tence expressed otherwise than in the identical words of its framer.
The next rule to be borne in mind, in order not to stumble in reading the Syllabus, is one that needs a touch of elementary logic to be understood. It is thus conveyed: "When a proposition is pronounced false, its contradictory is declared to be true; its contrary may be, or may not be, true." I crave my reader's forbearance for this bit of scholasticism; one word of explanation will make it as clear as noonday, and I really could not have left it out without loss.
In short; one sentence is said to be contradictory to another when it conveys just as much as is wanted, and no more than is wanted, to affirm the falsehood of the opposite one. For example, if I read this sentence: "All the Catholic members of the House of Commons voted for the disestablishment of the Irish Church;" its contradictory might be thus formulated:
"Not all the Catholic members voted for disestablishment." The latter does not state that many members or even that more than one member withheld his vote; it simply denies that all voted. Between two contradictions there is no medium; if one is true, the other is false; and hence when a sentence is condemned as false, its contradictory is thereby defined as true.
But it is otherwise with two contrary propositions. Propositions are said to be contrary when one not only asserts the falsehood of the other, but affirms more than was necessary to make its opposite false. Thus, these two propositions: "All the members voted," "None of the members voted," are said to be contrary; the second denies a great deal more than was required to
