Equivalence of Propositions

1. Equivalence of Propositions – the formulation of a new proposition, with the same meaning as the original, by interchanging the subject and predicate terms of the latter and/or by the use or removal of negatives.

1. conversion – interchanging the subject and predicate terms of the original but leaving its quality unchanged.

convertend original proposition	S is P
converse resultant proposition	Ps is Sp

1.a. simple done by simply interchanging subject and predicate terms because they have the same quantity. Note that the quantity of the converse should be the same as the quantity of the convertend.

E – E	No dog is a cat – No cat is a dog.
I - I	Some pictures are clear prints – Some clear print are pictures.

1.b. partial – the unioversal quantity of the convertend becomes particular in the converse.

A – I

All horses are animals – Some animals are horses.

It is advisable to reduce a proposition to its logical form before attempting conversion. Simple conversion is applied to a singular proposition whose predicate is also singular.

2. obversion – formulating a new proposition [obverse] by retaining the subject term and quantity of the original proposition [obvertend], changing its quality, and using as predicate term the contradictory of the original predicate term. The procedure for obversion is as follows:

1. Retain the subject quality of the obvertend.

2. Change the quality.

3. As new predicate, use the contradictory of the predicate of the obvertend.

A – E	All me are sinful.	-	All me are not sinless.
I - O	Some house are white.	-	Some houses are not non-white.
E – A	No person is indispensable.	-	All persons are dispensable.
O - I	Some jewels are not rare.	-	Some jewels are non-rare.

3. contraposition – the formulation of a new proposition [contraposit] whose subject is the contradictory of the predicate of the original proposition [contraponend]. There are two types of contraposition and the corresponding procedures are as follows:

Type 1:

1. Obvert

2. Convert the obverse.

[contraponend] A - E [contraposit]

E - I

O - I

A - E
Every dog is an animal.	Every dog is not a non-animal.	Every non-animal is a dog.
E - I
No dog is a cat.	All dogs are non-cats.	Some non-cats are dogs.
O - I
Some men are not voters.	Some men are non-voters.	Some non-voters are men.

Type 2:

1. Obvert.

2. Convert the obverse.

3. Then obvert the converse of the obverse.

[contraponend] A - A [contraposit]

E - O

O - I

A - A
Every man is mortal.	Every man is not immortal.	Every immortal is not a man.	Every immortal is a non-man.
E - O
No dog is a cat.	All dogs are non-cats.	Some non-cats are dogs.	Some non-cats are not non-dogs.
O - I
Some men are not voters.	Some men are non-voters.	Some non-voters are men.	Some non-voters are not non—men.