Chapter 15 — Reasoning About Values and the Course Synthesis
The module's primary reading · ~45–55 minutes · Objective 9 (with Objective 2 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 arguments that say what someone ought to do. A moral argument (an argument about what is good, right, or required) usually joins a value premise (a claim about what is good, right, or required) to a factual premise (a claim about what the situation is). Each kind of premise needs its own support, and many arguments about right and wrong turn out to be arguments about facts. You learn three ways of laying out moral reasons, how to state the other side at its strongest, and how to build and defend an argument of your own. Then you put the whole course together: which test fits which kind of argument.
Why you already care about this
Three choices land on you in one term. A friend asks to copy your lab report the night before it is due. Your club of 5 wins a 600-dollar prize and has to decide how to split it. A coworker proposes a plan at a team meeting, and you think it will not work.
None of these is a question about what is. Each is a question about what you ought to do. You have probably heard someone say that questions like these are "only opinion", so there is nothing to argue about. That feels true when people disagree loudly. It is not true. A moral claim has reasons behind it, and reasons can be strong or weak.
Since Week 1 you have tested arguments about what is: their form, their words, their samples, their causes, their numbers, their sources, their explanations, and your own biases. This week you test arguments about what ought to be. Then you argue the running question in full, with its strongest objection and a reply.
By the end of this chapter you will be able to:
- separate a moral argument's value premise from its factual premise and say what supports each;
- tell a value disagreement from a factual disagreement;
- lay out the consequence-based, duty-based, and character-based frameworks, each with its strongest case and standard objections;
- argue both sides of a question from each framework without declaring a winner;
- steelman an opposing view before replying to it;
- build and defend the running question with its map, its strongest objection, and a reply;
- choose the test that fits each kind of argument you have met this term.
Carry this line with you: a value is not a fact — test each one its own way.
Where we are
- Already covered: Week 1 taught you to find an argument, Week 2 to put it in standard form and map it, and Weeks 3 to 5 to test deductive reasoning. Weeks 6 to 8 taught language and the fallacies, Weeks 9 to 11 samples, causes, and numbers, Weeks 12 and 13 sources and science, and Week 14 the biases in your own reasoning.
- This week: you reason about values, meet three ethical frameworks as tools, steelman the other side, build and defend the running question in full, and match every kind of argument to its test.
- How they connect: a moral argument is still an argument, so Week 2's standard form and supplied premise do the first job. Week 7's straw man becomes the mistake that steelmanning cures, and Week 14's "consider the opposite" becomes the habit of stating the other side at its strongest.
- Where we're going next: Week 16 holds the cumulative final, which draws on all nine course objectives, so this week's synthesis is your map for review.
Two earlier ideas carry most of the weight. From Week 2: a premise the arguer left unstated can be supplied and marked "(supplied)", and the principle of charity asks you to choose the most reasonable reading the words allow. From Week 7: a straw man answers a weaker or distorted version of the opposing position instead of the position actually stated. Keep both in view; this chapter puts them to work.
1. Take a moral argument apart: value premise and factual premise
Your friend asks to copy your lab report. You say no, and you give a reason: "Copying a lab report is cheating, and I shouldn't help someone cheat." Look closely, and two different kinds of claim are hiding in that sentence.
One claim says what the situation is: copying the report would count as cheating under the course's rules. You could check that by reading the rules. The other claim says what you ought to do: you should not help someone cheat. No rule book or measurement settles that one by itself. You support it with reasons, such as fairness to the classmates who did their own work.
A moral argument is an argument whose conclusion says what someone ought to do or what is good, right, or required, usually built by joining a value premise to a factual premise.
A value premise is a premise that says what is good, right, or required, such as a rule about what a campus should provide; it is supported by reasons and principles rather than by observation alone.
A factual premise is a premise that says what the situation is, such as what something costs or how many hours someone worked; it is supported by evidence that could show it true or false.
Worked example — the copied lab report (illustrative). Put your reason in standard form.
P1: Copying your lab report would count as cheating under the course's rules.
P2 (supplied): A student should not help another student cheat.
So,
C: You should not let your friend copy your lab report.
- Find the value premise. P2 says what a student should do, so it is the value premise. You supplied it, because the reason as spoken left it half stated.
- Find the factual premise. P1 says what the situation is, so it is the factual premise.
- Ask what supports each. P1 is checked against the course's written rules. P2 is supported by reasons, such as fairness to classmates and the point of doing the work yourself.
In words: the argument needs both premises, and each one is supported in its own way.
Here is the move that matters most. When two people disagree about a moral conclusion, ask which premise they disagree about. Often it is the factual one. Suppose your friend says, "It's not cheating if I only check my numbers against yours." Your friend may accept P2 and dispute P1. That is a disagreement about what the rules say, and the rules can be read.
Misconception check — a moral claim is "only opinion". Students often say that a claim about right and wrong is a matter of opinion, so it cannot be argued. That is tempting, because people do disagree about values, sometimes for a long time. But an opinion is a claim someone holds, and its reasons can still be strong or weak. A moral argument has premises you can find, factual premises you can check, and value premises you can support or question.
Memory hook: every "ought" rides on an "is"; check both.
2. Split the running question into value and fact
You have argued about the campus library all term. Should it stay open around the clock during finals week? This week you can see what kind of argument it is.
Worked example — the running question in standard form (illustrative). Here is the campus-newsletter argument with every premise on its own line.
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.
- Check the cost premise. 2 staff × 8 hours × 5 nights × 20 dollars an hour = 1,600 dollars, so P4 matches the inputs it rests on.
- Find the value premise. P3 says what the campus should do, so it is the value premise.
- Find the factual premises. P1, P2, and P4 say what the situation is, so they are the 3 factual premises.
- Count. That is 1 value premise and 3 factual premises, 4 premises in all.
In words: the argument's one value premise is P3, and its other three premises are claims you could check with evidence.
Now do the same for the strongest objection, written charitably. You met its first two steps in Week 14. Here it is in full, with the value premise it needs supplied.
O1: Overnight hours encourage all-night studying.
O2: Losing sleep can hurt exam performance.
O3 (supplied): The campus should not provide a service that helps students harm themselves.
So,
OC: The campus library should not stay open around the clock during finals week.
Worked example — where the dispute lies (illustrative). Lay the argument and the objection side by side.
- Sort the objection. O1 and O2 are the 2 factual premises, and O3 is the 1 value premise.
- Set the value premises side by side. P3 says the campus should provide needed study space at modest cost. O3 says it should not provide a service that helps students harm themselves. A reader can accept both P3 and O3 at once.
- Find the factual split. The sides part ways on O1, a factual claim about whether an open library adds all-night studying or only moves it to a less safe place.
- Say what would settle it. That is a factual question that evidence about where students study can settle.
In words: two people who share both value premises can still reach opposite conclusions, because they disagree about a fact.
A value disagreement is a dispute about which standard of good, right, or fair to apply, which can remain even when both sides agree on every fact.
A factual disagreement is a dispute about what the situation is, which evidence could settle; many moral disagreements turn out to be of this kind.
An honesty note: finding that a dispute is factual does not end it on the spot. Someone still has to gather the evidence, and the evidence can be hard to get. But it tells you what kind of evidence to look for, which is more than shouting about values can do.
Misconception check — a value disagreement read as a factual one, or the reverse. Students often assume that a heated moral argument must be about values. That is tempting, because the conclusion uses words like "should". But the heat often comes from a factual premise, such as O1 here. The reverse mistake happens too: two people trade facts for an hour when they really disagree about a standard. Ask which premise each side rejects before you decide what kind of disagreement it is.
Memory hook: share the value, split on the fact — then go get the fact.
3. When fact and value pull apart: the club prize
Your club enters a campus design contest and wins. Now comes the hard part: splitting the money. Two members disagree, and both sound fair.
Worked example — the club prize (illustrative). A club of 5 members wins a 600-dollar prize.
- Equal shares. Equal shares give 600 ÷ 5 = 120 dollars each.
- The hours. The sign-in log shows 20, 10, 10, 5, and 5 hours, and 20 + 10 + 10 + 5 + 5 = 50 hours.
- Shares by hours. Shares by hours give 600 ÷ 50 = 12 dollars an hour, so 20 × 12 = 240, 10 × 12 = 120, and 5 × 12 = 60 dollars.
- Check the total. 240 + 120 + 120 + 60 + 60 = 600, so the shares by hours add back up to the whole prize.
Here are the two splits side by side.
| Member | Hours on the log | Equal share (dollars) | Share by hours (dollars) |
|---|---|---|---|
| Member A | 20 | 120 | 240 |
| Member B | 10 | 120 | 120 |
| Member C | 10 | 120 | 120 |
| Member D | 5 | 120 | 60 |
| Member E | 5 | 120 | 60 |
In practice (your tools). In a free spreadsheet, put each member on a row with their hours in one column. Add a cell that totals the hours. In the next column, divide the prize by the number of members for the equal share. In the last column, divide the prize by the total hours and multiply by each member's hours. Total each share column to check that it comes back to 600.
- Find the value question. Whether equal shares or shares by hours is fair is the value question.
- Find the factual question. Whether the log's 50 hours are accurate is the factual question.
- Classify a challenge. A member who disputes the log is making a factual objection, not a value one.
In words: the arithmetic is settled, the hours are a fact the log can check, and the choice of rule is the value question the club has to argue.
Notice that the numbers do not pick the rule. The share-by-hours column gives Member A 240 dollars, which is 240 ÷ 120 = 2 times the equal share. That ratio is a fact. Whether a twofold share is fair is a value judgment about effort, membership, and teamwork. A limitation worth saying: this course will not tell your club which rule to choose. It will help your club see which part of the argument is about the log and which part is about fairness.
Misconception check — the numbers settle the moral question. Students often think that once the shares are computed, the fair answer is obvious from the table. That is tempting, because arithmetic feels final. But the table shows what each rule gives, not which rule is right. The value premise, "shares should follow effort" or "members share equally", still needs its own reasons.
Memory hook: the math shows the options; the value picks among them.
4. Use three frameworks as tools, not verdicts
Your coworker's plan has a flaw, and you are deciding whether to say so in the meeting. One voice in your head asks what will happen if you speak up. Another says you owe your team honesty. A third asks what a good colleague would do. Those three voices are the three ethical frameworks this course uses.
An ethical framework is an organized way of judging actions that tells you which considerations to weigh, used in this course as a tool for laying out reasons rather than as a machine that settles a case.
There are 3 frameworks.
- A consequence-based framework is a way of judging an action by its outcomes for everyone affected; critics note that outcomes are hard to predict and that it can seem to allow harming a few for a gain to many.
- A duty-based framework is a way of judging an action by whether it keeps duties or rules, some of which hold regardless of outcomes; critics note that duties can conflict and that keeping a rule can lead to a bad outcome.
- A character-based framework is a way of judging an action by what a person of good character, such as an honest, fair, and caring person, would do; critics note that it can give little specific guidance in a hard case.
Each framework has a strongest case as well as standard objections. Here they are side by side.
| Framework | It judges an act by | Its strongest case | Its standard objections |
|---|---|---|---|
| Consequence-based | its outcomes | outcomes for everyone affected matter | outcomes are hard to predict; it can seem to allow harming a few for a gain to many |
| Duty-based | whether it keeps duties or rules | some things should not be done to people even for good outcomes | duties can conflict; keeping a rule can lead to a bad outcome |
| Character-based | what a person of good character would do | it looks at the whole person and their judgment over time | it can give little specific guidance in a hard case |
Worked example — the coworker's plan through each framework (illustrative). You think your coworker's plan will not work.
- Consequence-based. Speaking up may save the team wasted effort, and it may also embarrass your coworker in front of others. You weigh both outcomes, perhaps by raising the concern privately first.
- Duty-based. You may have a duty of honesty to the team, and also a duty of respect to your coworker. If the duties pull apart, the framework names the conflict without settling it.
- Character-based. You ask what an honest and kind colleague would do. Honesty pulls toward speaking up, and kindness toward a way and a moment that help the plan improve.
In words: each framework turns you toward different reasons, and none of them decides the case by itself.
Misconception check — one framework is the correct one. Students often pick the framework that matches their first instinct and treat it as the last word on ethics. That is tempting, because each framework sounds right when you read its strongest case. But each also faces standard objections that thoughtful people take seriously. This course presents all three as tools for organizing reasons and prescribes none.
Memory hook: outcomes, duties, character — three lenses, no verdict.
5. Argue both sides from each framework
A framework is not a team jersey. The same framework can give reasons on both sides of a question. Watch it happen on the running question.
Worked example — the running question from each framework (illustrative). Run the library question through each lens in turn.
- Consequence-based. The case for C weighs a quiet, safe place for many students against a cost of 1,600 dollars. The objection weighs the harm of lost sleep.
- Duty-based. The case for C rests on a duty to provide what students need at modest cost. The objection rests on a duty not to help people harm themselves.
- Character-based. The case for C asks what a caring campus would do. The objection asks what a campus that values rest and moderation would do.
In words: each framework supports a version of both sides, so no framework decides the question here.
Here is the same comparison as a table.
| Framework | The case for keeping the library open | The case in the objection |
|---|---|---|
| Consequence-based | a quiet, safe place for many students, at a cost of 1,600 dollars | the harm of lost sleep before exams |
| Duty-based | a duty to provide what students need at modest cost | a duty not to help people harm themselves |
| Character-based | what a caring campus would do | what a campus that values rest and moderation would do |
Two caveats keep this honest. First, the frameworks organize reasons; they do not weigh them for you. Second, a framework does not make a factual premise true. A consequence-based case still needs evidence about what overnight hours do to sleep.
Pause and choose one of these to think through, (a) or (b):
- (a) Pick one framework and write the strongest case it gives for keeping the library open, then the strongest case it gives against.
- (b) Pick one framework and explain which factual premise its case for the library depends on most, and what evidence would test that premise.
Misconception check — a framework decides the case. Students often expect that once they choose a framework, the answer falls out. That is tempting, because a framework sounds like a formula. But as the table shows, each framework gives reasons on both sides here. A framework tells you which considerations to weigh. You still have to weigh them, and you still have to check the facts.
Memory hook: a framework is a lens, not a judge.
6. Steelman before you reply
In Week 7 you met a weak way to answer the objection: "They want the library to be a dorm." That answer is easy to knock down, because nobody said it. This week you learn the opposite habit.
Steelmanning is stating the opposing view in its strongest form, ideally in terms its holders would accept, before replying to it; it is the opposite of a straw man and does not mean agreeing.
Worked example — the straw man and the steelman (illustrative). Compare two summaries of the library objection.
- The straw man. "They want the library to be a dorm" answers a claim no premise makes.
- The steelman. The steelman is O1, O2, and O3 stated in terms the objection's holders would accept: overnight hours encourage all-night studying, losing sleep can hurt exam performance, and the campus should not provide a service that helps students harm themselves.
- The test. Would someone who holds the objection say, "Yes, that's my view, put better than I put it"? For the steelman, yes. For the straw man, no.
In words: a reply to the steelman answers the real objection, and a reply to the straw man answers nobody.
Worked example — the coworker's plan (illustrative). A coworker proposes moving the team's weekly meeting online to save travel time.
- The straw man. "They don't care about the team."
- The steelman. "An online meeting saves each member's travel time, and the team can keep one in-person meeting a month for planning."
- Your reply to the steelman. Online meetings can make quick questions harder to ask, so you suggest a trial and a check of how it went.
In words: once you have stated the plan at its strongest, your reply can improve it instead of insulting the person who proposed it.
Steelmanning builds on Week 14's first debiasing habit, consider the opposite. Here you do it out loud, for the other side, before you answer. It also makes your own argument stronger: an argument that answers the best objection has survived a real test.
Misconception check — steelmanning means agreeing. Students often worry that stating the other side at its strongest gives the argument away. That is tempting, because you are saying their reasons well. But stating a view fairly is not adopting it. You can steelman the objection and still reply that it fails, exactly as you can call an argument valid while rejecting its conclusion.
Memory hook: reply to the best version, or you have replied to nothing.
7. Build and defend your own argument
All term, the running question has picked up parts. It began as a passage in Week 1 and got standard form and a map in Week 2. Week 3 tested it, Week 6 made "modest cost" precise, Week 12 traced a claim, and Week 14 added an objection. Now it gets built in full.
Worked example — the running question built and defended (illustrative). Assemble every part in order.
- Standard form. P1 to P4 and C, as in Section 2, with P3 marked (supplied).
- The map. The map is P1, P2, and P3 linked, working together to support C; P4 supports P3's "modest cost" condition; the objection is an arrow marked "against" pointing at C; and the reply is an arrow marked "against" pointing at the objection.
- The objection. O1, O2, and O3 (supplied), leading to OC, stated at its strongest.
- 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.
- Where it is weakest. The reply rests on the factual claim that closing the library would move all-night studying rather than end it, and that claim needs evidence.
In words: the argument now has every part a strong argument needs, and its last line names the premise a careful critic should press on.
Described in words, the map reads like this. Three boxes, P1, P2, and P3, are joined and send one arrow to C, because they work together. A fourth box, P4, sends an arrow to P3's "modest cost" condition. A box holding the objection sends an arrow marked "against" to C. A box holding the reply sends an arrow marked "against" to the objection.
Notice what the reply does. It targets O1, the factual premise, rather than O3, the value premise. The reply can accept that the campus should not help students harm themselves. It argues that closing the building would not stop the studying, only move it somewhere less safe.
A caveat: this course takes no side on the running question, and neither does this chapter. A student who argues for closing the library at night, with the objection built into a full argument and a reply to the best case for staying open, does the same work. What counts is the reconstruction, the test, and the reply, never the side.
Misconception check — naming your weakest point weakens your argument. Students often hide the premise they are least sure of. That is tempting, because admitting a weak spot feels like losing. But every real argument has one, and a reader will find it. Naming it shows that you tested your own case, and it tells the reader exactly what evidence would settle the question.
Memory hook: map it, object to it, reply, and name the weak link.
8. Put the course together: which test fits which argument
You now have a full toolkit. The skill this section adds is choosing the right tool. Different kinds of argument fail in different ways, so each one gets its own test.
The course synthesis is the matching of each kind of argument with the test that fits it, from the counterexample method for a claim that must follow to the value-and-fact split for a claim about what ought to be.
There are 11 kinds of argument, each with its test.
| Kind of argument | The test that fits it | Taught in |
|---|---|---|
| a claim that must follow | the counterexample method | Weeks 3 and 4 |
| an "all" or "some" claim | a Venn diagram | Week 5 |
| a claim that hangs on a key word | a precise definition | Week 6 |
| a reply aimed at a person or a distorted view | the fallacy check | Weeks 7 and 8 |
| a claim about a group from a sample | the sampling check | Week 9 |
| a causal claim | the confounding check | Week 10 |
| a claim in numbers | percentage points and natural frequencies | Week 11 |
| a claim from a source | the source check | Week 12 |
| an explanation offered as true | testability and the best-explanation test | Week 13 |
| your own reasoning | the bias check | Week 14 |
| a claim about what ought to be | the value-and-fact split | Week 15 |
Worked example — the synthesis run on the running question (illustrative). Ask what kind of claim each part of the library argument makes.
- The inference. P1 to P3 lead to C deductively once the cost is granted to be modest, and P4's link to "modest cost" is inductive.
- The number. P4's 1,600 dollars is checked by arithmetic.
- The word "only". P2's "only" is a factual claim for the source check.
- The causal premise. O1 is a causal claim for the confounding check.
- The values. O3 and P3 are value premises for the frameworks.
In words: one argument can call on five different tests, because each premise is a different kind of claim.
That is the deepest habit this course has tried to build. Before you ask whether an argument is good, ask what kind of claim each part makes. Then reach for the test that fits it.
Misconception check — one test fits every argument. Students often grab the tool they know best and use it on everything, such as calling every bad argument a fallacy. That is tempting, because a favorite tool feels reliable. But a causal claim can pass a validity test and still fail the confounding check, and a moral claim can pass every factual check and still rest on a disputed value premise. Match the test to the claim.
Memory hook: name the claim, then pick the test.
Key terms
- moral argument — An argument whose conclusion says what someone ought to do or what is good, right, or required, usually built by joining a value premise to a factual premise. (first used: 1. Take a moral argument apart: value premise and factual premise)
- value premise — A premise that says what is good, right, or required, such as a rule about what a campus should provide; it is supported by reasons and principles rather than by observation alone. (first used: 1. Take a moral argument apart: value premise and factual premise)
- factual premise — A premise that says what the situation is, such as what something costs or how many hours someone worked; it is supported by evidence that could show it true or false. (first used: 1. Take a moral argument apart: value premise and factual premise)
- value disagreement — A dispute about which standard of good, right, or fair to apply, which can remain even when both sides agree on every fact. (first used: 2. Split the running question into value and fact)
- factual disagreement — A dispute about what the situation is, which evidence could settle; many moral disagreements turn out to be of this kind. (first used: 2. Split the running question into value and fact)
- ethical framework — An organized way of judging actions that tells you which considerations to weigh, used in this course as a tool for laying out reasons rather than as a machine that settles a case. (first used: 4. Use three frameworks as tools, not verdicts)
- consequence-based framework — A way of judging an action by its outcomes for everyone affected; critics note that outcomes are hard to predict and that it can seem to allow harming a few for a gain to many. (first used: 4. Use three frameworks as tools, not verdicts)
- duty-based framework — A way of judging an action by whether it keeps duties or rules, some of which hold regardless of outcomes; critics note that duties can conflict and that keeping a rule can lead to a bad outcome. (first used: 4. Use three frameworks as tools, not verdicts)
- character-based framework — A way of judging an action by what a person of good character, such as an honest, fair, and caring person, would do; critics note that it can give little specific guidance in a hard case. (first used: 4. Use three frameworks as tools, not verdicts)
- steelmanning — Stating the opposing view in its strongest form, ideally in terms its holders would accept, before replying to it; it is the opposite of a straw man and does not mean agreeing. (first used: 6. Steelman before you reply)
- course synthesis — The matching of each kind of argument with the test that fits it, from the counterexample method for a claim that must follow to the value-and-fact split for a claim about what ought to be. (first used: 8. Put the course together: which test fits which argument)
Summary
- A moral argument joins a value premise to a factual premise; each needs its own support.
- Many moral disagreements are really about a factual premise.
- In the running question, P3 is the value premise and P1, P2, and P4 are factual.
- Arithmetic shows a rule's results; it does not choose the rule.
- The consequence-based, duty-based, and character-based frameworks are tools, not verdicts.
- Each framework can give reasons on both sides of one question.
- Steelmanning states the other side at its strongest; it is not agreeing.
- A defended argument has a map, its strongest objection, a reply, and a named weak point.
- Name the kind of claim first, then pick the test that fits it.
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.
- A neighborhood group argues: "Children cross the corner by the park on the walk to school, so the city should paint a crosswalk there" (illustrative). Put the argument in standard form with the unstated value premise supplied. Then say which premise is factual, which is the value premise, and what would support each.
- Three roommates share an internet bill of 60 dollars a month (illustrative). One works from home 20 hours a week and the other two 5 hours each. Work out equal shares and shares by hours. Then say which part of their disagreement is a value question and which is a factual question.
- At a gym's members' meeting, someone says: "People who want the late hours cut only want to punish night-shift workers" (illustrative). Explain why this is a straw man, and write a steelman of the view that the late hours should be cut.
- Name the test from the course synthesis that fits each claim (all illustrative): (a) "Sales rose the month after the new window sign went up, so the sign caused the rise." (b) "A survey of 50 people at the gym shows that most people in town exercise daily." (c) "The bonus should go to whoever closed the most sales."
Answers (worked reasoning — read after attempting)
- P1: Children cross the corner by the park on the walk to school. P2 (supplied): The city should paint a crosswalk where children cross on the walk to school. So, C: The city should paint a crosswalk at the corner by the park. P1 is the factual premise: a count of who crosses there, at what times, would support or undercut it. P2 is the value premise: it is supported by reasons such as children's safety and the city's duty to its residents, and someone could question it by asking whether a crosswalk is the best way to keep them safe.
- Equal shares: 60 ÷ 3 = 20 dollars each. Hours: 20 + 5 + 5 = 30 hours. Shares by hours: 60 ÷ 30 = 2 dollars an hour, so 20 × 2 = 40 dollars for the roommate who works from home and 5 × 2 = 10 dollars for each of the others; 40 + 10 + 10 = 60. Whether equal shares or shares by use is fair is the value question. Whether the hours are really 20, 5, and 5 is the factual question, and a week of tracking could settle it.
- It is a straw man because it answers a motive nobody stated instead of the reasons people gave. A steelman: "Keeping the gym open late costs staff wages and safety coverage for few members, and that money could keep the gym open longer on weekends, when more members use it." Someone who holds the view could accept that wording. You can steelman it and still reply that night-shift workers have few other times to exercise.
- (a) The confounding check, because it is a causal claim; a holiday season or a sale could explain the rise. (b) The sampling check, because a sample taken at a gym is biased toward people who exercise. (c) The value-and-fact split: "whoever closed the most sales" names a value standard for who deserves the bonus, and the sales counts are the factual premise.
Next up in this module: the lecture, the slide deck, the Readings & Resources page, the lecture tutorial, the practice set, and the quiz. Next week there is no new chapter: Week 16 holds the cumulative final, and the course synthesis is the test-matching method to review with.
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