| 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:
“Mental health depends upon the maintenance of a balance within the personality between the basic human urges and egocentric wishes on the one hand and the demands of conscience and society on the other hand.”
—Selma H. Fraiberg (20th century)
“Jesus wept; Voltaire smiled. From that divine tear and from that human smile is derived the grace of present civilization.”
—Victor Hugo (1802–1885)
“Your views are now my own.”
—Marvin Cohen, U.S. author and humorist.
In conversation, after having taken a strong position in an argument and heard a complete refutation of his position.
“The very existence of society depends on the fact that every member of it tacitly admits he is not the exclusive possessor of himself, and that he admits the claim of the polity of which he forms a part, to act, to some extent, as his master.”
—Thomas Henry Huxley (1825–95)