Deductive and inductive reasoning
Deduction claims its conclusion follows with necessity; induction claims only probability. Deductive arguments are valid or invalid; inductive ones are strong or weak.
Deduction and induction compared
| Point | Deductive | Inductive |
|---|---|---|
| Claim | Conclusion follows necessarily | Conclusion is probable |
| Judged as | Valid or invalid; sound if also true | Strong or weak; cogent if also true |
| New information | Conclusion already contained in premises | Conclusion goes beyond premises |
| Adding a premise | Cannot spoil a valid argument | Can strengthen or weaken it |
| Typical forms | Syllogism, modus ponens, modus tollens | Generalisation, analogy, causal, statistical |
Valid argument forms
| Form | Pattern |
|---|---|
| Modus ponens | If P then Q; P; so Q |
| Modus tollens | If P then Q; not Q; so not P |
| Hypothetical syllogism | If P then Q; if Q then R; so if P then R |
| Disjunctive syllogism | P or Q; not P; so Q |
| Constructive dilemma | If P then Q, and if R then S; P or R; so Q or S |
Validity, soundness, truth
A valid argument can have false premises and a false conclusion. The one thing it cannot have is true premises with a false conclusion.
Mill's methods of inductive (causal) inquiry
- Agreement: the one factor common to all cases of the effect is its likely cause.
- Difference: the one factor present when the effect occurs and absent when it does not.
- Joint method: agreement and difference used together.
- Residues: subtract known causes; what remains explains the remaining effect.
- Concomitant variation: when one thing varies whenever another varies, the two are probably causally connected.
How NET asks this: you classify a passage as deductive or inductive, or decide whether an argument is valid, sound or merely true, often as statements or assertion-reason.
Typical MCQ: “'Every swan I have seen is white, so all swans are white.' Deductive or inductive?” Inductive generalisation: the conclusion goes beyond the cases seen and is only probable.
Typical MCQ: “Can a valid argument have a false conclusion?” Yes, if at least one premise is false. Validity rules out only true premises with a false conclusion.
Ponens puts forward (affirms) the antecedent; tollens takes away (denies) the consequent. Affirming the consequent and denying the antecedent are the two traps.