Page:Mind (New Series) Volume 15.djvu/532

518 HUGH MACCOLL : SYMBOLIC EEASONING. simple elementary notions on which my formulae and opera- tions are founded, his whole reasoning is, from beginning to end, irrelevant. On page 153, for example, he mixes up logic with psychology and defines a statement as impossible when, and only when, nobody can believe it. 1 Now, the belief in witchcraft is not yet dead. It follows therefore from Mr. Shearman's definition that it is still possible for old women to ride through the air on broomsticks, and that so long as the belief lasts, the possibility will last also. 1 Mr. Shearman's exact words are as follows : " As an instance of the way in which statements described by these three terms are to be dealt with, take the following : ' It is impossible that x is y '. This would appear in such a form as ' A thinker who can believe that x is y does not exist' ." The " three terms " to which Mr. Shearman refers are the words certain, impossible, variable, respectively denoted by my symbols t , 77, & (see 15-18).