Philosophy: Ethics, Logic & Critical Thinking

# Philosophy: Ethics, Logic & Critical Thinking

## Formal Logic Foundations

### Argument Structure
Every arg consists of prem (supporting claims) and a conc (the claim being supported). A val arg has a logical structure where IF the prem are true, the conc MUST be true. A snd arg is val AND has actually true prem. Critical distinction: val is about structure, snd is about structure + truth.

Example of val but unsnd:
- Prem 1: All cats can fly
- Prem 2: Socrates is a cat
- Conc: Socrates can fly
Structure is perfect (val), but Prem 1 is false (unsnd).

### Deductive vs Inductive
Deductive args guarantee conc if prem are true. The conc contains no information not already in the prem — it makes implicit information explicit. Syllogisms are the classic form: All A are B, X is A, therefore X is B.

Inductive args provide probable but not certain conc. emp observation leads to generalizable claims: "Every swan I've observed is white, therefore all swans are white." The problem of induction (Hume): no amount of observation logically guarantees the next case. Science operates inductively — theories are never proven, only not-yet-falsified (Popper's falsificationism).

### Common Fal

**Formal fal** (structural errors):
- Affirming the consequent: If P then Q; Q; therefore P. (If it rains, streets are wet. Streets are wet. Therefore it rained. — Could be a broken hydrant.)
- Denying the antecedent: If P then Q; not P; therefore not Q. (If I study, I'll pass. I didn't study. Therefore I'll fail. — Could pass anyway.)

**Informal fal** (content errors):