Skip to primary content
Skip to secondary content

Joel David Hamkins

mathematics and philosophy of the infinite

Joel David Hamkins

Main menu

  • Home
    • About
    • My Curriculum Vita
    • Contact
    • Comment Board
  • Publications
    • Publication list
    • Recent publications
    • Publications by topic
      • Automorphism towers
      • Infinitary computability
      • Infinitary utilitarianism
      • Large cardinals
    • My Research Collaborators
  • Talks
    • Talks
    • Recent and Upcoming Talks
    • Videos
  • Appointments and Grants
    • About Me
    • My Academic Appointments
    • Grants and Awards
  • Teaching
    • About My Courses
  • Students
    • About My Graduate Students
    • List of My Graduate Students
  • Mathematical Shorts
  • Math for Kids

Tag Archives: Rahul Sam

The Gödel incompleteness phenomenon, interview with Rahul Sam

Posted on January 14, 2024 by Joel David Hamkins
Reply

Please enjoy my conversation with Rahul Sam for his podcast, a sweeping discussion of topics in the philosophy of mathematics—potentialism, pluralism, Gödel incompleteness, philosophy of set theory, large cardinals, and much more.

Share:

  • Click to share on X (Opens in new window) X
  • Click to share on Facebook (Opens in new window) Facebook
  • Click to share on Reddit (Opens in new window) Reddit
  • Click to share on WhatsApp (Opens in new window) WhatsApp
  • Click to email a link to a friend (Opens in new window) Email
  • Click to print (Opens in new window) Print
  • More
  • Click to share on LinkedIn (Opens in new window) LinkedIn
  • Click to share on Tumblr (Opens in new window) Tumblr
  • Click to share on Pocket (Opens in new window) Pocket
  • Click to share on Pinterest (Opens in new window) Pinterest
Posted in Talks, Videos | Tagged large cardinals, multiverse, philosophy of mathematics, pluralism, potentialism, Rahul Sam | Leave a reply

Infinitely More

Proof and the Art of Mathematics, MIT Press, 2020

Buy Me a Coffee

Recent Comments

  • Lecture series on the philosophy of mathematics | Joel David Hamkins on Lectures on the Philosophy of Mathematics
  • How the continuum hypothesis might have been a fundamental axiom, Lanzhou China, July 2025 | Joel David Hamkins on How the continuum hypothesis could have been a fundamental axiom
  • Joel David Hamkins on Lectures on Set Theory, Beijing, June 2025
  • Joel David Hamkins on Lectures on Set Theory, Beijing, June 2025
  • Mohammad Golshani on Lectures on Set Theory, Beijing, June 2025

JDH on Twitter

My Tweets

RSS Mathoverflow activity

  • Comment by Joel David Hamkins on Is this theory of bottomless hierarchy, consistent?
    Ah, sorry, you had the comma before → not after, namely, ∃y∈A:ϕ,→.
  • Comment by Joel David Hamkins on Is this theory of bottomless hierarchy, consistent?
    I confess that I have long been a little confused by your manner of using colons and commas in formal expressions, since it is different from what I am used to in first-order logic or in type theory. For example, how am I to read the meaning of "∃y∈A:ϕ→,"? And how are we […]
  • Comment by Joel David Hamkins on Is every external downshifting elementary embedding j with j(x)=j[x], an automorphism?
    Ah, yes, of course. Thanks!
  • Answer by Joel David Hamkins for About forcing method
    Yes, part of your perspective is correct—we can make sense of forcing over any model of set theory. We can in effect internalize the concepts of forcing and express everything we need inside ZFC rather than in the metatheory. The assertion of "φ is forceable", meaning that it is true in some forcing extension, is […]
  • Comment by Joel David Hamkins on Is it possible to transform a statement of unsolvabilty to an equivalent one by using a bounded universal quantifier
    OK, I have posted the argument I had in mind for the multi-variable case.
  • Answer by Joel David Hamkins for Is it possible to transform a statement of unsolvabilty to an equivalent one by using a bounded universal quantifier
    Let me answer negatively for the case where the polynomial p is a polynomial in several variables p(x1,…,xn) over the integers. To begin, for any given program q, consider the c.e. set Eq that undertakes the algorithm of checking whether q(0) halts, then whether q(1) halts, then whether q(2) halts, and so forth, and each […]
  • Comment by Joel David Hamkins on How might mathematics have been different?
    Thanks for mentioning my CH thought experiment, Mike. The published version is open access online at doi.org/10.36253/jpm-2936.
  • Comment by Joel David Hamkins on Is it possible to transform a statement of unsolvabilty to an equivalent one by using a bounded universal quantifier
    I can post a (negative) answer for the multi-variable case, if that's what you mean. Unfortunately, it doesn't seem to settle the single-variable case.

Meta

  • Log in
  • Entries feed
  • Comments feed
  • WordPress.org

Subscribe to receive update notifications by email.

Tags

  • absoluteness
  • buttons+switches
  • CH
  • chess
  • computability
  • continuum hypothesis
  • countable models
  • definability
  • determinacy
  • elementary embeddings
  • forcing
  • forcing axioms
  • games
  • GBC
  • generic multiverse
  • geology
  • ground axiom
  • HOD
  • hypnagogic digraph
  • indestructibility
  • infinitary computability
  • infinite chess
  • infinite games
  • ITTMs
  • kids
  • KM
  • large cardinals
  • Leibnizian models
  • maximality principle
  • modal logic
  • models of PA
  • multiverse
  • open games
  • Oxford
  • philosophy of mathematics
  • pluralism
  • pointwise definable
  • potentialism
  • PSC-CUNY
  • supercompact
  • truth
  • universal algorithm
  • universal definition
  • universal program
  • Victoria Gitman
Proudly powered by WordPress
Buy Me A Coffee