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A count of people settles a question about people, and settles nothing about the world unless each of them looked.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
You will decide whether the number of people who believe something is a reason to believe it, by asking what the claim is about and what each of the people counted actually did. You will mark the step that counts a crowd repeating one rumor, leave alone the step that counts people who each checked, and say why the size of the number never decides the question.
Every house on Fell Row now says the tap water is unsafe to drink.
The first person to say so noticed the water looked cloudy one morning in June.
Nobody else has looked at their own tap, and nobody has had the water tested.
On Mill Lane, forty households were each sent a test strip and each dipped it themselves.
Thirty-eight of the forty strips came back clear.
The city council also asked both streets which evening they would rather the water be turned off for the repair.
Sixty-one of the eighty households answered Tuesday.
You can ask what a claim is resting on. This lesson asks it of a particular kind of support — a number of people — and the answer turns out to depend entirely on what those people did before they spoke.
| Term | What it means |
|---|---|
| Appeal to popularity | Treating widespread belief as sufficient proof of a claim. |
| Independent corroboration | Support with a separate evidential basis rather than another repetition of one source. |
| Population | The group a count or generalization is intended to describe. |
| Appeal to ignorance | Treating a lack of proof or disproof as sufficient support for the opposite verdict. |
| Search coverage | The places, cases, or records an inquiry actually examined. |
Read the three counts in the consultation. Every one of them is a number of people who all say the same thing, and the city council has to act on them tonight.
Somebody at that meeting will say the same thing about all three: you cannot settle anything by counting heads. Somebody else will say the opposite about all three: these are the people who live here, and they have spoken. Both of those positions are easy to hold and both are wrong about at least one of the counts — which is what makes this worth an hour.
The whole of the work is the middle question, asked separately of each count: what is this claim about, and what did each person counted actually do? Fell Row, Mill Lane and the Tuesday question answer it three different ways.
Counting people is sometimes exactly the right evidence and sometimes no evidence at all, and the number is never what decides which.
When the count is the evidence. Some claims are about people. What would the class rather do is settled by asking the class. What is the back field called is settled by what the people there call it. There is nothing else to consult.
When the count is evidence about the world. If each person looked separately, each is an observation. Forty people who tasted the soup are forty tastings, and forty tastings are strong evidence about the soup.
When the count is worth nothing. If nobody checked, the number is the number of people who heard, and hearing is not knowing. Everyone in the year says the test is on chapter four; nobody has seen the paper; so the year knows exactly what the first person to guess knew.
Another way: picture
Draw arrows from the thing itself to each person. If every person has their own arrow, the count is a count of observations. If all the arrows run from one person to the rest, you have drawn a rumor, and the shape is the same however many people you add along the bottom.
Another way: steps
Three questions:
| The count | What it is worth |
|---|---|
| Forty people each tasted the soup and all said it was salty | forty observations |
| Forty people were told the soup was salty and all repeat it | one observation |
| Forty people were asked whether they like salty soup | forty answers, and the question was about them |
Three arguments, one number, and three completely different amounts of evidence. Anybody who decided by the number would grade all three the same.
There is a fourth case worth naming: forty people who each checked but all used the same broken thermometer. That is forty observations with one fault running through all of them, which is why did they check separately and did they check the same way are both worth asking.
Before evaluating a count of opinions, write three labels: the question asked, the group counted, and the conclusion proposed. A survey asking 23 club members which evening they prefer supplies evidence about those members' stated preferences. If 19 choose Thursday, it is accurate to report that 19 of the 23 preferred Thursday in that survey. It is not accurate to report that every member preferred Thursday. Nor does the count by itself establish that Thursday is cheapest, most accessible, or best for every purpose.
The distinction matters because some conclusions are about preferences and others are about facts independent of those preferences. A majority can determine a decision under an agreed voting rule. It does not determine whether a building's wiring is defective. If the question is which name residents commonly use for a lane, usage is relevant evidence about the name. If the question is whether the lane floods after heavy rain, observations and records of flooding are relevant. The appropriate evidence follows the claim, not a universal rule that crowds are always right or always wrong.
Even a preference count needs careful interpretation. Were all eligible people asked? Did each person answer once? Was the wording neutral? Did nonresponders have different constraints from responders? A complete count of the 23 people present does not automatically represent the 40 members who stayed away. These questions do not dismiss the answers already received. They identify the population to which a conclusion may reasonably extend. Report the scope before deciding whether a wider generalization is justified.
Now consider an apparent factual consensus. Twelve people say a footpath is blocked. If each walked the relevant section separately and observed a fallen tree, their reports may provide substantial corroboration. If all twelve read the same unverified message, there is only one underlying source of that message. Repetition might accurately convey that source's statement, but it does not add twelve independent checks of the path. Trace the reports backwards until you find the observations or records they rely on.
Independence is about the evidential basis, not simply whether the people have ever spoken to one another. Two observers can know about an earlier report and still make useful separate measurements. Conversely, people working in different rooms can all inherit the same faulty data file. Ask which possible errors they share. If every measurement used the same miscalibrated thermometer, agreement does not remove that instrument error. Diverse methods or separately checked instruments can provide a different kind of corroboration.
Do not assume that an expert consensus is just an opinion poll. Agreement among relevant specialists may summarize extensive evidence, criticism, and replication. Its value depends on those processes, not merely the number of signatures. A classroom exercise that exposes a rumor does not establish that every shared conclusion is a rumor. The useful habit is to ask what produced the agreement and what evidence can be inspected, rather than treating unanimity itself as either proof or disproof.
A second kind of crowd claim rests on silence: 'Nobody has shown that the rumor is false, so it is true.' This is an appeal to ignorance when the absence of a disproof is treated as sufficient proof. The reverse form can also fail: 'Nobody has proved it true, so it is false.' A lack of decisive evidence may leave a claim unsettled. It does not automatically select whichever answer the speaker prefers. State the actual evidential result: the available inquiry has not settled this question.
Silence at a meeting is especially ambiguous. People might agree, feel uncertain, lack information, fear embarrassment, or have no opportunity to speak. Unless the meeting uses a clearly understood decision procedure, no objections is weaker than an explicit recorded vote. Even a properly recorded unanimous vote establishes the result under that procedure, not every factual assumption behind the proposal. A committee can unanimously adopt a forecast that later proves wrong.
However, absence of evidence can sometimes be evidence of absence. The relevant question is whether a suitable search would probably have detected the thing if it were present. If a small empty box is opened under good light and carefully inspected, finding no coin is evidence that there is no coin in that box. If nobody has ever inspected a locked warehouse, the absence of a reported coin tells us much less. The difference lies in the search's opportunity and sensitivity, not in a blanket rule about negative evidence.
Work through a library example. An authenticated current catalog and a complete shelf check find no copy of a particular book in a small branch. That supports the limited conclusion that the branch has no available copy within the checked locations and records. It does not show that the book has never existed or that no other branch owns it. An effective search supports a conclusion matched to its coverage. A search that overlooks storage rooms or recent returns requires a narrower statement still.
This connects back to counting people. Ten people saying 'I have heard no complaint' may all rely on the same unopened inbox. Their agreement adds little evidence that customers had no problems. A properly functioning complaint system with accessible reporting channels, regular monitoring, and known coverage makes a zero count more informative. Even then, some people may choose not to complain. A report should distinguish no recorded complaints from no dissatisfied customers.
To check an argument from silence, name the proposed claim, the search or reporting process, what would count as detection, and the limits of coverage. Then ask what follows from a failure to detect. Sometimes the answer is a justified narrow negative conclusion. Sometimes it is simply that the matter remains unknown. This method avoids both gullibility about unrefuted rumors and the equally mistaken insistence that missing evidence can never tell us anything.
A fictional community center must choose an evening opening schedule. A questionnaire completed by all 30 regular club members records 21 votes for Tuesday and 9 for Thursday. Separately, 60 social-media comments claim the heating system cannot run on Tuesday. All 60 link to the same undated post. A maintenance technician supplies the current control schedule, which shows Tuesday operation is available from five until nine.
The preference survey supports a precise claim: 21 of the 30 responding club members preferred Tuesday. Under a simple majority rule for that group, Tuesday wins. The count does not establish the preferences of other center users who were not part of the club survey. Nor does it establish the technical limits of the heating system. Those are separate questions requiring separate evidence.
The 60 comments do not represent 60 tests of Tuesday heating. They trace back to one undated source. The current schedule is directly relevant to the operating question, although a schedule is still distinct from a guarantee that every component is functioning. The committee should preserve that distinction if it commissions a practical check.
Suppose a member adds, 'Nobody has proved the old post wrong, so we must accept it.' That reverses the evidential task. A claim does not become established merely because a particular refutation has not been supplied. Here the dated schedule already provides relevant contrary information. The minutes can record the club preference, identify the repeated source behind the rumor, and ask the technician to clarify current operation. Counting, tracing sources, and checking the system each answer a different part of the decision.
Rejecting every count of people. Elections, surveys, taste tests and dictionaries are all counts of people, and all of them are evidence about what they are counts of.
Taking a big number as a big reason. Two hundred people repeating one sentence are one source with two hundred echoes.
Taking age for evidence. People have always said so is a fact about how long the saying has been around. It adds no observations to the pile.
Record the group counted.
All 23 members answered the question.
The result concerns this identified group.
Record the responses.
19 chose Thursday; 4 chose another day.
The count preserves disagreement rather than describing unanimity.
State the supported preference claim.
A majority of these members preferred Thursday.
19 exceeds half of 23.
Apply a stated decision rule if one exists.
Under simple majority choice, Thursday is selected.
An agreed voting rule can turn preferences into a group decision.
Limit the factual implications.
The vote does not establish that Thursday is cheapest.
Costs are not determined by the preference count alone.
Name the claim being repeated.
The footpath is blocked by a fallen tree.
This is a claim about the path rather than about popularity.
Trace the reports to their source.
All 12 people read one unverified message.
The reports share an evidential origin.
Count what has actually been added.
12 repetitions; no additional direct path checks stated.
Repeating a source does not independently verify its claim.
Compare a separate observation.
A walker visits the relevant section and photographs a fallen tree.
A separate observation can add evidence about the actual path.
Report the distinction.
The photograph is new evidence; the repetition count describes circulation.
The two counts concern different aspects of the situation.
State the first negative report.
Nobody has reported a coin in a locked warehouse.
The report does not state that a suitable search occurred.
Identify the missing detection opportunity.
The warehouse has not been inspected.
A coin could be present without generating any report.
Limit the first conclusion.
Coin presence remains unsettled by that silence.
No report is not a reliable test when nobody could detect the object.
State the second search precisely.
A small empty box is opened and inspected under good light.
The search covers the relevant space with a plausible chance of detecting a coin.
Record the negative result.
No coin appears anywhere in that box.
The result follows an effective inspection rather than mere inattention.
Draw the appropriately bounded conclusion.
Evidence supports no coin in this box, not no coin anywhere.
A negative search result supports only a conclusion within its coverage.
State what the friends claim.
The phone charges fully in ten minutes.
Charging time is an empirical claim that can be checked under specified conditions.
Trace the four reports.
All four copied the same post; none timed a charge.
Their agreement adds no separate timing measurement.
Name a useful next check.
Four arguments that count people. Match each to whether the count settles the question asked.
| The count settles it | The count does not settle it | |
|---|---|---|
| Nineteen of the twenty-three said Thursday, so Thursday is what the class would rather do. | ||
| Everyone round here says the bridge is safe, so the bridge is safe. | ||
| Everybody at the club calls the back field the paddock, so that is what it is called. | ||
| Most people think the tide is lowest at noon, so it is lowest at noon. |
All 30 regular club members answer a survey: 21 prefer Tuesday and the remainder Thursday. Separately, 60 comments copy one undated heating post. Complete the scope check.
Find the Thursday response count.
Total respondents minus Tuesday supporters = thursday members.
The two stated options exhaust this survey's responses.
Record the preference population actually counted.
The survey covers population regular members.
It does not automatically describe other center users.
Trace the comments to their underlying source.
The 60 comments copy sources post.
Repeating one source does not create sixty separate equipment checks.
*Almost everybody at the club calls the back field the paddock. So the back field is called the paddock.* Is the count of people a good reason here?
All 23 club members answered a preference survey: 19 chose Thursday. Separately, a checked booking sheet shows Thursday hire costs 80 credits and Tuesday hire costs 60. Construct only the support links justified by these sources.
This task has no paper form; do it on a device.
Twelve residents repeat one message saying the path is flooded; none visited it. A walker separately visits the path today and supplies a dated photograph of floodwater. Draw the supported connections to the claims shown. Repetition by itself does not add a path inspection.
This task has no paper form; do it on a device.
Four counts, from a hospital waiting room rather than a village. For each, say whether the people counted checked anything themselves, and then whether the count is evidence for the claim.
| How many people | Did each of them check for themselves? | Is the count evidence? | |
|---|---|---|---|
| Thirty patients who each waited in the room say it was over an hour | 30 | ||
| Two hundred people repeating what the local paper printed about the wait | 200 | ||
| Twelve nurses who each read their own thermometer say the ward is cold | 12 | ||
| Ninety people who all heard it from the same porter say the lift is broken | 90 |
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A small branch library checks its current catalog, every shelf, and the returns trolley for a particular book, finding no copy. Another branch has not been checked. Separately, an online rumor about the book's author has neither evidence nor a disproof. Construct only the supported link; do not treat every unrefuted rumor as true.
This task has no paper form; do it on a device.
You can say when a count of people is the right evidence and when it is a rumor with echoes, and you can explain why two hundred people repeating one article are worth one article. Tell somebody why a vote settles what a class would rather do and not whether it is a good idea. Next: answering the position somebody actually holds.
15. A phone claim repeated four times, step 3
Find the original test conditions or conduct a suitable timed test.
A relevant measurement addresses the charging claim more directly than counting repetitions.