2. In E, or ‘No A is B,’ both subject and predicate enter wholly. ‘No A whatsoever is any one out of all the Bs;’ ‘search the whole collection of Bs, and every B shall be found to be something which is not A.’
3. In I, or ‘Some A is B,’ both subject and predicate enter partially. ‘Some of the As are found among the Bs, or make up a part (the whole possibly, but not known from the preceding) of the Bs.’
4. In O, or ‘Some A is not B,’ the subject enters partially, and the predicate wholly. ‘Some As are none of them any whatsoever of the Bs; every B will be found to be no one out of a certain portion of the As.’
It appears then that,
In affirmatives, the predicate enters partially.
In negatives, the predicate enters wholly.
In contradictory propositions, both subject and predicate enter differently in the two.
The converse of a proposition is that which is made by interchanging the subject and predicate, as follows:
| The proposition. | Its converse. |
|---|---|
| A Every A is B | Every B is A |
| E No A is B | No B is A |
| I Some A is B | Some B is A |
| O Some A is not B | Some B is not A |
Now, it is a fundamental and self-evident proposition, that no consequence must be allowed to assert more widely than its premises; so that, for instance, an assertion which is only of some Bs can never lead to a result which is true of all Bs. But if a proposition assert agreement or disagreement, any other proposition which asserts the same, to the same extent and no further, must be a legitimate consequence; or, if you please, must amount to the whole, or part, of the original assertion in another form. Thus, the converse of A is not true: for, in ‘Every A is B,’ the predicate enters partially; while in ‘Every B is A,’ the subject enters wholly. ‘All the As make up a part of the Bs, then a part of the Bs are among the As, or some B is A.’ Hence, the only legitimate converse of ‘Every A is B’ is, ‘Some B is A.’ But in ‘No A is B,’ both subject and predicate enter wholly, and ‘No B is A’ is, in fact, the same proposition as ‘No A is B.’ And ‘Some A is B’ is also the same as its converse ‘Some B is A;’ here both terms enter partially. But ‘Some A is not B’ admits of no converse whatever; it is perfectly consistent with all assertions upon B and A in which B is the subject. Thus neither of the four following lines is inconsistent with itself.