Lesson 2.4 day 1
The Named Argument Forms
Focus: law of syllogism, law of detachment, denying the consequent, disjunctive syllogism — Lewis Carroll — geometry as the law of syllogism applied 465 times
The named argument forms failed in Year 1 not because they are difficult but because they arrived on top of students who were already carrying conditionals, biconditionals, and the valid/sound distinction. This lesson gives them their own space — one thinking task, one gallery walk, one set of guided notes and CYU to begin in class. The task leads students to discover the law of syllogism before it is named.
The chain task is structured deliberately. Part 1 gives a three-step chain where each conclusion feeds directly into the next hypothesis. Groups who write this out and then collapse it to a single step are discovering the law of syllogism from the structure of the problem. Part 2 breaks the chain: the two given premises do not connect. Groups who get stuck in Part 2 feel exactly why the middle term matters — the consequent of the first premise must match the hypothesis of the second. That frustration is the intuitive understanding of the law before it is named.
Day 1 consolidation: gallery walk, then guided notes naming all four valid argument forms. Students begin the Day 1 CYU in the remaining time. The Day 1 CYU covers the law of detachment and law of syllogism. The Lewis Carroll puzzle is the extension for groups that finish early — it is resolved at the start of Day 2.