Logic: Deductive and Inductive Reasoning, Syllogism
Deduction and induction
Deduction aims at validity: if the premises are true, the conclusion must be true. Induction is probabilistic: premises make the conclusion likely. The exam tests categorical syllogism: four proposition forms-A (universal affirmative), E (universal negative), I (particular affirmative), O (particular negative); terms major, minor, middle; figures; distribution; five rules.
Rules to apply
- A valid syllogism has three and only three terms, each with the same meaning.
- The middle term must be distributed at least once.
- No term may be distributed in the conclusion if undistributed in the premise (illicit major/minor).
- Two negative premises yield no conclusion; a negative premise requires a negative conclusion.
- Particular premises cannot yield a universal conclusion.
Worked example
'All men are mortal; Socrates is a man; therefore Socrates is mortal.' Form: All M are P; All S are M; therefore All S are P (Barbara, figure 1). M is distributed in the first premise; S and P are distributed in the conclusion only if universal. Valid.
Traps
Do not confuse validity with truth: a valid argument can have false premises. Do not call inductive strength 'validity'. Do not commit undistributed middle: 'All dogs are animals; all cats are animals; therefore all cats are dogs.' Do not ignore existential import in A propositions when translating to Venn diagrams.