| Basic and Derived Argument Forms | ||
|---|---|---|
| Name | Sequent | Description |
| Modus Ponens | If then ; ; therefore | |
| Modus Tollens | If then ; not ; therefore not | |
| Hypothetical Syllogism | If then ; if then ; therefore, if then | |
| Disjunctive Syllogism | Either or, or both; not ; therefore, | |
| Constructive Dilemma | If then ; and if then ; but or ; therefore or | |
| Destructive Dilemma | If then ; and if then ; but not or not ; therefore not or not | |
| Bidirectional Dilemma | If then ; and if then ; but or not ; therefore or not | |
| Simplification | and are true; therefore is true | |
| Conjunction | and are true separately; therefore they are true conjointly | |
| Addition | is true; therefore the disjunction ( or ) is true | |
| Composition | If then ; and if then ; therefore if is true then and are true | |
| De Morgan's Theorem (1) | The negation of ( and ) is equiv. to (not or not ) | |
| De Morgan's Theorem (2) | The negation of ( or ) is equiv. to (not and not ) | |
| Commutation (1) | ( or ) is equiv. to ( or ) | |
| Commutation (2) | ( and ) is equiv. to ( and ) | |
| Commutation (3) | ( is equiv. to ) is equiv. to ( is equiv. to ) | |
| Association (1) | or ( or ) is equiv. to ( or ) or | |
| Association (2) | and ( and ) is equiv. to ( and ) and | |
| Distribution (1) | and ( or ) is equiv. to ( and ) or ( and ) | |
| Distribution (2) | or ( and ) is equiv. to ( or ) and ( or ) | |
| Double Negation | is equivalent to the negation of not | |
| Transposition | If then is equiv. to if not then not | |
| Material Implication | If then is equiv. to not or | |
| Material Equivalence (1) | ( is equiv. to ) means (if is true then is true) and (if is true then is true) | |
| Material Equivalence (2) | ( is equiv. to ) means either ( and are true) or (both and are false) | |
| Material Equivalence (3) | ( is equiv. to ) means, both ( or not is true) and (not or is true) | |
| Exportation | from (if and are true then is true) we can prove (if is true then is true, if is true) | |
| Importation | If then (if then ) is equivalent to if and then | |
| Tautology (1) | is true is equiv. to is true or is true | |
| Tautology (2) | is true is equiv. to is true and is true | |
| Tertium non datur (Law of Excluded Middle) | or not is true | |
| Law of Non-Contradiction | and not is false, is a true statement | |
Read more about this topic: Propositional Calculus
Famous quotes containing the words basic, derived, argument and/or forms:
“It is not an exaggeration to say that play is as basic to your child’s total development as good food, cleanliness, and rest.”
—Joanne E. Oppenheim (20th century)
“Ex oriente lux may still be the motto of scholars, for the Western world has not yet derived from the East all the light which it is destined to receive thence.”
—Henry David Thoreau (1817–1862)
“A striking feature of moral and political argument in the modern world is the extent to which it is innovators, radicals, and revolutionaries who revive old doctrines, while their conservative and reactionary opponents are the inventors of new ones.”
—Alasdair Chalmers MacIntyre (b. 1929)
“For forms of Government let fools contest;
Whate’er is best administered is best.”
—Alexander Pope (1688–1744)