Logic and Scientific Thinking

Empirical, Conceptual, and Normative Claims

Bogdan G. Popescu

bgpopescu@tec.mx

Tecnologico de Monterrey

Learning Outcomes

Overview

Label premises empirical, conceptual, or normative (E / C / N).

Catch the hidden ought — the moment an argument slides from is to should.

Reconstruct a real policy argument start to finish — standard form, hidden premises, labels.

Judge where an argument is weakest — after making it its strongest.

NARRATION: Welcome back. Last session you learned to spot arguments and rebuild them in standard form. Today, two more moves. By the end you will be able to label every premise as empirical, conceptual, or normative; catch the moment an argument slides from what is to what should be; reconstruct a real policy argument start to finish; and judge where an argument is weakest — after first making it its strongest. Timing plan, honest numbers (180-min slot): Outcomes ~3 / Recap ~4 / Warm-up: reconstruct from memory ~10 (LOAD-BEARING — a week has passed; do not trim it) / Part 1 (three kinds: table 6, clean cases 5, Hume 7, Where This Bites 5) ~23 / Part 2 (Euthyphro as exercise) ~10 / BREAK 15 / Warm-up round (two quick excerpts) ~10 / Team activity (assign 3, work 20, presentations ~14, debrief ~8) ~45 / Exit check ~5 / Four Moves close ~4 / References ~1. Total ~130; ~50 slack — spend it on the team activity debrief, not on new content. Accordion if behind: cut the second warm-up excerpt; never cut the recap or the exit check.

Recap: The Toolkit

For every “therefore”: conclusion? premises? unstated assumption?

Standard form — one line per premise, (hidden) ones included, conclusion at the bottom.
Enthymeme — an argument that leaves a premise unstated.
Charity — attribute the strongest plausible hidden premise. Then judge.

Today: two new moves. Sort premises into kinds — and probe where arguments break.

Warm-Up: Reconstruct from Memory

“The team started losing after the new coach arrived. So the coach should be fired.”

Alone, use standard form to recreate the argument:

premises
conclusion
hidden premises

Warm-Up — Reconstructed

P1.	The team started losing after the new coach arrived.
P2.	(hidden) The new coach caused the losing.
P3.	(hidden) A coach who causes the team lose should be fired.
C.	The coach should be fired.

P1 is only a clue: losing came after the coach arrived.
P2 does the causal work: it turns timing into blame.
P3 does the normative work: it turns blame into firing.

Where the Argument Can Break

P1.	The team started losing after the new coach arrived.
P2.	(hidden) The new coach caused the losing.
P3.	(hidden) A coach who causes the team lose should be fired.
C.	The coach should be fired.

Attack	What it targets
“The best players were injured.”	Challenges P2
“The team got worse before the coach arrived.”	Challenges P2
“A new coach needs time to rebuild team.”	Challenges P3
“A coach should be fired only after repeated poor seasons.”	Shows that P3 is too strong.

The argument is not one chain. It is two jumps:

flowchart LR
  A["after coach"] -->|"P2: causal"| B["because of coach"]
  B -->|"P3: normative"| C["fire coach"]

Data Helps — But Only in the Right Place

Question	Type of issue
Did losses increase after the coach arrived?	Descriptive
Did the coach cause the losses?	Causal
Should a losing coach be fired?	Normative

Data can help with the first two questions.

But data alone cannot answer the third.

(The first two are both empirical — the third is not.)

The Key Lesson

Premise	Role
P1	Evidence
P2	Causal bridge
P3	Normative rule
C	Final judgment

To evaluate an argument, ask:

What is stated?
What is hidden?
Which premise does the conclusion actually depend on?

Part 1: Three Kinds of Claims

Three Kinds of Claims

The test for each: what would decide it?

Kind	Decided by	From last session’s debate
Empirical	evidence, observation	“Our Navy is smaller than in 1917.” — count the ships
Conceptual	meaning, definition	(hidden P3) “Strength” means what the military can do, not how many units it has
Normative	moral or political principles, together with relevant facts	“We should not cut the military budget.”

Your coach argument had two of these — empirical (its descriptive + causal claims) and normative. The debate adds the third: a conceptual claim about what “strength” means.

Normative claims are not mere taste — they can be argued well or badly. But no amount of data alone gets you to should.

NARRATION: The test for each kind is: what would decide it? Empirical claims are decided by evidence and observation — count the ships. Conceptual claims are decided by meaning and definition — what does “strength” even mean? Notice that one is the debate’s hidden P3. Normative claims need principles together with facts — “we should not cut the budget.” All three kinds were on that debate stage. One caution: normative claims are not mere taste. They can be argued well or badly — but no amount of data alone gets you to “should.” The debate examples are deliberate retrieval: students spent last session holding all three claims, so the categories land on familiar material. P3 is a BORDERLINE case — if a student objects that it sounds normative (“how strength SHOULD be measured”), celebrate and label it C/N: mixed labels are legal (next slide makes that official), and “what does ‘strength’ mean?” vs. “what should we do?” is exactly the distinction to draw. Honesty caveat if pressed: “decided by” is aspirational for all three kinds — normative disputes especially can remain reasonable after good argument. The point is WHAT KIND of considerations bear on the claim, not that agreement is guaranteed.

Three Clean Cases

Before the messy ones — classify each:

Empirical
Conceptual
Normative

“Antarctica is losing ice every year.”
“‘Unemployed’ doesn’t mean everyone without a job — it means people seeking work and not finding it.”
“The restaurant should refund us — it served an allergen we disclosed.”

NARRATION: Before the messy real-world cases, three clean ones — pause and classify each before I answer. Antarctica losing ice: empirical — observation decides it. What “unemployed” covers: conceptual — that is about the meaning of a word. The restaurant should refund us: normative — a “should,” resting on a principle and on facts. Now the honest rule for real arguments: many premises are mixed. Label the dominant function, or use two labels when both genuinely matter. You will need that flexibility within the hour. Stabilize the categories on indisputable cases BEFORE the policy material — borderline cases only teach once the clean ones feel solid. Case 3 is deliberately a miniature argument: the should is normative even though an empirical fact (the disclosed allergen) does most of the visible work — one breath of “kinds travel together.” The mixed-labels rule is the load-bearing line: it is what makes the team activity’s labeling defensible instead of a guessing game about the professor’s key.

Hume’s Is–Ought Gap (1739)

Reading the moral philosophy of his day, Hume kept catching:

Pages of moral philosophy contain is claims: facts about
- God
- society
- human nature.
Then, without warning: “…therefore we ought to…”:
- the jump is never explained.

“…of a sudden I am surprised to find that instead of is, and is not, I meet with no proposition that is not connected with an ought, or an ought not.”

— A Treatise of Human Nature (1739), p. 302

That unexplained jump is where the normative premise enters unstated.

David Hume, by Allan Ramsay (1766). Public domain, via Wikimedia Commons.

NARRATION: This observation is nearly three centuries old. David Hume, reading the moral philosophy of his day, kept catching the same move: page after page about what is — and then suddenly, “therefore we ought to…” — with the jump never explained. That unexplained jump is where normative premises get smuggled. You watched one last session: the Navy is smaller… so we ought not cut the budget. One protection, though: this is not a fallacy verdict. Facts can earn an “ought” — once the bridge premise is stated. The sin is incompleteness. And “smuggled” usually just means the speaker assumed you shared the value. The protective fragment matters — without it, students infer that EVERY is-to-ought argument is broken. Model the repaired version aloud if needed: “this causes serious avoidable harm (E) + we should prevent serious avoidable harm at proportionate cost (N, stated!) = we should prevent it” — a perfectly good argument, because the bridge is visible. Quote lightly trimmed: the original’s “the usual copulations of propositions” (= linkings of propositions) is cut for readability — restore verbally if a student checks the text. The sequence is intuition first, quote as confirmation: Hume noticed authors piling up facts and then sliding into “ought” with no bridge. The missing bridge IS the hidden normative premise — same object, 1739 vocabulary. The Romney example: P(is) Navy smaller + hidden normative premise (a country ought to fund what its military needs) = C(ought) don’t cut. Full Treatise and the is-ought excerpt are in readings/; the quote is on printed p. 302 in both PDFs (Book 3, Part 1 — excerpt PDF page 12, full-Treatise PDF page 319; Selby-Bigge 470 for scholarly citation).

Normative Policy Arguments

Every “the data says we should…” hides the same jump:

“Greater threats, so spend more on defence” — data can measure the threat, but not how much is the right amount, nor whether the trade-offs (education, health) are worth it.
“Crime rose as immigration rose, so restrict immigration” — correlation is not cause; and if the real cause is unclear, the policy may not even work.
“Social media causes anxiety, so ban it” — even granting the harm, is a ban the right fix — or would time limits or design rules do better?

Does This Mean We Can Question Everything?

Almost every argument can be unpacked further.

But a useful critique targets a premise that is:

Load-bearing:
- if it is false, the conclusion becomes weaker.
Contestable
- the argument has not yet given us enough reason to accept it.

Policy Arguments

Data rarely dictates a policy by itself.

A policy conclusion may depend on several bridges:

Causal: Did the suspected cause actually produce the problem?
Instrumental: Would the proposed policy solve it?
Comparative: Would it work better than realistic alternatives?
Normative: Are its benefits worth its costs, and who should bear them?

Part 2: Socrates Did This First

Socrates. Roman marble bust (1st century AD), Louvre Museum. Photo: Eric Gaba (Sting), via Wikimedia Commons, CC BY-SA 2.5.

Find the Hidden Premise

Athens, 399 BCE. Euthyphro is prosecuting his own father for letting a laborer die. Socrates asks him to define piety — doing what the gods approve:

Euthyphro: Piety is that which is dear to the gods.

Socrates: And the gods quarrel, Euthyphro — the same things are loved by some gods and hated by others?

In pairs, 3 minutes:

What premise does Euthyphro’s definition need but never state?
What happens to the definition when you utter that premise?

NARRATION: Athens, 399 BCE. Euthyphro is so certain the gods demand it that he is prosecuting his own father over a laborer’s death. Socrates asks him to define piety — doing what the gods approve — and gets: piety is what is dear to the gods. Socrates’ reply is on the slide. Now pause. What premise does Euthyphro’s definition need but never state? And what happens to the definition when you say that premise out loud? Work it out before advancing — you have all the tools. This is the session’s structure applied 2,400 years early — but now THEY do the finding, not you. Circulate; the answer usually arrives fast in one pair and spreads. Backstory in one breath if asked: Euthyphro’s father let a laborer (himself a killer) die in a ditch; Euthyphro thinks prosecuting him is what the gods demand — supreme confidence about piety, which is why Socrates’ question stings.

The Hidden Premise, Exposed

Euthyphro’s definition leans on a premise he never states:
- all the gods agree about what they love.
Socrates says it out loud: the gods do not agree.
Once that premise falls, the definition no longer tells us which actions are pious.

Notice: this is not an is–ought argument — Euthyphro is defining what piety is. A conceptual definition collapses because it rests on an empirical assumption about the gods. The kinds mix in real arguments.

NARRATION: The hidden premise: all the gods agree about what they love. Say it aloud and the definition collapses — in a world of quarreling gods, the same act comes out both pious and impious. The same recipe as the debate’s P3: find the unstated premise, say it aloud, watch what falls. One classification note: this is not an is-ought case. A conceptual definition collapses because it rests on an empirical assumption about the gods. The kinds travel together — which is exactly why you label premises one by one. Reveal AFTER the pair work — the slide is confirmation, not instruction. Greek polytheism does the work: Zeus and Hera need not agree, so “dear to the gods” is ill-defined the moment they quarrel. The P3 parallel is the teaching payoff: same recipe, cover-the-premise gesture included. Note the label question if the room is strong: “the gods agree” is an EMPIRICAL claim about the gods (within Greek theology) — and the definition it rescues is CONCEPTUAL. The kinds travel together. WHY THE HUNT WORKS BETTER IN PAIRS (Mercier & Sperber 2017): myside bias means your OWN premise menus feel complete — we produce reasons lazily and grade them on a curve; in their lab, people tricked into judging their own argument as a stranger’s rejected it more than half the time. That is why Socrates ran this as DIALOGUE, and why the team activity next runs in groups: the hidden premise is easiest to spot in someone else’s argument.

Moral Topic ≠ Normative Argument

Socrates is discussing piety, a moral concept.

But his argument asks whether Euthyphro’s definition works.

Normative question: What should we do?
Conceptual question: What does piety mean?
Socrates’ question:
- Can some things be loved by some gods and hated by others?

Team Activity

Two Quick Ones

Find the hidden premises, label what you can:

empirical
conceptual
normative

1 — “Australia now bars under-16s from social media. Teen anxiety has risen sharply since smartphones arrived, and governments must protect children from proven harms. Every democracy should follow.”

2 — “Millions of graduates paid off their student loans in full. Forgiving student debt now would reward those who did not and punish those who did. Washington must abandon the plan.”

NARRATION: Two quick rounds together first. Read each excerpt; find the hidden premises; label what you can — E, C, or N. Watch for a familiar move in the Australia one: “anxiety has risen since smartphones arrived” — that “since” is doing the same trick as “after” in the crime example. And in the student-debt one, ask whether “rewarding” and “punishing” are neutral descriptions — or whether the framing itself carries the argument. Pause and try both before you continue. ~10 minutes, oral, instructor-led — the rehearsal before teams work alone. Cold-call premises one at a time; label as you go. ANSWERS 1 (Australia): P1 (E) Australia bars under-16s; P2 (E) teen anxiety rose since smartphones; hidden (E, causal) social media CAUSED the rise — “since” is the coach move, after-is-not-because; P3 (N, near-explicit) governments must protect children from proven harms — “proven” smuggles that the harm is established; hidden (E, external validity) what worked/fits in Australia will work elsewhere, plus (N) democracies should adopt policies that effectively protect children. C: every democracy should follow. Weakest: the causal premise — or the transfer premise; reward either. ANSWERS 2 (student debt): P1 (E) millions repaid in full; P2 (C/N — conceptual framing with normative force) forgiveness constitutes “rewarding” non-payers and “punishing” payers: is not receiving a benefit a PUNISHMENT? The framing already carries the evaluation — first use of the mixed-labels rule, point at it; hidden (N) policies that reward imprudence are unfair, and unfair policies must be abandoned. C: abandon the plan. Weakest: the C/N framing premise — the whole argument rides on it. Both excerpts rehearse exactly what the team round grades; say so as you close the warm-up.

Team Activity: The Task

In teams of 3–4, each team takes one excerpt (next slides). Produce on one page:

The argument in standard form.
Hidden premises made explicit — charitably.
Every premise labeled: empirical, conceptual, or normative.
One sentence: where is the argument most vulnerable?

20 minutes, then each team presents in 2 minutes. (Excerpts adapted from recent commentary on AI and deepfakes.)

Excerpt A

“During the last election, deepfake videos of candidates were viewed millions of times before any fact-check appeared. A democracy cannot function when citizens cannot tell real statements from fabricated ones. Congress must therefore criminalize the production of deceptive political deepfakes.”

Task:

turn to standard form
what are hidden premises explicit
label each premise
what is the weakest point

Excerpt B

“Every new medium has triggered the same panic — the printing press, radio, Photoshop. Each time, society adapted and the doomsayers were wrong. AI-generated content is just the next chapter, so heavy regulation now would be premature.”

Task:

turn to standard form
what are hidden premises explicit
label each premise
what is the weakest point

Excerpt C

“Platforms profit directly from viral content. Deepfakes are engineered to go viral. It is only fair that platforms bear legal liability for the synthetic content they amplify and monetize.”

Task:

turn to standard form
what are hidden premises explicit
label each premise
what is the weakest point

All Three Excerpts

A — “During the last election, deepfake videos of candidates were viewed millions of times before any fact-check appeared. A democracy cannot function when citizens cannot tell real statements from fabricated ones. Congress must therefore criminalize the production of deceptive political deepfakes.”

B — “Every new medium has triggered the same panic — the printing press, radio, Photoshop. Each time, society adapted and the doomsayers were wrong. AI-generated content is just the next chapter, so heavy regulation now would be premature.”

C — “Platforms profit directly from viral content. Deepfakes are engineered to go viral. It is only fair that platforms bear legal liability for the synthetic content they amplify and monetize.”

Task — one page per team, 20 minutes, then 2-minute presentations:

turn to standard form
what are hidden premises explicit
label each premise
what is the weakest point

NARRATION: All three excerpts on one slide, with the task checklist. If you are working along at home: pick one excerpt, set a timer for twenty minutes, and produce the page — standard form, hidden premises, labels, weakest point. Then compare against a classmate’s before you look at any answers. Leave this slide up while teams work — every team sees its excerpt and the task without you cycling slides. The three single-excerpt slides before it are for assigning: walk them quickly, one team block per excerpt, then land here. SOLUTIONS (also on the hidden slide that follows in the qmd — flip it to visibility=“uncounted” and re-render to project it): A: P1 (E) deepfakes seen millions of times pre-fact-check; P2 (E/C — a causal claim about democratic functioning dressed as a definition; either label defensible, mixed is best) democracy can’t function when citizens can’t tell real from fake; hidden (E) criminalization would SUBSTANTIALLY REDUCE deceptive deepfakes — and gentler remedies wouldn’t suffice + (N) Congress should ban what breaks democracy; C: criminalize. WEAKEST: the smuggled “best remedy” premise — granting the whole problem, why criminalization over platform liability or labeling? And “deceptive” is undefined (satire? parody?). Warn teams off the lazy version (“enforcement is hard”) — imperfect enforcement doesn’t defeat laws, and note the agreement it exposes: everyone concedes the problem; the battle is the remedy. That echoes last session’s deeper lesson: opponents often concede the problem and fight only over the remedy. B: P1 (E) past media panics, society adapted; hidden (C) AI is relevantly like past media + (N) don’t regulate when adaptation likely (“premature” smuggles the threshold); C: regulation premature. WEAKEST: the analogy — scale, speed, personalization, zero cost. But B has SEVERAL legitimate weakest points (the universal “doomsayers were wrong,” the cherry-picked examples, the adaptation-beats-prevention assumption) — reward any well-defended choice; the skill is the defense, not matching the key. C: P1 (E) platforms profit from viral; P2 (E) deepfakes engineered viral; hidden link (E) so platforms profit FROM deepfakes; P3 (N, “only fair” flags it) whoever profits from a harm should be liable for it; C: platforms liable. WEAKEST: P3 proves too much (phone companies profit from calls scammers use — liable?); the principle needs narrowing, and “amplify” is the battleground: promoting is a stronger liability case than hosting. If teams add “liability would change behavior” — flag it: that premise belongs to a consequentialist argument, not this fairness one.

Four Moves, Complete

Two sessions, four moves — practiced on a presidential debate, policy prose, and Socrates:

Spot the argument — reasons for a disputed claim, or just noise?
Rebuild it — standard form, hidden premises said aloud, charitably.
Sort the premises — empirical, conceptual, normative — and catch the hidden ought.
Probe the weak point — often the therefore, not the facts.

Live speech comes too fast to check in real time — these moves let you slow it down and check it. Do that before you repost, vote, or argue back.

NARRATION: And that completes the arc. Four moves, practiced on a presidential debate, policy prose, and Socrates. Spot the argument. Rebuild it charitably in standard form. Sort the premises — empirical, conceptual, normative — and catch the smuggled ought. Probe the weak point — often the therefore, not the facts. Live speech will always flood you. The pause button is yours now: use it before you repost, before you vote, before you argue back. Close the two-session arc: point back at the previous session’s Quick Logic Check — same three questions, now a trained reflex with a sorting step attached. Moves 1-2 were the previous session; moves 3-4 were today; the team activity used all four. Next sessions: validity and truth (deduction vs. induction), then the checklist grows teeth in the fallacies sessions. The pause-button line calls back the flood — floods win live, standard form wins on paper. End there; don’t add content after the punchline.

References

Hume, D. (1739). A treatise of human nature, Book 3, Part 1.
Plato. (n.d.). Euthyphro.