***
Hypothetical Negative
Hypothetical Negative (p -> ~q)
Read as any of the following:
No p is q
If p then not q
The hypothetical negative says that when an antecedent (p) happens (is true) then some other thing (the consequent) (q) will necessarily not happen (that is it will be false). The hypothetical negative can be defined by taking the reading "If p then not q" and writing it as such.
Hence (p -> ~q).
| p | q | ~q | p -> ~q | Comments |
| T | T | F | F | The antecedent happens and the consequent also happens so the statement is false since both are true. |
| T | F | T | T | The antecedent happens but the consequent does not happen, so the statement is true. This is a simple statement of the definition . |
| F | T | F | T | The antecedent does not happen but the consequent does happen so the statement is true since if the antecedent of a conditional is false result is always true. |
| F | F | T | T | The antecedent does not happen and nor does the consequent so the statement is true since if the antecedent of a conditional is false result is always true. |
Derivation
| p | q | ~q | p -> ~q |
| T | T | T | F |
| T | F | F | T |
| F | T | T | T |
| F | F | F | T |
