The Star in the West

THE NEW WINE 231 tion of straight which has no reference to size , but only to quality , by defining “ a straight line is the shortest between two points ” (which is certainly untrue :? “ Two straight lines cannot enclose a space ,' is better ; for in the definition which he gives , Kant does not seem to have grasped the true conception of “ straight." ] Hume , Kant states , severed pure mathe matics from synthetic judgements à priori , and herein made a great mistake , as all mathematical judgements he asserts are synthetic . [ But is his dogmatism cor rect ? Crowley would disagree .] [(a.) Mathematics is analytic , because a parabola is but a name , and all its qualities are directly deducible from its definitions , etc. , etc. , and therefore contained therein , though not seen . ( 6) Mathematics is based on racial experience , and even on individual learning ; only a few highly developed brains can apprehend its propositions . It may be doubted whether any synthetic judgement exists at all ; for the moment it is made it becomes analytic . This is obvious of “ A ” and “ E ” propositions , and only not so of “ I” and “ 0,” be cause the subject is impure .] Kant then rejecting metaphysics as a true science ( p.21 ), asserts , however with confidence , “ that certain pure synthetic cognitions are really given à priori , namely , pure mathematics and pure natural science , ... both . . . partly apodictically certain through mere Reason .” [ However he fails to quote any such proposition ! And his “ apodictic certainty ” only means that the human mind is unable to transcend that limitation . Thus metaphysics is a mere branch of psychology , for one thing ; for another , every result 1 What relation is there between our conceptions of rectitude and length ? None , till geometry informs us .