Week 2 · Chapter

Chapter 2 — Analyzing Arguments

Critical Thinking Free sample edition

The module's primary reading · ~35–45 minutes · Objective 2 (with Objective 1 carried forward) · Read it first this week; the lecture, the slides, the tutorial, the quiz, and the Argument Workshop all build on it.

In plain language

This week is about writing an argument out so you can see every piece of it. You will learn standard form (a layout with each reason on its own numbered line and the main claim on the last line). You will learn to find an unstated premise (a reason the speaker needs but never says) and write it in, marked so everyone knows you added it. You will practise the principle of charity (reading an argument in its most reasonable form, without adding views the speaker never held). Finally, you will draw an argument map (boxes and arrows that show which reasons work together and which stand alone), and you will always say the map in words too.

Why you already care about this

It is 9 p.m., and a group chat for 4 roommates buzzes. One roommate writes: "We need a cleaning schedule. The kitchen has been a mess for 2 weeks, and nobody knows whose turn it is to take out the trash." Then nothing. 3 people read the message, and nobody answers for 20 minutes.

The message is an argument: a main claim and two reasons. But something is missing between them. A messy kitchen does not, by itself, prove that a schedule is the fix. Maybe the roommate thinks a schedule would solve the "whose turn is it" problem, or maybe the roommate means something stronger. You cannot reply well until you know which.

This chapter gives you the tools to say exactly what is missing. Last week you found the parts of an argument. This week you lay those parts out, fill the gaps fairly, and draw how the parts connect. None of that judges the argument yet; it tells you what the argument is, so later judging hits the right target.

By the end of this chapter you will be able to:

rewrite a passage in standard form, turning questions and commands into claims;
find an unstated premise or an unstated conclusion, write it out, and mark it "(supplied)";
choose, under the principle of charity, the weakest premise that connects the stated premises to the conclusion;
tell linked from independent premises, add an objection and a reply as arrows marked "against", and describe the map in words;
name the six parts of the Toulmin layout;
put the running question in standard form, supply its P3, and map it.

Carry this line with you: rebuild the argument they gave — not the one you wish they gave.

Where we are

Already covered: Week 1 taught you to find an argument: a conclusion, the premises offered for it, and how an argument differs from an explanation, a report, and an unsupported assertion.
This week: standard form, unstated premises and conclusions, the principle of charity, argument maps with objections and replies, and the Toulmin layout, all run on the running question.
How they connect: you cannot lay out an argument you have not found, so every reconstruction this week starts with the Week 1 question, "what does the writer want me to accept, and what is offered as the reason?"
Where we're going next: Week 3, Deductive and Inductive Reasoning, starts judging the arguments you lay out this week, beginning with validity and the counterexample method.

Week 1 gave you the definition of an argument and the habit of finding a conclusion by asking what the writer wants you to accept. It also found the running question's conclusion and three stated reasons, and this week picks up that passage where Week 1 left it.

1. Write it in standard form: one claim per line

A gym's flyer on a bulletin board (illustrative) reads: "Why pay more somewhere else? Members who sign up this month pay no joining fee, and our new evening classes run until 10 p.m. Join this month." The flyer is an argument, but its parts are scattered. One part is a question, one is a command, and the reasons are tucked into a single long sentence.

Standard form lists each premise on its own numbered line, P1, P2, P3; then a line that reads "So,"; then the conclusion on its own line, marked C. Indicator words are dropped, and every line is a complete declarative sentence.

That last rule matters. A question or a command cannot be true or false, so you rewrite it as the claim it carries, the way Week 1 taught you to spot an implied claim.

Worked example — the gym flyer (illustrative). Lay the flyer out step by step.

Find the conclusion. The flyer wants you to join this month. "Join this month" is a command, so rewrite it as a claim: "You should join this gym this month."
Find the stated premises. The flyer gives two reasons: members who sign up this month pay no joining fee, and the new evening classes run until 10 p.m.
Rewrite the question. "Why pay more somewhere else?" carries an implied claim: other gyms cost more to join. That is a third premise, and the flyer means it as one.
Drop the indicators and number the lines.

P1: Members who sign up this month pay no joining fee.

P2: The gym's new evening classes run until 10 p.m.

P3: Other gyms cost more to join.

So,

C: You should join this gym this month.

In words: the flyer is an argument with three premises and one conclusion, and two of its five lines were rewritten from a question and a command. Now you can say "P3 is the weak spot" instead of "something about that flyer bugs me."

Misconception check. Students often think standard form means rewriting an argument so it sounds better. That is tempting, because you do rephrase questions and commands. But each line stays as close to the arguer's words as a complete sentence allows. Standard form changes the layout, not the content.

Memory hook: one claim per line; the conclusion goes last.

2. Supply what is missing: unstated premises and conclusions

Back to the roommate's chat message from the start of the chapter. Here it is in standard form, with only the words the roommate wrote:

P1: The kitchen has been a mess for 2 weeks.

P2: Nobody knows whose turn it is to take out the trash.

So,

C: The apartment needs a cleaning schedule.

There is a jump. The premises describe a problem; the conclusion names a fix. Nothing on the page says this fix suits this problem.

Many everyday arguments leave a premise unstated because the arguer takes it for granted. An unstated premise is a premise an argument needs but leaves unsaid. When you write it out, you mark it "(supplied)" after its number, so no reader mistakes your words for the arguer's. A premise marked this way is a supplied premise.

Worked example — the roommate's missing premise (illustrative). Find the gap and fill it.

Name the gap. P1 and P2 say chores are going undone and nobody knows whose turn they are. C says a schedule is needed. The missing link is a claim that connects "nobody knows whose turn it is" to "a schedule is the answer."
Write the link as a claim. "A shared apartment should adopt a cleaning schedule when chores go undone because no one knows whose turn they are."
Mark it and place it.

P1: The kitchen has been a mess for 2 weeks.

P2: Nobody knows whose turn it is to take out the trash.

P3 (supplied): A shared apartment should adopt a cleaning schedule when chores go undone because no one knows whose turn they are.

So,

C: The apartment needs a cleaning schedule.

In words: two stated premises and one supplied premise reach the conclusion, and a housemate could accept P1 and P2 while still doubting P3.

Sometimes the conclusion is the missing piece. A sandwich shop's sign (illustrative) says: "Every sandwich is made with bread baked this morning. You deserve fresh food." The sign never says "buy here," but that is plainly the point. An unstated conclusion is a conclusion the arguer means to establish but never says out loud. You write it out on the C line and mark it the same way.

P1: Every sandwich at this shop is made with bread baked this morning.

P2: You deserve fresh food.

So,

C (supplied): You should buy your sandwiches at this shop.

Misconception check. Students often read a supplied premise as part of what the arguer said. That is tempting, because once P3 is on the page it looks like every other line. But the roommate never typed P3. If you criticize the roommate for "saying" P3, you are criticizing words you wrote; the "(supplied)" mark keeps that straight.

An honesty note: supplying a premise is interpretation, and two careful readers can supply slightly different ones. What matters is that each can say why theirs is the one the argument needs, which is where the next section comes in.

Memory hook: if you wrote it, mark it; the arguer did not.

3. Read with charity: the most reasonable version

Picture a bus rider speaking at a city transit meeting (illustrative): "The night bus should run until 2 a.m. on weekends. Many restaurant workers finish their shifts after midnight." There is a gap between the premise and the conclusion, so you need to supply a premise. But which one?

One candidate is "the city must run a bus whenever anyone wants a ride." Another is "the city should extend bus service when a sizable group of riders has no other practical way home." Both close the gap. The first is easy to knock down; nobody thinks a city must run a bus for one person at 4 a.m. The second is harder to dismiss, and it fits what the speaker seems to mean.

The principle of charity tells you which to pick. Among the readings the words allow, you choose the one that makes the argument as reasonable as possible, and you supply the weakest premise that connects the stated premises to the conclusion.

"Weakest" means the premise that claims the least while still closing the gap, which gives the arguer the best fair chance.

Worked example — charity at the transit meeting (illustrative). Run the principle step by step.

List the stated parts. P1: Many restaurant workers finish their shifts after midnight. C: The night bus should run until 2 a.m. on weekends.
Name the gap. P1 says some riders need late rides; C says the city should provide them. Missing: a claim that the city ought to serve such riders.
Pick the weakest premise that closes the gap. The sweeping premise (a bus for anyone at any hour) and the modest one (service for a sizable group with no other way home) both close it, but the modest one claims far less, so it wins.

P1: Many restaurant workers finish their shifts after midnight.

P2 (supplied): The city should extend bus service when a sizable group of riders has no other practical way home.

So,

C: The night bus should run until 2 a.m. on weekends.

In words: charity supplies the modest premise, and now the place to question the argument is P2's "sizable group" and "no other practical way home", not a silly claim the rider never made.

Charity has a hard limit. It rebuilds the argument the arguer actually gave; it never invents a view the arguer did not hold. Adding a premise about traffic safety the rider never mentioned would make it your argument, not theirs.

Misconception check. Students often think charity means agreeing, or going easy on an argument. That is tempting, because "charity" sounds like kindness. But charity is about accuracy: you read the argument at its most reasonable so that later you test the real thing. You can read with full charity and still reject the conclusion.

A caveat: "weakest" is a guide, not a formula. If the context shows the arguer holds a stronger premise, charity writes what they hold.

Memory hook: the most reasonable reading — nothing invented.

4. Draw the map: linked versus independent premises

Standard form lists the parts. A map shows how they connect. An argument map draws each claim as a box and each line of support as an arrow toward the claim it supports, and it is always described in words as well.

A map shows whether premises work together or alone. Take a rule from a restaurant kitchen (illustrative): "Every staff member on the closing shift gets a free meal. The night cook is on the closing shift. So the night cook gets a free meal." Cover up either premise and the other does nothing for the conclusion. Other arguments are different: cover up one reason and the rest still give some support.

Linked premises support the conclusion only together; remove one and the support collapses. On a map, linked premises sit in joined boxes with one arrow from the group to the conclusion. Independent premises each give some support on their own. On a map, each independent premise has its own arrow to the conclusion.

The test is the cover-up test: hide one premise and ask, "does the other premise still give any reason for the conclusion?" If not, they are linked. If so, they are independent.

Worked example — a four-day-week memo (illustrative). A team lead at a small design office writes a memo: "We should try a four-day week this summer. Most of the team asked for it at the last staff meeting. Our two biggest clients close their offices one weekday each summer week anyway. And the office would spend less on cooling with one fewer day open."

Standard form. P1: Most of the team asked for a four-day week at the last staff meeting. P2: The office's two biggest clients close their offices one weekday each summer week. P3: The office would spend less on cooling with one fewer day open. So, C: The office should try a four-day week this summer.
Cover-up test. Hide P1, and P2 and P3 still give reasons: lost client contact is small, and there is a cost saving. Hide P2 or P3 instead, and the others still offer some support.
Draw it. Three separate arrows, one from each box to C.

In words: P1, P2, and P3 each support C on its own, so the map has three independent arrows into C.

Maps also show disagreement. An objection is a reason offered against a premise or a conclusion, drawn as a box with an arrow marked "against" pointing at the claim it attacks. A reply is a reason offered against an objection, drawn as a box with an arrow marked "against" pointing at the objection.

Worked example — adding an objection and a reply (illustrative). A client manager at the same office objects: "Customers who call on the closed day will get no answer." The team lead replies: "The office phone can forward to one staff member on call that day."

The objection is a new box with an arrow marked "against" pointing at C.
The reply is a new box with an arrow marked "against" pointing at the objection, not at C.

In words: the objection attacks C, and the reply attacks the objection; the reply adds no new support for C, it removes a reason against it.

Misconception check. Students often draw linked premises as independent, giving each its own arrow. That is tempting, because every premise looks like "a reason." But the cover-up test exposes the mistake. In the closing-shift argument, neither premise supports the conclusion alone, so two separate arrows would claim support that is not there.

Misconception check — the silent map. Students often treat a map as a picture that needs no words. That is tempting, because a diagram feels self-explanatory. But a drawing hides which premises are joined from anyone who cannot see it or reads it differently. Every map in this course comes with a sentence such as "P1 and P2 work together to support C" or "P1 and P2 each support C on its own."

Memory hook: cover one up; if the other goes quiet, they are linked.

5. Lay it out another way: the Toulmin layout

Toulmin's The Uses of Argument (1958) lays out an argument as a claim, the data offered for it, the warrant that links them, and the backing, qualifier, and rebuttal around them. The Toulmin layout is a second way to see structure, good at showing the hedges and exceptions standard form can hide.

Here are the six parts in plain words:

Claim — what the arguer wants you to accept.
Data — the facts offered for it.
Warrant — the general rule that links the data to the claim.
Backing — support for the warrant itself.
Qualifier — a word that says how strongly the claim is made, such as "probably".
Rebuttal — the exception that would defeat the claim.

Worked example — a sports-radio prediction (illustrative). A sports-radio host says: "The home team will probably win this weekend. They have won their last 4 home games, and teams that keep winning at home tend to keep winning there, since they know the field and the crowd is behind them. Unless their starting goalkeeper is still injured, I like their chances."

Claim: the home team will win this weekend.
Data: they have won their last 4 home games.
Warrant: teams that keep winning at home tend to keep winning there.
Backing: they know the field, and the crowd is behind them.
Qualifier: "probably".
Rebuttal: unless the starting goalkeeper is still injured.

In words: the host's argument has all six Toulmin parts, and the layout makes the hedge ("probably") and the exception (the goalkeeper) easy to see.

The warrant plays the same role as a supplied premise in standard form: the general link between data and claim. Toulmin gives that link its own name.

Misconception check. Students often treat the Toulmin layout as a test that says whether an argument is good, so an argument with all six parts "passes." That is tempting, because a full layout looks complete. But the layout is a classroom tool for seeing structure, not a verdict. An argument can fill all six boxes and still be weak, and nothing in this course is graded from the Toulmin layout itself.

A limitation worth naming: real arguments rarely announce their backing or rebuttal, so you will often leave those parts blank or supply them, marked.

Memory hook: data needs a bridge to the claim; the warrant is that bridge.

6. Map the running question: standard form, P3, and the map

Now you run every tool from this chapter on the running question. Here again is the illustrative campus-newsletter passage Week 1 analyzed:

The campus library should stay open around the clock during finals week. During finals week many students need a quiet, safe place to study late at night. The library is the only quiet, safe, well-lit study space on campus large enough to meet that need. Keeping the library open overnight for the five nights of finals week costs about 1,600 dollars in staff wages.

Worked example — the running question in standard form and on a map (illustrative). Work through it in nine steps.

The conclusion. The claim the writer wants you to accept goes last, on its own line marked C: "The campus library should stay open around the clock during finals week."
The stated premises. The three stated reasons become P1 (the need), P2 (the only suitable space), and P4 (the cost), worded as in the block below.
The gap. P1 and P2 say there is a need and a place that could meet it, but nothing stated says the campus ought to meet that need. Without that, the stated premises do not reach C.
The supplied premise. P3 (supplied) is "The campus should provide study space students need during finals when it can do so at modest cost." It is the weakest premise that closes the gap, because it asks the campus to act only when the cost is modest.
The charity check. A stronger premise such as "The campus must give students any space they ask for, at any cost" would also close the gap, but the writer never said it, and it would be easy to knock down. Charity picks the modest version.
The tally. 3 stated premises + 1 supplied premise = 4 premises, and 4 premises + 1 conclusion = 5 lines in standard form.
The cost check behind P4. 2 staff × 8 hours a night = 16 staff hours a night; 16 × 5 nights = 80 staff hours; 80 × 20 dollars an hour = 1,600 dollars.

Here is the whole argument in standard form:

P1: During finals week many students need a quiet, safe place to study late at night.

P2: The library is the only quiet, safe, well-lit study space on campus large enough to meet that need.

P3 (supplied): The campus should provide study space students need during finals when it can do so at modest cost.

P4: Keeping the library open overnight for the five nights of finals week costs about 1,600 dollars in staff wages.

So,

C: The campus library should stay open around the clock during finals week.

P4 comes after the supplied premise because of its job: it holds up one part of P3 rather than sitting beside the others.

The map in words. P1, P2, and P3 work together to support C, so they are linked, with one arrow from the joined boxes to C. P4 supports P3's "modest cost" condition, with its own arrow from P4 to P3.
The objection and the reply. The objection, "overnight hours encourage all-night studying, and losing sleep can hurt exam performance, so the library would be helping students harm themselves", is a box with an arrow marked "against" pointing at C. The reply, "students who stay up will study somewhere; the question is whether that place is quiet and safe, and the library can post sleep reminders and set aside one quiet floor for rest without closing the building", is a box with an arrow marked "against" pointing at the objection.

Verdict in words: the argument has four premises, one of them supplied, and one conclusion; P1, P2, and P3 are linked, so the support for C collapses if any one of them fails, and the place to look hardest later is P3, the premise the writer never said out loud.

The cover-up test confirms the linked group. Hide P3, and nothing says the campus should act. Hide P2, and some other building might meet the need. Hide P1, and maybe nobody needs the building at night.

Misconception check. Students often think that mapping the running question means taking a side on it. That is tempting, because you worked to make the argument look its best. But a student who opposes overnight hours should produce the same standard form, the same supplied P3, and the same map as a student who supports them. Mapping is not judging, and the course takes no side; whether this support is good enough waits for the coming weeks. The same holds for the roommates' group chat: before anyone argues about the cleaning schedule, everyone should agree on what the argument says, supplied premise and all.

Memory hook: P1, P2, and P3 hold up C together; P4 holds up P3.

Key terms

standard form — A way of writing an argument with each premise on its own numbered line (P1, P2, P3), then a line reading So, and then the conclusion on its own line marked C, with indicator words removed so each step can be checked separately. (first used: 1. Write it in standard form: one claim per line)
unstated premise — A premise an argument needs but leaves unsaid, usually because the arguer takes it for granted; finding it often shows where an argument is weakest. (first used: 2. Supply what is missing: unstated premises and conclusions)
supplied premise — An unstated premise that the analyst writes out and marks (supplied) after its number, so no reader mistakes the analyst's words for the arguer's. (first used: 2. Supply what is missing: unstated premises and conclusions)
unstated conclusion — A conclusion the arguer means to establish but never says out loud, which the analyst writes out on the C line when putting the argument in standard form. (first used: 2. Supply what is missing: unstated premises and conclusions)
principle of charity — The rule of choosing, among the readings the words allow, the one that makes an argument as reasonable as possible, and of supplying the weakest unstated premise that connects the stated premises to the conclusion; it rebuilds the argument given and never invents a view or signals agreement. (first used: 3. Read with charity: the most reasonable version)
argument map — A drawing of an argument's structure with boxes for claims and arrows for support or attack, always described in words as well, so the reader can see which premises work together and which stand alone. (first used: 4. Draw the map: linked versus independent premises)
linked premises — Premises that support a conclusion only together, so that removing any one of them makes the support collapse; a map draws them as one arrow from joined boxes. (first used: 4. Draw the map: linked versus independent premises)
independent premises — Premises that each give some support to a conclusion on their own, so that removing one weakens the case without erasing the others; a map draws them as separate arrows. (first used: 4. Draw the map: linked versus independent premises)
objection — A reason offered against a premise or a conclusion; on an argument map it is a box with an arrow marked against pointing at the claim it attacks. (first used: 4. Draw the map: linked versus independent premises)
reply — A reason offered against an objection; on an argument map it is a box with an arrow marked against pointing at the objection it answers. (first used: 4. Draw the map: linked versus independent premises)
Toulmin layout — A second way to lay out an argument, from Toulmin's The Uses of Argument, that names the claim, the data offered for it, the warrant linking them, and the backing, qualifier, and rebuttal around them. (first used: 5. Lay it out another way: the Toulmin layout)

Summary

Standard form puts each premise on a numbered line, then "So,", then the conclusion marked C; every line is a complete claim.
An unstated premise or conclusion is written out and marked "(supplied)".
A supplied premise is your words, not the arguer's.
Charity picks the most reasonable reading and the weakest premise that closes the gap.
Charity never invents a view, and it is not agreement.
Linked premises support only together; independent premises each support alone.
Objections and replies are arrows marked "against"; every map is described in words.
The Toulmin layout names claim, data, warrant, backing, qualifier, and rebuttal; it shows structure and is not a test.
The running question has four premises, P3 supplied; P1, P2, and P3 are linked, and P4 supports P3.

Check your understanding

Work these before looking at the answers — they are ungraded, and the answers (with reasoning) are at the bottom of the page.

An animal shelter's poster (illustrative) says: "Thinking about a pet? Older cats are usually already litter-trained. They are calmer than kittens, too. Adopt an older cat." Put the poster in standard form.
A friend says (illustrative): "The band will sell out the arena. They sold out their last three shows." Supply the missing premise under the principle of charity, and say why you did not choose "Any band that has ever sold out a show will sell out every show."
A hiking club's plan (illustrative) says: "The trail is open this weekend. The club van is free this weekend. So the club can run its hike this weekend." Linked or independent? Use the cover-up test.
A school robotics team argues (illustrative): "Our trip to the regional contest is affordable. The team will sell 75 snack boxes at 4 dollars each, and the bus costs 260 dollars." Put the argument in standard form, supply the unstated premise, and check the arithmetic the argument depends on.

Answers (worked reasoning — read after attempting)

The command becomes the conclusion: "You should adopt an older cat." The question "Thinking about a pet?" only sets the scene, so it gets no line. Standard form: P1: Older cats are usually already litter-trained. P2: Older cats are calmer than kittens. So, C: You should adopt an older cat.
A charitable supplied premise is "P2 (supplied): A band that sold out its last three shows will probably sell out its next one." It closes the gap and claims only what the friend seems to mean. The sweeping premise about any band that ever sold out a show claims far more than needed and is easy to knock down, so charity sets it aside.
Linked. Cover up "the trail is open": a free van does not help if the trail is closed. Cover up "the van is free": an open trail does not help if the club cannot get there. Each premise goes quiet without the other, so the map needs one arrow from the joined boxes.
The sales: 75 × 4 = 300 dollars. The bus costs 260 dollars, and 300 − 260 = 40 dollars left over, so the sales cover the bus. Standard form: P1: The team will sell 75 snack boxes at 4 dollars each. P2: The bus to the regional contest costs 260 dollars. P3 (supplied): A trip is affordable when the team's sales cover its cost. So, C: The trip to the regional contest is affordable. Whether the team will really sell all 75 boxes is a separate question about P1.

Next up in this module: the lecture, the slide deck, the Readings & Resources page, the lecture tutorial, and the practice set. Next week you start judging the maps you drew, with validity and the counterexample method, the test that asks whether the premises could all be true while the conclusion is false.

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