Wilfrid Hodges - 2001 - 'Classical Logic Logic I - First-Order Logic'

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1、ClassicalLogicI:First-OrderLogicChapter1ClassicalLogicI:First-OrderLogicWilfridHodges1.1.First-OrderLanguagesTheword‘logic’inthetitleofthischapterisambiguous.Initsfirstmeaning,alogicisacollectionofcloselyrelatedartificiallanguages.Therearecertainlanguagescalledfirst-orderlanguages,a

2、ndtogethertheyformfirst-orderlogic.Inthesamespirit,thereareseveralcloselyrelatedlanguagescalledmodallanguages,andtogethertheyformmodallogic.Likewisesecond-orderlogic,deonticlogicandsoforth.Initssecondbutoldermeaning,logicisthestudyoftherulesofsoundargument.First-orderlanguagescanb

3、eusedasaframeworkforstudyingrulesofargument;logicdonethiswayiscalledfirst-orderlogic.Thecontentsofmanyundergraduatelogiccoursesarefirst-orderlogicinthissecondsense.Thischapterwillbeaboutfirst-orderlogicinthefirstsense:acertaincollectionofartificiallanguages.InHodges(1983),Igaveadescri

4、ptionoffirst-orderlanguagesthatcoversthegroundofthischapterinmoredetail.Thatotherchapterwasmeanttoserveasanintroductiontofirst-orderlogic,andsoIstartedfromargumentsinEnglish,graduallyintroducingthevariousfeaturesoffirst-orderlogic.Thismaybethebestwayinforbeginners,butIdoubtifitisthe

5、bestapproachforpeopleseriouslyinterestedinthephilosophyoffirst-orderlogic;bygoinggradually,oneblursthehardlinesandsoftensthecontrasts.So,inthischapter,Itaketheoppositerouteandgostraighttothefirst-ordersentences.LaterchaptershavemoretosayaboutthelinkswithplainEnglish.Thechiefpioneer

6、sinthecreationoffirst-orderlanguageswereBoole,FregeandC.S.Peirceinthenineteenthcentury;butthelanguagesbecamepublicknowledgeonlyquiterecently,withthetextbookofHilbertandAckermann(1950),firstpublishedin1928butbasedonlecturesofHilbertin1917–22.(Sofirst-orderlogichasbeenaroundforabout70

7、years,butAristotle’ssyllogismsforwellover2000years.Willfirst-orderlogicsurvivesolong?)Fromtheirbeginnings,first-orderlanguageshavebeenusedforthestudyofdeductivearguments,butnotonlyforthis–bothHilbertandRussellusedfirst-orderformulasasanaidtodefinitionandconceptualanalysis.Today,compu

8、ter9WilfridHodgessciencehasstillmoreuses