3.2 Evaluating Inferences: Deductive Validity & Other Grounds

A. Validity — the deductive standard An inference is deductively valid if the conclusion must be true whenever the premises are true. Test by trying to imagine the premises true and conclusion false — if impossible, valid.Valid forms (memorise — they are the grammar of legal logic): | Form | Pattern | |---|---| | Modus ponens | If P then Q; P; ∴ Q | | Modus tollens | If P then Q; not-Q; ∴ not-P | | Disjunctivesyllogism | P or Q; not-P; ∴ Q | | Hypothetical syllogism | If P then Q; if Q then R; ∴ if P then R | | Categorical syllogism | All M are P; S is M; ∴ S is P |Invalid forms (the fallacies of form):• Affirming the consequent — If P then Q; Q; ∴ P. (If he committed the murder he fled; he fled;∴ he committed it — innocent people also flee).• Denying the antecedent — If P then Q; not-P; ∴ not-Q. (If she signed, she is bound; shedidn't sign; ∴ not bound — maybe bound by ratification!).• Undistributed middle — All judges are lawyers; all prosecutors are lawyers; ∴ all prosecutors are judges. (No.)B. Other grounds — when deduction does not apply Most real inferences are not deductive; they are judged by strength instead of validity:•…