Chapter 9-Obversion, Conversion, and Contraposition

Chapter 9-Obversion, Conversion, and Contraposition

Obversion

To obvert a sentence you must:

1. Change the quality of the sentence

- affirmative to negative

- negative to affirmative

"all s is p" "no s is p"

"some s is p" "some s is not p"

After Step 1:

All S is P No S is P

No S is P All S is P

Some S is P Some S is not P

Some S is not P Some S is P

2. Negate the predicate

-add a "not" in front of the predicate

"all s is p" "no s is p" "no s is NOT p"

Negating the predicate

Group work

Contraposition of A

Obversion, unlike the other two work on all four proposition types:

They dont look like they are equivalent; but logically they are

After Steps 1 and 2 have been applied:

original sentence: All men are mortal

step 1 obvert: No men are non-mortal

step 2 convert: No non-mortals are men

step 3 obvert: All non-mortals are non-men

A and O Basic contraposition

All S is P All non-P is non -S

Some S is not P Some non-P is S

With your group you will make a presentation of the assigned chapter based on the review at the end of chapter 9.

You will have 10 minutes to work

Group 1- chapter 4

Group 2- chapter 5

Group 3-chapter 6/7

Group 4-chapter 8

Group 5- chapter 9 summary

Intro

Contraposition

Double Negation of the Predicate in I Statements

Two statements are logically the same: logically equivalent

Three ways to convert propositions into their logical equivalents:

1. Obversion

2. Conversion

3. Contraposition

Three steps:

1. Obvert the statement

2. Convert the statement

3. Obvert the statement again

Only used with A and O statements

With I statements- two negations in the predicate after obversion

"Some S is P"......"Some S is not non P"

To change from affirmative to negative in particular statements you negate the predicate (step 1)

Some S is P........Some S is not P

Negate the predicate again (step 2)

Some S is not P..........Some S is not non-p

Conversion

Four ways of phrasing the predicate when obverting I statements

1. Simply place two 'not's' at the beginning of the predicate-term

2. Make the second 'not' a 'non' and attach it to the predicate word with a dash.

3. Place an 'im,' 'un,' 'in,' or an 'ir' at the beginning of the predicate-term.

4. Apply the rule of double negation

Conversion is easier than obversion: only one step

1. interchange the subject and the predicate

"No S is P" "No P is S"

" Some S is P" " Some P is S"

**Only works for E and I statements

Partial conversion of A statements:

If A is true it can be converted to I but in a slightly different way:

*Interchange S and P and change the statements quantity.

"All dogs are animals" "Some animals are dogs"

Be careful that you do not negate the predicate-term by using an antonym.

do not negate 'large' to 'small'

Double Negation

Sometimes adding another 'not' makes the statement sound awkward.

The rule of double negation says that a term which is not negated is equivalent to a term that is negated twice (and vice-versa).

"not not P" is logically equivalent to "P"

In O statements- end up with triple negation if we don't use the double negation rule

" Some S is not P"....."Some S is not not not P"

In practical terms: O statements don't change from the original

" some S is not P"....."Some S is not P"