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Thedifferencebetweenthemathematicalandtheintuitivemind.[1]—Intheonetheprinciplesarepalpable, butremovedfromordinaryuse; sothatforwantofhabititisdifficulttoturnone’smindinthatdirection: butifoneturnsitthithereversolittle, oneseestheprinciplesfully, andonemusthaveaquiteinaccuratemindwhoreasonswronglyfromprinciplessoplainthatitisalmostimpossibletheyshouldescapenotice.
Butintheintuitivemindtheprinciplesarefoundincommonuse, , andnoeffortisnecessary; itisonlyaquestionofgoodeyesight, butitmustbegood, fortheprinciplesaresosubtleandsonumerous, ; thusonemusthaveveryclearsighttoseealltheprinciples, andinthenextplaceanaccuratemindnottodrawfalsedeductionsfromknownprinciples.
Allmathematicianswouldthenbeintuitiveiftheyhadclearsight, fortheydonotreasonincorrectlyfromprinciplesknowntothem; andintuitivemindswouldbemathematicaliftheycouldturntheireyestotheprinciplesofmathematicstowhichtheyareunused.
