Lesson 2.4 day 2
Carroll puzzle resolved, valid vs. fallacy comparison table, full CYU
Focus: law of syllogism, law of detachment, denying the consequent, disjunctive syllogism — Lewis Carroll — geometry as the law of syllogism applied 465 times
Day 2 is not really designed to teach new material. It is designed to get another day practicing and applying what we have been building in logic. After our first year trying this, it was clear that students needed more time with the named forms of the arguments and fallacies. If it feels a little repetitive that is a feature not a bug.
Open Day 2 by resolving the Carroll puzzle with the whole class. The solution requires two moves: writing the contrapositive of premise (b) to get ‘if it does not waltz, it is not an officer’, then chaining through premises (c), (a), and (b’) via the law of syllogism. Neither tool alone is sufficient. The solution demonstrates a genuine proof move: you do not always have premises in the order you need them. Rewriting to the contrapositive is standard.
Lewis Carroll designed these puzzles in the 1890s specifically to teach symbolic logic. He understood that the content is only memorable when the form is entertaining. The absurdity is a feature: students have to trust the logic because the subject matter offers no help. That experience is exactly what geometric proof will ask of them.
Close Day 2 with the comparison table: valid forms on the left (law of detachment, denying the consequent, law of syllogism, disjunctive syllogism), fallacies on the right (affirming the consequent, denying the antecedent, undistributed middle). One minute on the board, not a re-teaching. State it directly: the valid forms use the conditional or its contrapositive — the two equivalent forms. The fallacies use the converse or the inverse — the two forms that are not equivalent to the original. If you remember that, you do not need to memorize the fallacy names as separate facts. That said, you should learn the names. Being able to communicate precisely is part of being well educated.
Day 2 consolidation: the comparison table, then the full CYU covering all four valid argument forms. Additional Carroll-style puzzles are available in the Teacher Reference Notes for groups that want more practice.