> Now, you might mean that most mathematicians suspect that adding CH to ZFC is more intuitive/natural/useful than adding !CH to ZFC, but that's a quite differe

> Now, you might mean that most mathematicians suspect that adding CH to ZFC is more intuitive/natural/useful than adding !CH to ZFC, but that's a quite different statement. I guess I'm a constructivist about this. You can't just wave your hands and take !CH as an axiom. Remember what that means: you reject that there is no set with cardinality between the integers and the reals, so you're implying there is such a set. I realize not all mathematicians share this point of view, but if you can't somehow construct the intermediate set you're claiming exists, or show that it can be constructed, then you don't really have any grounds for taking !CH to be true. Without a positive reason for believing such a set exists, I have a hard time pretending that !CH could possibly be a "useful" (your word) axiom to add to ZFC. By contrast, imagining that CH might be true is easy. You don't have to construct any never-before-seen mathematical objects to make your point. You just presume, without fear of being contradicted by ZFC, that the integers are countably infinite, and the reals are uncountably infinite but only sort of "minimally" so (there are higher orders of uncountable infinity, but none lower). You may never be able to prove CH (certainly not with ZFC, and almost certainly not with any other logical system), but at least the model makes sense: there's no cardinality in between that of the integers and the reals. Which is not to say that CH is particularly useful! In fact, maybe the most interesting thing about the paper is the idea that the CH could be meaningfully connected to anything in an applied form of math like machine learning. Does that weird connection between CH and ML have any practical consequences for ML in general, or the EMX learning algorithm in particular? Probably not, especially since assuming CH is true just implies EMX should work, so it's fine to keep using it to solve learning problems. In other words, if you wanted to convince an ML practitioner that their learning algorithms might be unreliable because the Continuum Hypothesis might be false, I think they would be within their rights to request you show them an actual set with cardinality between the integers and the reals. When you couldn't, they would then be within their rights to ignore your objection.