Validity
Validity is a formal property of deductive arguments. An argument is valid if and only if there is no possible situation in which all premises are true and the conclusion is false. Validity is about logical form, not about whether the premises are actually true. A valid argument preserves truth: feed in true premises, and a true conclusion is guaranteed.
How It Appears Per Course
PHIL 252
The central concept of Unit 3. Validity is introduced as the “truth-preserving method” — the guarantee that good deductive structure delivers. The unit pairs it with soundness and teaches both counter-example testing and truth-value mapping.
Validity vs. Soundness
| Validity | Soundness | |
|---|---|---|
| What it requires | No possible true-premise / false-conclusion situation | Valid + all premises actually true |
| Depends on | Logical form only | Form AND factual truth |
| Can have false premises? | Yes | No |
| Guarantees true conclusion? | Only if premises are true | Yes — always |
Soundness is a subset of validity. All sound arguments are valid, but not all valid arguments are sound.
Counter-Examples
The definitive test for invalidity. A counter-example is a possible situation (doesn’t have to be real) where the premises are true and the conclusion is false. One counter-example is sufficient to prove an argument invalid. No counter-examples exist for a valid argument — by definition.
Five Valid Argument Forms
| Name | Structure | Memory Hook |
|---|---|---|
| Modus Ponens | If P→Q. P. ∴ Q | ”Method of Affirming” — affirm the antecedent |
| Modus Tollens | If P→Q. ¬Q. ∴ ¬P | ”Method of Denying” — deny the consequent |
| Hypothetical Syllogism | If P→Q. If Q→R. ∴ If P→R | Chain of conditionals |
| Disjunctive Syllogism | P or Q. ¬P. ∴ Q | Eliminate one option (exclusive or) |
| Constructive Dilemma | If P→Q. If R→S. P or R. ∴ Q or S | Two conditionals + a disjunction |
Two Invalid Forms (Formal Fallacies)
| Name | Structure | Why Invalid | Mimics |
|---|---|---|---|
| Affirming the Consequent | If P→Q. Q. ∴ P | Q can be true for other reasons besides P | Modus Ponens |
| Denying the Antecedent | If P→Q. ¬P. ∴ ¬Q | Q can still hold even if P is absent | Modus Tollens |
Key test: For both invalid forms, a counter-example can always be constructed. E.g., for Affirming the Consequent: “If it rains, the ground is wet. The ground is wet. ∴ It rained.” Counter-example: a sprinkler could have run.
Truth-Value Mapping
Systematically test all possible combinations of T/F values for all variables. If any combination produces all-true premises with a false conclusion → the argument is invalid.
Antecedent and Consequent
In a conditional “If P, then Q”:
- Antecedent: the “if” part (P)
- Consequent: the “then” part (Q)
Valid moves: affirm the antecedent (MP) or deny the consequent (MT).
Invalid moves: affirm the consequent or deny the antecedent.
Cross-Course Connections
Argument — validity is the formal standard for deductive arguments
Cogency — informal standard that complements validity for inductive contexts
Syllogism — categorical syllogisms are tested for validity with Venn diagrams
InformalFallacies — informal fallacies fail validity in content/context, not just form
Key Points for Exam/Study
- Validity ≠ truth: a valid argument can have all false premises
- Soundness = validity + true premises → the gold standard
- One counter-example is enough to disprove validity
- The five valid forms must be memorized: MP, MT, HS, DS, CD
- The two invalid forms are “impostors” that look like valid forms — know what makes them fail
- Disjunctive Syllogism requires exclusive or — both can’t be true simultaneously