Thereason, therefore, , andthat, accustomedtotheexactandplainprinciplesofmathematics, andnotreasoningtilltheyhavewellinspectedandarrangedtheirprinciples, ; theyarefeltratherthanseen; , andtojudgerightlyandjustlywhentheyareperceived, withoutforthemostpartbeingabletodemonstratetheminorderasinmathematics; becausetheprinciplesarenotknowntousinthesameway, , atoneglance, andnotbyaprocessofreasoning, , andthatmenofintuitionaremathematicians, becausemathematicianswishtotreatmattersofintuitionmathematically, andmakethemselvesridiculous, wishingtobeginwithdefinitionsandthenwithaxioms, , butitdoesittacitly, naturally, andwithouttechnicalrules; fortheexpressionofitisbeyondallmen, andonlyafewcanfeelit.
Intuitiveminds, onthecontrary, beingthusaccustomedtojudgeatasingleglance, aresoastonishedwhentheyarepresentedwithpropositionsofwhichtheyunderstandnothing, andthewaytowhichisthroughdefinitionsandaxiomssosterile, andwhichtheyarenotaccustomedtoseethusindetail, thattheyarerepelledanddisheartened.
Butdullmindsarenevereitherintuitiveormathematical.
Mathematicianswhoareonlymathematicianshaveexactminds, providedallthingsareexplainedtothembymeansofdefinitionsandaxioms; otherwisetheyareinaccurateandinsufferable, fortheyareonlyrightwhentheprinciplesarequiteclear.
Andmenofintuitionwhoareonlyintuitivecannothavethepatiencetoreachtofirstprinciplesofthingsspeculativeandconceptual, whichtheyhaveneverseenintheworld, andwhicharealtogetheroutofthecommon.
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