If this sentence is true, then Santa Claus exists as a nazi.

Yes, it is the season. "So if this sentence is true, then Santa Claus both exists and is a nazi." And if the sentence above were true, then Santa Claus would exist and be a nazi. *But it doesn't say "It is false* that if this sentence is true, then Santa Claus both exists and is a nazi." Thus,

Physics with intuitionistic vs. classical mathematics:

"Nicolas Gisin [has] argued that we should be formulating physics without using infinities or infinitely precise numbers." in http://backreaction.blogspot.com/2020/12/is-infinity-real_5.html Nicolas Gisin on physics with intuitionistic vs. classical mathematics: https://arxiv.org/abs/2011.02348