Conversion

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.