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. Some A is not B and Every B is A Some A is not B and No B is A Some A is not B and Some B is A Some A is not B and Some B is not A. We find then, including converses, which are not identical with their direct propositions, _six_ different ways of asserting or denying, with respect to agreement or non-agreement, total or partial, between A and, say X: these we write down, designating the additional assertions by U and Y. │Identical. │ Identical. │ A Every A is X│E No A is X│I Some A is X│O Some A is not X U Every X is A│„ No X is A│„ Some X is A│Y Some X is not A We shall now repeat and extend the table of page 8 (A), &c., meaning, as before, the denial of A, &c. From A or (O) follow A, (E), I (O) From E or (I) (A), E, (I), O, (U), Y From I or (E) (E) I From O or (A) (A), O From U or (Y) (E) I, U (Y) From Y or (U) (U) Y Having thus discussed the principal points connected with the simple assertion, we pass to the manner of making two assertions give a third. Every instance of this is called a syllogism, the two assertions which form the basis of the third are called premises, and the third itself the conclusion.