Understanding the profound rules of conversion

Conversion is a kind of immediate inference. It has one premise and a conclusion. The premise of conversion is called convertend and the conclusion is called converse. In other words, the proposition to which conversion is applied or the proposition which is to be converted is called convertend and the result or the conclusion is called converse.

We may define conversion as a kind of immediate inference in which the subject and predicate terms of the convertend are inter charged, the quality of the converse is same as that of the convertend and also it satisfies the principle of distribution (i.e. no term is distributed in the converse unless it is distributed in the convertend. An immediate inference satisfying the following rules (or conditions) is called conversion.

i. The subject and the predicate terms of the convertend inter charge their position in the converse. This means that the subject term of the convertend becomes the predicate of the converse and the predicate term of the convertend becomes the subject of the converse.

ii. The quality of the converse is the same as that of the quality of the convertend. In other words, if the convertend is affirmative then the converse is affirmative and if the convertend is negative then the converse is also negative.

iii. The quantity of the converse will be determined according to the principle of distribution, i.e. no term is distributed in the converse if it is not distributed in the convertend.

From the definition and the rules of Conversion as stated above, it follows that given a convertend, the converse of it is obtained just by interchanging the subject and predicate of the convertend so that the quality of the converse should be same as that of the convertend.

Moreover, the principle of distribution should not be violated. Thus, to find the converse of any given convertend, we have to find answers to these following questions, viz. what should be the subject of the converse? What should be the predicate of the converse? What should be the quality of the converse? And what should be the quantity of the converse? Since we have four types of propositions, A, E, I and O. let us check to find out the converse (if any) of these four types of propositions.

Conversion of A-Proposition:

Let an A-proposition ‘All S is P’ be our convertend. To find its converse, let us interchange the subject and the predicate of the convertend according to the first condition of the definition of Conversion.

Hence, ‘S’ being the subject of the convertend becomes the predicate of the converse and ‘P’ being the predicate of the convertend becomes the subject of the converse. Then according to the second condition, the quality of the converse must be affirmative because the convertend v affirmative. So the negative propositions E and O are ruled out as the converse of A proposition by this condition.

So far as the quantity of the converse is concerned we have the options, that the converse is either an A-proposition or an I proposition. The first option is also ruled out, recause, if the converse of an A-proposition would be an A-proposition then P being the subject of the converse will be distributed in the converse without being distributed in the convertend. This will violate the rule of distribution. So only I-proposition can be the converse of an A-proposition. So, we conclude that the conversion of an A-proposition is an I-proposition. For example,

A   All S is P. Convertend

I    Some P is S. Converse

A   All men are mortal. Convertend

I    Some mortal beings are men. Converse

Note that in some special cases the conversion of an A-proposition is also an A- propositions. Consider any A-proposition asserting a definition (e.g. “All triangles are plane figures bounded by three straight lines”) or an A-proposition where the subject and predicate are co-referential (e.g. “All creatures with a heart are creatures with kidneys) as our convertend.

To get the converse, the subject and the predicate of the convertend are being transposed i.e. the subject of the convertend becomes the predicate of the converse and the predicate of the convertend becomes the subject of the converse. The quality of the converse is the same as that of the convertend.

Thus, the converse of an A-proposition is either A-proposition or an I- proposition. For example, if we derive an I-proposition such as “Some plane figures bounded by three straight lines are triangles” from an A-proposition, “All triangles are plane figures bounded by three straight lines,” then the converse seems to be odd as it gives the impression in our ordinary use of language that there can be plane figures bounded by three straight lines which are not triangles. Hence in such case (or cases) the converse of an A-proposition is an A-proposition. For example,

A “All triangles are plane figures bounded by three straight lines.” Convertend

A “All plane figures bounded by three straight lines are triangles.” Converse

A “All creatures with a heart are creatures with kidneys.” Convertend

A “All creatures with kidneys are creatures with a heart.” Converse

To sum up we may say in general that the converse of an A-proposition is an I-proposition but in some cases (where the subject and predicate terms of the convertend are co-referential of the convertend asserts a definition) the conversion of an A-proposition is an A-proposition.

Conversion of E-Proposition:

Let an E-proposition say “No S is P” be our convertend. To find its converse, let us interchange the subject and predicate of the convertend. So, ‘P’ and ‘S’ will be subject and predicate of the converse respectively. By the second condition the converse will be negative £ the convertend is negative.

So far as quantity of the converse is concerned, it should be universe (i.e. an E-proposition) because in this case the principle of distribution is not violated. Because the converse both the subject and predicate terms are distributed and these are also distributed in the convertend. Hence there is no violation of the principle of distribution. Thus, the converse fan E-proposition is an E-proposition.

E No S is P Convertend

E No P is S    Convserse

E No married person is a bachelor. Convertend

E No bachelor is a married person. Converse

Conversion of I-Proposition:

Let an I-proposition “Some S is P” be our convertend. To find its converse let us interchange the subject and predicate of the convertend. Thus, ‘P’ and ‘S’ will be the subject and predicate of the converse respectively by the condition (i) of the definition of conversion.

The converse must be affirmative as the convertend is affirmative by condition (ii) of the definition of conversion. But so far as the quantity of the converse is concerned, we have two options; Case-1 – the converse is an A-proposition and Case 2 – the converse is an I-proposition. If case- holds (i.e. if the converse is an A-proposition) then P being the subject of the converse will be distributed without being distributed in the convertend.

Hence the principle of distribution will be violated. So, Case-1 cannot hold. In other words, the converse of an I-proposition cannot be an A-proposition. If case 2 holds, then the converse of an I-proposition is an I-proposition. In this case, the principle of distribution is not violated, because converse being an I-proposition distributes no term. So the question of violation of the principle of distribution does not arise. Therefore, converse of an I-proposition is an I-proposition, For example,

I Some S is P.   Convertend

I Some P is S.   Converse

I Some men are rich. Convertend

I Some rich persons are man. Converse

Let an O-proposition “Some S is not P” be our convertend. Then to find its converse we have to interchange the subject and predicate in the convertend. Hence, ‘P’ and ‘S’ would be our subject and predicate of the converse respectively. Further, the converse would be negative as the convertend is negative according to the condition (ii) of the definition of conversion.

So far as its quantity is concerned we have two cases for consideration viz. Case I converse is an E- proposition and Case-2, converse is an O-proposition. In either case, S being the predicate term of the converse will be distributed in the converse without being distributed in the convertend. Thus, in both the cases the principle of distribution would be violated. Therefore, O-proposition admits (or has) no converse. In other words, an O-proposition cannot be converted.

Now we may say that the converse of A, E and I-proposition are I, E and I-proposition respectively. Hence, two forms of conversion are being recoginsed. These are (i) Simple conversion and (ii) Conversion per limitation (or Conversion per Accidents).

Conversion is called simple conversion if both the convertend and the converse have the same quantity. For example, E and I proposition admit simple conversion. The conversion of an E-proposition is an E-proposition and so also the conversion of an I-proposition is again an I-proposition. Sometimes, the conversion of an A-proposition admits simple conversion if the subject and predicate terms of the convertend have the same denotation, i.e. they are co-referential. For example,

A All triangles are plane figures bounded by three straight lines. Convertend

A All plane figures bounded by three straight lines are triangles, converse.

In this example, the subject and predicate terms of the convertend have the same deno­tation or they are co-referential.

So, the conversion of A-proposition in these cases would be again an A-proposition. In other words, if the denotation of the subject and predicate terms of the convertend are equal (or co-referential) then the conversion of an A-proposition is also an A-proposition. But, in general the conversion of an A-proposition is an I-proposition. We may summaries the immediate inferences relating to conversion in a tabular form as given below.

	Converted	Converse
A	All S is P	Some P is S	I
E	No S is P	No P is S	E
I	Some S is P	Some P is S	I
O	Some S is Not P	Nil	Nil