chapter  5
42 Pages

Verification in Geometry

Inordertofindhowmetaphysicaljudgmentscanbeverified,Kant considershowgeometricalknowledgeisobtained.Hedoessobecause therearetworespectsinwhichgeometricalknowledgeresemblesthe knowledgewhichmetaphysicsseeks.First,whatoneknowsbyageometricaljudgmentoneknowsmustbeso.Hencegeometricaljudgments canonlybeverifiedapriori.Second,geometricaljudgmentsaresynthetic. Kantdoesnotdenythatgeometryalsoavailsitselfofanalyticjudgments. Whathepointsoutisthatitisonlybymeansofsyntheticjudgmentsthat geometryisabletoenlargeknowledge.Thereis,however,animportant. differencebetweenmetaphysicsandgeometry.Metaphysicshasnotsucceededinarrivingatauthoritativeknowledge.Geometry,ontheother hand,longagoenteredonthepathofascience.HenceKantthinksthat geometrystandsinnoneedofaninvestigationofhowitobtains knowledge.Heinquireshowgeometricaljudgmentsareverifiedonlyfor thelightitcanthrowonhowmetaphysicaljudgmentsmaybeverified.1It willbeusefultoconsiderhow,assynthetic,Kantholdsthatgeomatrical judgmentsareverified,andthentoconsiderhowheholdsthattheyare verifiedapriori.