DEFINING BASIC KINDS OF PROPERTIES

1、1DEFININGBASICKINDSOFPROPERTIESJiříRaclavskýAbstract:ThispaperfollowsinPavelTichý’sconceptofdistinguishingbetweentrivial(i.e.constant)andnon-trivialproperties.ThisclassificationhasbeenextendedbyPavelCmorejwhodistinguishedtwokindsofnon-trivialproperties,namelypurelyempiricalandpartlyessential(whicharepartlyempirical)properties(partlyessentialpropertyisessentialforcertainindividual(s),butthatitisnotforother(s)).Thepresentstudyprovidesrigorousformaldefinitionsoftrivial/non-trivial,essential/non-es。

2、sential,andpurelyempirical/partlyessential/purelyessentialpropertieswithrespecttothepossiblepartialityoftheseproperties.Inaddition,adefinitionoftriviallyvoidpropertiescompletingtheclassificationofthekindsofpropertiestoformaquadrupletisproposed.Furthermore,theintroductionoftheconceptofaccidentalpropertiesgivesrisetoanother(yetnotequivalent)quadruplet:purelyaccidental/partlyessential(i.e.partlyaccidental)/purelyessential/voidproperties.PavelTichý,alogicianwhodevelopedaspecificintensionallogic,name。

3、lytransparentintensionallogic(hereafterTIL),usedhislogicnotonlyforalogico-semanticanalysisofnaturallanguagebuthealsoappliedittoproblemsinseveralphilosophicalareas.Thefieldweareconcernedwithinthispapercanbecalled‘thelogicofproperties’.Intensionallogicmaybeviewedasaconceptualtoolhelpingtodevelopintensionalmetaphysics.Accordingtoitsmainassumption,anindividualcaninstantiatevariousproperties.Propertiesaremodelledasfunctionsfrompossibleworldsandhaveclassesofindividualsastheirvalues(extensions).Sincepo。

4、ssessingofapropertybyanindividualiswhatconstitutesafact,apreciseconceptualhandlingofpropertiesisofgreatimportanceforthecoreofmetaphysics.Tichýhimselfusedsomeclassificationsofpropertiesofhisownbuthedidnotwriteasystematicpaperonit(hiskeyclassificationemergedfromhiscommentsonthedoctrineofbareindividuals).PavelCmorej,afollowerofTichý,paidcloseattentiontopropertiesanddefinedotherkindsofthem.Naturally,propertiescanbeclassifiedaccordingtovariouscriteriabutonlysomeofthesehavebeendiscussedbythefollowerso。

5、fTichý.Thetopicisthereforestillopenforfurtherdevelopment.Theaimofthispaperistosummarizeandextendup-to-dateknowledgeofthisareaandofferexactdefinitionsofthekindsofproperties(withrespecttopartiality),whichisanecessarystepforfurtherinvestigations.Theconceptualconstructionisbasedonafewsimplelogicalconceptslikeidentity,connectivesandquantifiers.Thegradualinvolvementinthequestionhelpsustoguaranteetheadequacyofproposeddefinitions.Thewholeconstructionculminatesinthedefinitionsofthreerelatedcategoriesofpr。

6、operties(whicharefurtherdivided):trivial/non-trivialproperties(i.e.2propertieswithconstantorwithnon-constantrangeofextensions),essential/non-essentialproperties(i.e.propertieswhichare,orwhicharenot,necessarilypossessedbyacertainindividual),andpurelyempirical/partlyessential/purelyessential/triviallyvoidproperties(i.e.propertieswithentirelycontingentextensions,propertiespossessedbysomeindividualsnecessarilybutbyotherscontingently,propertiesinstantiatedbyanindividualnecessarily,propertiesnotinstan。

7、tiablebyanyindividual).SpecialattentionispaidtopartlyessentialpropertieswhichhavealreadybeeninvestigatedbyCmorej.1Thetwokindsofvoidpropertiesandaccidental/non-accidentalpropertiesrepresentanewcontributionextendingCmorej’sclassification.Theydosonotonlyincompletingtheoriginallytripledivisionintotheabovementionedquadrupletofkindsofpropertiesbecausethereisalsoanotherquadrupletconceivable.Thisquadrupletdividespropertiesintopurelyaccidental/partlyessential(i.e.partlyaccidental)/purelyessential/voidpro。

8、perties(nownon-triviallyvoidpropertiesarenotcoveredbythefirstcategoryasintheprecedingquadruple,butbythelastone).TRANSPARENTINTENSIONALLOGICNaturallanguagebymeansofwhichweformulateourtheorieswasnotoriginallydesignedforsuchartificialservice.Itwasspontaneouslydevelopedbyordinarypeopleforeasycommunicationoffactswithoutgoingintosubtletiesweneedtosortout.Thedangerofnaturallanguageambiguityforphilosophers’theorieswasstressedbyFrancisBacon.Subsequently,GeorgWilhelmLeibnizpromotedtheideaof‘conceptualscri。

9、pt’,aninstrumentdesignedtohelptheoreticianstosolvetheirabstractquestions.ThismovementwasjoinedbyGottlobFrege,whodevelopedthefirstmodern‘shorthand’writing.Nevertheless,Frege’soriginalproposalhastobemodifiedbecausepredicatelogiccannotsufficientlyhandleitemswithinrealisticempiricalframework,whichisinvestigatedbyintensionalmetaphysics.BelowweareusingthenotationoftransparentintensionallogicdevelopedbyTichýattheverybeginningof1970th(see[Tichý2004],[Tichý1988]).TILcanbecharacterizedasahigherorderintens。

10、ionallogicwithatemporalparameter.Itishigherorderlogicforitquantifiesnotonlyoverindividualsbutalsooverpropertiesofindividualsoroverpropertiesofproperties,etc.Predicatelogiccanbeviewedasacalculuswhose(model-theoretic)interpretationisbasedonobjectsbelongingtothecategoryofindividuals(markedι),ortruth-values(markedο).TILalsoadoptsatomiccategoriesofpossibleworlds(ω)andrealnumbers1TheauthorishappytoexpressherehiswarmestcongratulationstoPavelCmorejontheoccasionofhis70thbirthdayandispleasedtodedicatethisp。