Post by Fringe Pioneer on Feb 16, 2011 2:31:36 GMT
In symbolic logic, you can have simple truth functional statements (statements that can be true or false). Arbitrary constants that represent a simple statement are represented by a single capital letter.
To make more complex truth functional statements, you can apply any number of any of the various logical operators.
Variables can represent a truth functional statement of any complexity, and are represented by a single lowercase letter.
An argument is a set of premises (given truth functional statements) and the conclusion that they are supposed to derive, also a truth functional statement.
A person likes math or likes literature.
If a person likes math and literature, then a person likes philosophy.
A person neither not likes math nor not likes literature.
/∴ A person likes philosophy.
A person can perform calculus.
A person cannot make good poetry.
/∴ A person likes to eat cake.
An argument can be valid or invalid. An argument is invalid if there is an instance where all premises can be simultaneously true and the conclusion false; otherwise, an argument is valid.
The validity of an argument can be tested either by creating truth tables or by proofs. When using proofs, various rules of inference must be used to derive the conclusion from the premises.
To make more complex truth functional statements, you can apply any number of any of the various logical operators.
Variables can represent a truth functional statement of any complexity, and are represented by a single lowercase letter.
Operator | Operation |
~ | Negation (NOT) |
· | Conjunction (AND) |
∨ | Disjunction (OR) |
⊃ | Material Implication (IF...THEN) (IMPLIES) |
≡ | Material Equivalence (IF AND ONLY IF) |
x | ~x |
False | True |
True | False |
x | y | x · y |
False | False | False |
False | True | False |
True | False | False |
True | True | True |
x | y | x ∨ y |
False | False | False |
False | True | True |
True | False | True |
True | True | True |
x | y | x ⊃ y |
False | False | True |
False | True | True |
True | False | False |
True | True | True |
x | y | x ≡ y |
False | False | True |
False | True | False |
True | False | False |
True | True | True |
An argument is a set of premises (given truth functional statements) and the conclusion that they are supposed to derive, also a truth functional statement.
A person likes math or likes literature.
If a person likes math and literature, then a person likes philosophy.
A person neither not likes math nor not likes literature.
/∴ A person likes philosophy.
A person can perform calculus.
A person cannot make good poetry.
/∴ A person likes to eat cake.
An argument can be valid or invalid. An argument is invalid if there is an instance where all premises can be simultaneously true and the conclusion false; otherwise, an argument is valid.
The validity of an argument can be tested either by creating truth tables or by proofs. When using proofs, various rules of inference must be used to derive the conclusion from the premises.