argument and Hilbert's Hotel
01:29 • 2min
Understanding Sets and Cardinality in Mathematics
03:08 • 3min
Exploring Actual and Potential Infinities
06:26 • 23min
Understanding Set Differences in Infinity
28:56 • 22min
Exploring Actual Infinities and Hilbert's Hotel
51:14 • 30min
Philosophical Insights on Hilbert's Hotel
01:20:51 • 21min
Exploring Actual and Potential Infinities
01:42:02 • 33min
Understanding Mathematical Induction and Infinite Collections
02:15:05 • 5min
The Infinite Future and Divine Knowledge
02:20:01 • 19min
Rethinking Time and Existence
02:38:40 • 23min
Exploring the Possibility of Actual Infinites in Philosophy
03:01:54 • 5min
Exploring Modal Induction and Causal Principles
03:06:56 • 1min
Exploring Infinite Causal Regressions
03:08:26 • 6min