PHIL 252 Unit 3 — Validity as a Truth-Preserving Method
Core Argument of This Unit
Deductive logic provides a truth-preserving method: feed in true premises and a valid argument form guarantees a true conclusion. The unit distinguishes deductive from inductive arguments, defines validity and soundness, teaches five valid forms and two invalid forms, and introduces truth-value mapping and counter-examples as testing tools.
Key Ideas
Deductive vs. Inductive Arguments:
- Deductive: If premises are true, conclusion must be true. Conclusion contains no new information not already in premises. Can be overturned only by falsifying a premise.
- Inductive: If premises are true, conclusion is probable — not guaranteed. Can be overturned by new evidence. Essential in science.
Standard Form: Premises listed vertically above a horizontal line; conclusion below. Makes argument structure transparent for analysis.
Validity: A formal property. An argument is valid if and only if there is no possible situation where the premises are true and the conclusion is false. Validity is about logical form, not the actual truth of premises. A valid argument can have false premises.
Soundness: An argument is sound if it is (1) valid AND (2) all premises are actually true. Sound arguments necessarily have true conclusions. Soundness is the gold standard for deductive arguments.
Counter-Examples: The definitive test for invalidity. A counter-example is a possible situation where premises are true but the conclusion is false. One counter-example is sufficient to prove invalidity.
Five Valid Deductive Forms
| Name | Structure |
|---|---|
| Modus Ponens | If P→Q. P. ∴ Q |
| Modus Tollens | If P→Q. ¬Q. ∴ ¬P |
| Hypothetical Syllogism | If P→Q. If Q→R. ∴ If P→R |
| Disjunctive Syllogism | P or Q. ¬P. ∴ Q (exclusive or) |
| Constructive Dilemma | If P→Q. If R→S. P or R. ∴ Q or S |
Two Invalid Forms (Formal Fallacies)
| Name | Structure | Why Invalid |
|---|---|---|
| Affirming the Consequent | If P→Q. Q. ∴ P | Q can be true for other reasons besides P |
| Denying the Antecedent | If P→Q. ¬P. ∴ ¬Q | Q can still be true even if P is false |
Both impersonate their valid counterparts: Affirming the Consequent mimics Modus Ponens; Denying the Antecedent mimics Modus Tollens.
Truth-Value Mapping
Map all possible T/F combinations for the variables. If any row produces all-true premises with a false conclusion, the argument is invalid.
Key Terms
Foundational for Unit 7
- Inductive arguments are the heart of scientific reasoning — Unit 7 will extend this
- Enumerative induction (generalizing from observations) is previewed here
- Understanding why deductive validity cannot be achieved in science motivates the study of inductive standards
- Distinguishing valid form from true premises (validity vs. soundness) is critical when evaluating scientific studies