If they're all inconsistent then the real world is inconsistent and therefore the real world doesn't exist since inconsistent systems don't have models. But all the women who think that the damsel in distress trope is harmless fun/perpetuates sexist stereotypes do exist, and they are models so I don't think the theory is inconsistent.

Yes, you're right (except it's not a joke). Not sure why the other person seems to be dismissive about model theory, reducing an entire field of mathematics to "people are different and think different things".

But I still wonder : Are there any axioms that can decide the statement about damsels in distress, just like how axioms can be added to ZFC that decide CH, like V=L and proper forcing axioms as I pointed out?

Yes but I still think it goes deeper than that. Are there any axioms that can decide the statement about damsels in distress, just like how axioms can be added to ZFC that decide CH, like V=L and proper forcing axioms as I pointed out?

I want to understand why some women seem to enjoy movies and video games that use the damsel in distress trope, despite knowing that in feminist theory it's often considered harmful. I realized that Godel and Cohen proved a very similar result and wonder if their techniques can be applied here as well

Actually, now that I think of it, we can add axioms to ZFC that decide CH. For example, V=L implies it's true, and proper forcing axioms imply that it's false. Can we also add additional axioms to decide whether or not the damsel in distress trope is harmless fun, or sexist against women?

I think it goes deeper than that. There are people who disagree with the axiom of choice, finitists who disagree with the axiom of infinity, etc. But it's a proven theorem (not independent) that ZFC proves the existence of uncountably infinite sets, non-measurable sets, etc. On the other hand, ZFC doesn't prove nor disprove CH.

So it's much deeper than merely "people are different and think different things".

I mean in the same way that the continuum hypothesis is independent of ZFC. Godel constructed a model of ZFC where it's true, and Cohen constructed a model where it's false. We now have two models, both equally valid and satisfying all the axioms of ZFC, but in one, CH is true and in the other, CH is false, proving that CH is independent of ZFC.

Likewise, we can find one woman who enjoys the damsel in distress trope and think it’s harmless fun, and we can find another women who thinks it perpetuates sexist stereotypes against women. Just like in the case above, we have two women, whose views are equally valid, but coming to opposite conclusions. Therefore, we can conclude, just like Godel and Cohen did, that the statement about damsels in distress is independent of the axioms.