[FOM] an interesting article

[Kreinovich, Vladik]

Dear Friends, The 1st issue of 2018 The Review of Symbolic Logic has an interesting article titled "Can modalities save naïve set theory"; it is posted, e.g., in http://harveylederman.com/Can%20Modalities%20Save%20Naive%20Set%20Theory.pdf

This article was motivated by a question posted a few years ago by Grigory "Grisha" Mints from Stanford: what is instead of the usual naïve comprehension principle according to which for every property P(x) there exists a set y for which x is in y iff P(x) (and which Russell has shown to be inconsistent), we postulate that for every property P(x) there is a set y for which x is in y iff necessarily P(x).

The conclusion of the article - in a nutshell - is that this idea does not seem to lead to good set theory: no matter what the authors tried, they got either an inconsistent theory or a theory too weak to be useful as foundations of mathematics. However, there are still open problems, so maybe there is hope.
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