4 Laws Governing Logical Oppositions

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  • Topic: Logic, Truth, Contradiction
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C. FOUR LAWS GOVERNING LOGICAL OPPOSITIONS
1. Law of Contradiction 3. Law of Sub-Alternation 2. Law of Contrariety 4. Law of Sub-Contrariety

1. Law of Contradiction
→ Two contradictory propositions cannot be both true and both false at the same time. * If A is true, O is false * If A is false, O is true * If O is true, A is false * If O is false, A is true * If E is true, I is false * If E is false, I is true * If I is true, E is false * If I is false, E is true

2. Law of Contrariety
→ States that two contrary propositions cannot be both true but they may be both false at the same time. * If A is true, E is false
* If E is true, A is false
* If A is false, E is doubtful
* If E is false, A is doubtful
3. Law of Sub-Alternation
a) States that the truth of the universal carries or implies the truth of the particular but not vice versa. * If A is true, I is true
* If E is true, O is true
* If I is true, A is doubtful
* If O is true, E is doubtful
b) States that the falsity of the particular carries or implies the falsity of the universal but not vice versa. * If I is false, A is false
* If O is false, E is false
* If A is false, I is doubtful
* If E is false, O is doubtful

4. Law of Sub-Contrariety
→ States that two contrary propositions can’t be both false but they maybe both true at the same time. * If I is false, O is true
* If O is false, I is true
* If I is true, O is doubtful
* If O is true, I is doubtful

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