Logic and Scientific Thinking

Final Review

Bogdan G. Popescu

bgpopescu@tec.mx

Tecnologico de Monterrey

Five Skills

By the end of the course, you can:

Reconstruct arguments — including the premises a speaker never states.
Name the fallacy — and say what would decide the question.
Take apart persuasion — the appeals, and where misinformation fails.
Evaluate evidence: correlation, samples, polls, sources.
Apply it all to a real specimen — cold, in the speaker’s own words.

Five Weeks

16 sessions · 11 readings · two exams · five weeks.
Readings from Plato to 2019. None of it filler.
A logic course usually takes a semester.
Half of you said the pace was too fast. Fair.
That was the design, not an accident.
Hence the repetition, the drills, and today.

NARRATION: Say the numbers plainly and do not apologise for them — five weeks carrying a semester is a structural fact about this course, not a failing. On the second bullet, name a few out loud so the span lands: Plato and Aristotle, Hume twice, Schopenhauer — then Huff on statistics, a 1937 propaganda manual, Sagan, Kahneman. Twenty-four centuries, eleven pieces, each one carrying a session. Say why that mix is deliberate: the classics are where these problems were first stated clearly, and the moderns are where they show up in the world the students actually live in. Nobody assigned a chapter to fill a week. Then own the survey result out loud: twelve of the twenty-four who answered said the pace was too fast. Students respect being told the truth about a complaint they made far more than they respect hearing it ignored. Then say what was done with it, because that is the part that is actually to your credit: the repetition, the end-of-session drills, and this whole session, which is the slow pass over everything. They told us the in-class exercises were what helped most — fifteen of twenty-four named them — so today is seven drills and not a lecture.

One Reading, One Tool

Every reading was the source of one session’s instrument:

Sagan — the checklist you run before believing a claim. (S1)
Plato — why listing examples never says what a thing is. (S2)
Hume, twice — is/ought, then why induction never proves. (S3–4)
Vaughn — the words for grading: valid, sound, strong. (S5, S7)
Kahneman — why a good story beats a good argument. (S6)
The same holds for Sessions 10–13. Work out which.

NARRATION: This slide exists because of the mid-course survey. Four students wrote, in different words, that they could not see how a reading related to its session — “no les veo tanta relación” — and one asked outright for time on the readings and their connection to the class. That is a fair complaint about something that was never said out loud, so say it now: nothing was assigned to fill a week. One reading, one instrument, every time.

Then make the point the span is for. The list runs from Plato to 2019, and that is the argument, not the decoration: Aristotle names the three appeals, a 1937 propaganda pamphlet shows them industrialised for radio, and Kahneman shows why they work on us at all. Huff’s sampling problem from 1954 is the same problem as an online poll in 2019. Twenty-four centuries and the moves do not change — which is evidence that they are structural, not fashions. A course of only modern readings would leave that invisible.

The last bullet is deliberate: do NOT supply the four pairings for Sessions 10 to 13. That is exactly what Part G asks, and Drill 6 is where they work it out.

What You Can Do Now

Read a study and say what would settle it.
Name the move in words the speaker would recognise.
Tell a bad argument from a false conclusion.
Not logic class: the next contract, diagnosis, viral claim.

Exam Format

Closed book, individual, in class.
Covers Sessions 10–13.
Tests the concepts, the vocabulary, and their application to short cases.
The required readings for those sessions are examinable.

Session 14 is a workshop and is not examined. Neither is anything from the midterm.

Grading

Component	Weight
Midterm exam	30%
Final exam	30%
Reading	20%
Attendance	10%
Participation	10%

Two exams, 60% together — and neither one is cumulative.

Reading 20% — tested on the exams. Attendance and participation 20% — earned in the room.

Teaching Evaluation

forms.gle/3VzPTovn8FxbWSUG9

Part 1: The Whole Toolkit

Where the Catalogue Stands

Family	Fallacies	Where
Faulty reasoning	false cause · circular reasoning	S7
Misused sources	ad hominem · appeal to authority	S7
Distorted claims	straw man · red herring · slippery slope · equivocation · false dilemma	S10
Emotional appeals	appeal to fear · appeal to pity · bandwagon	S10

Eight are examinable. The first four were the midterm and do not come back.

Distorted Claims

Straw man — answers a weaker version nobody argued for.
Red herring — changes the subject to something easier.
Slippery slope — asserts a chain to disaster without defending any link.
Equivocation — one word, two senses, sliding between them.
False dilemma — offers two options when more exist.

Emotional Appeals

Appeal to fear — accept this or something terrible happens.
Appeal to pity — accept this because someone is suffering.
Bandwagon — accept this because everyone else has.

An emotion in an argument is not automatically a fallacy. The question is whether the feeling is doing work that a reason should be doing.

The Two Guards

The fallacy fallacy — naming the move does not refute the conclusion.
The verbal dispute — not every disagreement is substantive.

A bad argument for a claim leaves the claim exactly where it was. It still might be true.

Three Ways an Argument Fails

Where it breaks	What to say
False premise	that claim is not true
Misleading scope	every word is true, and the comparison is missing
Hidden link	the step carrying the conclusion is never stated

Middle row is the hard one. “Complaints rose 300%” is arithmetic — until you ask 300% of what?

The Gish Gallop

Four checks — ask all four before you use the name:

Who — name the speaker and the setting.
Speed — faster than any rebuttal could keep up with.
Strategy — the quantity IS the point.
Weakness — several claims would not survive checking.

The defence is not to answer everything. Pick one claim, demand its evidence, and say why you picked it.

Ethos, Pathos, Logos

Appeal	The speaker offers	Grounded when
Ethos	who I am	you can check the credential and the grounds
Pathos	what you feel	the feeling is real and comes with something you can check
Logos	the reasoning	the steps are given and checkable

One test for all three rows: a grounded appeal hands you something you could go and check — a record, a number, a plan. An ungrounded one hands you a feeling, or a name, and asks you to stop there.

What Grounded Looks Like

Session 12’s own pairs — same appeal, opposite verdict:

	Grounded	Ungrounded
Ethos	the cardiologist who shows how she knows	the rented white coat in the advert
Pathos	a real danger — plus what to do	fear doing all the work
Logos	“here is the calculation — check it”	“studies show…”

Read down the Ungrounded column: a name, a feeling, a gesture at evidence. Not one of them hands you anything you could go and look at.

Four Explanations of a Correlation

Ignore the colour and the two clouds become one upward line. The correlation is real. The cause is the weather.

The Four, In Order of Habit

X causes Y — the reading everyone reaches for first.
Reverse causation — Y causes X. Ask which came first.
Confounder — a third thing causes both. Name it.
Chance — small numbers, or enough tries that a streak was coming.

Only random assignment or control licenses number 1, because it is the only thing that removes 2, 3 and 4 at once.

Reading a Study

Four questions, in this order:

Who was studied? — who is in the sample, who chose them, and who is missing?
What was actually measured? — is the number the thing, or a proxy for it?
Compared to what? — what tells us the programme made the difference?
How was the result selected? — the planned test, or the one that looked best?

Who? What? Compared to what? How was it selected?

Funding is a reason to look harder at the method. It is not, by itself, a refutation.

The Readings

Schopenhauer, A. (c. 1831/1896). The art of controversy (T. B. Saunders, Trans.). Swan Sonnenschein. Required — S10.
Institute for Propaganda Analysis. (1937). How to detect propaganda. Propaganda Analysis, 1(2), 5–8. Required — S11.
Aristotle. (n.d.). Rhetoric, Book I, Chs. 1–2. Required — S12.
Huff, D. (1954). The sample with the built-in bias. In How to lie with statistics (Ch. 1). W. W. Norton. Required — S13.

Part 2: Practice

Six drills. Answers on the slide immediately after each.

Drill 1 — Name the Move

1. P1: I am proposing a bike lane on Constitución.
P2: So you want a city where nobody is allowed to own a car.

2. P1: She raised the safety inspection at the meeting.
P2: I would rather talk about who leaked it to the press.

3. P1: Can I park here?
P2: The sign says fine for parking here, so it is fine to park here.

4. P1: Should we let one student submit late?
P2: If we let one submit late, by December nobody will hand anything in on time.

5. P1: He broke the rule, so he should be disqualified.
P2: He trained eight years for this.

Drill 1 — Answers

	P2’s move	Why
1	straw man	answers “ban all cars”, which nobody proposed
2	red herring	the inspection is abandoned, not misrepresented
3	equivocation	fine = a penalty, then fine = acceptable
4	slippery slope	a chain to disaster, no link defended
5	appeal to pity	the training is real and irrelevant to the rule

1 vs. 2 is the pair worth remembering: straw man deforms the claim, red herring drops it.

Part A — On the Exam

A1. “Either we raise the fare or the metro stops running.”
A2. “Four of the six departments have already adopted it, so we should too.”

Write only this:

A1 – false dilemma A2 – bandwagon

A name each. No sentences, no reasons — and each of the eight is used exactly once, so a name you have already spent is a name you cannot spend again.

Drill 2 — Fair Move, or Not?

1. P1: Her argument for the cut is a straw man of what the department said.
P2: So she is wrong about the budget.

2. P1: The project failed.
P2: Failed by what — cost, schedule, or whether anyone uses it?

3. P1: This poll shows we are ahead.
P2: It was run by the party it favours. How were the respondents selected?

4. P1: This poll shows we are ahead.
P2: It was run by the party it favours, so the numbers are fiction.

Drill 2 — Answers

	P2’s move	Why
1	not a fair move	the fallacy fallacy — the budget claim may still be true
2	fair move	fixes the word before arguing about it
3	fair move	the interest raises a question, and the question is asked
4	not a fair move	the interest is treated as the finding

3 and 4 differ by one clause. That clause is the whole lesson.

Drill 3 — Which Appeal, and Is It Grounded?

1. “I have taught this course for twenty years.”

2. “I inspected this bridge myself in January. Here is the report and the photographs.”

3. “Think of the families who cannot sleep for the noise. The night-flight ban starts in April — here is the schedule.”

4. “If this passes, you will not recognise your own neighbourhood.”

5. “Nine studies agree.”

6. “Twelve of the fifteen buses on this route ran late last month. Here is the timetable and the operator’s log.”

Drill 3 — Answers

	Appeal	Verdict	Why
1	ethos	ungrounded	seniority offered instead of grounds
2	ethos	grounded	hands you the means of checking her
3	pathos	grounded	real feeling, attached to a specific plan
4	pathos	ungrounded	the fear does all the work
5	logos	ungrounded	which nine, on whom, measuring what?
6	logos	grounded	the count is given, and so is where to go and check it

Grounded does not mean right. A careful liar can hand you a checkable number too.

Part C — On the Exam

C1. “Trust me, I have been doing this since before you were born.”

Write three things:

ethos · ungrounded — age is offered in place of any reason to think the claim is true.

Two labels, one sentence. Two points for the pair, two for the reason.

Wording: the paper says grounded / ungrounded. The Session 12 slides said honest / counterfeit. Both are accepted.

Drill 4 — Explain the Correlation

1. “Countries with more Nobel laureates eat more chocolate. So chocolate makes you brilliant.”

2. “People who see a physiotherapist have more back pain than people who do not. So physiotherapy causes back pain.”

3. “A sports magazine compared thirty pre-match habits with whether teams won. Eating pasta came out on top. So pasta wins matches.”

4. “Plots randomly assigned the new fertiliser yielded more than the control plots. So the fertiliser works.”

Drill 4 — Answers

	Explanation	The rival, named
1	confounder	national wealth — rich countries buy chocolate and fund laboratories
2	reverse causation	the back pain is why they went
3	chance	thirty habits were compared, so one had to come out on top
4	X causes Y	random assignment removed the other three

“Correlation is not causation” earns nothing. Naming the rival earns the mark.

Part E — On the Exam

E1. “Towns with more streetlights report more night-time crime. So streetlights attract crime.”

Write both:

confounder — town size. Bigger towns have more lights and more crime of every kind.

Naming the confounder is worth as much as the label. “Confounder” alone scores one of two — and there are ten of these on the paper, so it adds up fast.

Drill 5 — Read the Study

The city reports that its after-school programme raised attendance by 9%. Schools chose whether to join. Attendance was recorded by the programme’s own coordinators. The 9% compares joining schools with their own attendance the year before. The figure reported is the one for primary schools, where the effect was largest.

(a) How did these schools end up in the study? (b) What was actually measured? (c) Compared to what? (d) Why is the reported figure 9% and not some other number?

Drill 5 — Answers

(a) How they ended up in the study. Schools chose. The joiners differ from the non-joiners before the programme does anything — an organised school is likelier both to join and to have good attendance already.
(b) What was measured. Attendance was recorded by the people delivering the programme, and nobody independent checked it.
(c) Compared to what. Against their own previous year — so any city-wide trend, or any rebound from a bad year, is counted as programme effect. The comparison needed is similar schools that did not join, over the same months.
(d) Why 9% and not another number. Primary schools are the subgroup where the effect was largest — several were looked at and the best was published. So you cannot say the programme raises attendance by 9%, nor that it works especially well for primary schools.

Part F — On the Exam

One study. Four questions. 14 points, and the four are not worth the same.

1. and (b) want a named problem plus why it matters — two marks for the problem, one for the why. Three points each.
1. is worth four: two for naming the comparison actually made — each student against their own past — and two for the real comparison that is needed instead.
1. wants both halves: the subgroup was picked after the results were seen, and what that does not let you conclude: not that the app raises marks by 11%, and not that it works especially well for engineers.

Budget your time backwards from here. Parts A and G take five minutes between them.

Drill 6 — Match the Reading

1. Schopenhauer, The Art of Controversy
2. Institute for Propaganda Analysis (1937)
3. Aristotle, Rhetoric I.1–2
4. Huff, “The Sample with the Built-in Bias”

  (a) how a poll is steered by who gets asked, long before the questions are written
  (b) the moves of someone who wants to win when being right is not the goal
  (c) what a speaker has to work with: who they are, what you feel, what follows
  (d) the named tricks a campaign uses to carry a crowd along
  (e) the four rival explanations to rule out before believing a correlation

Drill 6 — Answers

	Reading
1	Schopenhauer	(b) the moves of someone who wants to win
2	Propaganda Analysis (1937)	(d) the named tricks that carry a crowd
3	Aristotle	(c) who they are, what you feel, what follows
4	Huff	(a) who gets asked, before the questions are written

Left over: (e) — the four rivals for a correlation. That is Session 13 class material, not a reading. The leftover is never a reading, so there is no title to recognise.

Part G — On the Exam

Match each required reading to what it is mainly about. One option is left over.

The leftover is not a reading at all — it is a topic from class. There is no title to recognise, so the only way through is knowing what each of the four is about.

Four required: Schopenhauer · the 1937 propaganda article · Aristotle · Huff. One line each is the whole revision.

Conclusion

Practise, don’t re-read. Redo the drills with the answers covered.
Name the eight out loud, by family. distorted claims · emotional appeals
Say what would settle it — for a fallacy, for a correlation, for a study.
Name the rival. Never “correlation is not causation” on its own.
One line per reading — what it was about, nothing more.

The question the whole paper asks, in every part: and what would decide it?