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1、1NewworkforatheoryofuniversalsINTRODUCTIOND.M.Armstrongoffersatheoryofuniversalsastheonlyadequateanswertoa'compulsoryquestion'forsystematicphilosophy:theprob-lemofOneoverMany.1Ifindthislineofargumentunpersuasive.ButIthinkthereismoretobesaidforArmstrong'stheorythanhehimselfhassa
2、id.ForasIbearitinmindconsideringvarioustopicsinphilos-ophy,Inoticetimeandagainthatitofferssolutionstomyproblems.WhateverwemaythinkoftheproblemofOneoverMany,universalscanearntheirlivingdoingothermuch-neededwork.Idonotsaythattheyareindispensable.Theservicestheyrendercouldbematche
3、dusingresourcesthatareNominalisticinletter,ifperhapsnotinspirit.2ButneitherdoIholdanypresumptionFirstpublishedinTheAustralasianJournalofPhilosophy61(1983),pp.343-377.Re-printedwithkindpermissionfromTheAustralasianJournalofPhilosophy.IamindebtedtocommentsbyGilbertHarman,LloydHum
4、berstone,FrankJack-son,MarkJohnston,DonaldMorrison,KimSterelny,andothers;andespeciallytodiscussionandcorrespondencewithD.M.Armstrongoverseveralyears,withoutwhichImightwellhavebelievedtothisdaythatsettheoryappliedtopossibiliaisallthetheoryofpropertiesthatanyonecouldeverneed.1D.M
5、.Armstrong,UniversalsandScientificRealism(CambridgeUniversityPress,1978),henceforthcitedas'Universals';seealsohis"Against'Ostrich'Nominalism:AReplytoMichaelDevitt",PacificPhilosophicalQuarterly61(1980)pp.440-449.2Inthispaper,IfollowArmstrong'straditionalterminology:'universals'
6、arerepeatableentities,whollypresentwhereveraparticularinstantiatesthem;'Nominalism'istheagainstuniversals,totheeffectthattheyaretobeacceptedonlyifwehavenoalternative.Ithereforesuspendjudgementaboutuni-versalsthemselves.Ionlyinsistthat,onewayoranother,theirworkmustbedone.Ishalli
7、nvestigatethebenefitsofaddinguniversalstomyownusualontology.Thatontology,thoughNominalistic,isinotherre-spectsgenerous.Itconsistsofpossibilia—particular,individualthings,someofwhichcompriseouractualworldandothersofwhichareunactualised3—togetherwiththeiterativehierarchyofclasses
8、builtupfromthem.ThusIalreadyhaveatmydisposalatheoryofp
