My typical interaction with books and articles on model theory: them: 1+3=4 me: yup them: Rubik's cube forms a group me: u-huh them: polynomials form a ring me: yeah yeah them: let's call an entity 𝔚-sammlungswürdigkeit if it's a set equipped with infinite functions and infinite infinitary relations me: ... what kind of letter is that supposed to be now? them: now, since we have a notion of 𝔉-zusammengehörigkeit, we can write down 𝔉 ⊨ ∀x.∃y.∃z.(ζ(y) ∧ ∀w.ϕ(w,z,x)) and call it a "thing". me: .... wait, why did you swap one funky-letter thing with another, and why is this particular construction just a "thing"? them: don't worry, you obtain it by interpreting this STANDARD property of classical first-order logic in an OBVIOUS WAY me: ... them: (continuing for another half an hour) ...and thus, we've concluded that the sentence "YOUR EXISTENCE ON THIS PLANET IS WARRANTED" is unprovable! me (slowly backing towards the door, trying not to make sudden movements): A brilliant lecture, professor! Couldn't agree more with all of the things you've said!