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The Routledge Companion to of Language

Gillian Russell, Delia Graff Fara

Logical Form

Publication details https://www.routledgehandbooks.com/doi/10.4324/9780203206966.ch1_3 Kirk Ludwig Published online on: 24 Feb 2012

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Maryloves John 1. they appeartoenterintothesamesystematicentailments. superficially differentforms,suchas6–8,areassignedthesamelogicalformbecause they enterintodifferentsystematicentailmentrelations.Andsomesentenceswith 2, 4–6,9and10,1112,1314,areassigneddifferentlogicalformsbecause truth conditionsoneach.Somesentenceswiththesamesuperficialform,suchas1and be assigneddifferentlogicalformsbecausethesamewordscontributedifferentlyto who arevisitingcanbeboring”and“itboringrelatives”)whichshould is lovedbyeveryone”and“everyonesuchthattheresomeoneheloves”;“relatives analysis.) Forexample,somesentences,like2and3,havemultiplereadings(“someone below towhetherlogicalformmaybeassociatedwithsomefurtherlevelofsyntactical matically, fromthesurfaceorsuperficialgrammaticalformofasentence.(Wereturn falsity ofasentence. of logicalformtosemanticstructurerelevanttheevaluationgenerallytruthor more generalaccountofvalidargumentformshasledtoageneralizationthenotion ment underwrittenbytheirsemanticforms.Thepressuretoprovideaneverdeeperand that is,semanticentailmentrelationsbetweenthepremisesandconclusionofanargu- Interest inlogicalformhasbeendrivenhistoricallybyinterestvalidargumentforms, It isastapleofthetraditionsinceFregethatlogicalformdiffers,sometimesdra- LOGICAL FORM Kirk Ludwig 1.3 Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 reveal thequantificational commitments ofnaturallanguagesentences(seeDavidson made inthetheorybetrue,” itfollowsthatonegoaloftherecoverylogicalform is to bound variablesofthetheory mustbecapableofreferringinorderthattheaffirmations according towhich“atheory iscommittedtothoseandonlyentitieswhich the we endorsearetrue.Given Quine’s(1948:33)criterionofontologicalcommitment, ering theontologyembedded innaturallanguages,whatmustexistifthesentences ponent ofwhatStrawson(1959)called“descriptivemetaphysics,” theprojectofuncov- 2001c: 31).) tion oflogicalformandconceptualanalysis(Davidson [1980]2001b:105–6,[1984] structure ofthoughtblursthedistinctionDavidson drew laterbetweeninvestiga- sell [1918–19]1985:87–8).(Importantly,Russell’sand Wittgenstein’sinterestinthe express relationstopropositions,aviewheheldatone pointbutlaterrejected(Rus- Russell, forexample,acrucialquestionaboutlogicalform waswhetherbeliefsentences in inferencepatternsamongsentencesinducedbythe meaningsoflogicalterms.For expressed withthem.Thisinterestinlogicalformisclearly broaderthananinterest sentences wastakentorevealboththeformsofpossiblefactsorrealityandthoughts ophy ofmind(Russell[1918–19]1985;Wittgenstein[1921]1961).Thelogicalform Logical Atomism,logicalformwasdirectlyconnectedwithmetaphysicsandthephilos- bald” (5,6,and12introduceadditionalcomplexities). tributing anyentitytothemeaningofsentence,incontrastto,say,“LouisXIVwas it andisbald,”inwhichthegrammaticalsubjectoforiginalnottreatedascon- structure, “ThereisakingofFranceandwhateveridenticalwith to thisdivergencelater)butaquantificationalsentencewithinternaltruth-functional ject–predicate sentence(orevenanounphrase+verbconstruction—wereturn according towhichthelogicalformof“TheKingFranceisbald”notthatasub- The mostfamousexemplarofthisactivityisRussell’sTheoryDescriptions study offormspropositions—or,ashecalledthem,“logicalforms.”Heclaimedthat External World,defined“philosophicallogic”asthatportionoflogicconcernedthe Bertrand Russell,inthesecondofhis1914Lowelllectures, 4.002). them. WittgensteinputsthisvividlyinhisTractatusLogico-Philosophicus([1921]1961: ciated withadivergencebetweentheformofthoughtsandsentencesexpressing In theearlyanalytictradition,divergenceofsurfaceandlogicalformwasasso- Even apartfromLogicalAtomism,investigationoflogical formisanimportantcom- In theearlytwentiethcentury,especiallyinshort-livedbutinfluentialtheoryof render itexplicitandpure. sophical logictoextractthisknowledgefromitsconcreteinteguments,and explicit, isinvolvedinallunderstandingofdiscourse.Itthebusinessphilo- some kindofknowledgelogicalforms,thoughwithmostpeopleitisnot for entirelydifferentpurposes. outward formoftheclothingisnotdesignedtorevealbody,but clothing itisimpossibletoinfertheformofthoughtbeneathit,because Language disguisesthought.Somuchso,thatfromtheoutwardformof KIRK LUDWIG 30 Our Knowledgeofthe ([1914] 1993:53)

(1905), Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 though, onlyatemporaryillusionofprogress.AsAyerputit, cal formsifandonlythepropositionsorpossiblefactstheyexpressdo.Thisgivesus, possible factsastheprimarybearersoflogicalform.Sentencesthenhavesamelogi- analysis ofactionsentences. 1977; Higginbotham1993).Wewillconsideradramaticexamplebelowintheevent the objectsofthoughtand themeaningsof(declarative)sentences.Thissuggests propositions (intheFrege–Russell tradition)wereintroducedtobesimultaneously But thisleavesuswiththequestion of why philosophersoftentalk ofsuchrenderingsasgivingthelogicalformoriginal. nal anditstranslations(ifthey are)sharelogicalform.Sensitivityto this pointexplains can onlysaywhatthelogicalformisrelativetoasystem of regimentation.Yet,theorigi- the patternsoftermsinthem,sincetheyaredistinct andthechoicearbitrary.We The logicalformof“thekingFranceisbald”cannotbeidentified witheither,or 16. 15. (x)((f(x) &y)(f(y) “x =y”),asin15and16. “f(x)” for“xisakingofFrance,”“b(x)”bald,”and “i(x,y)”inprefixnotationfor be renderedintoastandardinfixlogicalnotationor Polishorprefixnotation(with many thatwoulddoequallywell.Russell’sanalysisof“TheKingFranceisbald”can the notionoflogicalformrelativetochoicefavoredlanguage,andthereare terms ofthepatterninit,perhapslogicalterms,thenthismakes the formofsentenceinideallanguageis(Grandy1974).Ifwethinkit language ofthesameform. have thesameformifandonlytheyaretranslatedbysentencesofregimented tion ofasentenceoutitsparts,wouldbeanexample.Naturallanguagesentences designed tomakesharedvalidity-relevantsemanticfeaturescorrespondtheconstruc- or semanticrolesoftermsinthem.Aninterpretedformallanguageforafirst-orderlogic, guage istohavenoambiguitiesandencodeinitssyntaxalldifferencesthelogical and sometimesto 1972; Audi1995:511–12;Sainsbury2001).Thesesentencesaresometimessaidtobe, of thesentencesthattranslateitifisstructurallyambiguous(Kalish1952;Harman specially regimented,“ideal,”typicallyformallanguage,thattranslatesit—ortheforms which thelogicalformofanaturallanguagesentenceisin Ayer’s lastremarkpointstoapopularwayoftalkingaboutlogicalform,according One responsetothedivergenceofsurfaceandlogicalformistreatpropositionsor The ideathatlogicalform attaches firsttopropositionspointsaresolution,for This isnot,however,asatisfactoryaccount,foritleavesuswiththequestionofwhat originally cast. and thatthesearenotalwaysthegrammaticalformsinwhichsentences grounds, whichformsofsentencesconveythisinformationmostperspicuously, are usedtostatethem.Whathappens,inpractice,isthatwedecide,onother forms .otherthanthroughthegrammaticalofsentenceswhich This wouldbeallverywell,ifwehadanymeansofdeterminingthelogical xKKf(x)yCf(y)i(x,y)b(x) give, thelogicalformsoforiginals.Theidealorregimentedlan- x =y))&b(x)) LOGICAL FORM what itgivesandhowisdoingit. 31 (1984: 29–30) Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 replaced byametalanguagesentencethattranslatesit. language sentencesintroducesacomplicationwhichwereturntobelow)and“p”is constructed outofitssemanticallyprimitivecomponents(theneedtoregimentnatural all sentencesoftheform(T),where“s”isreplacedbyadescriptionsentenceLas guage expressionswhichtranslatethem.Withanadequatelogic,thetheorywillentail conditions forthesemanticallyprimitiveexpressionsoflanguagebyusingmetalan- an objectlanguageLisafinitelyaxiomatizedtheorywhoseaxiomsprovidesatisfaction Restricting attentiontoacontext-insensitivelanguage,aninterpretivetruththeoryfor tive Tarski-styletruththeory(Tarski[1934]1983,1944;Davidson1967b,1970,1973). of acompositionalmeaningtheoryforthelanguagethattakesformaninterpre- The suggestioninfullisthatthelogicalformofasentencerevealedcontext replaces “p”translatess,wecanreplace“istrue language. of logicalformisbestplacedinthecontextaninterpretivetruththeoryforanatural conditions forsentences. sive semantictheorythatdetailshowwordsandstructurescontributetofixingtruth looking midwaybetweenthesentenceandpropositionitexpressestoacomprehen- vocabulary ofLconsiststhe variables,“x,”“x of thesignificantfeatures thesentence”([1980]2001a:146). of asentenceistoknow,inthe contextofacomprehensivetheory,thesemanticalroles suggestion, thisistoknowthe logicalformofthesentence:“Toknow ditions, andinthissenseshows whatitssemanticstructureis.AccordingtoDavidson’s tic roleofeachprimitiveexpressioninthesentencefixing itsinterpretivetruthcon- tent oftheaxiomsforwordsins.Thecanonicalproof aT-sentenceshowstheseman- more detailandtherelationofthiswayputtingproject toDavidson’sown.) though wecannottaketheextensionuphere.SeeLepore andLudwig2005:chs.4–5for sentence. (Themoralsdevelopedextendtoalanguagewith context-sensitiveelements, sentence andwesaythatitprovidesinterpretivetruthconditions foritsobjectlanguage A sentenceoftheform(T)inwhichthisreplacementyields atruesentencewecallT- In (T),“istrue An influentialsuggestionofDonaldDavidson’salongtheselinesisthatthenotion A simpleinformaltheory,A1–A8, stipulatedtobeinterpretive,willillustrate.The A canonical (T) sistrue Tarski. is byrecursivelycharacterizingatruthpredicate,alongthelinessuggested see itinthelightofatheoryforitslanguage.Awaytoprovidesuch that sufficesforthelanguageasawhole.Toseesentenceinthislightisto language asawhole,outofelementsdrawnfromfinitestock(thevocabulary) number ofapplicationssomeafinitedevicesthatsufficeforthe the sentence—itstruthorfalsity—asowedtohowitiscomposed,byafinite Above all.suchanaccountmustleadustoseethesemanticcharacterof What shouldweaskofanadequateaccountthelogicalformasentence? proof issuesinaT-sentenceforsbydrawingintuitivelyonly onthecon- L ” is a metalanguage truth predicate for sentences of L. Given that what ” isametalanguagetruthpredicateforsentencesofL.Given thatwhat L iffp KIRK LUDWIG 32 L iff” with“means iff” (Davidson 1968,[1984]2001c:94) 1 ,” “x 2 ,” ..,names“Ned”and“Sally,” L that” and preserve truth. that”andpreservetruth. Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 A8. For any sentence Ned to“x”andSally“x then ‘loves’istrueofNedandSallytakeninthatorder.Thus,afunctionfassigns relation.If‘NedlovesSally’istrue, The satisfactionrelationgeneralizesthe‘trueof’ 5 Foranyfunctionf,forformulaI,fsatisfies A5. “[v lovesv']”isequivalentto“v where “v”and“v'”aremetalinguisticvariablesfornames(terms)ofL, “‘Ned’ form astructuraldescriptionofsentence.Thus,“[NedlovesSally]”isequivalentto with parenthesesaround“”followedbyavariable,e.g.,“(x).”Squarebracketswill “~” and“&”(fornegationconjunction),anexistentialquantifierformed the one-placepredicate“ishonest,”two-place“loves,”connectives 3 Foranyfunctionf,term v,fsatisfies A3. Foranyfunctionf,f(“Sally”) =Sally. A2. Foranyfunctionf,f(“Ned”) =Ned. A1. f assignstoD.“I”and\takeobjectlanguageformulasasvalues. ments tonamesforthefunctionswequantifyover.Forany use functionsfromtermstoobjectsassatisfiersofformulas.AxiomsA1–2specifyassign- 4 Foranyfunctionf,termsv, v',fsatisfies A4. 7 Foranyfunctionf,forformulaI,variablev,fsatisfies A7. 6 Forany functionf,foranyformulas A6. as havingthedistinctforms. same form,andaxiomsfordistinct truth–functionalconnectivesanddistinctquantifiers form, axiomsforpredicates withthesamenumberofargumentplacesashaving the relevant semanticstructure is totreatthesingularreferenceaxiomsashavingsame framework allowsforvarious classifications.Anaturalclassificationfortracingtruth- form ofs. are usedintheproofofaT-sentenceforsandhowthey areemployedrevealthelogical of thevocabularyitemforwhichitisanaxiom.Then theformsofaxiomswhich mining truthconditionsofsentencesinwhichitappears andthelogico-semanticform The formoftheaxiomsmaybesaidtogiverole objectlanguagetermindeter- tions forquantifiedformulas.A8connectssatisfaction with truthofclosedsentences. structed withtruth-functionalconnectives.A7provides recursivesatisfactioncondi- two-place predicates.A5–6providerecursivesatisfaction conditionsforformulascon- ence axiomsfor“Ned”and“Sally.”A3–4arepredicatesatisfaction axioms,forone-and axioms. derived sentencesbyrulesappliedsoastopermitdrawingonlyonthecontentof side and(ii)eachmemberofitisanaxiomorderivedfromaxiomspreviously member isasentenceoftheform(T)withnosemanticvocabularyonrighthand like fexceptatmostinwhatitassignstov. A parameterincharacterizing semanticformistheclassificationofaxioms.The Axioms A1–4arebaseaxioms;axiomsA5–7recursive axioms.A1–2arerefer- A canonicalproofisasequenceofmetalanguagesentencessuchthat(i)thelast { such thatf'isav-variantoff,satisfies f satisfies satisfies ‘loves’ L { \. L I. ‘Sally’”—the concatenationof“Ned,”“loves,”and“Sally.”Similarly, I, 1 I istrue ” satisfies“xlovesx { ‘loves’ L LOGICAL FORM iffeveryfunctionfsatisfies { 33 L ,” etc. ‘iff’ abbreviates“ifandonlyif.”We v',” etc.‘iff’ I, [vishonest]ifff(v)honest. \, fsatisfies L L 1

[vlovesv']ifff(v)f(v). .” Afunctionf'isav-variantofiff I. L [~I]iffitisnotthecasethat L [ D, [f()]referstotheobject I & L

L I. \] ifffsatisfies [(v) I] iffforsomef' L I andf ' is Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 In termsofthisnotion,thesuggestionisthat(loc.cit.) sentence “[(x)(Nedlovesx)&(x A2. TheninstantiatingA8tothesentence,aseriesofvalidsubstitutionsyieldsT- us whatthingthelogicalformofasentence isbutratherwhenanytwosentencesin This yieldsanunrelativized characterization ofsamenesslogicalform.Itdoesnot tell and Ludwig2002b:67). tive languagesintermsoftheiradmittingcorrespondingcanonicalproofs(Lepore Davidson’s proposalistofixsamenessoflogicalformtwosentencesintheirrespec- to abstractawayfromincidentalfeaturesofcanonicalproofs.Asuggestionextending lier inidentifyinglogicalformwithsentencesaparticularideallanguage.Wewant both themetalanguageanditslogic.Weseemtofacesameproblemaswedidear- at whichitisapplied. which theyareaxioms,andhowcontributeisgivenbytheplaceinderivation arriving ataT-sentenceforit.Theaxiomsgivethetypeofcontributionterm object languagesentenceinwhataxiomsofformsareappliedatpoints loves xandsomeyissuchthatSally.” some xissuchthatNedlovesx”andsimilarlyfor[( A1 for“Ned”wecanthendeduce“Foranyfunctionf,fsatisfies[(x)(Nedlovesx)]iff quantifier toeachoftheconjunctsonrighthandside.WithA4for“loves”and tiate A6for“&”tothissentence.ThenwewouldinstantiateA7theexistential A proofofaT-sentencefor[(x)(Nedlovesx)&(x The notionofformwearriveatbythismethod,asDavidsonnoted,isrelativeto What isthepointofexercise?Theproofdisplayssemanticstructure For anysentencess iff s (d) P thereisacanonicalproofP (c) there areinterpretivetruththeoriesT iff (a) P A proofP c thebaseaxioms employedateachstageareofthesamesemantictype,and (c) ateachstageofproofidenticalrulesareused; (b) b thereisacanonical proofP (b) theysharethesame logic; (a) for s 2 inL df df 2 tions totruthconditions). terms forwhichtheyspecifysatisfactionconditions(withrespecttocontribu- recursive axiomsemployedateachstageinterpretidenticallyobjectlanguage inT 1 1 2 correspondstoP andP 1 2 ofaT-sentencefors

2 aresentencesequencesidenticalinlength; 1 , s 2 , languagesL 2 . 1 inT 2 1 1 KIRK LUDWIG oftheT-sentencefors oftheT-sentencefors )(x 1 1 1 lovesSally)]istrueiffsomexsuchthatNed correspondstoaproofP , L 1 34 forL 2 , s 1 inL 1 andT 1 hasthesamelogicalformas 1 1 2 )(x )(x forL 1 1 2 1 lovesSally)]wouldinstan- lovesSally)]withA4and inT inT 2 suchthat 2 2 1 foraT-sentence , suchthat: ; Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 the samelogicalformass lence relation—thelogicalformofs languages arethesameinlogicalform.Anentitycanbeintroducedusingthisequiva- solve certainpuzzles.Forexample, if17isalogicaltruth,aninstanceofthelaw the is kingofFrancebald.Additional evidencecomesfromthepowerofanalysis to and onlyifthereisakingof France,thereisatmostonekingofandwhoever Evidence forthisisthatthe targetsentenceappearstobetrueasamatterofmeaning if method. but twoexampleswillgivetheflavorofenterprise andshowthepowerof (Grice 1989:chs.1–4).Thereisnosimplegeneralway todescribehowdothis, meaning andresponsesbasedinpartonwhatispragmatically impliedbyaspeaker tive contexts—forthetheorymustdistinguishresponses tosentencesbasedsolelyon (ii) bytheneedtotakeintoaccountroleofpragmatic factorsincommunica- expressions intoacomprehensivesemanticandsyntactic theoryforthelanguage,and on judgmentsandobservationsofusageisconstrained (i)bytheneedtoincorporate ity andentailmentsinpatternsofusage.Recoveringtheserulesfromreflection sentences andtheirinterpretation,areexpressedinjudgmentsaboutgrammatical- use, realizedinspeakers’linguisticcompetencies.Theseinvolveboththegrammarof and structures.Themeaningofatermorstructureismattertherulesforits that axiomsusetermsandstructurestranslateorinterpretobjectlanguage ited onlyinthelightofsemantictheoryforregimentedsentence. and (b)tobethesameasthatoforiginal.Thepropertyindicated,however,isexhib- producing asentencewhosesemanticstructureispresumed(a)tobewellunderstood (we reviewanexamplebelow). attendant dangerthatfamiliarstructureswillproveaProcrusteanbedfortheoriginal heavily onstructureswealreadyknowhowtoincorporateintoatruththeory,withthe sentences isexpressedinappropriateregimentation.Inpractice,regimentationsdraw 1984: ch.1).Muchoftheworkuncoveringlogicalformnaturallanguage lation firstintoaregimentednotationtowhichthetruththeorycanbeapplied(Lycan how wordscontributetotruthconditionsinnaturallanguagesentencesrequireatrans- Minimally, structuralambiguityandsyntacticelisionthatleavesinexplicitaspectsof Ludwig 2002b:74–6;2003). that ofacorrespondingproof,togeneralizetheaccountnondeclaratives(Leporeand definition ofacanonicalproofcanbegeneralizedtofulfillmenttheory,andlikewise “if youaregoingtothestore,buysomemilk,”“Investeverypennyearn.”Then they canappearinmolecularsentences,andwequantifyintomoodmarkers:e.g., using themachineryoftruththeory.Thisisrequiredevenfornon-declarativessince for imperativesandinterrogatives.Complianceconditionsarespelledoutrecursively ditions ofdifferentsorts:truthconditionsfordeclaratives,andcompliance theoretic semanticstofulfillment-theoreticsemantics.Sentenceshavefulfillmentcon- Return firsttoRussell’sanalysisof‘ThekingFranceis bald’in15,repeatedhere. What aretheconstraintsonregimentation?Aninterpretivetruththeoryrequires Thus, givingasentence’slogicalformwithregimentedsentencecomesdownto Our illustrationelidesanimportantstageintheapplicationtonaturallanguages. This approachcanbeextendedtoimperativesandinterrogativesbyextendingtruth- 15. (x)((f(x)&y)(f(y) 2 inL 2 —but thisprovidesnoadditionalinsight. x=y))&b(x)) LOGICAL FORM 1 inL 1 35 =thelogicalformofs 2 inL 2 iffs 1 inL 1 has Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 wide scope),asshownin18aand18b. treated asmodifyingthepredicate(takingnarrowscope)orwholesentence The answeronRussell’stheoryisthattheseconddisjuncthastworeadings,as‘not’ a kingofFrance? excluded middle,howdoweavoidtheconclusionthatitisalogicaltruththere x: xisaphilosopher],”which restrictsthedomaintophilosophersandrequiresmost to stricted quantifiers.“Mostphilosophers” mustbetreatedadistinctsemanticunit,“[Most are neitherphilosophersnor rich—nortoanyotherrepresentationusingonlyunre- equivalent to“Mostxaresuch thatxisaphilosopherandrich”becausemostthings the originalisfalse,whilethis istruebecausemostthingsarenotphilosophers.It not is notequivalentto“Mostxaresuchthatifaphilosopher, thenxisrich”because equivalent toanyfirst-orderconstrualusingunrestricted quantifiers(Rescher1962).It miner (Neale1990:38–44,2002).However,“Mostphilosophers arerich”isnotlogically should havethesamesemanticstructure,differingonly inthequantificationaldeter- to aresolution.Primafacie,“Allphilosophersarerich”and “Mostphilosophersarerich” Reflection onrelatedconstructionsgivessubstancetothis concernandshowstheway duction oflogicalconnectivescanseemunmotivated from thestandpointofsyntax. losophers arerich”as“Somexissuchthataphilosopher andxisrich.”Thisintro- “All philosophersarerich”as“Forallx,ifxisaphilosopher, xisrich”and“Somephi- strual intermsofunrestrictedquantifiers.Thepracticegoes backtoFrege,whorendered France ortherearetwomore,onemustbemorespecifictoavoidmisunderstanding. and, thus,attentionisfocusedonthepredicate.Ifonedeniesitbecausetherenokingof hirsute, sincethepointofsentenceistopickoutsomethingascribeapropertyit, is bald,onewilltypicallybetakentodenyingitbecausethinksthekingofFrance of conversationalpragmatics(Grice1989:chs.1–4).IfonedeniesthatthekingFrance pattern ofresponse,moreover,canbeexplainedonRussell’stheorytogetherwitha example, “MyfatheristhepresentkingofFrance”(Neale1990:26–7).Theidentified some assertionsofsentencescontaininganondenotingdefinitedescriptionarefalse:for it butbysaying“ThereisnokingofFrance.”Againstthis,wefeelhesitationin no kingofFrance,werespondtoassertions“TheFranceisbald”notbydenying king ofFranceisamerepresuppositionratherthananentailmentit.Forwhenthere of “ThekingFranceisbald”notfalsebutlacksatruthvaluebecausethatthere predicate orthewholesentencemakesnodifferencetoitsevaluation. bald” thencontrastswith“LouisXIVisnotbald,”wherewhether“not”modifiesthe ing aswetake“not”tomodify“gold”orthewholesentence.“ThekingofFranceisnot bald” isassimilatedto“Allthatglittersnotgold,”whichhasatrueandfalseread- truth butnotcommittedtotherebeingakingofFrance.“TheFranceis of France,isnotalogicaltruth,whileifwegiveittheconstrualin18b, If wegiveittheconstrualin18a,then17,thoughiscommittedtotherebeingaking There areothergroundstomodifyRussell’saccount,however. Russelloffersacon- Strawson (1950)objectedfamouslythatwhenthereisnokingofFrance,anassertion 18b. ~(x)((f(x)&(y)(f(y) 18a. (x)((f(x)&y)(f(y) ThekingofFranceisbaldorthenotbald. 17. x=y))&~b(x)) x=y))&b(x)) KIRK LUDWIG 36 Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 (1967). entailments likethosebetween 25and26ontheonehand,27other of agentandobject(orpatient) oftheactionasseparateconjunctstoaccommodate In acommentonDavidson’s suggestion,Casteñedasuggestedseparatingoutthe role entailment of22by20and21ismadetransparent. exhibited asplayingthesamesemanticroleineachof these sentences,andtheformal an existentialquantifier;22isanalyzedasin24,andso“violent,” “withaknife,”etc.,are Modifier dropentailmentisthenaninstanceofconjunction eliminationinthescopeof abbreviated discussion;seeLeporeandLudwig2002aforaquantificationaltreatment). the adverbialsascontributingpredicatesofevents,in23(wesetasidetenseforthis involve animplicitexistentialquantifierovereventsintroducedbytheactionverb,and explains inauniformwaythefunctionofrecurringwords21–22,ifwetake20to bials in20.Davidsonsuggestedthattheseentailmentsfallintoafamiliarpattern,which event described.Itcanscarcelybeanaccidentthatvariantsoftheseappearintheadver- stabbing Caesar,and“wasviolent,”donewithaknife,”etc.,arepredicatesofthe interest because22containsadescriptionofanevent:namely,theeventBrutus’s admit ofadverbialmodification).That20togetherwith21entails22isparticular they areamatterofform(thisholdseventverbsgenerally,andstatethat That theseentailmentsareindependentoftheparticularadverbialsandverbshowsthat obtained byremovingoneormoreofthem,andtogetherwith21entails22. ment. In20,theactionverbismodifiedbyfouradverbials;20entailseachsentence semantic functionofadverbsaction,andinparticulartoexplainmodifierdropentail- action sentences(Davidson1967a).Theeventanalysiswasintroducedtoexplainthe Reimer andBezuidenhout2004Ludlow(Chapter3.7)inthisvolume. theory forthelanguagecanprovideacorrection.Forfurtherdiscussion,seeNeale1990, semantic form,andhowplacingtheprojectincontextofacomprehensive We seehereanexampleofhowregimentationinafamiliarnotationcandistortlogico- tions withoutreadinganytruthfunctionalstructureintoourunderstandingofthem. (x isbald).”WecanthusretainRussell’squantificationalaccountofdefinitedescrip- a ](xisrich)”and“ThekingofFrancebald”as“[Thex:xFrance] “[All x:xisaphilosophers](xrich)”and“Somephilosophersarerich”as“[Some satisfy thefollowingpredicate.Butweshouldthenconstrue“Allphilosophersarerich”as Another celebratedexampleofthediscoverylogicalformiseventanalysis 4 [thee:stabbing(e,Brutus, Caesar)](violent(e)&with(e,aknife)at(e, 24. Curia ofPompey)&on(e,theidesMarch)). (e)(stabbing(e, Brutus,Caesar)&violent(e)with(e, aknife)&at(e,the Brutus’sstabbingofCaesarwasviolent,donewithaknife,attheCuria 22. BrutusstabbedCaesaronlyonce. 21. BrutusstabbedCaesar[violently][withaknife][attheCuriaofPompey] 20. the CuriaofPompey)&on(e, theidesofMarch)) of Pompey,ontheidesMarch. [on theidesofMarch] LOGICAL FORM 37 Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 like thatfrom28to29arestructural butnotlogical.Still,thisdistinctiondoesseem terms, structuralconsequences onthepatternsoftypestermsinthem.Entailments ical andstructuralconsequences. Logicalconsequenceshingeonthepresenceoflogical 30 containsanylogicalterms. Onthisground,Evans(1976)distinguishedbetween log- But thisistosaythat28and 30sharelogicalformonthecriterionintroduced,not that Of course,therepresentation ofthelogicalform28in30containsaconstant. any logicalterms. entails 29.Thisisintuitivelyaformallyvalidargument, butneither28nor29contain notion ofalogicalconstant,isnarrowerthanthatformal validity.Forexample,28 ‘logically valid’. lane 2010foranoverview.)Consequently,thereisnosettledviewontheextensionof ing theideathatleadtodifferentextensions.(SeeGomez-Torrente2002andMacFar- neutral, andontheclassificationofcertainterms,therearevariouswaysdevelop- constant.” Whilethereisgeneralagreementontherequirementthatlogicbetopic and nonlogical.However,thereisnosettledviewonthecorrectextensionof“logical conclusion true.Logicalvalidityisthereforerelativetoadivisionoftermsintological fixed theinterpretationsofitslogicalterms,makespremisestruewithoutmaking the standardaccountifnouniformreinterpretationofitsnonlogicalelements,holding object languagesentences. with anadequatelogicwillprovideaccountoftheformalentailmentrelationsamong entailments therearebasedontheformsofsentences.Thus,truththeorytogether to themeaningsoftermsandstructuresoverwhichitoperates,willdeterminewhat of thetruththeory,whichisneededtocarryoutproofsT-sentences,iffullyadequate or moresentences.Thetruththeorydoesnotstatetheserelations.However,thelogic in thecaseofmodifierdropentailmentabove.Similarlyforasetsentencesandone semantic structure(perhapsonareading),itstruthmayrequiretheofanother,as in termsofsemanticstructure.Invirtuethemeaningasentencewithcertain ments. Thetruth-theoretic(orfulfillment-theoretic)accountcharacterizeslogicalform overt quantifiersortermsforeventsinthem. action sentences,wearecommittedtotheexistenceofevents,thoughthereno . Iftheeventanalysisiscorrect,then,aswearecommittedtotruthof chapters (2.8and3.9)inthisvolumeforfurtherdiscussionrefinements.) the semanticsofadverbialmodification.(SeeLudwig2010andGraffFaraSchein’s This hasbecomeastandardfeatureoftheeventanalysis,nowdominateview However, nomatterwhatthecriterion,logicalvalidity, ifunderstoodintermsofthe What istherelationofthistologicalvalidity?Anargumentlogicallyvalidon Let usreturnnowtorelatethisconceptionoflogicalformformallyvalidargu- The eventanalysisshowsvividlytherelationbetweenlogicalformanddescriptive 0 Brutusishonorableand a man 30. Brutusisaman 29. Brutusisanhonorableman 28. (e)(agent(e,he)) (e)(object(e,thespaceship)&flying(e)) 27. The spaceship flew Hedidsomething 26. (e)(agent(e,he)&object(e,thespaceship) Heflewthespaceship 25. flying(e)) KIRK LUDWIG 38 Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 logical formfornaturallanguages, andviceversa. if LFhastherelevantproperties,willinteractinastraightforward waywithatheoryof important empiricalconstraintonthem(seee.g.Hornstein 2002).WorkonLF,then, can guideregimentationsthatserveasinputtoaninterpretive truththeoryandan encodes structuralsemanticfeaturesofsentences.This providesarepresentationthat to logicalform.IfLFisreal,thenapsychologicallyreal levelofsyntacticaldescription structure, relativetoasemantictheory,applieshereas well. Still,LFisclearlyrelevant logical formwithasentenceinformallanguagewhich makesexplicititssemantic analyzed intermsofLF.Wecanalsonotethatourearlier argumentagainstidentifying not havelogicalform.Thenotionoftheform asentence,then,isnottobe empirically inadequate.Thiswouldnot,however,bea reason tosaythatsentencesdid rules ofsyntaxaredefined.ItisconceivablethatthehypothesisLFbeshownto surface form,isapsychologicallyreallevelofrepresentationbyspeakersoverwhich Form andLF).Asusuallyunderstood,alevelofsyntacticrepresentation,distinctfrom empirical issue(manylinguists,followingChomsky(1995),nowpositonlyPhonetic This motivatescallingit“LogicalForm.” to semanticinterpretation,suchasquantificationalstructure(May1985,1987,1989). the languageinsensethatLFrepresentationmakesexplicitwhateverisrelevant tation ofsyntaxinChomskiangrammarthatprovidesaninterfacewithasemanticsfor be identifiedwiththelogicalformsofsentences(Neale1993).LFisalevelrepresen- called “LogicalForm”or“LF,”distinctfromsurfacestructureanddeepstructure,might the Chomskianprogram,ithasbeensuggestedthatsyntacticrepresentationsatalevel tional grammarcouldbeidentifiedwithlogicalform.Morerecently,changesin was madebyGilbertHarman(1975),whosuggestedthatdeepstructureintransforma- The firstsuggestionofanalignmentbetweenthetheorysyntaxandlogicalform revealed. Thechoicelieswiththepurposesforwhichdistinctionisdeployed. the roleofeachexpressionandstructure,whetherclassifiedaslogicalornot,isfully “logical.” Inacomprehensivetruthorfulfillment-theoreticaccountofthelanguage, about themachineryoflanguagebychoicewhattermstobringunderheading ity. Whenweareclearaboutwhatdistinctionseachdraws,nothingfurtherisrevealed initial observationthattherearetermsformsalientpatternsrelevanttovalid- competing criteriaintheliteratureidentifiestruecoinoflogic.Eachrefines of expressionsused(LeporeandLudwig2002b:sec.IVappendixC). tue ofapatterncreatedbycertainterms,orstructureinthetypes of formallyvalidarguments,anddistinguishthem,asEvansdoes,intothoseinvir- indifferently byapatternformedpartlywithoutorentirelyparticularterms, terminology whetherwespeakoflogicalsyntaxasasemanticstructurecharacterized seems amatterofwhatdeviceisusedtosubservepurpose.Thus,it one casebytheuseofatermandinotherarrangementcategoriesterms significant fromthestandpointofsemantictheory.Thatpatterniscreatedin 1.8 Compositionality 1.2 Semantics and Pragmatics That therearelevelsofsyntacticrepresentation,howmany,andrealized,isan A finaltopicistherelationofnonovertlevelssyntacticdescriptiontologicalform. Returning tologicalconstants,thereseemslittlepointininsistingthatoneofthe Related Topics LOGICAL FORM 39 Downloaded By: 10.3.98.104 At: 07:39 25 Sep 2021; For: 9780203206966, chapter1_3, 10.4324/9780203206966.ch1_3 ——. (2005)DonaldDavidson:Meaning,Truth, Language, andReality ——. (2002b)“WhatIsLogicalForm?,” inG.Preyer(ed.) Lepore, E.,andK.Ludwig(2002a) “OutlineofaTruthConditionalSemanticsforTense,”inQ.Smith (ed.) Kalish, D.(1952)“LogicalForm,” Mind, 61:57–71. Higginbotham, J.(1993)“GrammaticalFormandLogicalForm,”in J. Tomberlin(ed.)PhilosophicalPerspec- Hornstein, N.(2002)“AGrammaticalArgumentforaNeo-Davidsonian SemanticsInLogicalFormand ——. (1975)“DeepStructureasLogicalForm,”inD.Davidsonand G.Harman(eds.)SemanticsofNatural Harman, G.(1972)“LogicalForm,”FoundationsofLanguage,9:38–65. Grice, P.(1989)StudiesintheWayofWords,Cambridge:HarvardUniversityPress. Grandy, R.(1974)“SomeRemarksaboutLogicalForm,”Noûs,8(2):157–64. Gomez-Torrente, M.(2002)“TheProblemofLogicalConstants,” Evans, G.(1976)“SemanticStructureandLogicalform,”inJ.McDowell andG.Evans(eds.)Truth ——. (2001c)InquiriesintoTruthandInterpretation,2nded.,NewYork:ClarendonPress.Originalpublica- ——. (2001b)EssaysonActionsandEvents,2nded.,Oxford:Clarendon.Originalpublication,1980. ——. (2001a)“CommentsandReplies,”inEssaysonActionsEvents,NewYork:ClarendonPress. ——. (1977)“TheMethodofTruthinMetaphysics,”MidwestStudiesPhilosophy,2:244–54.Reprinted ——. (1973)“InDefenseofConventionT,”inTruth,SyntaxandModalit,Amsterdam:North-Holland ——. (1970)“SemanticsforNaturalLanguages,”inLinguagginellaSocietaeTecnica,Milan:Comunita. ——. (1968)“OnSayingThat,”Synthese,19:130–46.Reprintedin(Davidson2001c). ——. (1967b)“TruthandMeaning,”Synthese,17:304–23.Reprintedin(Davidson2001c). Davidson, D.(1967a)“TheLogicalFormofActionSentences,”inN.Rescher(ed.)TheLogicDecisionand Chomsky, N.(1995)TheMinimalistProgram,Cambridge:MITPress. Casteñeda, H.-N.(1967)“CommentsonDonaldDavidson’s‘TheLogicalFormofActionSentences’,”inN. Ayer, A.J.(1984)PhilosophyintheTwentiethCentury,NewYork:VintageBooks. . Frege,Russell,andWittgenstein. ThePhilosophyofLanguageforMetaphysics 7.4 TheRoleofLinguistics 6.3 TheRoleofIntuitions 4.2 TheRoleofPsychology 4.6 4.3 3.11 Indexicals and 3.9 Adverbs Demonstratives 3.7 Descriptions 3.4 Quantifiers 2.8 Event and 2.2 Theories Semantics Determiners 1.10 Context-Sensitivity of Truth Audi, R.(ed.)(1995)TheCambridgeDictionaryofPhilosophy Press. Tense, TimeandReference,Cambridge:MITPress. tives: LanguageandLogic,Atascadero:Ridgeview. Language,” inG.PreyerandPeter(eds.)LogicalFormLanguage , Oxford:Clarendon,345–64. Language, Dordretch:Reidel. 1–37. Meaning, London:OxfordUniversityPress. tion, 1984. Original publication,1980. (Davidson 2001c). Publishing Company.Reprintedin(Davidson2001c). Reprinted in(Davidson2001c). Action, Pittsburgh:UniversityofPittsburgh.Reprintedin(Davidson2001b). 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