Week 13 · Chapter

Chapter 13 — Science and Explanation

Critical Thinking Free sample edition

The module's primary reading · ~40–50 minutes · Objective 8 (with Objective 3 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 how to tell whether a claim about the world has been tested. A hypothesis (a proposed explanation still being tested) earns trust when it makes a prediction (what you should see if it is true) that could have failed and did not. A fair test compares a group that got a treatment with a control group (a group that did not), so that you can see what would have happened anyway. When several explanations compete, you choose the one that fits the evidence best and then keep testing it. You also learn the warning signs of claims that only look scientific.

Why you already care about this

Three claims reach you in one week. An ad for a cold supplement fills its page with 12 happy customers' stories. A seller says an energy bracelet works and that no test can measure its effect. A friend says the old dorm must be haunted, since no one has ever proven it is not.

Each claim asks you to believe something about how the world works. Each one also comes with something that feels like evidence: real people's stories, a confident seller, a dare that no one can answer. You have probably believed a claim like one of these, at least for a while. That is normal. Stories are vivid, and a claim no one has disproved can feel like a claim that must be true.

Since Week 1 you have tested arguments: their form, their words, their samples, their causes, their numbers, and their sources. Last week you asked where a claim comes from. This week you ask a sharper question: what would test it?

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

tell a hypothesis from a prediction and judge whether a claim is testable;
read a failed prediction and a passed prediction with the forms from Week 4;
explain what a control group, a placebo, and blinding add to a test;
choose the best of several rival explanations by fit, simplicity, scope, and consistency;
tell a scientific theory from a guess and use the warning signs of pseudoscience;
spot the appeal to ignorance and say who carries the burden of proof;
name the deep question beneath every inductive argument.

Carry this line with you: ask what would prove it wrong — not only what would prove it right.

Where we are

Already covered: Week 3 taught you validity and inductive strength, and Week 4 taught you modus tollens and affirming the consequent. Week 7 taught you the appeal to authority, Weeks 9 and 10 taught you to check samples and causal claims, Week 11 taught you to read numbers, and Week 12 taught you to check sources.
This week: you test explanations themselves: what a hypothesis predicts, what a fair comparison looks like, which rival explanation is best, and who must prove what.
How they connect: Week 4's two forms become the logic of a test, and Week 10's controlled comparison becomes the control group and the placebo.
Where we're going next: Week 14 turns the same tests inward, on the biases in your own reasoning.

Two earlier ideas carry most of the weight this week. From Week 4: in "if P, then Q", modus tollens reasons "not Q, so not P" and is valid, while affirming the consequent reasons "Q, so P" and is invalid. From Week 10: a controlled comparison holds other factors fixed, or spreads them evenly by random assignment, so that a difference in outcome can be traced to the one factor that differs. Keep both in view; this chapter puts them to work.

1. Ask what would prove it wrong: hypotheses and testability

Your laptop fan has started roaring. You guess that a browser tab is running something heavy. That guess is a hypothesis. Then you think: if a tab is the cause, closing the browser should quiet the fan. That is a prediction. You close the browser and listen.

Two words name what you did.

A hypothesis is a proposed explanation that is still being tested, such as the guess that a smoke alarm chirps because its battery is low.

A prediction is what you should observe if a hypothesis is true, stated before you look, so that the observation can count for or against the hypothesis.

The test you ran could have gone either way. The fan might have kept roaring. That possibility is what made it a test. A claim earns trust from evidence only if the evidence could have gone against it.

A testable claim is a claim that some possible observation could show to be wrong; a claim that fits every possible observation is not tested by any of them.

Worked example — the energy bracelet (illustrative). A seller says an energy bracelet "boosts your energy, and no test can measure its effect."

Find the claim. The bracelet boosts your energy.
Ask for a prediction. If it works, what should you observe? Wearers should feel or perform better than people wearing a look-alike bracelet.
Ask what would count against it. The seller has an answer ready: no test can measure the effect. Every possible result is ruled out in advance.
Say the verdict. The claim is untestable as stated, and an untestable claim is not a proven one.

In words: the seller has protected the claim from every test, so no observation can count for it either.

The philosopher Popper built a famous proposal on this idea. Falsifiability is the property of making predictions that some possible observation could show to be false, which Popper proposed as the test that separates science from non-science. He set it out in Logik der Forschung, first published in German in Vienna in the mid-1930s, and in his English edition, The Logic of Scientific Discovery, in 1959.

An honesty note: falsifiability is one influential proposal, not a settled test. Philosophers of science have criticized it, noting that many pseudosciences have been tested and shown false rather than being untestable. A claim can be testable and still be wrong. Use the question "what would show this wrong?" as a strong first check, not as a machine that sorts all of science.

Misconception check — "no one can disprove it" means it is proven. Students often hear "no test can show this is wrong" as a sign of strength. That is tempting, because a claim that survives every challenge sounds powerful. But a claim that no possible result could count against has not survived anything. It has avoided the test. "Unfalsifiable" never means "proven"; it means the claim tells you nothing you could check.

Memory hook: a real test is one you could fail.

2. Read the logic of a test: when a prediction fails and when it passes

Week 4 gave you two forms that look alike and behave very differently. Modus tollens is valid. Affirming the consequent is invalid. A scientific test uses one or the other, and knowing which tells you how much the result can carry.

Every test rests on a conditional: if the hypothesis is true, then the prediction comes true. The hypothesis is P, the antecedent. The prediction is Q, the consequent.

Worked example — the smoke alarm, a failed prediction (illustrative). Your hypothesis is that the kitchen smoke alarm chirps because its battery is low.

The prediction. If the battery is low, then a new battery will stop the chirping.
The test. You put in a new battery, and the chirping goes on.
Standard form.

P1: If the battery is low, then a new battery will stop the chirping.

P2: A new battery did not stop the chirping.

So,

C: The battery is not the cause.

Name the form. This is "if P, then Q; not Q; so not P": modus tollens, a valid form.

In words: if both premises are true, the conclusion must be true. A failed prediction counts against the hypothesis, and here it rules the battery out.

Worked example — the smoke alarm, a passed prediction (illustrative). Now suppose the chirping stops after the new battery goes in.

Standard form. P1: If the battery is low, then a new battery will stop the chirping. P2: A new battery did stop the chirping. So, C: the battery was low.
Name the form. This is "if P, then Q; Q; so P": affirming the consequent, an invalid form.
Find the counterexample. Taking the alarm down to change the battery may have reset it. In that case both premises are true and the conclusion may be false.

In words: a passed prediction supports the hypothesis without proving it. The support is inductive. It can be strong, and it grows when the hypothesis passes many different tests that could each have failed.

A caveat on the failed test, too. Modus tollens is valid, but its first premise can be false. Maybe the new battery was dead in the package. A careful tester checks that the test itself worked before treating a failed prediction as the end of a hypothesis.

Misconception check — a passed prediction proves the hypothesis. Students often reason, "it predicted the result, and the result happened, so it is true." That is tempting, because a correct prediction feels like a win. But that reasoning affirms the consequent: another cause could produce the same result. A passed test is real support, and it is never a guarantee. A failed test, by a valid form, counts against the hypothesis unless the test itself went wrong.

Memory hook: a miss can refute; a hit can only support.

3. Compare with a control: placebos, blinding, and the lone success story

Your roommate swears by a new pillow. "I slept great the first night!" Maybe the pillow helped. Maybe it was a quiet night, or a tired day, or the hope of a good night's sleep. One night with no comparison cannot tell those apart.

A single story like that has a name.

An uncontrolled observation is a single case or a set of cases, such as a customer testimonial, with no comparison group, so that it cannot show what would have happened without the treatment.

Three tools turn stories into a test.

A control group is a comparison group that does not get the treatment being tested, so that what happens without the treatment can be set beside what happens with it.
A placebo is a look-alike treatment with no active ingredient, given to a comparison group so that the effect of a treatment can be told apart from the effect of expecting one.
Blinding means keeping the people in a study, and often the people who measure the results, from knowing who got the treatment, so that expectations cannot tilt the measurements.

These build on Week 10's controlled comparison. Random assignment spreads other factors evenly between the groups. The placebo and the blinding make sure that expecting to feel better is spread evenly, too.

Worked example — the supplement ad and the trial (illustrative). An ad for a cold supplement prints 12 customer testimonials from people whose colds went away after taking it. Each story is one uncontrolled observation, with no comparison group.

The design. 120 adults with colds are randomly assigned, 60 to the supplement and 60 to a placebo pill that looks the same.
The blinding. Neither the adults nor the staff who check their symptoms know who got which.
The supplement group. Within a week, 51 of 60 in the supplement group feel better, and 51 ÷ 60 × 100 = 85 percent.
The placebo group. In the placebo group, 51 of 60 feel better, and 51 ÷ 60 × 100 = 85 percent.
Compare. 85 percent recovered in both groups, so the supplement group did no better than the placebo group.

In words: the 51 placebo takers who recovered could have written testimonials too. The ad's 12 stories show that colds end, not that the supplement ends them.

Here is the trial set out as a table.

The illustrative cold-supplement trial: adults in each group and how many felt better within a week
Group	Adults	Felt better within a week	Share who felt better
Supplement	60	51	85 percent
Placebo	60	51	85 percent

In practice (your tools). In a free spreadsheet, put each group on its own row. Type the number of adults in one column and the number who felt better in the next. In a third column, divide the number who felt better by the number of adults and multiply by 100. Label each column in words so the two rows can be compared at a glance.

Misconception check — one success story is a test. Students often take a vivid story as evidence that a treatment works. "My aunt took it, and she got better." That is tempting, because the story is real and the recovery happened. But most colds end within days whatever people take. Without a control group, a story cannot show what would have happened anyway. Ask "compared with what?" before you count a story as a test.

A limitation worth saying: a trial like this one can show that a treatment did no better than a placebo for these adults over this week. It cannot settle every question. A different dose, a different illness, or a much larger trial could tell more. A good test answers one clear question well.

Memory hook: no comparison, no conclusion.

4. Choose the best explanation: fit, simplicity, scope, and consistency

You come home and the kitchen floor is wet near the fridge. Did the dog knock over its water bowl? Did the freezer defrost? Is a pipe leaking? You look around: the bowl is full, the freezer is cold, and the drip comes from under the sink. You settle on the leaking pipe, because it explains what you see.

That everyday move has a long history.

Inference to the best explanation is reasoning from the evidence to the hypothesis that would best explain it, judged by fit with the evidence, simplicity, scope, and consistency with what else is known.

Abduction is Peirce's name for reasoning from a surprising observation to a hypothesis that would explain it, a form related to inference to the best explanation.

Peirce is named here with his word and no year. The modern phrase comes from Harman (1965), "The Inference to the Best Explanation", The Philosophical Review.

Four criteria do the judging.

Fit with the evidence: does the hypothesis account for the clues, and does any clue count against it?
Simplicity: does it explain the clues with one cause, or does it need a pile of extra assumptions?
Scope: how much of the evidence does it explain?
Consistency with what else is known: does it agree with what you already have good reason to believe?

Scope is how much of the evidence a hypothesis explains; a hypothesis with wider scope accounts for more of the observations without extra assumptions.

Worked example — the car that will not start (illustrative). A car will not start.

The clues. There are 3 clues: the engine only clicks, the dashboard lights are dim, and the headlights were left on overnight. The fuel gauge reads half full.
The rivals. There are 3 rival hypotheses: a dead battery, an empty fuel tank, and a failed starter motor.
The dead battery. A dead battery explains 3 of the 3 clues and fits the gauge.
The failed starter. A failed starter explains 1 of the 3 clues, the clicking, and leaves the dim lights unexplained.
The empty tank. An empty tank explains none of the clues, and the half-full gauge counts against it.
Judge. The dead battery wins on fit, simplicity, scope, and consistency with what you know about cars, the 4 criteria.
Test it. It is still a hypothesis, so you test it: if a jump-start gets the car going, the hypothesis gains support.

In words: the dead battery is the best of 3 rival explanations of the car's 3 clues, and a jump-start is the next test.

Here is the same comparison as a table.

Three rival hypotheses for the illustrative car, and which of its three clues each one explains
Hypothesis	Engine only clicks	Dashboard lights dim	Headlights left on overnight	The half-full fuel gauge
Dead battery	explains it	explains it	explains it	fits
Failed starter	explains it	leaves it unexplained	leaves it unexplained	fits
Empty fuel tank	leaves it unexplained	leaves it unexplained	leaves it unexplained	counts against it

The same reasoning works far from the garage. A store's weekly sales drop sharply. A rival store opening nearby, a price rise, and road work blocking the entrance are three rival hypotheses. If the drop began the week the road work started, and sales at the chain's other store held steady, the road work fits more of the clues (illustrative).

Misconception check — the best explanation is the proven one. Students often treat "the best of the rivals" as "the truth". That is tempting, because the best explanation can feel like a solved case. But inference to the best explanation is inductive. A rival you never thought of may fit the clues even better, and new evidence can overturn the winner. The best explanation is the one to test next, not the one to stop testing.

Memory hook: list the rivals, weigh the clues, then test the winner.

5. Tell a theory from a guess, and read the warning signs

A friend shrugs off a well-supported idea in science: "It's only a theory." The word sounds weak, like "only a hunch". In science it means nearly the opposite.

A scientific theory is a well-tested, broad explanation of many observations, as opposed to a guess or a hypothesis that is still being tested.

So the ladder runs from guess, to hypothesis, to theory, and a claim climbs it only by passing tests that could have failed.

Some claims borrow the look of science without the climb.

Pseudoscience is a claim or practice presented with the look of science that lacks the testing science requires, such as a product said to work in a way no test can measure.

The warning signs of pseudoscience are five signs that call for a closer look: no possible result could count against the claim, testimonials stand in for controlled tests, methods and data are kept secret, persecution is claimed in place of evidence, and the claim never changes despite contrary evidence.

Worked example — the bracelet's ad, checked for the signs (illustrative). The bracelet's ad says no test can measure its effect, fills its page with customer stories, and claims that big labs want to hide the truth.

No possible result could count against it. The ad says no test can measure its effect. Present.
Testimonials stand in for controlled tests. The page is customer stories, with no comparison group. Present.
Methods and data kept secret. The ad shows no method and no data, but it does not say it refuses to share them. Not shown either way.
Persecution in place of evidence. "Big labs want to hide the truth." Present.
No change despite contrary evidence. A single ad cannot show how a claim changes over time. Not shown either way.

In words: that is 3 of the 5 warning signs: no possible result could count against it, testimonials stand in for controlled tests, and persecution is claimed in place of evidence. Three signs are a strong reason to investigate, not a proof that the bracelet fails.

Models are taught as models here. The list of warning signs is a classroom tool for deciding where to look harder. It does not settle a real case on its own. A new idea with few tests yet is not pseudoscience for that reason alone, and a claim that shows a sign may still turn out to be true.

Misconception check — "theory" means a guess. Students often hear "it's only a theory" as a fair dismissal. That is tempting, because in everyday talk a theory is a hunch. But in science a theory is the top of the ladder: a broad explanation that has passed many tests. The weak word in science is "guess", and the word for a tested-but-not-settled idea is "hypothesis".

Memory hook: guess, hypothesis, theory — each rung is earned by a test.

6. Ask who carries the burden: the appeal to ignorance

A friend says the old dorm is haunted. You ask how they know. "Prove it isn't." The conversation has quietly flipped. They made the claim, and now you are asked to disprove it.

That flip is the last fallacy in the course's set.

The appeal to ignorance (ad ignorantiam) is the fallacy of concluding that a claim is true because no one has shown it false, or false because no one has shown it true.

The burden of proof is the duty of the person who makes a claim to offer support for it; a lack of disproof does not shift that duty to the listener.

Locke (1690) named the ad ignorantiam argument in An Essay Concerning Human Understanding, the same work in which Week 7 met his name for the appeal to authority.

Worked example — the haunted dorm (illustrative). "No one has ever proven that the old dorm is not haunted, so it must be haunted."

Standard form. P1: No one has ever proven that the old dorm is not haunted. So, C: The old dorm is haunted.
Ask what supports C. The only support offered is a lack of disproof.
Name it. The passage commits the appeal to ignorance (ad ignorantiam).
Place the burden. The burden of proof lies with the person claiming the dorm is haunted.

In words: a lack of disproof is not evidence for a claim, so the passage gives no reason at all to think the dorm is haunted.

The passage tally closes here. The haunted dorm is 1 Week 13 passage, and 19 passages keyed through Week 12 + 1 = 20 passages keyed through Week 13, which is the whole fallacy set of 20.

Every fallacy in this course has a non-fallacious neighbor, and this one does too. Sometimes "we looked and found nothing" is good evidence.

Worked example — the careful search (illustrative, discussed and never keyed). An inspector checks every beam in a building for termite damage, finds none, and concludes the building probably has no termites.

Ask whether the search could have found it. Termite damage shows in the beams, and every beam was checked.
Judge. The search would likely have found damage if it were there, so the conclusion is reasonable, though not certain.

In words: absence of evidence counts as evidence when someone looked where the evidence would be. The haunted-dorm passage names no search at all.

Misconception check — a lack of disproof is proof. Students often accept "you can't prove it's false" as a win for the claim. That is tempting, because an unanswered dare feels like a win for the person who made it. But many false claims cannot be quickly disproved. Ask who made the claim, and ask them for support. Then ask whether anyone searched where evidence would be.

Memory hook: whoever claims it carries it.

7. Face the deep question: Hume's problem of induction

Every morning you expect the sun to rise, the floor to hold, and your coffee to taste like coffee. You have never checked tomorrow. You expect it to resemble the past because the past has been reliable. But why should the past be a guide to the future?

That question is old, and it sits under everything in the second half of this course.

The problem of induction is Hume's question of what justifies expecting the future to resemble the past, the expectation that every inductive argument leans on.

Hume raised the problem of induction, asking what justifies expecting the future to resemble the past, in A Treatise of Human Nature (1739 to 1740) and in shorter form in An Enquiry Concerning Human Understanding (1748). Those dates are taught in words here, and no quiz asks for them.

Worked example — finding the expectation under this week's reasoning (illustrative). Look back at three moves from this chapter.

The passed test. The smoke alarm stopped chirping after a new battery, so you trust the battery hypothesis next time. That trust assumes alarms will behave as they did.
The trial. 85 percent recovered in both groups in the trial, and you expect a similar result in other adults. That expectation assumes the future will resemble the trial.
The best explanation. A dead battery explained the car's clues, because dead batteries have caused such clues before.

In words: each step is inductive, and each one leans on the expectation that the world will keep working as it has.

Hume's question does not tell you to stop reasoning this way. Philosophers still disagree about the best reply, and this course takes no side. What the question does is explain why inductive conclusions are never guaranteed. A strong, cogent argument gives good reason to believe its conclusion, and that is the most any inductive argument can do.

Misconception check — if induction cannot be proven, it is worthless. Students who meet Hume's question sometimes conclude that every inductive argument is as good as any other. That is tempting, because the question has no settled answer. But the problem asks why induction works, not whether some inductive arguments are better than others. A large, random sample still beats one anecdote, and a controlled trial still beats a page of testimonials.

Memory hook: Hume's question is under every inductive argument — strong arguments still beat weak ones.

8. Put it together: one science check

You now have four questions, and they fit on an index card. Run them on any claim about how the world works.

What does it predict, and could any observation show it wrong?
Compared with what? Was there a control group, a placebo, and blinding?
What are the rival explanations, and which fits the evidence best?
Who carries the burden of proof, and is a lack of disproof offered as proof?

Worked example — the whole check on this week's claims (illustrative). Run the four questions on the claims you met in this chapter.

The bracelet. The seller rules out every test, so the claim is untestable as stated, and its ad shows 3 of the 5 warning signs.
The supplement. The trial's 85 percent in both groups shows the supplement did no better than a placebo, and the ad's 12 testimonials have no comparison group.
The car. The dead battery is the best of 3 rival explanations of the car's 3 clues, and a jump-start tests it.
The dorm. The haunted-dorm passage commits the appeal to ignorance, and the burden of proof lies with the person making the claim.

In words: the bracelet's claim is untestable as stated. A failed prediction refutes by a valid form, while a passed one only supports. The trial's 85 percent in both groups shows the supplement did no better than a placebo. The dead battery is the best of 3 rival explanations, and the haunted-dorm passage commits the appeal to ignorance.

Notice what the check does not do. It does not show that the bracelet cannot work, that no cold remedy helps, or that the dorm is not haunted. It shows how much support each claim has. A claim that fails the check is not thereby shown false. It is shown to be unsupported so far.

Misconception check — a claim that fails the check is false. Students often decide that a claim with no good test behind it must be wrong. That is tempting, because the claim was oversold. But "not yet supported" and "shown false" are different verdicts. The trial counts against the supplement because the supplement was tested and did no better. The bracelet was never tested at all, so the honest verdict is "no evidence either way, and a seller who blocks the test".

Memory hook: predict, compare, rival, burden — four questions, one card.

Key terms

hypothesis — A proposed explanation that is still being tested, such as the guess that a smoke alarm chirps because its battery is low. (first used: 1. Ask what would prove it wrong: hypotheses and testability)
prediction — What you should observe if a hypothesis is true, stated before you look, so that the observation can count for or against the hypothesis. (first used: 1. Ask what would prove it wrong: hypotheses and testability)
testable claim — A claim that some possible observation could show to be wrong; a claim that fits every possible observation is not tested by any of them. (first used: 1. Ask what would prove it wrong: hypotheses and testability)
falsifiability — The property of making predictions that some possible observation could show to be false, which Popper proposed as the test that separates science from non-science. (first used: 1. Ask what would prove it wrong: hypotheses and testability)
uncontrolled observation — A single case or a set of cases, such as a customer testimonial, with no comparison group, so that it cannot show what would have happened without the treatment. (first used: 3. Compare with a control: placebos, blinding, and the lone success story)
control group — A comparison group that does not get the treatment being tested, so that what happens without the treatment can be set beside what happens with it. (first used: 3. Compare with a control: placebos, blinding, and the lone success story)
placebo — A look-alike treatment with no active ingredient, given to a comparison group so that the effect of a treatment can be told apart from the effect of expecting one. (first used: 3. Compare with a control: placebos, blinding, and the lone success story)
blinding — Keeping the people in a study, and often the people who measure the results, from knowing who got the treatment, so that expectations cannot tilt the measurements. (first used: 3. Compare with a control: placebos, blinding, and the lone success story)
inference to the best explanation — Reasoning from the evidence to the hypothesis that would best explain it, judged by fit with the evidence, simplicity, scope, and consistency with what else is known. (first used: 4. Choose the best explanation: fit, simplicity, scope, and consistency)
abduction — Peirce's name for reasoning from a surprising observation to a hypothesis that would explain it, a form related to inference to the best explanation. (first used: 4. Choose the best explanation: fit, simplicity, scope, and consistency)
scope — How much of the evidence a hypothesis explains; a hypothesis with wider scope accounts for more of the observations without extra assumptions. (first used: 4. Choose the best explanation: fit, simplicity, scope, and consistency)
scientific theory — A well-tested, broad explanation of many observations, as opposed to a guess or a hypothesis that is still being tested. (first used: 5. Tell a theory from a guess, and read the warning signs)
pseudoscience — A claim or practice presented with the look of science that lacks the testing science requires, such as a product said to work in a way no test can measure. (first used: 5. Tell a theory from a guess, and read the warning signs)
warning signs of pseudoscience — Five signs that call for a closer look: no possible result could count against the claim, testimonials stand in for controlled tests, methods and data are kept secret, persecution is claimed in place of evidence, and the claim never changes despite contrary evidence. (first used: 5. Tell a theory from a guess, and read the warning signs)
appeal to ignorance (ad ignorantiam) — The fallacy of concluding that a claim is true because no one has shown it false, or false because no one has shown it true. (first used: 6. Ask who carries the burden: the appeal to ignorance)
burden of proof — The duty of the person who makes a claim to offer support for it; a lack of disproof does not shift that duty to the listener. (first used: 6. Ask who carries the burden: the appeal to ignorance)
problem of induction — Hume's question of what justifies expecting the future to resemble the past, the expectation that every inductive argument leans on. (first used: 7. Face the deep question: Hume's problem of induction)

Summary

A hypothesis is a proposed explanation; a prediction is what it says you should observe.
A testable claim could be shown wrong by some possible observation.
A failed prediction refutes by modus tollens; a passed one only supports.
Testimonials are uncontrolled observations; a fair test needs a control group.
A placebo and blinding separate a treatment's effect from the effect of expecting it.
Judge rival explanations by fit, simplicity, scope, and consistency, then test the winner.
A scientific theory is well tested; the warning signs of pseudoscience call for a closer look.
A lack of disproof is not proof; the burden lies with the person making the claim.
Hume's problem of induction explains why no inductive conclusion is guaranteed.

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 phone will not charge (illustrative). Your hypothesis is that the cable is broken, so you predict that a new cable will charge the phone. You try a new cable, and the phone still does not charge. Put the reasoning in standard form, name the form, and say what you may conclude. Then say what form the reasoning would take if the new cable had worked and you concluded the old cable was broken.
A sleep-tea brand's website posts 30 reviews from people who say they slept better after drinking it (illustrative). Explain why the 30 reviews prove little, and name three features a fair test of the tea would add.
A houseplant's lower leaves are turning yellow (illustrative). The clues: the soil is soggy, the pot has no drainage hole, and the yellowing started after a new watering schedule. You check the leaves closely and find no insects. Three rival hypotheses are overwatering, too little light, and pests. Which is the best explanation, and why? Name one test that could support it.
Which of these passages commits the appeal to ignorance, and why is the other reasonable? (a) "No one has proven this new energy drink harms anyone, so it must be safe." (b) "The lifeguard swept the whole pool floor with an underwater camera and found no lost ring, so the ring is probably not in the pool." (Both illustrative.)

Answers (worked reasoning — read after attempting)

P1: If the cable is broken, then a new cable will charge the phone. P2: A new cable did not charge the phone. So, C: The broken cable is not the cause. This is modus tollens, "if P, then Q; not Q; so not P", a valid form, so you may rule out the cable, as long as the new cable itself works. If the new cable had worked and you concluded the old cable was broken, the reasoning would be "if P, then Q; Q; so P", which affirms the consequent and is invalid. A loose plug that the swap pushed back in could also explain the result, so a passed test only supports the hypothesis.
Each review is an uncontrolled observation: there is no comparison group, so the reviews cannot show how those people would have slept without the tea. People who slept badly may also be less likely to post. A fair test would add a control group that drinks a look-alike tea with no active ingredient (a placebo) and random assignment of who gets which. It would also add blinding, so that neither the drinkers nor the people measuring sleep know who got the real tea.
Overwatering is the best explanation. It fits all three clues: soggy soil, no drainage hole, and yellowing that began with the new watering schedule. Pests are unlikely, because a close check found no insects. Too little light explains none of the three clues and needs an extra assumption, such as the plant having been moved. One test: water less and give the pot a drainage hole; if new leaves stop yellowing, the hypothesis gains support, though that passed test supports it without proving it.
Passage (a) commits the appeal to ignorance. It concludes "safe" from a lack of disproof, when the burden of proof lies with whoever claims the drink is safe. Passage (b) is reasonable: the lifeguard searched the whole floor with a camera, so the search would likely have found the ring if it were there. Absence of evidence counts as evidence only when someone looked where the evidence would be.

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, in Bias and Decision-Making, the science check turns inward as a test of your own reasoning, starting with confirmation bias and a classic rule-discovery experiment.

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