obverting

Thus, if _No S is not-P_ be given us to recover the obvertend or to find the corresponding affirmative; the proposition being formally negative, we apply the rule for obverting negatives: 'Remove the negative sign, and for the predicate substitute its contradictory.'

Logic Deductive and Inductive Carveth Read 1889

It may not, at first, be obvious why the process of alternately obverting and converting any proposition should ever come to an end; though it will, no doubt, be considered a very fortunate circumstance that it always does end.

Logic Deductive and Inductive Carveth Read 1889

By thus obverting (k) and simply converting (s) (in sum, contrapositing) the major premise, and obverting the minor premise, we get a syllogism in Ferio, thus:

Logic Deductive and Inductive Carveth Read 1889

Similarly, to obtain the obvertend of _All S is not-P_, apply the rule for obverting Affirmatives; and this yields _No S is P_.

Logic Deductive and Inductive Carveth Read 1889

Formally to draw a conclusion, we must have affirmative grounds, such as in this case we may obtain by obverting both premises:

Logic Deductive and Inductive Carveth Read 1889

For thus to explain the _Modus tollens_, reduce it to the _Modus ponens_ (contrapositing the major premise and obverting the minor):

Logic Deductive and Inductive Carveth Read 1889

Celarent, they are easily reducible to one another by obverting their major premises and the new conclusions, thus:

Logic Deductive and Inductive Carveth Read 1889

It is needless to intimidate the reader by drawing up these four moods in battle array: they always admit of reduction to the foregoing moods by obverting the hypotheticals.

Logic Deductive and Inductive Carveth Read 1889