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.


Avsnitt(420)

324 | Elizabeth Mynatt on Universities and the Importance of Basic Research

324 | Elizabeth Mynatt on Universities and the Importance of Basic Research

It is not manifestly obvious that universities should be where most scholarly research is performed. One could imagine systems that separated out the tasks of "teaching students" and "generating new k...

11 Aug 20251h 13min

AMA | August 2025

AMA | August 2025

Welcome to the August 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 Patr...

4 Aug 20253h 39min

323 | Jacob Barandes on Indivisible Stochastic Quantum Mechanics

323 | Jacob Barandes on Indivisible Stochastic Quantum Mechanics

The search for a foundational theory of quantum mechanics that all physicists can agree on remains active. Over the last century a number of contenders have emerged, including Many-Worlds, pilot-wave ...

28 Juli 20252h 58min

322 | Philip Pettit on Language, Agency, Politics, and Freedom

322 | Philip Pettit on Language, Agency, Politics, and Freedom

When we think of the capacities that distinguish humans from other species, we generally turn to intelligence and its byproducts, including our technological prowess. But our intelligence is highly co...

21 Juli 20251h 20min

321 | David Tong on Open Questions in Quantum Field Theory

321 | David Tong on Open Questions in Quantum Field Theory

Quantum field theory is the basis for our most successful theories of fundamental physics. And yet, there are things we don't understand about it. Some of these puzzles are relatively well-known, whil...

14 Juli 20251h 19min

AMA | July 2025

AMA | July 2025

Welcome to the July 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 Patreo...

7 Juli 20254h 3min

320 | Solo: Complexity and the Universe

320 | Solo: Complexity and the Universe

Our universe started out looking very simple: hot, dense, smooth, rapidly expanding. According to our best current model, it will end up looking simple once again: cold, dark, empty. It's in between -...

30 Juni 20252h 14min

319 | Bryan Van Norden on Philosophy From the Rest of the World

319 | Bryan Van Norden on Philosophy From the Rest of the World

It is common to refer to philosophy as "a series of footnotes to Plato." But in the original quote, Alfred North Whitehead was more careful: he limited his characterization to "the European philosophi...

23 Juni 20251h 12min

Populärt inom Vetenskap

p3-dystopia
dumma-manniskor
svd-nyhetsartiklar
doden-hjarnan-kemisten
allt-du-velat-veta
rss-ufo-bortom-rimligt-tvivel-2
bildningspodden
det-morka-psyket
rss-vetenskapsradion
kapitalet-en-podd-om-ekonomi
rss-vetenskapsradion-2
sexet
rss-experimentet
medicinvetarna
paranormalt-med-caroline-giertz
har-vi-akt-till-mars-an
dumforklarat
hacka-livet
naturmorgon
halsorevolutionen