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:
“Unlike femininity, relaxed masculinity is at bottom empty, a limp nullity. While the female body is full of internal potentiality, the male is internally barren.... Manhood at the most basic level can be validated and expressed only in action.”
—George Gilder (b. 1939)
“All moral discipline, all moral perfection derived from the soul of literature.”
—Thomas Mann (18751955)
“Our argument ... will result, not upon logic by itselfthough without logic we should never have got to this pointbut upon the fortunate contingent fact that people who would take this logically possible view, after they had really imagined themselves in the other mans position, are extremely rare.”
—Richard M. Hare (b. 1919)
“Ring out a slowly dying cause,
And ancient forms of party strife;
Ring in the nobler modes of life,
With sweeter manners, purer laws.”
—Alfred Tennyson (18091892)