THE CONVENIENCE OF THE TYPESETTER; NOTATION AND TYPOGRAPHY IN FREGE’S GRUNDGESETZE DER ARITHMETIK

Abstract. WediscussthetypographyofthenotationusedbyGottlobFregeinhis GrundgesetzederArithmetik . § 1. Background to the GrundgesetzederArithmetik . GrundgesetzederArithmetik wastohavebeenthepinnacleofGottlobFrege’slife’swork—arigorousdemonstrationofhowthefundamentallawsofclassicalpuremathematicsofthenaturalandrealnumberscanbederivedfromprincipleswhich,inFrege’sview,werepurelylogical.Hislogicalsystem,called Begriffs-schrift ,i.e.,“concept-script”,wasfirstintroducedin1879inhisbookwiththistitle[19].Itincludesthefirstoccurrenceinformallogicofquantifiers, 1 withwhichmultipleandembeddedgeneralitycouldbeexpressed—noear-lierlogicalsystemwascapableofthis.Italsooffersthefirstformulationofalogicalsystemthatcontainsrelationsratherthanmerelymonadicpredicates.Inaddition,Fregeherepresentshiscelebrateddefinitionoftheancestralofarelation.Takentogether,thesedevelopmentsmadelogicexpressivelyade-quateformathematicsforthefirsttimeinhistory[13,pp.xxxv–xxxvi]. Begriffsschrift isthuswidelyacknowledgedasthegreatestadvanceinlogicsinceAristotle—asW.V.Quineputit[43,p.vii]:Logicisanoldsubject,andsince1879ithasbeenagreatone.In1884Fregepublishedthebook

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