I remain unconvinced, given that we continue to explore the meaning and possibility of cardinalities beyond aleph 0. See, e.g., [1], and its implications for CH

I remain unconvinced, given that we continue to explore the meaning and possibility of cardinalities beyond aleph 0. See, e.g., [1], and its implications for CH. It strikes me that since we are still learning about cardinalities above aleph 0, we may have made mistakes at 0 itself and that there may be an “aleph -1”, an infinite cardinality less than aleph 0, which could apply, e.g., to the set of primes. This would require proving that the bijection technique is not properly constructivist. That is considered constructivist has long bothered me, but I lack the detailed background in the field to articulate the objection. [1] https://www.quantamagazine.org/how-many-numbers-exist-infinity-proof-moves-math-closer-to-an-answer-20210715/ https://www.quantamagazine.org/how-many-numbers-exist-infini...