DSCI 220, 2025 W1
September 16, 2025
Goal for today: treat valid logical arguments like legal moves in a game.
You’ll identify moves, build quick proofs, and design traps.
A valid argument is a legal inference. Content can change; form is what makes it valid.
If the lab is open, I’ll go. The lab is open. So I’ll go.
If the exam is today, the forum is quiet. The forum isn’t quiet. So the exam isn’t today.
Use these all class as a reference.
p→q, p infer qp→q, ¬q infer ¬pp→q, q→r infer p→rp∨q, ¬p infer qp, q infer p∧qp∧q infer p (or q)p infer p∨q (any q)p∨q, ¬p∨r infer q∨r(p→r), (q→s), (p∨q) infer r∨sCommon traps:
Affirming consequent: p→q, q ∴ p ❌
Denying antecedent: p→q, ¬p ∴ ¬q ❌
From p→q and p, infer q.
Ex:
If the bus is full, I’ll walk. The bus is full. So I’ll walk.
From p→q and ¬q, infer ¬p.
Ex:
If office hours moved, Slack has an announcement. No announcement. So they didn’t move.
From p→q and q→r, infer p→r.
Ex:
If tidy then joins are simpler; if simpler joins then faster viz; so tidy ⇒ faster viz.
From p∨q and ¬p, infer q.
Ex:
Dinner is sushi or tacos. Not sushi. So tacos.
∧-Intro: from p, q infer p∧q
∧-Elim: from p∧q infer p (or q)
From p infer p∨q.
Ex: I rode my scooter today, so I either rode my scooter or I’m a unicorn.
Note validity cares about form, not plausibility of the added disjunct.
From p∨q and ¬p∨r infer q∨r.
Ex:
Either study or soccer; if study then library. So soccer or library.
From (p→r), (q→s), (p∨q) infer r∨s.
Ex:
If sunny then picnic; if rainy then museum; sunny or rainy; so picnic or museum.
Affirming the consequent ❌
from p→q, q infer p
Denying the antecedent ❌
from p→q, ¬p infer ¬q
∧-Elim: \((p\wedge q)\rightarrow p\) is this always true?
Affirming Consequent: \(((p\rightarrow q)\wedge q)\rightarrow p\) is this always true?
| \(p\) | \(q\) | \(p\rightarrow q\) | \((p\rightarrow q)\wedge q\) | \(((p\rightarrow q)\wedge q)\rightarrow p\) |
|---|---|---|---|---|
| F | F | |||
| F | T | |||
| T | F | |||
| T | T |
How to play: post in chat…
(a) valid or not, (b) if valid, name the rule, (c) formal pattern.
If the lecture live-streams, the chat is busy. The chat is busy. So it live-streams.
❌ Fallacy: Affirming the consequent (p→q, q ∴ p)
If the Canucks win, downtown is loud. Downtown isn’t loud. So the Canucks didn’t win.
✅ MT (p→q, ¬q ∴ ¬p)
Dinner is sushi or tacos. Not sushi. So tacos.
✅ DS (p∨q, ¬p ∴ q)
If it rains, I’ll bus. If I’m late, I’ll bus. It’s raining or I’m late. So I’ll bus.
✅ CD with r=s=bus
If a film is MCU, it has a post-credits scene. This is MCU. So post-credits.
✅ MP (p→q, p ∴ q)
Either I practice guitar or code. If coding, then coffee. So either practice or coffee.
✅ RES: (g ∨ c) and (f v ¬c)
I stretched and hydrated. So I stretched.
✅ ∧-Elim
If a dataset is tidy then joins are simpler. If joins are simpler then viz faster. So if tidy then viz faster.
✅ HS
In the chat, each person adds exactly one line using a Rule Card.
Premises
1. D→R (deadline ⇒ review session)
2. R→C (review ⇒ crowded café)
3. D
Goal: C
Premises
1. P∨Q (pizza or quinoa)
2. ¬P∨R (if pizza then ramen)
3. ¬Q (no quinoa)
Goal: R
Your mission:
- Write one valid two-premise argument (any rule).
- Write a look-alike fallacy with the same topic words.
- Bring to class on Wednesday morning!
In chat (or poll), complete both: