SYMBOLIC EEASONING. 515 degree ; the statement A* is of a degree higher. The state- ment A. 1 2 , since it means (A**')*, is of the first degree as regards its subject A**' ; but since it also means (A*) yz , it is of the second degree as regards A*, and of the third degree as regards the root-statement A. Now, suppose A stands for Q^. In that case, though A is the root- statement as regards A*"*, it is a statement of the second degree as regards the root-statement Q ; and A*" 2 , .which is of the third degree as regards A, is of the fifth degree as regards Q ; for, expressed in terms of Q, it means Q ^ 2 . 15. Let me here say a few words in reply to the logicians who maintain that statements can only be classed as true and false, and that my introduction of such classes as certainties, impossibilities, and variables, and of any others that may concern our argument or researches, is wrong, or at any rate, outside the proper domain of logic, and especially of symbolic logic. This is very much as if one argued that since animals are only divisible into two classes, males and females, it is no business of true zoology to consider the respective characteristics of such creatures as lions, tigers, and leopards, to say nothing of others still more objection- able. All such attempts to surround symbolic logic by a Chinese wall of exclusion are futile. 16. Another argument against my system is that variable statements, statements which are sometimes true and some- times false, have no real existence ; that a statement if once true is true always, and if once false is false always. But surely this is a mere play upon words, and it does not seem to me very accurate even as that. A servant, in reply to an inquiry at the street door in the morning, says, and says truly, that " Mrs. Brown is not at home ". The same servant, in reply to the same inquiry in the afternoon, says again, and this time, in obedience to instructions, says falsely, that " Mrs. Brown is not at home ". She makes exactly the same statement as in the morning, because she uses exactly the same form of words ; but this statement, this form of words, which was true in the morning, because in the morning it conveyed true information, is false in the after- noon, because in the afternoon it conveyed false information. 17. Let us look at the matter from another point of view. Suppose we have no data but our definitions or symbolic and linguistic conventions. Let A, B, C respectively denote the three statements " 7 is greater than 5," " 6 is greater than 9," "a; 2 is greater than x". Is it not clear that with these meanings of the symbols we may truly and confidently make the three-factor compound statement A'B^C*? For,
