2.8 KiB
2.8 KiB
- A syllogism is an instance of a form of reasoning in which a conclusion is drawn from two given or assumed propositions; a common or middle term is present in the two premises but not in the conclusion, which may be invalid.
- Aristotle
Double Negation ¬ Elim ¬ ¬ p p
| Propositions | Premises | Conclusion |
|---|---|---|
| p | \neg\neg p |
p |
| T | T | T |
| F | F | F |
Hypothetical syllogism; this says that if p implies q and q implies r, then it can be logically concluded that p implies r. p ⇒ q q ⇒ r p ⇒ r
| Propositions | Premises | Conclusion | |||
|---|---|---|---|---|---|
| p | q | r | p \implies q |
q \implies r |
p \implies r |
| T | T | T | T | T | T |
| T | T | F | T | F | |
| T | F | T | F | T | |
| T | F | F | F | T | |
| F | T | T | T | T | T |
| F | T | F | T | F | |
| F | F | T | T | T | T |
| F | F | F | T | T | T |
- Involves linking implications together in a sequential manner, much like the links in a chain.
p ∨ q q Therefore, p
| Propositions | Premises | Conclusion | ||
|---|---|---|---|---|
p |
q |
p \lor q |
q |
p |
| T | T | T | T | T |
| T | F | T | F | T |
| F | T | T | T | F |
| F | F | F | F | F |
p ⇒ q q ⇒ p Therefore, p ∧ q
| Propositions | Premises | Conclusion | ||
|---|---|---|---|---|
| p | q | p \implies q |
q \implies p |
p \land q |
| T | T | T | T | T |
| T | F | F | T | F |
| F | T | T | F | F |
| F | F | T | T | F |
p \implies q
r \implies s
p \lor r (p disjunction (or) r)
Conclusion: q \lor s
The "Constructive Dilemma": If the disjunction of the antecedent of two implications holds then the disjunction of the conclusions also must hold