Logic and Scientific Thinking

Midterm Review

Bogdan G. Popescu

Tecnologico de Monterrey

Exam Format

Closed book, individual, in class.
Covers Sessions 1–7.
Tests the concepts, the vocabulary, and their application to short cases.
The required readings for those sessions are examinable.

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.

Part 1: The Whole Toolkit

Finding the Argument

An argument gives reasons for a claim.

Conclusion	the claim being defended
Premises	the reasons offered for it

Find the conclusion first. Everything else is premises or noise.

Not Everything Argues

	Example	Why it isn’t an argument
Description	“It’s raining outside.”	states a fact, defends nothing
Opinion	“Messi is the best ever.”	a judgement, no reasons attached
Contradiction	“No, it isn’t.”	denies the claim, gives no reason
Explanation	“I was late — heavy traffic.”	says why an agreed fact happened

A contradiction is one word away from an argument: because.

The test for explanations: is the conclusion actually in dispute?

Session 2’s four non-arguments, with its own examples. Move fast through the first three — a description states what is there and asks you to accept nothing; an opinion is a conclusion with no reasons pinned to it, which is why “Messi is the best ever” starts fights but settles none; a contradiction at least aims at the claim but offers nothing behind it. That is the Argument Clinic room from Session 2, and it is worth saying the fix out loud, because it is one word: the moment “no it isn’t” becomes “no it isn’t, BECAUSE…”, it starts to be an argument. Spend the remaining time on EXPLANATION, which is the one that costs marks. “I was late because there was heavy traffic” gives a cause for something nobody disputes — we all agree I was late; the only question is why. An argument tries to make you accept a conclusion you might not accept yet. So the test is the second fragment: is the conclusion actually in dispute? If everyone already grants it, you are looking at an explanation and there is nothing to grade.

Standard Form

“We should not cut the military budget — our Navy is smaller than in 1917.”

P1.	Our Navy is smaller than in 1917.
P2.	(hidden) Fewer ships means a weaker military.
P3.	(hidden) Cutting the budget would shrink the fleet further.
P4.	(hidden) We should not weaken the military.
C.	We should not cut the military budget.

Three Kinds of Claim

One question sorts them: what would settle this?

	The answer	Example
Empirical	go and look	“Our Navy is smaller than in 1917.”
Conceptual	agree what the word means	“‘Strength’ means what a military can do.”
Normative	argue about what matters	“We should not weaken the military.”

A claim packed with facts can still be normative. Look for the value word.

The Hidden Ought

You cannot get a should out of premises that only say is.

Every normative conclusion needs at least one normative premise.
If you can’t find one stated — it is hidden.
Naming it is how you find where to disagree.

Guarantee or Good Bet

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  A["AN ARGUMENT<br/>what does it promise?"]
  A -->|"a GUARANTEE"| D["DEDUCTIVE"]
  A -->|"a GOOD BET"| I["INDUCTIVE"]
  D --> D1["the link<br/>VALID or INVALID"]
  I --> I1["the link<br/>STRONG or WEAK"]
  D1 --> D2["+ true premises<br/>= SOUND"]
  I1 --> I2["+ true premises<br/>= COGENT"]
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The Four Steps

Every argument, in the same order:

Deductive or inductive? (a guarantee, or a good bet?)
Does the link hold? (deductive → valid? · inductive → strong?)
Are the premises true?
One-word verdict: sound · cogent · or neither.

Step 1 decides which test steps 2 and 3 run.

Validity Is Not Truth

Truth values tell you almost nothing about validity.

Premises	Conclusion	What you can conclude
false	either	nothing — could be valid, could be invalid
true	true	nothing — could be valid, could be invalid
true	false	invalid — guaranteed

“All cats are reptiles; all reptiles speak French; so all cats speak French.” — hypothetical syllogism

Every line false — and perfectly valid.

The Five Shapes

One rule, five moves: “If it rains, the street gets wet.”

	The move
Modus ponens	It rained → street is wet	valid
Modus tollens	Street is dry → it didn’t rain	valid
Hypothetical syllogism	rain → wet → slippery	valid
Affirming the consequent	Street is wet → it rained	trap
Denying the antecedent	It didn’t rain → street is dry	trap

Both traps forget the burst pipe — the street can be wet without rain.

Five patterns on one rule, so the only thing changing down the table is the MOVE. Read the valid three first: it rained, so the street is wet — forward, fine. The street is dry, so it did not rain — backwards WITH both ends negated, also fine, and that is modus tollens. Chain two rules and you get a third rule, not a fact. Then the two traps, and here is the payoff of using one rule for all five: they fail for the SAME reason, and it fits in two words. A burst pipe. The street is wet, so it rained? A pipe burst. It did not rain, so the street is dry? A pipe burst. Say “burst pipe” twice and most of the room will keep it — the conditional only ever promised that rain is ENOUGH to wet the street, never that rain is the ONLY thing that can. Compression for the board: you may run the arrow forwards, or backwards with both ends negated. Never backwards as it stands, and never negate both ends going forwards. The next five slides take each shape on its own, with the session five diagrams — one rule throughout, so the only thing changing is the move.

Modus Ponens

P1: If something is a dog, then it is a mammal.
P2: Fido is a dog.
C: Fido is a mammal.

modus ponens

Shape: If P, then Q. P. so Q

Valid — the if is met, so the then follows.

Modus Tollens

P1: If something is a dog, then it is a mammal.
P2: Fido is not a mammal.
C: Fido is not a dog.

modus tollens

Shape: If P, then Q. Not Q. so Not P

Valid — the logic behind falsification.

Hypothetical Syllogism

P1: If dog, then mammal.
P2: If mammal, then animal.
C: If dog, then animal.

hypothetical syllogism

Shape: If P, then Q. If Q, then R. so If P, then R

Valid — but every added link is another premise that can fail.

Look at the Conclusion

Two rules: “If it rains, the street gets wet.” · “If the street is wet, it is slippery.”

	Add this	You conclude
Modus ponens	It rained.	The street is wet.
Hypothetical syllogism	nothing — just the second rule	If it rains, the street is slippery.

Still an “if”? Hypothetical syllogism. A flat claim? Modus ponens.

Thirty seconds, and worth them because Part C asks for the name and this is the pair students swap. Same two rules for both moves, so the only thing changing down the table is what you add to them — the same trick as the five-shapes slide. Modus ponens: somebody tells you it actually rained, and you walk out with a fact about the street. Hypothetical syllogism: nobody tells you anything about today’s weather, you just line the second rule up behind the first, and you walk out with a longer rule. We never claimed it rained. The test on the last line is the same one they saw in Session 5, deliberately — read the conclusion. If it still has an “if” in it, they chained. If it is a flat claim about the world, they crossed. The failure to name out loud: seeing two “if” statements and reaching for modus ponens because the first premise looks familiar.

Affirming the Consequent

P1: If something is a dog, then it is a mammal.
P2: Fido is a mammal.
C: Fido is a dog.

But Fido could be a cat — a dog is only one way to be a mammal.

affirming the consequent (invalid)

Shape: If P, then Q. Q. so P

Trap — reads the rule backward.

Denying the Antecedent

P1: If something is a dog, then it is a mammal.
P2: Fido is not a dog.
C: Fido is not a mammal.

But Fido could be a cat — not a dog, still a mammal.

denying the antecedent (invalid)

Shape: If P, then Q. Not P. so Not Q

Trap — forgets Q can hold without P.

Tool vs. Trap

Each trap reverses its valid counterpart (all share the rule: If P, then Q):

Valid tool	Invalid counterpart	Where it goes wrong
Modus ponens — P, so Q	Affirming the consequent — Q, so P	reads the rule backward
Modus tollens — Not Q, so Not P	Denying the antecedent — Not P, so Not Q	forgets Q can hold without P (the cat)

Two questions catch most errors: (1) Am I going the direction the conditional states? (2) Was P the only route to Q, or just one?

NARRATION: Put each valid tool beside the trap that imitates it, because on the exam the traps will not announce themselves — they arrive looking like the tool they copy. Modus ponens goes forward, condition to result; affirming the consequent runs backward from the result and invents certainty about its cause. Modus tollens observes that a guaranteed result is missing and rules the condition out; denying the antecedent merely removes one route and wrongly assumes no other exists. Then the two questions, and these are the ones to write at the top of the answer sheet. Am I moving in the direction the conditional states? And did the conditional name the ONLY route to the result, or just one route? Those two catch almost every error in Drill 3. And the fallback if a question stalls in the exam: draw two circles, put a dot somewhere, and read the answer off the picture.

Necessary vs. Sufficient

“If it’s a dog, then it’s a mammal.”

Dog is sufficient for mammal — dog guarantees mammal.
Mammal is necessary for dog — no mammal, no dog.
The traps come from swapping the two.

The Four Families

Family	Fallacies
Faulty reasoning	false cause · circular reasoning
Misused sources	ad hominem · appeal to authority
Distorted claims	(Session 10 — not on this exam)
Emotional appeals	(Session 10 — not on this exam)

Four fallacies are examinable. The other eight come after the midterm.

The Three-Step Diagnosis

Name the move.
Quote the words that commit it.
Say what would decide the question.

Naming alone is not a refutation — step 3 is where the marks are.

The Readings

Sagan, C. (1995). The fine art of baloney detection. In The demon-haunted world: Science as a candle in the dark (Ch. 12). Random House.
Plato. (n.d.). Euthyphro.
Hume, D. (1739). A treatise of human nature, Book III, Part I, Section I.
Hume, D. (1748). An enquiry concerning human understanding, Section IV, “Sceptical doubts concerning the operations of the understanding.”
Vaughn, L., & MacDonald, C. (2019). The power of critical thinking (Canadian ed.). Oxford University Press. (Ch. 3, “Making sense of arguments,” pp. 58–106.)
Kahneman, D. (2011). The characters of the story. In Thinking, fast and slow (Ch. 1). Farrar, Straus and Giroux.
Vaughn, L., & MacDonald, C. (2019). The power of critical thinking (Canadian ed.). Oxford University Press. (Ch. 5, “Fallacies and persuaders,” pp. 151–186.)

Part 2: Practice

Six drills. Answers on the slide immediately after each.

Drill 1 — Label the Claim

Mark each E, C, or N.

1. Our Navy is smaller than it was in 1917.

2. “Strength” means what a military can do, not how many units it owns.

3. We should not weaken the military.

4. Turnout was lower this year than last.

Drill 1 — Answers

		Why
1	E	Count the ships.
2	C	Fixes what the word means.
3	N	A value word — and no amount of data settles it.
4	E	Look up the figures.

Part A — On the Exam

A1. Costa Rica abolished its army in 1948.
A2. A subsidy is, by definition, a payment from government to a producer.
A3. Voting should be compulsory.

Write only this:

A1 – E A2 – C A3 – N

One letter each. No sentences, no reasons.

Drill 2 — Family and Verdict

Deductive or inductive? Then: sound, cogent, or neither? (Assume the stated premises are true.)

1. “All squares have four sides. This figure is a square. So it has four sides.”

2. “All dogs are mammals. This animal is a mammal. So it’s a dog.”

3. “This mountain pass has closed for snow every winter for thirty years. So it will probably close this winter too.”

4. “Two of my friends got sick after eating there. So that restaurant probably has bad hygiene.”

Drill 2 — Answers

	Family	Verdict	Why
1	deductive	sound	“Square” forces “four sides”.
2	deductive	neither	Invalid — a cat is a mammal too.
3	inductive	cogent	Thirty winters, same pass, same cause.
4	inductive	neither	Weak — two cases, no base rate.

A broken link ends it. Nothing rescues an invalid argument.

Part B — On the Exam

B1. “Every treaty the senate ratifies is binding. The senate ratified this treaty. So this treaty is binding.”

Write only this:

B1 – deductive, sound

Two things: the type, then the verdict. Assume the stated premises are true.

Drill 3 — Name the Shape

Name the pattern, then say valid or trap.

1. “If it’s a dog, then it’s a mammal. Rex is a dog. So Rex is a mammal.”

2. “If the video is fake, the detector flags it. The detector flagged it. So the video is fake.”

3. “If the vaccine caused the outbreak, the vaccinated would get sick. They didn’t. So it didn’t.”

4. “If she deleted the files, she’s guilty. She didn’t delete them. So she’s not guilty.”

5. “If it’s a dog, it’s a mammal. If it’s a mammal, it’s an animal. So if it’s a dog, it’s an animal.”

Drill 3 — Answers

	Shape
1	Modus ponens	valid
2	Affirming the consequent (Trap 1)	trap
3	Modus tollens	valid
4	Denying the antecedent (Trap 2)	trap
5	Hypothetical syllogism	valid

Both traps run the arrow backwards — or delete a route that was never the only one.

Part C — On the Exam

C1. “If the shipment left on Monday, it arrives Thursday. It did not arrive Thursday. So it did not leave on Monday.”

Write only this:

C1 – modus tollens, valid

The name, then valid or trap. Tool 2 is accepted for the name.

Drill 4 — Name the Fallacy

False cause · circular reasoning · ad hominem · appeal to authority

1. “Brawndo’s got what plants crave — it’s got electrolytes. And electrolytes are what plants crave.”

2. “There’s no proof because it’s covered up, and we know it’s covered up because there’s no proof.”

3. “The mayor’s figures show the curfew cut crime. But the mayor’s a crook — ignore them.”

4. “More doctors smoke this brand than any other, so it must be safe.”

Drill 4 — Answers

		Why
1	circular reasoning	Every turn renames the claim. Nothing new arrives.
2	circular reasoning	Two claims, each propped up by the other.
3	ad hominem	Attacks the mayor, not the figures. Crooks can still hold correct data.
4	appeal to authority	The survey was real — and brand preference is not a safety finding.

Circles need not repeat words — 1 and 2 are the same move in different clothes.

Part D — On the Exam

D1. “This brand must be the best — a famous footballer endorses it.”

Write only this:

D1 – appeal to authority

The name only. No quotation, no explanation — that is Part E’s job.

Drill 5 — Run the Three Steps

“Crime fell after the curfew. The curfew works.”

Name the move.
Quote the words.
Say what would decide it.

Drill 5 — Answers

Step
Name	False cause
Quote	“Crime fell after the curfew. The curfew works.”
Decide	Was crime already falling before? What happened in comparable cities with no curfew?

“After” is not “because.” Rule out the rivals, or you have not shown anything.

Part E — On the Exam

“Museum attendance rose 30% the year after the café opened. The café is what brought the crowds in.”

Write three separate lines:

E(a) – false cause
E(b) – “The café is what brought the crowds in”
E(c) – I would check two things: 1) whether attendance was already rising before the café opened, and 2) whether other museums in the city rose by the same amount that year.

Drill 6 — Reconstruct

“Violent video games should be restricted for minors — children who play them behave more aggressively at school.”

Put it in standard form. Find the hidden premise.

Drill 6 — Answers

P1.	Children who play violent games behave more aggressively at school. (E)
P2.	(hidden) Behaving more aggressively is caused by the games, not merely correlated. (E)
P3.	(hidden) We should restrict what makes children more aggressive. (N)
C.	Violent video games should be restricted for minors.

The conclusion is a should. So at least one premise must be a should.

Part F — On the Exam

“Street stalls should be inspected like restaurants — after all, they serve food to the public.”

Write the argument out, then the label:

P1. Street stalls serve food to the public.
P2. Anything that serves food to the public should be inspected like a restaurant.
C. Street stalls should be inspected like restaurants.
Ans: N

P1 is in the sentence. P2 is the one nobody said.

Part G — On the Exam

G1. Vaughn & MacDonald, Ch. 5 G2. Hume, Treatise

  (a) why facts alone never settle what ought to be done
  (b) a catalogue of the named ways an argument goes wrong
  (c) how formal logic developed after Aristotle

Write only this:

G1 – b G2 – a

One letter each. One option is always left over — so the last answer cannot be had by elimination.

Conclusion

Practise, don’t re-read. Redo the exercises with the answers covered.
Say the four steps out loud, in order, from memory. family · link · premises · verdict
Rehearse the four fallacies — name, then what would decide it. false cause · circular · ad hominem · appeal to authority
One line per reading — what it was about, nothing more.

Logic and Scientific Thinking

Exam Format

Grading

Part 1: The Whole Toolkit

Finding the Argument

Not Everything Argues

Standard Form

Three Kinds of Claim

The Hidden Ought

Guarantee or Good Bet

The Four Steps

Validity Is Not Truth

The Five Shapes

Modus Ponens

Modus Tollens

Hypothetical Syllogism

Look at the Conclusion

Affirming the Consequent

Denying the Antecedent

Tool vs. Trap

Necessary vs. Sufficient

The Four Families

The Three-Step Diagnosis

The Readings

Part 2: Practice

Drill 1 — Label the Claim

Drill 1 — Answers

Part A — On the Exam

Drill 2 — Family and Verdict

Drill 2 — Answers

Part B — On the Exam

Drill 3 — Name the Shape

Drill 3 — Answers

Part C — On the Exam

Drill 4 — Name the Fallacy

Drill 4 — Answers

Part D — On the Exam

Drill 5 — Run the Three Steps

Drill 5 — Answers

Part E — On the Exam

Drill 6 — Reconstruct

Drill 6 — Answers

Part F — On the Exam

Part G — On the Exam

Conclusion

Encuesta