Week 4 Argument Workshop: Testing a Letter About Drip Lines in a Community Garden

Part 1 — The Big Picture

Rules and proposals are full of "if" sentences, and a handful of patterns built on them do most of the work. This week you learned four forms that never lead from true premises to a false conclusion, and two look-alikes that can. In this workshop you lay out a short letter about drip lines in a community garden, find the four inferences inside it, name each one's form, test each with the counterexample method, build a short argument of your own with its strongest objection and a reply, and then catch a chatbot making the slips this week warns about.

Time budget: Plan for about 90 minutes.

Part 2 — The Task

Guiding question: In an illustrative letter asking a community garden to switch to drip lines, which of the four inferences follow a valid form and which only look like they do, and what case shows the difference?

Workshop data: Ten sentences from an illustrative letter about drip lines in a community garden

Source: An illustrative letter to a community garden's newsletter, written for this workshop and printed in full in Part 4; it comes from no real person, garden, group, or newsletter.

• Rows: 10 sentences, one row each in the sorting table
• Columns: sentence, role in the argument, and the inference it belongs to
• Source text: the full letter: The community garden should switch its vegetable beds to drip lines this summer. If the beds use drip lines, the garden will use less water. If the garden uses less water, its monthly water bill will drop. So if the beds use drip lines, the monthly water bill will drop. Either the garden lowers its water bill or the board raises member dues. The board has voted not to raise member dues. So the garden must lower its water bill. A nearby community garden's water bill dropped last summer, so that garden must have switched to drip lines. One member objects: if we keep hand watering, the beds stay healthy, and we are not keeping hand watering, so the beds will not stay healthy. A drip kit costs 15 dollars a bed, and the garden has 12 beds.

Part 3 — Materials & Procedure

Tools and materials

• Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them

Ways of working

• map-the-argument
• test-the-reasoning
• build-and-defend

Procedure

1. Read the whole letter in the first table of Part 4 twice: once for what it wants, and once sentence by sentence. Tool: Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them. Check: You can say in one sentence what the letter asks the garden to do.
2. In the Role column of the sorting table, label each sentence as the main conclusion, a premise, the conclusion of a smaller inference, the objection, or a cost detail, and in the last column name the inference it belongs to, if any. Tool: Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them. Check: Exactly one row is labelled the main conclusion, and every row has a role.
3. Fill in the forms table: for each of the four inferences, write its pattern in words with sentence letters, such as "if P, then Q; Q; so P", name the form, and mark it valid or invalid. Tool: Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them. Check: Every inference has a pattern, a form name, and a verdict that matches the form.
4. Type each inference's verdict into a free spreadsheet, one row per inference, and count the verdicts with formulas such as =COUNTIF(B2:B5,"valid") and =COUNTIF(B2:B5,"invalid"); record the counts. In another cell, type a formula that multiplies the 12 beds by the 15 dollars a bed to find the cost of a drip kit for every bed. Tool: Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them. Check: Your counts match the rows you labelled by hand, and the kit cost appears in its own cell.
5. Fill in the testing table: for each invalid inference, describe a case with every premise true and the conclusion false; for each valid inference, try to describe one and say why you cannot. Tool: Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them. Check: Each invalid inference has a counterexample checked line by line, and each valid inference has a reason no counterexample exists.
6. Write your own short argument on the same question in the build table: a conclusion, two premises that make a valid form, the form's name, the strongest objection someone could raise, and your reply. You may argue for either answer. Tool: Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them. Check: Your argument follows a valid form, and the objection is stated as fairly as its best defender would state it.
7. Open one approved chatbot, paste the Part 6 prompt below your completed tables, and check its answer against your own work and the checks in Part 6. Tool: Pen and paper or any free diagramming tool for argument maps and Venn diagrams; a free spreadsheet (Google Sheets, or any free spreadsheet) for the frequency, risk, and two-way tables; the Stanford Encyclopedia of Philosophy and the Internet Encyclopedia of Philosophy for named concepts; and one approved chatbot used as a sparring partner whose arguments the student maps and tests before trusting them. Check: You have at least two chatbot statements to quote and correct.

Fallback route

When to use it: Use this route if no spreadsheet is available.

Count the valid and invalid inferences in your forms table by hand, write the counts in the tally table, and multiply the 12 beds by the 15 dollars a bed with the steps shown. Then complete every other table, analysis question, and the critique step, and submit the same items for equal credit.

This route earns the same credit as the primary route.

Part 4 — The Scaffold

The letter comes first: give each of its ten sentences a role before you test anything.

Student scaffold table 1

Sentence	Role in the argument	Inference it belongs to, if any
S1. The community garden should switch its vegetable beds to drip lines this summer.
S2. If the beds use drip lines, the garden will use less water.
S3. If the garden uses less water, its monthly water bill will drop.
S4. So if the beds use drip lines, the monthly water bill will drop.
S5. Either the garden lowers its water bill or the board raises member dues.
S6. The board has voted not to raise member dues.
S7. So the garden must lower its water bill.
S8. A nearby community garden's water bill dropped last summer, so that garden must have switched to drip lines.
S9. One member objects: if we keep hand watering, the beds stay healthy, and we are not keeping hand watering, so the beds will not stay healthy.
S10. A drip kit costs 15 dollars a bed, and the garden has 12 beds.

Write each inference's pattern in words, then name its form and give its verdict.

Student scaffold table 2

Inference	Sentences	Pattern in words	Form name	Valid or invalid
Inference A	S2 to S4
Inference B	S5 to S7
Inference C	S8
Inference D	S9

Test each inference with the counterexample method.

Student scaffold table 3

Inference	Case with every premise true and the conclusion false, if one exists	Verdict in words
Inference A
Inference B
Inference C
Inference D

Tally what you found so you can check your tables.

Student scaffold table 4

Count	Your number
Sentences in the letter
Inferences tested
Valid inferences
Invalid inferences
Sentences outside the four inferences
Cost of a drip kit for every bed, in dollars

Build your own short argument on the same question and defend it.

Student scaffold table 5

Part	Your words
Your conclusion
Your first premise
Your second premise
The valid form your argument follows
The strongest objection
Your reply

Part 5 — Analysis Questions

1. Using your tally table, how many inferences did you test, how many are valid and how many invalid, and how many sentences sit outside the four inferences? Show the arithmetic, including the cost of a drip kit for every bed.
2. Inferences C and D both lean on an "if" sentence. For each one, which part of the conditional does its other premise affirm or deny, and how does that tell you its form?
3. Explain why you found no case with every premise of Inference A true and its conclusion false, and say whether Inference A would still be sound if sentence 2 turned out to be false.
4. Describe the counterexample you used for Inference C and the one you used for Inference D, and explain why Inference D is not modus tollens even though it contains a "not".
5. Choose one and answer it in 3–4 sentences. (a) Name two things that naming the forms in this letter cannot tell you about whether the garden should switch to drip lines, and say what you would need to check for each. (b) Describe an "if" rule from your own life that someone read backward, and say what case would have shown the backward reading was wrong.

Part 6 — AI-Critique Moment

Choose one equal-credit critique route. Route A: ask an approved AI tool to critique your completed work, then check its response against your own evidence. Route B is the no-AI equivalent printed below.

Approved tools: Claude, Gemini, ChatGPT, Grok, Microsoft Copilot.

Prompt to paste:

I've pasted my completed Week 4 Argument Workshop tables above. They test an illustrative letter to a community garden's newsletter that asks the garden to switch its vegetable beds to drip lines. Please do six things. First, name the form of each of the four inferences in the letter (sentences 2 to 4, sentences 5 to 7, sentence 8, and sentence 9) and say whether each one is valid. Second, tell me whether sentence 8 is valid because its conclusion is probably true, and whether sentence 9 is modus tollens. Third, tell me whether the letter commits any fallacy, and whether the member's objection in sentence 9 is an attack on the letter writer. Fourth, write a neutral one-paragraph summary of the letter and of the member's objection. Fifth, tell me what percentage of water gardens save with drip lines and what experts or studies say about drip watering. Sixth, tell me whether the drop in the nearby garden's bill proves that drip lines cause lower water bills.

Test the response for these likely failures:

• Chatbots often call sentence 8 valid because its conclusion sounds likely, and they often call sentence 9 modus tollens because it contains a "not".
• Chatbots often stick an informal fallacy label on the either-or step in sentences 5 to 7, or call the member's objection a personal attack on the letter writer.
• Chatbots often sum up the member as someone who "doesn't care about saving water".
• Chatbots often say the nearby garden's lower bill proves that drip lines cause lower water bills.
• Chatbots often announce that drip lines "cut water use by half" or "save 30 percent" with no starting amount.
• Chatbots often cite "a study" on drip watering or quote a gardener who never appears in the letter.
• Chatbots often add that "gardening experts agree drip lines are best" to strengthen the letter.
• Chatbots often declare that the garden "definitely should" switch because two inferences are valid, or that the writer and the member are "equally right".
• Chatbots often turn the one nearby garden in sentence 8 into a claim that every garden's bill drops after a switch.
• Chatbots often write a "neutral" summary that calls drip lines "the smart choice" or calls the member "resistant to change".

Write 3–5 sentences that quote at least two statements from the chatbot you used, say what is wrong with each and correct it with evidence from the letter, your tables, or this week's chapter, and name one thing the chatbot got right.

Equivalent route (no AI required)

No AI account is required for this workshop. Instead of the chatbot, critique this flawed analysis of the letter, printed here in full: "The letter's main conclusion is sentence 7, that the garden must lower its water bill. All four inferences are valid. Sentence 8 is valid because the nearby garden's bill really did drop, so it must have switched, and sentence 9 is modus tollens because it has a not in it. Since the premises sound true, every step is sound and the garden will certainly save money. The member in sentence 9 is attacking the letter writer, and that member doesn't care about saving water. Because the nearby garden's bill dropped, drip lines cause lower bills, and one garden proves that every garden saves. Gardening experts agree drip lines are best, a study found they cut water use by half, and gardens save 30 percent on average. A neutral summary: this is a smart plan that resistant members keep blocking, so the garden should definitely switch." Mark it up: quote each flawed sentence, name what is wrong (the wrong main conclusion, an invalid form called valid, denying the antecedent called modus tollens, a sound verdict built on unchecked premises, any criticism called an attack on the person, a straw version of the other side, a cause read into one lower bill, a sweeping claim from one garden, an unnamed expert, an invented study or statistic, a percentage with no base, false certainty, or a summary that takes a side), cite the evidence from the letter, your tables, or this week's chapter, and write a corrected sentence beneath it. This route assesses the same objectives (Objective 1 and Objective 3) as the chatbot critique, takes comparable effort (about 30 minutes and 200–300 words), is scored by the same scoring criteria for the same credit, and its own submission artifact is the marked-up flawed analysis, posted in place of the chatbot share link and report.

Part 7 — What to Submit

• All five completed tables
• Written answers to all five analysis questions
• The chatbot critique report with its share link, or the equivalent route's marked-up flawed analysis

Deliverable:

A short Argument Workshop report on the drip-line letter: five completed tables (the sentence sort, the forms, the tests, the tally, and your own argument), written answers to five analysis questions, and a critique of a chatbot's evaluation of the same letter, or, on the equivalent route, a marked-up correction of the printed flawed analysis. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text. Choose a written, recorded, or visual form for your answers; every form is graded by the same scoring criteria.

Rubric

The rubric below shows how each submitted part is evaluated; bands are full, partial, or none.

Workshop evaluation criteria

Criterion	Full	Partial	None
Laying the letter out and finding its inferences	Every sentence has a fitting role, the four inferences are named with their sentences, the main conclusion, the objection, and the cost detail are placed correctly, and each pattern is written in words with sentence letters.	The inferences are found, but a role is misplaced, a pattern is written with the parts swapped, or the objection is treated as support.	No sorting or forms table is recorded, or it is copied from a chatbot without any checking.
Naming and confirming the valid forms	The hypothetical syllogism and the disjunctive syllogism are named correctly, each is called valid with the reason no counterexample exists, and validity is kept separate from whether the premises are true.	The valid forms are called valid, but a name is wrong, no reason is given, or valid is confused with true.	No test of the valid inferences is submitted.
Refuting the formal fallacies with counterexamples	Affirming the consequent and denying the antecedent are named correctly, each is refuted with a counterexample checked line by line, and denying the antecedent is kept apart from modus tollens.	The invalid inferences are called invalid, but a name is wrong, a counterexample has a false premise or a true conclusion, or denying the antecedent is called modus tollens.	No test of the invalid inferences is submitted.
Building and defending your own argument	Your conclusion and two premises are claims that fit a named valid form, the strongest objection is stated as fairly as its best defender would state it, and the reply engages it; either side earns this band.	The argument is present, but its form is invalid or misnamed, the objection is weakened into a straw version, or the reply ignores it.	No argument of your own is submitted.
Critique of the chatbot or of the printed flawed analysis	On either route, at least two statements are quoted and corrected with evidence from the letter, the tables, or the chapter, and one correct statement is acknowledged; both routes earn this band equally.	On either route, errors are named but corrected without evidence, or only one error is caught.	No critique appears, or pasted output is submitted without any checking.
Reflection on what naming forms can show	The chosen reflection option is answered in 3–4 sentences that name a specific limit or a specific case and tie it to a check the student could run.	The reflection is answered but stays general or names nothing to check.	No reflection is submitted.

Quality Gate

• Every sentence in the sorting table has a role, and exactly one is labelled the main conclusion.
• Every inference has its pattern written in words with sentence letters, a form name, and a verdict that matches the form.
• Each invalid inference has a counterexample with every premise true and the conclusion false, checked line by line.
• Each valid inference has a stated reason that no counterexample exists, kept separate from whether its premises are true.
• Your own argument follows a valid form, states the strongest objection fairly, and replies to it, and it takes either side without penalty.
• No statistic, study, expert, or quotation is invented anywhere in the submission.
• The critique quotes the chatbot or the flawed analysis and corrects at least two statements with evidence from the letter, the tables, or the chapter.