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

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

Ultrafinitism with a largest number

The theory of finite arithmetic is a form of ultrafinitism asserting that there is a largest natural number. But where should the numbers stop and why…

Dec 19, 2025 • Joel David Hamkins

Ultrafinitism

Ultrafinitism is the philosophical view that only comparatively small or accessible numbers exist.

Dec 12, 2025 • Joel David Hamkins