| 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:
“... in Northern Ireland, if you don’t have basic Christianity, rather than merely religion, all you get out of the experience of living is bitterness.”
—Bernadette Devlin (b. 1947)
“Jesus wept; Voltaire smiled. From that divine tear and from that human smile is derived the grace of present civilization.”
—Victor Hugo (1802–1885)
“Because a person is born the subject of a given state, you deny the sovereignty of the people? How about the child of Cuban slaves who is born a slave, is that an argument for slavery? The one is a fact as well as the other. Why then, if you use legal arguments in the one case, you don’t in the other?”
—Franz Grillparzer (1791–1872)
“Let us say it now: to be blind and to be loved, is indeed, upon this earth where nothing is complete, one of the most strangely exquisite forms of happiness.”
—Victor Hugo (1802–1885)