Note 287 — Chapter IX

The validity of the above result will perhaps be more clearly seen by substituting for the hypotheticals their (assertoric) disjunctive equivalents, namely, Either A is not true or C is true, Either A is not true or C is not true. As a concrete example, we may take the propositions, “If this pen is not cross-nibbed, it is corroded by the ink,” “If this pen is not cross-nibbed, it is not corroded by the ink.” Supposing that the pen happens to be cross-nibbed, we cannot regard either of these propositions as false. It will be observed that their disjunctive equivalents are, “This pen is either cross-nibbed or corroded by the ink,” “This pen is either cross-nibbed or not corroded by the ink.” Take again the propositions, “If the sun moves round the earth, some astronomers are fallible.” “If the sun moves round the earth, all astronomers are infallible.” The truth of the first of these propositions will not be denied, and on the interpretation of hypotheticals with which we are here concerned the second cannot be said to be false. It may be taken as an emphatic way of denying that the sun does move round the earth.