PhilosophicalDefinition
Categoryreferstothecommonnatureonwhichthingsareclassifiedandarranged,thatis:categoryistheessenceofthekindofthings.Becausetheessenceofakindisoftencomposedofmultipleproperties,andtheessenceandthevariouspropertiesthatconstituteitarealwaysrelatedtoeachotherinacertainstructuralway,thiswayistocombine{positive/negative}.Therefore,thecategorycanalsobedefinedas:the{positive/negative}naturestructureonwhichthestandardandplanningthingsarebased.
Thesymbolicdefinitionofthecategoryis:A{B/C}.Read:AisthecombinationofBandC,thatis,A↔{B/C}.Abbreviation:He{positive/negative}.
Meaning:IfthepositiveconceptBcoversitsnegativeconceptC,thenitconstitutesacategory,whichcanbecollectivelyreferredtobyA.
Thesymbol/intheformulacoversandtheopposite:/{→∧⊕},wherea⊕b=(¬a∧b)∨(a∧¬b).Thesymbol{}representstherange,andA{}istheabbreviationofA↔{}.Itcanbeseenfromtheabovethatthestructureofthecategoryincludesallfivebasiclogicaloperations:non-,or∨,and∧,etc.↔,han→all.Forcomparison,therangeis{}intheconceptofset,setA={B,C...},rangesize=∣A∣.Setisjustaconceptinvolvingtheproblemofconceptselection.
The"combination{positive/negative}"structureofthecategoryisnotexactlythesameasHegel's"positiveandnegativecombination"developedfromKant.Theformerisasymbolicabstractcategoryconcept,whichcanbeusedforformaldeductionandinductivereasoning,anditisalsothebasisforthelattertobeestablished,whilethelatterisonlyathree-stagetheoryaboutpropositions,whichisonlythemanifestationofthecategoryconceptinpropositionalreasoning.
Categoryisthemostabstractpropositionalstructuralconcept.Itisthemostimportantandcoreconceptinphilosophyanditslogicalsystem.
Inadditiontocategories,otherpropositionalstructuralconceptsinclude:theopposite:A{B⊕C};contradiction:A{B∧¬B};thesame:A{B↔C};covering:A(B→C};Opposition:A(B∨C};Kind:A(B∨C...};Individual:A{B∧C...}etc.Theabstractionlevelislow.
Acategoryislikea"livingcell"inlogic,whichcanbesplitintotwonewcategories,whichiscalleddeduction;andtwocategoriesarelikeaspermandaneggcombinedintoafertilizedegg,whichcanbecombinedBecomeanewcategory,whichiscalledinduction.
Forexample:"nature{ontology/thischange}"canbededucedas"ontology{lian/limit}"and"thischange{combination/分}"Category;"spirit{past/record}"and"reality{present/fact}"canbesummarizedasacategoryof"being{spiritual/reality}".
TheexamplethatbestreflectstheimportanceofthecategoryNothingismore:itsstructuralformisthesourceoftheword"form"of"formallogic"!
Thepropositionalconstantsofformallogicaredividedintofourcategories:specialanduniversal,affirmativeandnegative,andhypothesis(Sufficientandnecessary),choiceandjoint.These8judgmentsarejusttheconfirmationofthestructuralformofthecategoryA↔{B/C}combined{positive/negative},sotheyarecalledformaljudgments,andthecorrespondingformsLogiciscalled"formal"logic.Asshowninthefollowingtable:
CategoryHistory
Whatisphilosophy?Expressedincategoryexpressionis:philosophy{Knowledge/System}:Philosophy{Perception/Knowledge},System{Individual/Relationship}.
Humanbeingshaveaprocessofunderstandingthings,andthisprocessisalways:fromperceptiontoconcreteTounderstandtheabstract,andthenunderstandtheabstractconcrete."Theconcreteoftheabstractknowledge"iscommonlyreferredtoas“wisdom”or“philosophicalknowledge.”FurthervariousphilosophicalknowledgeformsthetheoryThesystemproduces"philosophy"or"thestudyofwisdom."Theprocessofexpressingthisprocessinacategoryis:philosophicalknowledge{perception/reasoning},system{individual/relationship};philosophy{philosophicalknowledge/system}.
Forexample,theprocessofunderstanding"category":
1.Perception:thingsalwayshavedifferentproperties;2,knowledge:thesepropertiesarealwaysthesame.Oppositelyappearinpairs.3.Philosophy:Thesepropertiesalwaysappearingroupsofthreeina{positive/negative}structureintheformof"品",andthe"productsets"arecombinedintoone.Acomplete"recoveryskynetwork."Fromtheperspectiveofnaturetheoryphilosophy,formandspiritlogic,anyentity{individual/system}isaliving"category".Forexample,becausethescopeofactionofthenucleuscoverstheroleofelectronsRange,sotheyaresynthesizedintoanatomicsystem;becausetherangeofactionofthesuncoverstherangeofactionofplanetssuchasgold,wood,water,fire,earth,etc.,theyaresynthesizedintoasolarsystem.BecausetherangeofactionofhumanbraincellscoversallothercellsinthebodyRangeofeffect,sotheysynthesizeintoalivinghumanbodysystem.etc..
InthehistoryofWesternphilosophyandlogic,theunderstandingofcategoryconceptshasbeenconstantlyimprovedandclear.AlthoughAristotlefirstproposedtheconceptofcategorymorethan2,000yearsago,itsdefinitionisempirical.Ithasalwaysbeenknownthatitsroleisimportant,buthehasneverbeenabletogiveanaccurateandabstractdefinitionofrationality.Itisimpossibletorevealitsfullphilosophicalandlogicalsignificance.Bymorethan200yearsago,KantandHegelhadexpandedtheirspecificunderstandingofcategories,buttheywerestillunabletoabstracttheirpreciselogicaldefinitions.
InEasternChina,theunderstandingoftheconceptofcategoryhasalonghistory,andtheChinesepeoplehaveaverystrongconceptofcategory.InancientChina’syinandyangtheory:everything{yin/yang}isactuallyalreadyacategory,anditisregardedasanultimateabstractcategory.Threebegetsallthings.Allthingsbearyinandembraceyang,andtheythinkthattheyareharmonious."Inotherwords,LaoTzubelievesthateverythinghasthecommonnatureof"yin/yang",andeverythingcanbededucedfromthe"inspirationandharmony"betweenthepairofyinandyang.Positiveyinandanti-yanguniteeverything.Theone,two,threeinLaoTzu’ssentencemeans:acategorythatcontainsthetwopropertiesofyinandyangcanproducethethirdthing---thisiscalledtheTao.Tao:UseanultimatecategorythatcontainstwooppositepropertiesofYinandYangtodeduceeverythingandexplaintheworld.
Ihaveafurtherunderstandingofthecategory,discoveredthe"propositionalstructure"ofthecategoryandgaveitssymbolicformaldefinition,sothatitcanenterthecomputer'scalculationprocess.Thisisanindependentandinnovativeachievementmadebytoday'smainlandChinesephilosophers,andithasforward-lookingandepoch-makingsignificance.Forthefirsttimeinthousandsofyears,weChinesehaveourowncontemporaryphilosophicallogicsystem.Sincethisphilosophicallogicsystemcoversontologicalformallogic,intermsofpracticality,themoreimportantonesare:first,itisexpectedtobreakthroughthewesternmonopolyoncomputersoftwaretheory;second,itisexpectedtotheorizethelivingscienceofChinesemedicineandmakeItstranscendenceisonlyWesternmedicinetheorizedbydeadbodyscience.
Examplesofcategories
Philosophershavedifferentviewsonwhatisthebasiccategoryof"being".Hereweenumeratesomedifferentpointsofview:
Materialobjects
Materialobjectsdoexist;thereasonforsayingthey"exist"isverysimple,becausetheyare"At"ourside.Ahouse,aperson'sbody,atree,acloud.Saidtheyexistonlybecausetheyarephysicalobjects.Wecallitanobject,orsubstance,orconcretething,orentity(notethatthisisdifferentfromtheusageinphilosophy).
Mind
Mindisapartofus,usedforperceptionandthinking.Somephilosophersbelievethattheyareexistence.Accordingtocommonsense,eachofus"has"aheart.Ofcourse,mostphilosophersjustassumethatmindisanothercategorybesidesphysicalobjects.Descartesisoneofthem(thisviewiscalleddualism).Otherphilosophersbelievethatspiritualconceptscanbereducedtomaterialconcepts(thisviewiscalledmaterialism).Inaddition,somephilosophersbelievethatthemindisnota“thing”thatcanbedistinguishedseparatelyfromtheindividual.Theybelievethatspiritualityandmaterialitystemfromaconcomitantrelationship—justliketheconcomitantrelationshipbetweenabankandabuilding.
Class
Allpeopleandallplanetsbelongtotheclass.Amongtheplanets,thereareMercury,Venus,Earth,andotherplanetsthatmaybescatteredintheuniverse.Inadditiontothemembersoftheclass,theclassitselfisoftenconsideredtobeanexistence.Inasense,planetsexist.Classesaregenerallyconsideredtobeanabstractexistence,likeacollection."Class"isalmostequivalentto"collection"inthesense.
Nature
The"red"ofaredapple,orsimplythe"red"commontoallredthings,isakindofnature.Youcanalsocallthisanattributeofthatapple.Whenyoutalkaboutthesize,color,weight,composition,etc.ofanobject,youaretalkingaboutitsnature.Somepeoplebelievethatnatureislikematter(thishappenstobethefocusofintensedebateincosmologicalissues),sothe"red"ofapplesexists.
Relationship
Thereisarelationshipbetweenanappleplacedonthetableandthetable.Therelationshipbetweentheappleandthetableistherelationshipof"placedon".Sosomepeoplesaythatthisrelationshipexists.Forexample,theWashingtonMonumentishigherthantheWhiteHouse,and"higherthan..."isarelationshipbetweenbuildings.Similarly,wecansaythatthisrelationshipexists.Thisisalsothefocusofcontroversyincosmologicalissues.
Properties,relationships,andclassesareallconsideredabstractratherthanconcrete.Mostphilosophersagreethatnatureandrelationshipareabstractexistence,whilematerialobjectshaveconcreteexistence.Thismaybeaparadigmthatdistinguishestwokindsofexistence:theexistencethatcanbecalled"is"andtheexistencethatcanbecalled"being."
Itisthereflectioninthethinkingofthemostgeneralprescriptivenatureofobjectivethings,animportantthinkingformforpeopletoexplainandgraspthedialecticalmovementoftheobjectiveworld,andanonlinetwistofthewebofunderstandingandmasteringphenomena.
CategoryTheory
AboutthetenbasicphilosophicalcategoriesproposedbyAristotlein"Categories":entity,nature,place,time,quantity,relationship,posture,Status,activeandpassive.Thepropositionalstructuraldefinitionsofcategoriescanbeorganizedasfollows:
The"tencategories"directlyinvolvethefollowingcategories:existence{spiritual/reality},natureconnotation{ontology/thischange}:Ontology{connect/limit},originalchange{combined/min};extensionofnature{rawmaterial/value}:rawmaterial{texture∨space∨time},value{Quantity/Value};Texture{Quality/Density},Space{Distance/Volume},Time{time/period};natureextension{personality/collection},natureconnotation{general/variation},essenceb>Connotation{special/substantialchange}.;Relationship{absolute/relative};posture{independentecology/multipleecology}:independentecology{active/passive},publicecology{free/autocratic};conditions{continuous/discrete}.TheconceptmarkedbythescarletletterisrelatedtothetencategoriesofAristotle.
ItcanbeseendirectlyfromtheabovethatAristotle’stencategoriesarejustalistofcategoriesthatareatdifferentlevelsoflogicandarefarfromcomplete.Therefore,Kant,Hegelandotherphilosopherscontinuedtoexploreandstudythecategory.Specifically,thetencategoriesaredividedintotwoparts.Thefirstparthas5"entities,nature,location,time,andquantity",andthecoreis"entity";thesecondparthas5"relationships,attitudes,conditions,active,andpassive",andthecoreis"relationship"butImplied"change",changeisthecoreofthispart.Thebreakdownisasfollows:
First,entity,whichcontainsconceptssuchas"existence,ontology,individual,collective,nature,place,time,andquantity".Theseconceptsareatdifferentlevels.Realityreferstoexistence{spiritual/reality}atthehighestlevel,whilespiritandrealityarethingswiththepropertiesof"mass,space,time,quantity",andalowerlevel.Ontheonehand,thebodyreferstoitsconnotationandontheotherhanditreferstoitsextension.Theconnotationistheontology{connect/limit},thatis,anybodymustbeinternallyconnectedandexternallylimited,otherwiseitcannotbecalledabody,thatis,{connect/limit}isTheessentialattributeofthebody;theextensionisthebody{individual/collective}.Bodyandrealityliveatthesamelevel.Thispartinvolvesthetwosecond-levelabstractcategoriesof"natureandontology".However,itisnotcoveredinthe"CategoryChapter".
Second,"relationship,attitude,situation,active,passive"expressestherelationshipbetweenentitiesandtheirchanges,whichbelongtothelowercategoryinthecategoryof"change",becausetherelationship{absolute/relative}alwaysItisintheprocessofchange,andthehighestlevelofchangeis:thischange{combined/min}.Allchangesareinseparablefromitsorigin,Anychangeisnothingmorethan:integration(dissociation),separation(dissociation),integrationtoseparation(deduction),andseparationtointegration(induction).Intheprocessofchange,therelationshippresentsaposture{singleecology/multipleecology}:singleecology{active/passive},multiecology{free/authoritarian};andtheseattitudesareindifferentstatesofexistence{Continuous/discrete}.Thispartinvolvesthesecond-levelabstractcategoryof"intrinsicchange".However,itisalsonotfinishedinthe"CategoryChapter".
Summarizingthepreviousarticle,itcanbeseenthatthe"Categories"discussescategoriesofthethirdlevelandbelow,butithastouchedthecategoryofthesecondlevelof"three{naturalnature,ontology,originalchange}".Thatistosay:therearestill"twosteps"totheultimatecategory:fromtheentitytothethreebooks,andthenfromthethreebookstothesex{body/change}!