Logic and Scientific Thinking

Types of Knowledge

Bogdan G. Popescu

Tecnologico de Monterrey

Welcome

A Familiar Argument

A post you have probably scrolled past:

“Teen anxiety is up 50% since smartphones arrived. Phones are rewiring a generation — therefore schools should ban them.”

What would you question in this argument?

Three Different Moves

That argument contains:

A number you could check: “Teen anxiety is up 50%.”
A causal claim: Smartphones caused the increase.
A should: Therefore schools should ban them.

The question of this course: What should you believe — and what would decide it?

The Course

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.

The Path

%%{init: {"flowchart": {"useMaxWidth": true, "htmlLabels": false, "nodeSpacing": 30, "rankSpacing": 45, "padding": 24}, "themeVariables": {"fontSize": "16px", "edgeLabelBackground": "#ffffff"}}}%%
flowchart LR
  W1["WEEK 1<br/>knowledge,<br/>arguments, claims"] --> W2["WEEK 2<br/>deduction, validity,<br/>practice"]
  W2 --> W3["WEEK 3<br/>fallacies,<br/>review, midterm"]
  W3 --> W4["WEEK 4<br/>fallacies,<br/>misinformation,<br/>persuasion"]
  W4 --> W5["WEEK 5<br/>causation, reading<br/>a study, final exam"]
  style W1 fill:#1e293b,color:#f9fafb,stroke:#1e293b
  style W2 fill:#4a7c6f,color:#f9fafb,stroke:#4a7c6f
  style W3 fill:#4a7c6f,color:#f9fafb,stroke:#4a7c6f
  style W4 fill:#4a7c6f,color:#f9fafb,stroke:#4a7c6f
  style W5 fill:#b44527,color:#f9fafb,stroke:#b44527

Logistics

Meetings	Monday, Wednesday, Thursday — 8:30–10:00
Materials	Course site: one page per session — slides, readings (PDF), homework
Readings	Required = used in class, examinable · Optional = reference
Exams	Midterm Thu, Aug 27 · Final Thu, Sep 10 — both in class
Contact	bgpopescu@tec.mx — office hours by appointment

Rules

Attendance: more than three unexcused absences = assumed withdrawal.
AI tools: allowed with disclosure — undisclosed use is academic dishonesty.
Exams: closed book, individual.

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.

NARRATION: Sixty percent sits in the two exams, and the good news is that neither is cumulative — the midterm on August twenty-seventh covers Sessions 1 through 7, the final on September tenth covers 10 through 14. The midterm gets a review session the class before; before the final, Session 14 runs the whole toolkit on one real study, which does the same job in applied form. Closed book, individual, both of them. Twenty percent is the reading — and the way that is graded is on the exams themselves, so the required readings are not optional background, they are examinable. The last twenty is for showing up and doing the work of the session; attendance and participation are scored separately, so being here is the floor, not the grade. Do NOT re-state the AI rule here — it was covered on the previous slide; if a hand goes up about it, point back rather than repeating.

Exercise 1 — How Do You Know?

Four Claims

For each, one line: how do you know — or how to find out?

The sun will rise tomorrow.
2 + 2 = 4.
Your best friend is trustworthy.
Smoking causes cancer.

(3 minutes alone, then hands.)

The Takeaway

Same confidence — different sources.

The sunrise: you saw it, again and again.
2 + 2 = 4: you reasoned it out.
Your friend: experience + judgment.
Smoking causes cancer: you were told.

Part 1: Four Ways of Knowing

Four Sources

Source	You know because…	Example
Empirical	you observed it	“It is raining.”
Rational	you reasoned it out	“2 + 2 = 4.”
Intuitive	it feels true	“Something is off about him.”
Authoritative	a source told you	“Smoking causes cancer.”

The categories often overlap — we separate them today to see each kind of support.

Reason and Observation

Plato points to reasoning; Aristotle to the world. Raphael (1509–1511). Public domain, via Wikimedia Commons.

An old argument — this course uses both sources, checked.

Where Each Fails

Empirical: senses mislead — and you cannot observe everything.
Rational: proofs work only from premises already accepted.
Intuitive: fast and useful — but others cannot check it.
Authoritative: only as good as the source — most knowledge is this.

The Key Question

For any claim, ask:

What would decide it?

Can we observe or measure it? → test it.
Can we reason it out? → prove it.
Does a source tell us? → ask how they know.
Could nothing prove it wrong? → notice that.

Better question: not “Do I believe it?” but “What would change my mind?”

So What?

Sources differ in one crucial way: whether others can check.

Knowledge that invites checking has a name.

Part 2: Scientific Knowledge

Four Features

Knowledge is scientific when it is:

Checkable — it says something that could fail a test.
Public — methods and data are open to others.
Self-correcting — errors get found and fixed.
Hedged — conclusions are probable, not final.

Ideals of good practice — not a perfect definition of science.

NARRATION: Four features, each doing work. Checkable: a scientific claim sticks its neck out — it says something that observation could contradict. Public: the methods and data are laid open, so checking is possible for anyone, not just the author. Self-correcting: because checking is public, errors surface — science is the system that finds its own mistakes. Hedged: honest conclusions come with uncertainty attached; “probably” is a feature, not a weakness — a later session makes this precise. Note what is absent from the list: white coats, laboratories, difficult mathematics. Scientific is a property of how knowledge is organized, not of who produces it. And the second guardrail, said plainly: these four are useful ideals of good scientific practice, not a perfect definition covering every case — real science sometimes falls short of them, and that gap matters later in the course.

A Claim Must Risk Being Wrong

Compare:

“Coffee improves memory.” → We can test it. The result might show no improvement.
“Coffee improves your invisible energy.” → What observation could show this is wrong?

Checkable = there is some possible evidence that could prove you wrong.

Checkable Authority

Most of what anyone knows arrives on authority — including science.
The difference: scientific sources show their work.
This course teaches you to do the checking.

Science’s Limit

Facts alone do not decide what we should do.
Every policy question mixes facts with values.
Where exactly values enter — a later session covers this.

Now practice the sorting — five claims.

Exercise 2 — What Would Decide It?

Five Claims

In pairs, one line per claim:

What would decide it?

“Students remember more after drinking coffee.”
“The library closes at 10 p.m.”
“This bracelet brings good luck.”
“There were 127 students in yesterday’s lecture.”
“Using phones during class lowers exam scores.”

(5 minutes, then share-outs.)

ANSWERS / DEBRIEF:

“Students remember more after drinking coffee.” HOW TO DECIDE IT: Run an experiment. Compare memory performance with coffee vs. no coffee/placebo. One student’s experience is not enough. KEY IDEA: empirical testing. “The library closes at 10 p.m.” HOW TO DECIDE IT: Check a reliable source. Library website, posted hours, or library staff. KEY IDEA: sometimes authority is the easiest way to check a fact. “This bracelet brings good luck.” ASK: What would count as evidence that it does NOT bring good luck? Define “good luck” and make a prediction that could fail. If every outcome counts as evidence for the bracelet, the claim cannot really be tested. KEY IDEA: a checkable claim must be able to be wrong. “There were 127 students in yesterday’s lecture.” HOW TO DECIDE IT: Count or check records. Attendance sheet, sign-in record, or other reliable count. The precise number makes the claim easy to test. KEY IDEA: empirical factual claim. “Using phones during class lowers exam scores.” HOW TO DECIDE IT: Compare students with and without phone use under controlled conditions. Simply finding that phone users have lower scores is not enough. Other differences could explain the result. KEY IDEA: causation is harder to establish than correlation.

Worked Example

“Students who sleep 8 hours score higher on exams.”

What would decide it?
Compare exam scores for students with different amounts of sleep.

Then ask: could something else explain the difference?

Part 3: The First Tool

The Quick Logic Check

For every “therefore” you meet, ask:

What is the conclusion?
What premises support it?
What unstated assumption connects them?

A preview, not for mastery today — the next session is devoted to it.

Try It

“I caught a cold, so I took vitamin C every day. A week later the cold was gone. Therefore, the vitamin C cured me.”

Conclusion? The vitamin C cured me.
Premise 1? I took vitamin C every day.
Premise 2? A week later, the cold was gone.
Unstated assumption? The vitamin C — and not something else — cured it.

True but Undecided

Every stated premise is true.
But colds clear up on their own in about a week.
The story fits “vitamin C worked” and “time passed” equally well.
True premises, undecided conclusion — that is “doesn’t follow.”

The Argument, Revisited

“Teen anxiety is up 50% since smartphones arrived. Phones are rewiring a generation — therefore schools should ban them.”

Conclusion? Ban phones in schools.
Premise? Anxiety rose after smartphones spread.
Unstated assumptions? The rise caused the rise — and that causing justifies banning.
And the number? Up 50% — since when, measured how, in whom?

Same shape as the vitamin C: after is not because. Later sessions test both steps.

By the final week, you run these checks cold — on a passage you have not seen.

NARRATION: Close the loop with the tool you just learned. Run the three questions on the opening argument. The conclusion: ban phones in schools. The stated premise: anxiety rose after smartphones spread. And the unstated assumptions — there are two: that the one rise caused the other, and that causing harm justifies a ban. Then the fourth line, which the vitamin C case did not have: the number itself is a claim. “Up fifty percent” since when, measured how, in which population? A real figure can still be the wrong figure for the argument it is carrying. Now the recognition: this is the vitamin C argument wearing bigger clothes — something happened after something else, “after” became “because,” and “because” became “act.” True premises would still leave the conclusion undecided. Whether the causal step holds is a question for the causation session; where the should-step gets its support is a question for the claims session; whether the number survives contact is a question for the evidence session. None is decided tonight — what is decided is that you can now SEE all three, which most people arguing about this never do. Both exams ask you to do exactly this, cold, on passages you have not seen.

What You Leave With

Four sources of knowledge — and where each fails.
Scientific = checkable, public, self-correcting, hedged.
One question for every claim: what would decide it?
One habit for every “therefore”: the Quick Logic Check.

References

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.