Key notes on the profound rules of Obversion

Obversion is another type of immediate inference. The premise and the conclusion of obversion are known as obvertend and obverse respectively. In obversion we get an affirmative equivalent of a negative proposition or a negative equivalent of an affirmative proposition.

Obversion may be defined as a kind of immediate deductive inference satisfying following conditions:

(i) The subject of the obverse is same as that of the subject of the obventend. In other words, if the term ‘S’ is the subject of the obvertend then the same ‘S’ is the subject of the obverse.

(ii) The predicate of the obverse is the contradictory of the predicate of the obvertend. In other words, if P is the predicate of the obvertend, then the contradictory of P i.e. ‘not -P’ is the predicate of the obverse.

(iii) The quality of the obverse is the opposite of the quality of the obvertend. This means, if the obvertend is affirmative then the obverse is negative and if the obvertend is negative, the obverse is affirmative.

(iv) The quantity of the obverse is same as that of the quantity of the obvertend. In other words, if the obvertend is universal then obverse is universal and similarly, if the obvertend is particular, the obverse is particular.

Note that these conditions effectively give us a method of obtaining or finding an observe for any categorical proposition that is in standard form. The acceptability of the process of obversion involves the following argument.

As we know that when a predicate term P is affirmed (or denied) of the subject, its contradictory i.e. ‘not P’ is denied (or affirmed) of subject. This is so because any term ‘t’ and its contradictory ‘not-t’ are mutually exclusive.

Since the predicate of the obverse is the contradictory of the predicate of the obvertend, the moment we change the quality the obverse and the obvertend become equivalent. Because, here a kind of double negative rule (i.e. “a double negation is equivalent to affirmation”) is involved. Now let us see the application of the process of obversion as it pertains to different types of logical propositions such as A, E. I and O-propositions.

Obversion of A-Proposition :

A All men are mortal. Overtend

E No men are non-mortal. Obverse

Let an A proposition of the form ‘All S is P’ be our obvertend. To obtain its obverse, let us follow the following instructions. The subject of the obverse would be S, according to condition (i) Then “Not – P” being the contradictory of the predicate of the obvertend, would be the predicate of the obverse by use of the condition (ii) of the definition of obversion.

According to the condition (iii) the quality of the obverse is negative as the convertend is affir­mative. Further, according to the condition (iv) the quantity of the obverse would be same as that of the quantity of the obvertend. Thus, taking these conditions into consideration the obverse of an A-proposition of the form “All S is P’ is an E-proposition of the form “No S is not- P”. For example,

A All Sis P. Obvertend

E No S is not-P. Obverse

Similarly

A All men are mortal. Obvertend

E No men are non-mortal. Obverse

Obversion of E-Proposition:

Let the obvertend be an E-proposition of the form “No S is P”. To find the obverse of an E-proposition we follow the following instructions. By our condition (i) as given above ‘S’ would be the subject of the obverse because ‘S’ is the subject of the obvertend.

According to condition (ii) ‘Not-P’, being the contradictory of the predicate ‘P’ of the obvertend would be the predicate of the obverse. Further, according to the condition (iii) quality of the obverse would be affirmative as the obvertend is negative. Finally, according to the condition (iv), the quantity of the obverse would be the same as that of the quantity of obvertend. Thus, all these considerations imply that the obversion of an E-proposition is an A-proposition. For example,

E       No S is P. Obvertend

A       All S is not P. Obverse

Similarly,

E       No man is perfect. Obvertend

A .     All men are non-perfect. Obverse

Obversion of I-Proposition:

Let the obvertend be an I-proposition of the form “Some S is P”. Then to obtain its obverse, we follow the following instructions. Firstly, by the condition (i) ‘S’ would be the subject of the obverse. Then ‘P’ being the predicate of the obverted, “not-P” would be the predicate of the observe by the condition (ii) of obversion. Further, by condition (iii) the observe would be a negative proposition as the obvertend is an affirmative proposition (i.e I-proposition).

Finally, according to condition (iv) the observe would be particular as the obvertend is particular. Therefore, taking all these into account, we conclude that the obverse of an I-proposition, “Some S is P”, would be an O-proposition of the form “Some S is not not-p”, For example.

I – Some S is P. Obvertend

0 – Some S is not not-P. Obverse.

Similarly,

I – Some men are poor. Obvertend

O – Some men are not not-poor. Obverse

Obversion of an O-proposition:

“Some S is not P” is an O-proposition for which we now try to obtain its obverse. As explained earlier according to the condition (i) and (ii) of the definition of obversion, the subject and the predicate of the obverse would be “S” and “not-P” respectively. By the condition (iii), the obverse would be affirmative as the obvertend is negative. Finally, according to the condition, (iv) the obverse would be particular as the obvertend is particular. From all these considerations, we conclude that the obverse of an O-proposition is an I-proposition. For example,

0 – Some S is not P. Obvertend

I – Some S is not-P. Obverse.

Similarly,

0 – Some men are not wise. Obvertend.

I – Some men are not-wise. Obverse.

We may now summaries the immediate inferences relating to obversion in a tabular form as given below.

Obvertend	Obverse
A All S is P.	E No S is not-P.
E No S is P.	A All S is not-P.
I Some S is P	0 Some S is not not-P
0 Some S is not P.	I Some S is not-P.