282 | Joel David Hamkins on Puzzles of Reality and Infinity

282 | Joel David Hamkins on Puzzles of Reality and Infinity

The philosophy of mathematics would be so much easier if it weren't for infinity. The concept seems natural, but taking it seriously opens the door to counterintuitive results. As mathematician and philosopher Joel David Hamkins says in this conversation, when we say that the natural numbers are "0, 1, 2, 3, and so on," that "and so on" is hopelessly vague. We talk about different ways to think about the puzzles of infinity, how they might be resolved, and implications for mathematical realism.

Blog post with transcript: https://www.preposterousuniverse.com/podcast/2024/07/15/282-joel-david-hamkins-on-puzzles-of-reality-and-infinity/

Support Mindscape on Patreon.

Joel David Hamkins received his Ph.D. in mathematics from the University of California, Berkeley. He is currently the John Cardinal O'Hara Professor of Logic at the University of Notre Dame. He is a pioneer of the idea of the set theory multiverse. He is the top-rated user by reputation score on MathOverflow. He is currently working on The Book of Infinity, to be published by MIT Press.


Episoder(415)

333 | Gordon Pennycook on Unthinkingness, Conspiracies, and What to Do About Them

333 | Gordon Pennycook on Unthinkingness, Conspiracies, and What to Do About Them

Why are people wrong all the time, anyway? Is it because we human beings are too good at being irrational, using our biases and motivated reasoning to convince ourselves of something that isn't quite ...

27 Okt 20251h 10min

332 | Dmitri Tymoczko on the Mathematics Behind Music

332 | Dmitri Tymoczko on the Mathematics Behind Music

Music is math that you can dance to. The fact that certain notes sound good when played together, or in succession, is related to the mathematical properties of the frequencies to which they correspon...

20 Okt 20251h 21min

AMA | October 2025

AMA | October 2025

Welcome to the October 2025 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Pat...

13 Okt 20253h 37min

331 | Solo: Fine-Tuning, God, and the Multiverse

331 | Solo: Fine-Tuning, God, and the Multiverse

Certain features of our universe seem unnatural to us. These include "constants of nature" such as the cosmological constant and the mass of the Higgs boson, as well as features of the initial conditi...

6 Okt 20251h 54min

330 | Petter Törnberg on the Dynamics of (Mis)Information

330 | Petter Törnberg on the Dynamics of (Mis)Information

A characteristic of complex systems is that individual components combine to exhibit large-scale emergent behavior even when the components were not specifically designed for any particular purpose wi...

29 Sep 20251h 12min

329 | Steven Pinker on Rationality and Common Knowledge

329 | Steven Pinker on Rationality and Common Knowledge

Getting along in society requires that we mostly adhere to certainly shared norms and customs. Often it's not enough that we all know what the rules are, but also that everyone else knows the rules, a...

22 Sep 20251h 16min

328 | Mary Roach on Replacing Parts of Our Bodies

328 | Mary Roach on Replacing Parts of Our Bodies

Like any machine, bodies occasionally break down, and it's natural to go in search of a replacement part. Ancient societies featured simple prosthetics for teeth, noses, and limbs, while modern medici...

15 Sep 20251h 7min

AMA | September 2025

AMA | September 2025

Welcome to the September 2025 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by P...

8 Sep 20253h 30min

Populært innen Vitenskap

fastlegen
rekommandert
jss
tingenes-tilstand
rss-rekommandert
villmarksliv
liberal-halvtime
sinnsyn
forskningno
rss-paradigmepodden
fjellsportpodden
nevropodden
rss-nysgjerrige-norge
diagnose
vett-og-vitenskap-med-gaute-einevoll
abid-nadia-skyld-og-skam
tidlose-historier
dekodet-2
smart-forklart
hva-er-greia-med