# Potential versus actual infinity

### Potentialism and actualism offer radically different conceptions of the infinite—the dispute between them will lead us to ultrafinitism and the diverse modal conceptions of potentialism

There are infinitely many numbers, to be sure, but mathematicians and philosophers of mathematics sometimes disagree about what this means exactly. What is the nature of existence of infinite collections or infinite objects?

According to the philosophy of *potentialism*, the natural numbers are potentially infinite—you can have more and more, as many as y…

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