🎯 What Is Logic About?
Logic focuses on arguments, i.e., sets of statements where one (the conclusion) is supported by the others (premises).
Argument: a set of reasons offered to persuade someone of a claim.
📜 Definitions
- Premise: statement providing support.
- Conclusion: statement being supported.
- Indicator words:
- Premise indicators: since, because, for, given that…
- Conclusion indicators: therefore, hence, thus, so, it follows that…
🧩 Finding Arguments
Arguments occur everywhere — in editorials, conversations, debates, articles, etc.
When indicators are absent, apply the Principle of Charity:
In unclear cases, interpret the passage as the strongest possible argument.
🧮 Deductive vs. Inductive Character
For now, focus on deductive arguments — those meant to make the conclusion necessarily follow from the premises.
We determine validity by matching the reasoning to valid argument patterns.
⚙️ Common Valid Deductive Patterns
| Pattern | Structure | Example |
|---|---|---|
| Modus Ponens (MP) | If A → B; A ⇒ B | If it rains, it snows. It rains → it snows. |
| Modus Tollens (MT) | If A → B; ¬B ⇒ ¬A | If it rains, it’s humid. Not humid → no rain. |
| Hypothetical Syllogism (HS) | If A → B; If B → C ⇒ If A → C | If rain → humid; humid → cloudy → rain → cloudy |
| Disjunctive Syllogism (DS) | A ∨ B; ¬A ⇒ B | Either I go to show or study. Not show → study. |
| Chain Argument | Combination of HS + MP | If A→B, B→C, A → therefore C |
| Exclusive Or | A ⊕ B; A ⇒ ¬B | Either stay home or go out (not both). I stayed → not out. |
| Constructive Dilemma (CD) | If A→B & If C→D; A∨C ⇒ B∨D | If study→do well, if party→fail; either study or party ⇒ do well or fail |
| Universal Syllogism (US) | All A→B; All B→C ⇒ All A→C | All humans→mammals; mammals→animals ⇒ humans→animals |
| Predicate Instantiation (PI) | All A→B; x is A ⇒ x is B | All humans→mortal; Socrates→human ⇒ Socrates→mortal |
🚫 Invalid Patterns
| Fallacy | Form | Explanation |
|---|---|---|
| Affirming the Consequent | If A→B; B ⇒ A | Invalid reverse of MP |
| Denying the Antecedent | If A→B; ¬A ⇒ ¬B | Invalid reverse of MT |
🧱 Adding Missing Premises (Enthymemes)
Use the Principle of Charity to insert implied premises that make an argument fit a valid form.
Example:
“It rains. Thus, it is humid.”
→ Add premise: “If it rains, then it is humid.”
🧭 Summary — Argument Identification Strategy
- Identify indicator words.
- Spot conclusion and premises.
- If unclear, apply charity.
- Fit to a valid argument pattern or note it as inductive.
🧩 Lecture 1B — Diagramming Arguments
🧠 Purpose
To visualize relationships between premises and conclusions — showing how reasoning connects.
🔗 Basic Notation
- Arrow (→) = “supports”
1 → 2means Premise 1 supports Conclusion 2.
- Conjoint support: premises work together.
1 + 2 → 3
- Independent support: premises separately support conclusion.
1 → 3
2 → 3
🧮 Examples
Conjoint Support
“All humans are mortal. Socrates is human. Thus Socrates is mortal.”
→ 1 + 2 → 3
Independent Support
“Schools need funding because they need more equipment and more teachers.”
→ 1 → 3
2 → 3
⚖️ Multiple Arguments
Sometimes a conclusion of one argument becomes a premise in another.
Example:
- All mammals are animals.
- All animals are mortal.
- Thus all mammals are mortal.
- All humans are mammals.
- ∴ All humans are mortal.
Diagram:
1 + 2 → 3
3 + 4 → 5
→ Two arguments (two conclusions: 3 and 5).
🧩 Counting Arguments
# of arguments = # of conclusions in a passage.
💬 Practice Diagrams
Example 1 – Capital Punishment
- Deters murder.
- Lower murder rate worthwhile.
- Less costly than imprisonment.
- Murderers owe less to taxpayers.
- Equivalent punishment required.
- Forfeiting life = equivalent punishment.
- ∴ Capital punishment justified.
Diagram (simplified):
(1+2) → (3+4) → (5+6) → 7
or separately:
1+2 → 7, 3+4 → 7, 5+6 → 7
Example 2 – Gov’t Programs
- Efforts to save whooping cranes are effective.
- Demonstrates government funding success.
- ∴ Programs should continue.
→ Diagram:1 → 2 → 3
Example 3 – Police Officers
- People complain when police absent.
- Same people complain when police act.
- ∴ Police are “damned if they do/don’t.”
→2 + 3 → 1
Example 4 – Wars
- Soviet invasion unjust (imperialism).
- WWII just (anti‑imperialism).
- Some wars right, some wrong → cautious entry to war.
→2 + 4 → 1&3 → 5
🧾 Diagram Summary Table
| Support Type | Description | Diagram |
|---|---|---|
| Conjoint | Premises jointly support conclusion | 1 + 2 → 3 |
| Independent | Premises separately support same conclusion | 1 → 3, 2 → 3 |
| Chained | A conclusion from one argument is premise in another | 1 + 2 → 3; 3 + 4 → 5 |
🪶 Diagramming Process
- Identify each claim.
- Label premises/conclusions.
- Determine how they connect (conjoint vs. independent).
- Use arrows/plus signs to show structure.
- Each distinct conclusion marks a new argument.
🧩 Combined Takeaway
- Lecture 1A → Recognize and reconstruct valid arguments.
- Lecture 1B → Diagram argument structure to visualize logical relationships.
Together they form the foundation of logical analysis — recognizing, reconstructing, and mapping argument reasoning clearly and charitably.