How to work with this page

This page is the workshop for Lesson 7 of the Logic unit. You work through it alone, in about 45 minutes, with your Lesson 7 handout beside you. It has one job: to make sure that after this lesson you can find the sentence in any moral argument where the ought comes in — and say whether it was earned or slipped in.

Each part is built the same way:

Explanation — short, with the lesson’s own examples.
Exercise — you type or choose, then press Check. Nobody sees your mistakes. The page counts your first try; that number is for you.

Two rules for this page

Retrieve before you look. Where the page says “from memory”, scroll the explanation away first. A wrong guess you then correct sticks better than a right answer you copied.

Every exercise says what goes in the field: a word from a closed list, yes or no, or a choice. Spelling counts as written; capitals do not.

The page has three stages. Stage 1 puts the lesson’s case on trial and asks you to take a seat before you have the tools. Stage 2 gives you the tools: the is–ought gap and the bridging premise, Moore’s open question, Searle’s derivation, the error-spotting. Stage 3 sends you back to your seat with the tools in hand. Your sheet tells you when each stage is due.

Recall — Lesson 6 from memory

Before anything new: eight questions on Lesson 6, without your notes. Guess first: how many of the eight will you get? …… of 8.

Exercise 1 — Lesson 6

Write one word or a short phrase in each field, in English, without looking anything up.

A paradox is not a : it is an argument that runs from sound-looking premises by valid-looking steps to a conclusion that is absurd.
“This sentence is false” is the paradox.
“One grain is not a heap; adding one grain to a non-heap never makes a heap; so a million grains are not a heap” is the paradox. It arises for any predicate.
The four responses to it, in the order the lesson gave them: there is a sharp boundary but we cannot know it — ; borderline statements are neither true nor false — ; truth comes in degrees — ; the boundary shifts with the conversation — .

Fewer than 5? Read the Lesson 6 key terms on your handout again before you go on — one minute, then come back and do not redo the exercise.

Stage 1 — The case first

Why the case comes first

A tool you have never needed is a tool you will not remember. Take your seat now; Stage 2 will give you the words for what you did.

Between 1932 and 1972 the United States Public Health Service left 399 Black men with syphilis untreated in Macon County, Alabama, so that researchers could observe the disease’s natural course — and went on doing so after penicillin became the standard of care in the late 1940s. The study’s architects did not lack facts. They knew what syphilis did to the body, they knew penicillin cured it, they knew their subjects were suffering. The study ran for forty years inside an institution committed to facts, and stopped only when a journalist, Jean Heller, exposed it in 1972.

Suppose you are one of the PHS doctors in 1955, asked to say why you will continue, or refuse to continue, withholding treatment. The lesson offers three seats. They agree that Tuskegee was a failure; they disagree about what kind:

The gap is real (Hume, Moore): no collection of medical facts entails “we ought to stop.” To refuse, you must bring a normative premise — consent is necessary for human research, or the subjects’ dignity outweighs the knowledge gained. That premise is a commitment, not a finding.
The gap is bridged by the practice (Searle): these men are the doctor’s patients, and “patient” is not a neutral description — it is an institutional fact that already carries what is owed. Nothing needs importing; the refusal is written into what medicine is.
There is no gap in the facts (Foot, Cornell realism): the facts at Tuskegee were already morally loaded — unnecessary suffering, deliberately inflicted. Nothing needed adding; the doctors failed to see what was on the table.

Exercise 2 — Read the case

Choose one answer per question.

Which of these is the lesson’s point about Tuskegee?

The doctors had every fact they needed, and the facts did not stop them The doctors lacked the medical knowledge to see the harm they were doing The doctors stopped as soon as penicillin became the standard of care

On the gap-is-real seat, what has to be added to the medical facts before “we ought to stop” follows?

More medical facts — the exact mortality figures, for instance A normative premise — for instance, that consent is necessary for human research Nothing — the facts already entail it

Now take your seat, in your notebook, before you go on. Two or three sentences: which seat, and one reason. Say where, on your seat, the obligation to stop comes from: a premise the facts cannot supply, the rules of the practice, or a fact already in plain view. You will come back to this at Stage 3.

Stage 2 · Part A — The gap

A1. Two kinds of sentence

A descriptive sentence says what is the case: it can be checked against the world. A normative sentence says what ought to be the case, what is right, wrong, good, permitted, required. The lesson’s whole rule turns on being able to tell them apart at a glance.

Descriptive (is)	Normative (ought)
Penicillin cures syphilis.	The doctors ought to have given penicillin.
The death penalty does not deter crime.	Punishments that do not deter should not be used.
People desire happiness.	We ought to promote happiness.

The trap

Words like natural, healthy, normal, standard look descriptive and are often used as verdicts. “It is natural to care for one’s children” describes; “it is right to” evaluates. When one word does both jobs, the gap is being crossed in the dark.

Exercise 3 — Is or ought?

Write exactly one of these two words in each field: descriptive or normative. The first row is done for you.

Sentence	Kind
Penicillin cures syphilis.	descriptive
The Tuskegee doctors ought to have treated their patients.
399 men were left untreated between 1932 and 1972.
Researchers ought to obtain the consent of their subjects.
Most people desire happiness.
Punishments that do not deter should not be used.
The death penalty does not deter crime.
Natural selection produced in us a tendency to care for our children.
It is wrong to cause unnecessary suffering.
Jones uttered the words “I promise to pay you five dollars.”
Jones ought to pay Smith five dollars.

A2. The rule: no ought from is alone

Hume’s observation, in the Treatise (1739): moral philosophers describe facts — about God, human nature, society — and then, without any visible step, slide into ought. The rule that came out of it:

No set of purely descriptive premises validly entails a normative conclusion. If the conclusion contains an ought and no premise does, the argument is invalid as it stands — there is a situation in which every premise is true and the conclusion false. This is Hume’s guillotine.

The only repair is to supply the missing premise:

The death penalty does not deter crime. [descriptive]
Punishments that do not deter crime should not be used. [normative — the bridge]
Therefore, the death penalty should not be used. [normative]

With line 2 the argument is valid. Line 2 is where the argument now lives: it cannot be settled empirically, only by moral argument — someone may accept line 1 and reject line 2, because punishment has other purposes.

The consequence that matters most

Every ethical argument contains at least one ethical premise. When you cannot find it, it has not gone away: it is unstated, and unstated means unexamined. Your first job with any ought-conclusion is to write the bridge out in full.

Exercise 5 — Bridged or not?

Three fields per argument, each yes or no: is the conclusion normative? is a normative premise stated? does the argument cross the gap without a bridge? The first row is done for you.

Argument	Conclusion normative?	Normative premise stated?	Crosses the gap without a bridge?
People desire happiness. So we ought to promote happiness.	yes	no	yes
The death penalty does not deter. Punishments that do not deter should not be used. So the death penalty should not be used.
Penicillin cures syphilis. These men have syphilis. So penicillin would cure these men.
Natural selection produced in us a tendency to care for our children. So it is right to care for our children.
One ought not cause avoidable suffering. Withholding penicillin caused avoidable suffering. So the doctors ought not to have withheld it.
Science can measure wellbeing. So science can tell us what we ought to do.
Researchers ought to obtain consent. The Tuskegee subjects gave none. So the study ought not to have been run.

Row 3 has no ought anywhere. Hume’s guillotine has nothing to cut: a descriptive conclusion from descriptive premises is ordinary reasoning. The rule only bites when the conclusion evaluates.

Part B — Moore’s test

B1. The naturalistic fallacy and the open question

G. E. Moore (Principia Ethica, 1903) made a point next door to Hume’s. Suppose you try to close the gap by definition: “good” just means “what produces pleasure” — then “pleasure is good” is true by definition, and no bridging premise is needed. Moore called every such definition the naturalistic fallacy: defining “good” in terms of a natural property (pleasure, survival, what God commands, what the institution sanctions).

His test is the open question argument. Take the proposed definition and ask the question it should have closed:

Definition of “good”	The question	Open or closed?
what produces pleasure	“Is pleasure good?”	open — it still makes sense to ask
what natural selection produced	“Is what selection produced good?”	open
(for comparison) bachelor = unmarried man	“Is an unmarried man a bachelor?”	closed — a real definition leaves nothing to ask

If “good” really meant N, “is N good?” would be a closed question — trivially yes, like asking whether a bachelor is unmarried. For every natural N, the question stays open. So “good” does not mean N. Repeat for any N you like.

The trap

A definition is not an argument. “Good means what promotes survival, so caring for children is good” has the shape of a proof and the content of a stipulation. Moore’s question is how you catch it: but is promoting survival good? If that still asks something, the definition has not done the work.

Part C — Searle’s bridge

C1. Deriving “ought” from “is” inside a practice

John Searle (“How to Derive ‘Ought’ from ‘Is’”, 1964) accepted Hume’s rule for brute facts and denied it for institutional facts. His derivation, in five steps:

Jones uttered the words “I hereby promise to pay you, Smith, five dollars.”
Jones promised to pay Smith five dollars.
Jones placed himself under an obligation to pay Smith five dollars.
Jones is under an obligation to pay Smith five dollars.
Jones ought to pay Smith five dollars.

Step 1 is a brute fact: sounds came out of a mouth. Step 2 is an institutional fact — a fact that exists only inside the practice of promising. What takes you from 1 to 2 is a constitutive rule: uttering those words, in those circumstances, counts as making a promise. A constitutive rule does not tell you what to do; it makes the practice what it is, as the rules of chess make a move a move. And because promising just is placing oneself under an obligation, the ought at step 5 is not imported from outside: it was encoded in step 2.

The lesson’s Tuskegee version: “patient” is an institutional fact of the same kind. These men are the doctor’s patients, and that description already carries what is owed.

Where the seat gets hard

The Public Health Service — the institution itself, with its review structures — read its own rules as permitting the study for forty years. Whoever takes Searle’s seat must say whose reading of the practice governs, and why the institution’s own reading does not settle it. That is Exercise 9, not this one.

Part D — Spot the error

D1. How arguments go wrong in this lesson

Seven things students say, and the one mistake in each. Learn to name them: naming is what lets you find them in your own writing.

Exercise 8 — Name the mistake

Write exactly one of these four labels in each field: is read as ought (a fact is treated as if it were already a verdict), bridge claimed as fact (the normative premise is stated, but presented as something science or the facts established), definition mistaken for argument (a definition of “good” is made to do the work of a moral argument), gap seen where none is (a properly bridged argument is accused of jumping from is to ought). The first row is done for you.

The student writes	The mistake
“The doctors knew penicillin cured syphilis; that fact alone shows they were obliged to give it.”	is read as ought
“Neuroscience has now proven that we ought to maximise wellbeing.”
“‘Good’ just means ‘what promotes survival’, so caring for children is good — no further argument needed.”
“‘Punishments that don’t deter should not be used, so the death penalty should go’ — that’s Hume’s fallacy, it jumps from is to ought.”
“Every human society has punished theft, so punishing theft is right.”
“Consent is required for research — that is not a value, it is a medical fact, so the case against Tuskegee is purely empirical.”
“‘One ought not cause avoidable suffering; withholding penicillin did; so the doctors ought not to have’ — invalid, because Hume says you can never reach an ought.”

Rows 2 and 6 are the ones to watch in your own essays. The premise may be right — but it is a moral commitment, and calling it a fact hides the one line the other side is entitled to dispute.

Exercise 9 — Where does the rule need a judgment call?

The drill can find the bridge. It cannot tell you whether the bridge holds. Decide for each:

“Consent is necessary for research on human beings.” A student asks: is that premise true?

Yes — every ethics board now requires it, so it is settled No — it is not a fact, so it cannot be true Cannot say yet — the premise is a moral commitment, not a fact; that is where the argument moves, and it has to be defended ethically, not empirically

“These men are the doctor’s patients, so he ought to treat them.” Does Searle’s move settle the Tuskegee case?

Yes — “patient” encodes what is owed, and the ought follows No — the PHS sanctioned the study, so the practice permitted it Cannot say yet — it depends on which practice’s constitutive rules govern, and why the institution’s own reading of its rules does not settle the question

“Wrongness just is the unnecessary infliction of suffering.” Does the open question refute this?

Yes — “but is unnecessary suffering wrong?” still asks something, so the identity fails like any definition No — Moore wrote in 1903 and the argument is out of date Cannot say yet — it depends on whether identifying the moral property with the natural one dissolves Hume’s gap or merely relocates the normative premise inside the description of the facts, and the lesson leaves that contested

This is the philosophy

The answer key to Exercise 9 says cannot say yet three times. That is not a dodge. The drill has taken you to the one line the facts cannot settle — the bridging premise, the reading of the practice, the loaded description. Defending that line is the work; the drill can only tell you where it is.

Stage 3 — Back to the case

Exercise 10 — The retrieval checks

Two questions from your handout, from memory. Write your answer in the box in full sentences; the bar fills as your words match the model answer’s key words. Then compare.

“Natural selection has produced in us a tendency to care for our children. Therefore, it is natural — and right — to care for our children.” Name the fallacy this argument commits, and state the missing premise that would be needed to make it valid — and where that premise would have to come from.

State Moore’s Open Question Argument: the test it runs on any proposed definition of “good,” and what the question’s remaining open is supposed to show.

Your verdict, with the tools

Take out what you wrote at Stage 1. Now rewrite it in three sentences:

Your seat (the gap is real · the practice bridges it · there is no gap in the facts).
Your reason — and say where the obligation enters: name the bridging premise, or the constitutive rule and whose reading of it, or the feature of the facts that was already evaluative.
The bill your seat hands you. Gap-is-real: the minimal premise you would read to the 1955 board, which another doctor could reject — and what you would say to that doctor. Practice: which practice’s rules govern, when the institution read its own rules as permitting the study. No-gap: what made the moral content of the facts invisible to doctors who thought themselves reasonable.

Then check your own paragraph:

Did you say where the ought enters — premise, rule, or fact — rather than “obviously they should have stopped”? The facts alone are the one thing this lesson says cannot do it.
If you stated a premise, did you call it a commitment and not a fact?
Did you treat the three seats as rivals about what kind of failure Tuskegee was, not three roads to the same comfortable verdict?
Did you pay the bill in your own words, not the sheet’s?

Only now: compare with the three model paragraphs — two good ones, one bad one.

Done?

You can now:

tell a descriptive sentence from a normative one at a glance;
state Hume’s rule and supply the bridging premise any is–ought argument is missing;
run Moore’s open question on a proposed definition of “good”, and say what closed looks like;
reconstruct Searle’s five steps and name the constitutive rule that licenses the first move;
catch a bridging premise being passed off as a fact — in your own essays first;
say where, on your seat, the obligation to stop the study comes from — and what it costs you to say so.

Go back to your sheet.