Three Acts of the Mind Mental Act: Verbal Expression: • Simple Apprehension •Term • Judgment • Proposition • Deductive Inference • Syllogism

Slide 9-1

Obversion, Conversion & Contraposition The Three relations of equivalence Obversion Double Negation Conversion Contraposition Review of Chapters 4-9 Slide 9-2

1 Equivalence: Three ways to convert logical statements into their logical equivalents Obversion Conversion Contraposition

Slide 9-3

Obversion

Change the quality of the statement Negate the predicate Slide 9-4

2 How to change the quality of a statement If the statement is affirmative, simply make it negative If the statement is negative, simply make it affirmative Be careful not to change the quantity of the statement: AÅÆE, IÅÆO Slide 9-5

Examples of how to change the quality of a statement: All S is P Æ No S is P No S is P Æ All S Is P Some S is P Æ Some S is not P Some S is not P Æ Some S is Slide 9-6 P

3 How to change the quality of a statement

Simply place a ‘not’ in front of it.

Slide 9-7

How to obvert an A statement Change the quality: All S is P Æ No S is P Then negate the predicate: No S is P Æ No S is not P

Slide 9-8

4 How to obvert an E statement Change the quality: No S is P Æ All S is P Then negate the predicate: All S is P Æ All S is not P

Slide 9-9

How to obvert an O statement Change the quality: Some S is not P Æ Some S is P Then negate the predicate: Some S is P Æ Some S is non-P

Slide 9-10

5 The Rule of Double Negation

A term that is not negated is equivalent to a term that is negated twice and vice- Slide 9-11 versa.

How to perform double negation 1. Place two ‘not’s at the beginning of the predicate-term 2. Make the second ‘not’ a ‘non’ and attach it to the predicate term with a dash 3. Place an ‘im’, ‘un’, ‘in’, or ‘ir’ at the beginning of the predicate term 4. Apply the rule of double negation

Slide 9-12

6 How to obvert an I statement Change the quality: Some S is P Æ Some S is non-P Then negate the predicate: Some S is not P Æ Some S is not non-P

Slide 9-13

Conversion

Interchange the subject and predicate

Slide 9-14

7 How to convert an E and I statements Interchange the subject and the predicate: No S is P Æ No P is S Some S is P Æ Some P is S

Slide 9-15

Partial conversion of A statements Interchange the subject and the predicate and change the quantity:

All S is P Æ Some S is P Slide 9-16

8 Contraposition Obvert the statement Convert the statement Obvert the statement again

Slide 9-17

How to convert an A statement

Original Statement: All men are mortal

Obvert: No men are non-mortal Convert: No non-mortals are men Obvert: All non-mortals are non-men

Slide 9-18

9 Obversion, Conversion & Contraposition

Equivalents A E I O

Obversion 3 3 3 3

Conversion 3 3

Contraposition 3 3

Slide 9-19

10