Infinitely More
Subscribe
Sign in
Home
The Book of Infinity
A Panorama of Logic
Infinite Games
Proof and the Art
Philosophy of Mathematics
My books
Music videos
Archive
Leaderboard
About
Ultrafinitism as arithmetic potentialism
We may fruitfully view the philosophy of ultrafinitism in a potentialist light, helping to illuminate its philosophical commitments.
Jan 12
•
Joel David Hamkins
8
1
Anthropomorphizing the Russell paradox
Anthropormorphization in mathematics—an excerpt from my podcast with Lex Fridman, a sweeping conversation on infinity, philosophy, and mathematics.
Jan 5
•
Joel David Hamkins
15
6
Two visions of ultrafinitism intricately intertwined
These two concepts of ultrafinitism—one positing a largest number, another asserting totality for addition and multiplication but not exponentiation—are…
Dec 29, 2025
•
Joel David Hamkins
10
3
Ultrafinitism with a largest number
According to the theory of finite arithmetic (FA), there is a largest natural number, and consequently addition and multiplication are only partially…
Dec 19, 2025
•
Joel David Hamkins
10
6
Ultrafinitism
Ultrafinitism is the philosophical view that only comparatively small or accessible numbers exist.
Dec 12, 2025
•
Joel David Hamkins
20
7
9
Most Popular
View all
Zeno's paradox
Jan 7, 2023
•
Joel David Hamkins
30
14
5
The surreal numbers
Jan 6, 2024
•
Joel David Hamkins
35
6
5
The Book of Numbers
Jan 2, 2023
•
Joel David Hamkins
43
12
4
Potential versus actual infinity
Apr 14, 2023
•
Joel David Hamkins
25
20
5
The Book of Infinity
See all
Take my Infinity final exam!
How well can you answer the questions on the final exam for my Infinity course?
Dec 21, 2024
•
Joel David Hamkins
17
15
2
Throwing Darts at the Real Line
Mathematical philosophers have proposed various thought experiments suggesting different resolutions of the continuum hypothesis. Can we hope…
Sep 25, 2024
•
Joel David Hamkins
8
10
3
What is the infinite?
What does it mean, exactly, to say that a set is infinite? Can we provide precise mathematical definitions of the finite and the infinite?
Sep 11, 2024
•
Joel David Hamkins
14
6
5
Infinite Games
See all
Tactics versus strategies—the case of chess
Does chess admit of winning or drawing tactics? Which information exactly do we need to include as part of the board position?
Aug 17, 2025
•
Joel David Hamkins
10
6
2
The tactical variation of the fundamental theorem
We prove the tactical variation of the fundamental theorem of finite games—for finite games with sufficiently rich board positions, one of the players…
Aug 10, 2025
•
Joel David Hamkins
7
2
2
Tactics versus strategies in the theory of games
How do tactics differ from strategies? Does the fundamental theorem of finite games hold for tactics? Must every finite game have a winning tactic for…
Aug 3, 2025
•
Joel David Hamkins
20
6
4
A Panorama of Logic
See all
Proof and the Art
See all
Philosophy of Mathematics
See all
Infinitely More
The mathematics and philosophy of the infinite
Subscribe
Recommendations
View all 13
Science without the gobbledygook
Sabine
Scientific Discovery
Saloni Dattani
The Nature-Nurture-Nietzsche Newsletter
Steve Stewart-Williams
TrueSciPhi.AI
Kelly Truelove
The Curious Mind
Álvaro Muñiz Brea
JDH Links
JDH web page
JDH on Twitter
JDH on Notes
JDH on MathOverflow
JDH on YouTube
JDH on Google Scholar
JDH at MIT Press
My Books
Lectures on the Philosophy of Mathematics, MIT Press 2021
Proof and the Art of Mathematics, MIT Press 2020
Proof and the Art of Mathematics: Examples and Extensions, MIT Press, 2021
A Mathematician's Year in Japan, Kindle KDP, 2015
Infinitely More
Subscribe
About
Archive
Recommendations
Sitemap
This site requires JavaScript to run correctly. Please
turn on JavaScript
or unblock scripts
