Here’s one way that this could be transformed into an exercise: Have the instructor read a proof (or a fake proof) from, say, formal logic or set theory, and ask the students to follow along step-by-step using a simple example (a la Richard Feynman). Then, at the end of the proof, the students have to explain whether the proof is or is not valid using their example. E.g.:
Instructor: forall x. p(x)
“Ok, let’s see, ‘all ice cream cones are delicious’.”
Instructor: not (not (forall x. p(x)))
“It’s not true that ‘not all ice cream cones are delicious’.”
Instructor: not (exists x. (not p(x)))
“Therefore, ‘there is never going to be an ice cream cone that is not delicious’. Valid!”
Here’s one way that this could be transformed into an exercise: Have the instructor read a proof (or a fake proof) from, say, formal logic or set theory, and ask the students to follow along step-by-step using a simple example (a la Richard Feynman). Then, at the end of the proof, the students have to explain whether the proof is or is not valid using their example. E.g.:
Instructor: forall x. p(x)
“Ok, let’s see, ‘all ice cream cones are delicious’.”
Instructor: not (not (forall x. p(x)))
“It’s not true that ‘not all ice cream cones are delicious’.”
Instructor: not (exists x. (not p(x)))
“Therefore, ‘there is never going to be an ice cream cone that is not delicious’. Valid!”