How many real numbers exist? New proof moves closer to an answer

Re:How many real numbers exist? New proof moves closer to an... by dwohnitmok on Thursday July 15, 2021 @01:58PM (#27847825)

This is not unsound in the usual sense of "logical soundness" (which applies to logical systems such as first-order logic, rather than specific theories in the system such as ZFC).

This is unsound in that it runs counter to certain philosophical commitments, namely that there should be some tangible, physical realization of all the natural numbers (although if you really go far in that direction you end up with ultrafinitism, which most set theorists would find unpalatable, so the philosophical implications of all this are rather tricky).

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Re:How many real numbers exist? New proof moves closer to an... by ummonk on Saturday July 17, 2021 @02:58PM (#27867949)

As you allude, it's rather ridiculous to make certain philosophical commitments but only apply them to natural numbers. I think ordinary finitism will do fine though, no need to go to ultrafinitism.

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