54 lines
2.8 KiB
Markdown
54 lines
2.8 KiB
Markdown
1. 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.
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2. Aristotle
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**Double Negation ¬ Elim ¬ ¬ p p**
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| Propositions | Premises | Conclusion |
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| ------------ | ------------ | ---------- |
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| p | $\neg\neg p$ | p |
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| T | T | T |
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| F | F | F |
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**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**
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| Propositions | | | Premises | | Conclusion |
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| ------------ | --- | --- | -------------- | -------------- | -------------- |
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| p | q | r | $p \implies q$ | $q \implies r$ | $p \implies r$ |
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| T | T | T | T | T | T |
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| T | T | F | T | F | |
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| T | F | T | F | T | |
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| T | F | F | F | T | |
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| F | T | T | T | T | T |
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| F | T | F | T | F | |
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| F | F | T | T | T | T |
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| F | F | F | T | T | T |
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1. Involves linking implications together in a sequential manner, much like the links in a chain.
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**p ∨ q q Therefore, p**
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| Propositions | | Premises | | Conclusion |
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| ------------ | --- | ---------- | --- | ---------- |
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| $p$ | $q$ | $p \lor q$ | $q$ | p |
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| T | T | T | T | T |
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| T | F | T | F | T |
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| F | T | T | T | F |
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| F | F | F | F | F |
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**p ⇒ q q ⇒ p Therefore, p ∧ q**
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| Propositions | | Premises | | Conclusion |
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| ------------ | --- | -------------- | -------------- | ----------- |
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| p | q | $p \implies q$ | $q \implies p$ | $p \land q$ |
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| T | T | T | T | T |
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| T | F | F | T | F |
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| F | T | T | F | F |
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| F | F | T | T | F |
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$p \implies q$
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$r \implies s$
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$p \lor r$ (p disjunction (or) r)
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Conclusion: $q \lor s$
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The "Constructive Dilemma": If the disjunction of the antecedent of two implications holds then the disjunction of the conclusions also must hold
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