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Chapter 6- Contradictory and Contrary Statements
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Chapter 6- Contradictory and Contrary Statements
The Rule of Contraries
Two statements are contrary to one another if they are both universals but differ in quality.
Only one combination of statements are contrary: A and E
*both universal, one affirmative and one negative
*Same quantity but different quality
The Second Law of Opposition
Relationships among the Four Categorical Statements
I
O
Examples..
Contraries cannot at the same time both be true, but can at the same time both be false.
A: All men are mortal
O: Some men are not mortal
Can these both be true or false?
E: No men are happy
I: Some men are happy
Can these both be true or false?
"All S is P" is true then "No S is P" must be false...vise versa
"All S is P" is false, "No S is P" could be either true or false.
Example:
"All men are mortal"
"No men are mortal"
Both cant be true. Both can be false though.
Introduction
First Law of Opposition
Rule of Contradiction
Contradiction cannot at the same time be true nor at the same time be false.
Contradictory statements are statements that differ in both quality and quantity.
Two types of relationships categorical statements can have...
1. Opposition
- four different kinds
2. Equivalence
-three different kinds
We will discuss the first two types of opposition
A: All S is P
O: Some S is not P
If A is false then O must be true and vise versa
*same for E and I
Introduction cont...
Statements that are in opposition affirm and deny the same predicate of the same subject.
There are four ways that A,I,E,O can be related in opposition.
-Contradictory
-Contrary
-Subcontrary
-Subalternate
Contraries
A
E
All S is P
No S is P
Contradictories
Some S is P
Some S is NOT P
Quality
Affirmative
Negative
Universal
E
A
Quantity
O
Particular
I