| 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:
“Of course I lie to people. But I lie altruistically—for our mutual good. The lie is the basic building block of good manners. That may seem mildly shocking to a moralist—but then what isn’t?”
—Quentin Crisp (b. 1908)
“There is, it seems to us,
At best, only a limited value
In the knowledge derived from experience....”
—T.S. (Thomas Stearns)
“Argument is conclusive ... but ... it does not remove doubt, so that the mind may rest in the sure knowledge of the truth, unless it finds it by the method of experiment.... For if any man who never saw fire proved by satisfactory arguments that fire burns ... his hearer’s mind would never be satisfied, nor would he avoid the fire until he put his hand in it ... that he might learn by experiment what argument taught.”
—Roger Bacon (c. 1214–1294)
“The time will come when the evil forms we have known can no more be organized. Man’s culture can spare nothing, wants all material. He is to convert all impediments into instruments, all enemies into power.”
—Ralph Waldo Emerson (1803–1882)