Dennett aims to solve this using heterophenemenology:

https://en.m.wikipedia.org/wiki/Heterophenomenology

In this framework, utterances can be studied without taking their truth value at face value.

Very interesting, I'll have to think a lot about that.

Oh, I'm not saying anything about how humans think, or model the world. FOL is a formal language. It can express the same things that natural language can express and you can do reasoning in it (actually- let's say "inference" because reasoning is a bit of a loaded term), but I make no claim that it's how humans really think.

I mean, I don't believe that is true any more that I believe calculus, or linear algebra are the way we think. Those are just formal systems that we can use to get various results about the world- but is that how we really think inside our heads? I kind of doubt it.

I'm just talking about the expressive power of first-order predicate calculus here, not about whether it's a good model for human intelligence.