Conversion
Chapter Forty-Five
Syllabus topic 3.3, "Eduction& types of Eductions. [Conversion, ...]"
Pages 215 to 218 of 334
In one line
To convert a proposition is to interchange its subject and predicate without changing its quality.
In the wording a student can write in an examination: conversion is the immediate inference in which the subject of the given proposition, called the convertend, becomes the predicate of the inferred proposition, called the converse, and the predicate becomes the subject, the quality remaining unchanged.
The two rules
Rule one: the quality must not change. An affirmative convertend gives an affirmative converse, and a negative gives a negative.
Rule two: no term may be distributed in the converse unless it was distributed in the convertend. This is the distribution rule of sequence 310, and it is what does all the real work.
Everything below follows from those two, applied to the distribution table.
The four propositions
E converts simply. "No S is P" gives "No P is S".
In E both terms are distributed, so nothing can be distributed in the converse that was not distributed in the convertend. The converse is again an E proposition, with both terms distributed, and the rule is satisfied. "No minor's agreement is enforceable" gives "no enforceable agreement is a minor's agreement."
I converts simply. "Some S is P" gives "Some P is S".
In I neither term is distributed, and neither is distributed in the converse either, so the rule is satisfied trivially. "Some agreements are contracts" gives "some contracts are agreements."
A converts only by limitation. "All S is P" gives "Some P is S", and not "All P is S".
Here is the derivation, and it is the examinable part. In A, the subject is distributed and the predicate is not. If the converse were "All P is S", then P, which is the subject of that universal, would be distributed. But P was undistributed in the convertend. That breaks rule two, so the universal converse is not available. The converse must therefore be particular, and a particular affirmative distributes neither term, which is permitted. "All contracts are agreements" gives "some agreements are contracts", and never "all agreements are contracts."
This is called conversion by limitation, or conversion per accidens, because quantity has been given up.
O has no converse at all. "Some S is not P" gives nothing.
The derivation is worth doing carefully because it is the one students cannot reconstruct. In O, the subject is undistributed and the predicate is distributed. The converse must be negative, by rule one, so it must be an E or an O.
If the converse were E, "No P is S", both terms would be distributed. But S was undistributed in the original. Breach.
If the converse were O, "Some P is not S", then S, as the predicate of a negative proposition, would be distributed. But S was undistributed in the original. Breach again.
Conversion
Both possibilities fail, so O cannot be converted, and this is not an oversight but a proof.
The table
| Convertend | Converse | Name | Why |
|---|---|---|---|
| A All S is P | I Some P is S | By limitation | P undistributed in the original, so it cannot be the subject of a universal |
| E No S is P | E No P is S | Simple | Both terms distributed in both |
| I Some S is P | I Some P is S | Simple | Neither term distributed in either |
| O Some S is not P | none | S undistributed in the original, distributed in every candidate converse |
The modern qualification
Conversion by limitation depends on the A proposition asserting that its subject class has members. Without existential import, "all S is P" may be true when there are no S at all, and "some P is S" would then assert an existence that the original did not.
So on the modern reading A has no converse either. E and I convert simply on both readings; A converts by limitation only on the traditional reading; O never converts.
As with the square of opposition, the traditional rules are what MU examines, and a complete answer states them and adds the qualification in a sentence.
Where a lawyer meets the failure to convert
The single commonest logical error in reading a statute is converting an A proposition as though it were an E.
"All registered documents are admissible" does not give "all admissible documents are registered". It gives only "some admissible documents are registered".
"Every person of the age of majority is competent to contract" does not give "every person competent to contract is of the age of majority". A company is competent to contract and has no age.
"All decrees are appealable" does not give "all appealable orders are decrees", and this one matters, because certain orders are appealable although they are not decrees.
The pattern in each case. The provision states that one class is inside another. Reading it backwards asserts that the two classes are the same, and a provision almost never says that. Where a provision does mean both directions it says so, by using "if and only if", "and no other", or a definition clause with "means". That is why the difference between "means" and "includes" at sequence 180 matters so much: "means" makes an equivalence, which converts in both directions, and "includes" does not.
A worked example
Section 91 of the Code of Civil Procedure 1908 provides that in the case of a public nuisance or other wrongful act affecting or likely to affect the public, a suit for a declaration and injunction may be instituted by the Advocate-General, or with the leave of the Court by two or more persons.
Conversion
Reduce. As an A proposition: All suits validly instituted under this section are suits instituted either by the Advocate-General or, with leave, by two or more persons.
Convert. By limitation only: some suits instituted by the Advocate-General or, with leave, by two or more persons are suits validly instituted under this section.
Read what the converse does and does not say. It says that at least some such suits are validly instituted. It does not say that every suit brought by the Advocate-General is valid under the section, and quite rightly: the section also requires a public nuisance or other wrongful act affecting the public, and a suit by the Advocate-General about something else is not within it at all.
The error the rule prevents. A submission that "the Advocate-General has instituted the suit, so it falls within section 91" converts an A proposition simply, and it drops the requirement about the subject matter of the suit. Stating the section as a proposition and applying the rule of conversion catches that in one step, before any authority is looked at.
Distinctions that carry marks
| Simple conversion | Conversion by limitation | |
|---|---|---|
| Quantity | Unchanged | Universal becomes particular |
| Applies to | E and I | A |
| Reason | Distribution permits it | The predicate of A is undistributed |
| Survives the modern reading | Yes | No |
| Conversion | Obversion | |
|---|---|---|
| Quality | Never changes | Always changes |
| Terms | Swapped | Predicate negated |
| Valid for | E, I simply; A by limitation; not O | All four |
What this does not mean
Conversion is not a way of strengthening a proposition. It restates it, and where it limits quantity it weakens it.
The failure of O to convert is not a defect of the rules. It is a proof: both candidate converses distribute a term that was undistributed, so no converse is available.
Simple conversion of A is not merely a bad habit. It is the standard misreading of statutory provisions, and it changes an inclusion into an identity.
Quick revision
Conversion: interchange subject and predicate, quality unchanged.
Two rules: quality never changes; no term distributed in the converse that was undistributed in the convertend.
E converts simply. I converts simply. A converts by limitation only, giving an I. O has no converse.
Why A is limited: its predicate is undistributed, so it cannot become the subject of a universal.
Why O fails: its subject is undistributed, and it would be distributed in every candidate converse, whether E or O.
Modern qualification: conversion by limitation needs existential import, so on the modern reading A has no converse either.
Conversion
Legal application: "all A are B" never gives "all B are A". This is the standard misreading of a statutory provision.
Test yourself
1. Define conversion and state its two rules.
Conversion is the immediate inference in which the subject and predicate of the given proposition are interchanged, the subject of the convertend becoming the predicate of the converse and the predicate becoming the subject. Its rules are that the quality must not be changed, so an affirmative gives an affirmative and a negative a negative, and that no term may be distributed in the converse unless it was distributed in the convertend.
2. Which propositions convert simply, and why?
E and I. In E both terms are distributed, so the converse, which is also an E and also distributes both, cannot distribute anything that was not already distributed. In I neither term is distributed, and neither is distributed in its converse, so the rule is satisfied trivially. In both cases the quantity is preserved and nothing is given up.
3. Why does A convert only by limitation?
Because in "all S is P" the predicate P is undistributed, being the predicate of an affirmative proposition. A universal converse "all P is S" would make P the subject of a universal and therefore distributed, which breaks the distribution rule. The converse must accordingly be particular, and "some P is S" distributes neither term, so it is permitted. Quantity has been given up, which is what "by limitation" records.
4. Prove that O has no converse.
In "some S is not P" the subject S is undistributed and the predicate P is distributed. The converse must be negative, so it is either E or O. If it were "no P is S", both terms would be distributed, including S, which was undistributed. If it were "some P is not S", then S, as the predicate of a negative proposition, would again be distributed. Both candidates breach the distribution rule, so no converse exists.
5. What is the modern qualification to the rules of conversion?
That conversion by limitation depends on the universal asserting that its subject class has members. On the modern reading a universal carries no such assertion, so "all S is P" may be true where nothing is S, while "some P is S" would assert that something exists. Conversion by limitation therefore fails, and on the modern reading only E and I convert, both simply.
6. Give a legal example of the error of converting an A proposition simply.
"Every person of the age of majority is competent to contract" does not yield "every person competent to contract is of the age of majority", since a company is competent and has no age. The pattern is general: a provision that places one class inside another is misread as asserting that the two classes are the same. Where a provision does mean both directions it says so, by a definition using "means" or by words such as "and no other".
The rest of this subject
These notes are cut from the University's printed syllabus. Open the syllabus itself, or the past papers, for the same subject.