Some thoughts from Gardner Campbell on Ivan Illich's concept of 'learning webs' supplemented with an interesting example of an exercise with a subversive outcome: "a game called Wff 'n Proof... 'In fact, for some children such games are a special form of liberating education, since they heighten their awareness of the fact that formal systems are based on changeable axioms and that conceptual operations have a gamelike nature." In my own education I got the same effect studying different interpretations of modal logic (K, S4, S5, B) - but this is better, because the students don't have to go to graduate school to get it. (I think my categorical converter is another example that shows how arbitrary axioms can change, and I have in my own notes (somewhere) a 'falsity-preserving' system of logic, just for fun).
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