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Questions tagged [finitism]

Finitism is a position in the philosophy of mathematics that only finite mathematical objects exist.

The following are some sources on finitism.

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How do proponents of finitism respond to the claim that their position is "dubiously coherent"?

Michael Dummett writes (page 349) Since primality is decidable, the statement that any particular natural number is prime must be determinately either true or false, since the decision procedure, if applied to that number, would have a determinate…
Frank Hubeny
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Is infinity an imperfect and unsubstantial epiphenomenon of the finite?

To my mind the concepts of the finite and the infinite are equally mysterious. But recently I was surprised to encounter the view that infinity may be something different from what I have instinctively thought it to be. So in view of Plato's…
exp8j
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Would Frege's version of the empty set contain "parafinitesimal elements," at least from the multiversal standpoint?

Frege's definition of the empty set was not a raw extensional one: he did not simply write the partial string {} and say, "That's it: that's the empty set." His account was more intensional: "There is a set that contains all and only true…
Kristian Berry
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