VALID FORMS | INVALID FORMS |
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Modus Ponens p→q p ∴q One premise is a conditional statement, the other premise affirms the antecedent, and the conclusion affirms the consequent. Also called Direct Reasoning, or Law of Detachment, among others. | Fallacy of the Converse (Affirming the Consequent)
p→q q ∴p One premise is a conditional statement, the other premise affirms the consequent, and the conclusion affirms the antecedent. |
Modus Tollens p→q ¬q ∴¬p One premise is a conditional statement, the other premise denies the consequent, and the conclusion denies the antecedent.. Also called Indirect Reasoning, or Contrapositive Reasoning, among others. | Fallacy of the Inverse (Denying the Antecedent)
p→q ¬p ∴¬q One premise is a conditional statement, the other premise denies the antecedent, and the conclusion denies the consequent. |
Hypothetical Syllogism p→q q→r ∴p→r One premise is a conditional statement, a second premise is a conditional statement whose antecedent matches the consequent of the other premise, and the conclusion results from this chain of reasoning. Also called Transitive Reasoning. | Misuse of Hypothetical Syllogism p→q p→r ∴q→r p→q r→q ∴p→r An incorrect attempt at Hypothetical Syllogism, in which two conditional premises agree in the antecedent, or agree in the consequent. Also called a False Chain. |
Disjunctive Syllogism p∨q ¬q ∴p One premise is a disjunction, the other premise denies one of the disjuncts, and the conclusion affirms the other disjunct. | Disjunctive Fallacy (Affirming a Disjunct) p∨q q ∴¬p One premise is a disjunction, the other premise affirms one of the disjuncts, and the conclusion denies the other disjunct. |
Disjunction Introduction p ∴p∨q |
Conjunction Elimination p∧q ∴p |
Conjunction Introduction p q ∴p∧q |
Constructive Dilemma (p→q)∧(r→s) p∨r ∴q∨s |
Universal Instantiation ∀xP(x) ∴P(c) |
Existential Instantiation ∃xP(x) ∴P(c) |
Existential Generalization P(c) ∴∃xP(x) |