The Eightfold Way - PhilArchive

volume17,no.25 december2017

The Eightfold Way:

Why Analyticity,

Apriority and Necessity

are Independent

Douglas Ian CampbellUniversity of Canterbury

©  2017  Douglas Ian CampbellThis work is licensed under a Creative Commons

Attribution-NonCommercial-NoDerivatives 3.0 License. <www.philosophersimprint.org/017025/>

1. Introduction

InthispaperIdefendwhatIfranklyadmitmayappearonfirstinspec-tiontobeapreposterousposition.Isayitmayappear“preposterous”advisedly,becauseeveryphilosopherIhavediscusseditwithhasear-nestly assured me it is preposterous — until, that is, the argument has beenexplained,whereuponmuchchinrubbingandheadscratchingensues.Iftheargumenthasaweakness,thenitis,Ithink,notobviouswhereitis.

Thepositionconcernsthethreegreatmodaldichotomies:

The metaphysical dichotomy. A true statement is necessaryiffitisimpossibleforittobefalse.Otherwiseitiscontingent.1

The epistemic dichotomy. A true statement is a prioriiffitcanbeknown independentlyof experience.Otherwise it isempirical (or a posteriori).

The semantic dichotomy. A true statement is analyticiffitistrueinvirtueofmeaningalone.Otherwiseitissynthetic.2

1. Bya‘statement’Imeanasentenceproducedinacontext.HereIfocusonlyontruestatements.Ifbothtrueandfalsestatementsareconsidered,thenwegetnotadichotomybutatrichotomy—betweennecessary truths, necessary false-hoods and contingencies.The samegoes,mutatis mutandis, for theepistemicandsemanticdichotomies.

2. It is presently somethingof a receivedview: (i) that thenecessary/contin-gent and a priori/empiricaldichotomiesapplyinthefirstinstanceto proposi-tions; (ii) that these twodichotomies also applyderivatively to statementsthatexpresspropositions,withastatementinheritingthemetaphysicalandepistemicstatusesofthepropositionitexpresses;but(iii)thattheanalytic/syntheticdichotomyinsteadappliesonly to statements, not to the propositions theyexpress.Iwon’tchallengethisreceivedviewinthepresentpaper.Ac-cordingly, Iwillwork always at the level of statements, not that of propo-sitions. However, I will argue elsewhere that the received view is poorlymotivated and that there are strong reasons for thinking that all three modal dichotomies apply in thefirst instance to propositions. It is also sometimessuggestedthattheanalytic/syntheticdichotomyappliestosentences.Thisisimplausible, since statementshavedeterminatemeaningswhile sentences(often)don’t(Hospers,1967,163).Forexample,anutteranceofthesentence‘Banks aremonetary institutions’might be either an analytically true state-mentorasyntheticfalsehood,dependingonwhetherthecontextisindicative

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Amodalcategory“hasmembers”ifstatementsbelonginginthatcat-egoryexist. It is “empty” if therearenostatementsof that type.Forexample,NAAhasmembersiffthereisatleastonestatementthatisnecessary,a prioriandanalytic.Ontheplausibleassumptionthat(1)issuchastatement,NAAdoesindeedhavemembers:

(1) Allbachelorsareunmarried.

ThepositionIwilldefendisthis:

Octopropositionalism: All eight modal categories havemembers.Noneisempty.

OctopropositionalismappearspreposterousbecauseitfliesinthefaceofreceivedopiniongoingrightbacktoHume.Humefamouslyheldthat there are just two types of statements, relations of ideas and mat-ters of fact.Theformerare(inmyterminology)NAAstatements,beingnecessary,a prioriandanalytic.Anexampleis(1).ThelatterareCESstatements, being contingent, empirical and synthetic. An example is(2):

(2)Thesunwillrisetomorrow.

Thedoctrinethatonlythesetwotypesofstatementsexist isHume’s fork.OctopropositionalismliesatoneextremityofaspectrumthathasHume’sforkattheotherextremity.3ForHume,thethreemodaldichot-omies are co-extensive and collapse into a single dichotomy—thatbetween relations of ideas andmatters of fact. For the octoproposi-tionalist,incontrast,thethreemodaldichotomiesaremaximallynon-coextensive.Theycomeapartevery which way.

3. TheQuineanpositionthatallthreemodaldichotomiesareill-posedliesattheextremityofadifferentspectrum.ForrecentrebuttalsofQuine,andofrelatedargumentsbyHarman (1973, 1996), see (Juhl&Loomis,2010), (G.Russell,2008)and(Chalmers,2012).

Thesethreedichotomiescanbecombinedtoproducethetri-dichoto-myofFigure1:

Figure 1. Themodaltri-dichotomy.

Figure1depictseightmodalcategories:

NAA:Necessary,A priori and AnalyticNAS:Necessary,A priori and SyntheticNEA:Necessary,EmpiricalandAnalyticNES:Necessary,EmpiricalandSyntheticCAA:Contingent, A priori and AnalyticCAS:Contingent, A priori and SyntheticCEA:Contingent, EmpiricalandAnalyticCES:Contingent, EmpiricalandSynthetic

ofMainStreetorariver’sedge.Thesentenceitself is thusneitheranalyticnorsynthetic.

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Kaplan(1977,509,540)hasalsoarguedthat(7)isa priori,contingentandanalytic,makingitaCAAstatement:

(7)Iamherenow.

Pullingtheseideastogether,weobtainthefollowingcandidatemem-bersofthedifferentmodalcategories:

NAA:Hume’s(1)NAS:Kant’s(4)NEA:-----------}Kripke’s(5)goesinoneNES:-----------}ofthesetwoplacesCAA:Kaplan’s(7),-----------}Kripke’s(6)goesinoneCAS:Descartes’(3),--------}ofthesetwoplacesCEA:CES:Hume’s(2)

Thislistcomesnowhereclosetovindicatingoctopropositionalism.Inthefirstplace,neitherDescartes,Kant,KripkenorKaplanprovidesuswithaputativeexampleofaCEAstatement.Second,ifKripkeisright,then(5)isamembereitherofNEAorofNES,butitcan’tbeamemberofboth—whichleavesoneofthesetwosectorsvacant.Third,itisnotobvioustheideasofDescartes,Kant,KripkeandKaplancanorshouldallbeacceptedconjointly—potentially leavingoneormoreofNAS,CAAorCASempty.

Inshort,althoughthesephilosophershaveproducedreasons forthinking statements aremoremodally diverse thanHume’s fork al-lows,noneofthemhaschallengedaweakerHumeandoctrinetotheeffect that some modal categories are empty. The octopropositionalistmustrefuteeventhisweakerdoctrine,which,inviewofhowwellithasstoodthetestoftimedownthecenturies,wouldappearaverytallorderindeed.

Setting aside the apparent unlikelihood of octopropositional-ism’sbeing shown to be true, why, if it were true, would its truth mat-ter? Its truthwouldbe important for thesamereasons thatKripke’s

In arguing for his ‟fork”,Hume(thearchempiricist)waspartlymo-tivatedbyawishtodenythatDescartes(thearchrationalist)wascor-rectinclaimingthat(3)isa priori:

(3)Athinkingthingexists.

IfDescarteswere rightabout(3)beinga priori,then,since(3)iscontin-gentandsynthetic,itwouldbeaCASstatement.4ThisHumetooktobeimpossible.5

Kant argued, contraHume, that statements of a third type exist:namely,NAS statements that are necessary and a priori on the one handbutsyntheticontheother.(4)isanexample.

(4)Causationexists.

Inmorerecenttimes,Kripke(1980)producedexamplesbothofstate-mentsthatarenecessarybutempirical—e.g.,(5)—andofstatementsthatarecontingentbuta priori—e.g.,(6).TheformeraremembersofeitherNEAorNES,dependingonwhethertheyareclassifiedasana-lyticorsynthetic.ThelatteraremembersofeitherCAAorCAS.

(5)WaterisH2O.

(6) The Standard Meter Bar is one meter long, if anythingis.6

4. See(Hintikka,1962;1963),(Kitcher,1983,30)and(Burge1988)forrationalreconstructionsofthecogitoargumentthatshedlightonhow(3)mightac-quireaCASstatus.

5. ForHume, (3) is insteadknownempirically,via introspection,making it aCESstatement.

6. Iaddan‘ifanythingis’clausetocoverreference-failurethatKripkedoesn’tinclude,althoughsee(Kripke,1980,110).Evans’ (1982,31) ‘Julius inventedthezip’examplewouldservejustaswellas(6),aswouldsimilarexamplesduetoSwinburne(1975,234,243).

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for constructingmembersof the remainingcategories. §3 considerstheproper framingof theanalytic/syntheticdistinction.§4presentsthecaseforthinkingNASstatementsexist.§5and§6dolikewiseforNEAandCAAstatements.§7wrapsthingsup.

2. Conjunction and disjunction

My argument for octopropositionalism hinges on the following‟trumpingrules”,whichtothebestofmyknowledgehaveheretoforegoneunnoticedintheliteratureonthethreemodaldichotomies:8

The conjunctive rules

T1. Inaconjunctionof twotruths,p and q,contingencytrumpsnecessity,inthesensethatifeitherp or qiscon-tingent,then‘p∧q’iscontingenttoo.

T2.Inaconjunctionoftwotruths,p and q,empiricalnesstrumps apriority, in the sense that if either p or q is empiri-cal,then‘p∧q’isempiricaltoo.

T3. Ina conjunctionof two truths,p and q, syntheticitytrumpsanalyticity,inthesensethatifeitherp or q is syn-thetic,then‘p∧q’issynthetictoo.

The disjunctive rules

T4.Inadisjunction,necessitytrumpscontingency,inthesense that if either p or qisnecessary,then‘p∨q’isneces-sarytoo.

T5.Inadisjunction,aprioritytrumpsempiricalness,inthesense that if either p or q is a priori,then‘p∨q’isa prioritoo.

8. Forexample,theyarenotdiscussedby(Swinburne,1975),(G.Russell,2008)or(Juhl&Loomis,2010).

discoveriesaboutstatementslike(5)and(6)havebeenimportant.Indemonstratingthatempiricalnecessitiesanda prioricontingenciesarepossible,Kripkeshowedthedangerinthecommonpracticeoftreat-ing apriority as a reliable guide tonecessity andvice versa. If octop-ropositionalismwerecorrect,thenthesamelessonwouldapplywithabsolutegenerality:no modal attribute of a statement would be a reli-able guide to any other.Thiswouldn’tentirelydebarusfromappealingtoheuristicssuchas‘ifastatementissynthetic,thenitisempirical’or‘ifastatementisnecessary,thenitisanalytic’.Butitwouldmeanthatsuchheuristicswouldneedalways tobe treatedwithcautionandacarefuleyetoknownclassesofcounterexamples.

Thetruthofoctopropositionalismwouldalsohavemajorimplica-tions with regards to the proper understanding of entailment. Threespeciesofentailmentcanbedistinguished,asfollows:7

ϕmetaphysicallyentailsψiffϕ⊃ψisnecessary.

ϕepistemicallyentailsψiffϕ⊃ψisapriori.

ϕsemanticallyentailsψiffϕ⊃ψisanalytic.

Becauseoctopropositionalism implies that noneof the threemodaldichotomiesisareliableguidetoanyother,italsoimpliesthatnoneofthesethreespeciesofentailmentisareliableguidetoanyother.Forin-stance,ifϕ⊃ψwereempiricalbutanalytic,thenϕwouldsemanticallyentailψwithoutepistemicallyentailingit.Orifϕ⊃ψwerenecessarybutsynthetic,thenϕwouldmetaphysicallyentailψwithoutsemanti-callyentailingit.Andsoon,foreverypairingofthedifferentspeciesofentailment.Octopropositionalismthereforehastheupshotthatthethreeentailmentrelationsarecompletelyseparableanddistinct.

Overview.§2explainsthestrategyIusetoargueforoctoproposition-alism—astrategywhichinvolvesshowingthatNAS,NEAandCAAstatementsexist,andthenusingthesestatementsas"rawingredients”

7. Iowethispointinpartto(Pollock,1974,300).

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Table2doesthesamefordisjunctions(withtheoperativetrumpingrulesbeingT4,T5andT6):

Table 2. Howthemodalcategoriesofp and q determine the mod-alcategoryofp∨q.

Tables1and2havebeenconstructedbysimplyapplyingtherelevanttrumpingrulestoeachpairof‟parent”statements,inordertodeducethemodalstatusofthe“child”statement.

Most entries in these tables are (relatively) uninteresting for one or bothofthesereasons:

(a)The“child”statementobtainedbyconjoiningordis-joining p with qbelongstothesamemodalcategoryaseither p or q.Forinstance,conjoininganNASstatementwithanNESstatementmerelyyieldsanotherNESstate-ment,gettingusnowhere.

(b)The“child”statementisaHumeanNAAorCESstate-ment, of which bountiful uncontroversial examples al-readyexist.

EntriesinTable1whicharenot“uninteresting”foreitheroftheserea-sonsareindicatedinbold.Thereareonlythreeofthem,andtheysaythefollowing:

T6. In a disjunction, analyticity trumps syntheticity, inthe sense that if either p or q is analytic, then ‘p∨q’ is analytictoo.9

Forexample,letpbeanycontingenttruth.Sincepiscontingent,itispossible for p tobefalse.Thus,it ispossibleforp∧q to be false, irre-spectiveofwhetherqisnecessaryorcontingent(p∧q being false if p is).Andso,p’sstatusasacontingenttruthisinheritedbyp∧q.Inshort,contingency trumps necessity within conjunctions, which is what T1says.

T2–T6areeasilyconfirmedusingsimilarexamples.Table1shows,foranypairoftruths,p and q,howthemodalcat-

egory that p∧qbelongstoisdeterminedbywhichcategoriesp and q belongto.TheoperativetrumpingrulesareT1,T2andT3.

Table 1.Howthemodalcategoriesofp and q determine the mod-alcategoryofp∧q.

9. The conjunctive rules containa clause, ‘of two truths’, that thedisjunctiveruleslack.Theclauseisincludedinordertoexcludecertainproblematiccas-es(e.g.,aswhenq=¬p)fromthescopeoftheconjunctiverules.

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Recipe 1. Start with “raw ingredients” consisting of: (i) any NASstatement;(ii)anyNEAstatement;and(iii)anyCAAstatement.Thenconstructa‟fullhouse”asfollows:

NAA:NAS∨NEA(byRule10)

NAS:-rawingredient-

NEA:-rawingredient-

NES:NAS∧NEA(byRule1)

CAA:-rawingredient-

CAS:NAS∧CAA(byRule2)

CEA:NEA∧CAA(byRule3)

CES:NAS∧NEA∧CAA(byRule4)

Recipe 2. Startwith"rawingredients”consistingof:(i)anyNESstate-ment;(ii)anyCASstatement;and(iii)anyCEAstatement.Thencon-structa“fullhouse”asfollows:

NAA:NES∨CAS∨CEA(byRule9)

NAS:NES∨CAS(byRule6)

NEA:NES∨CEA(byRule7)

NES:-rawingredient-

CAA:CAS∨CEA(byRule8)

CAS:-rawingredient-

Rule1:NAS∧NEA=NES

Rule2:NAS∧CAA=CAS

Rule3:NEA∧CAA=CEA

Table1alsoimpliesthefollowingpairofrulesforcreatingCESstate-ments(bothofwhichturnouttobemarginallyuseful):

Rule4:NAS∧NEA∧CAA=CES

Rule5:NES∧CAS=CES

Therearelikewisethree“interesting”entries inTable2, indicatedinbold,whichsay:

Rule6:NES∨CAS=NAS

Rule7:NES∨CEA=NEA

Rule8:CAS∨CEA=CAA

Table2alsogivesusthesetworulesforcreatingNAAstatements:

Rule9:NES∨CAS∨CEA=NAA

Rule10:NAS∨NEA=NAA

Puttingall these rules together,weobtain two “recipes”bywhicha“fullhouse”ofall eight typesof statementscanbeconstructed fromonlythree“rawingredients”.

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necessary toshowthatconditionC2obtains,whichwould(inpart)requiredemonstratingtheexistenceofsomeCEAstatement.Asnotedin§1,however,plausibleexamplesofCEAstatementsaredecidedlythinontheground.Forthisreason,Recipe2isunlikelytobeviable.Recipe1 (whichusesRule3 toconstructCEAstatements fromNEAandCAAingredients)willthereforebethefocusfromnowon.

On theassumption that (4), (5) and (7) areNAS,NEAandCAAstatements,respectively,Recipe1enablesalleightmodalcategoriestobefilledasfollows:11

NAA:Causationexists,orwaterisH2O.

NAS:Causationexists.

NEA:WaterisH2O.

NES:Causationexists,andwaterisH2O.

CAA:Iamherenow.

CAS:Causationexists,andIamherenow.

CEA:WaterisH2O,andIamherenow.

CES: Causation exists, and water is H2O, and I am herenow.

Forthereaderwhoishappytoacceptthat(4),(5)and(7)areindeedNAS,NEAandCAAstatements,thatcompletesmyargumentforoc-topropositionalism.But forreaderssceptical that(4), (5)and(7)arecorrectlyso-pigeonholed(probably,mostreaders),IneedtosaymorebywayofshowingthateachofRecipe1’srawingredientsisobtainable.

11. HereIuse(7),ratherthan(6),asaCAAstatement.Thechoiceisarbitrary.

CEA:-rawingredient-

CES:NES∧CAS(byRule5)10

LetconditionsC1andC2bedefinedasfollows:

C1:NAS,NEAandCAAstatementsexist.

C2:NES,CASandCEAstatementsexist.

IfC1obtains,thenalleightmodalcategoriescanbefilledusingRecipe1,sooctopropositionalismistrue.Likewise,ifC2obtains,thenalleightcategoriescanbefilledusingRecipe2,sooctopropositionalismistrue.Henceoctopropositionalismcanbedefendedeither by showing that C1obtainsorbyshowingthatC2obtains.Whoeverdeniesoctopropo-sitionalism must deny boththatC1obtainsandthatC2obtains.

Notice the dramatic shift in burdens of proof that has just beenachieved. It might have been thought that an octopropositionalistmustargueindependentlyfortheexistenceofeachoftheeightdiffer-enttypesofstatement.Thiswouldprovideheropponentwitheightindependentlinesofpossibleresistance.Butithasjustbeenshownthat in practice the octopropositionalist only needs to demonstratethat three categories of statements exist, for she can thenuse thesethreetoconstructtheotherfive.Moreoversheevenhasachoiceastowhichthreerawingredientstostartwith:NAS,NEAandCAA,ifsheusesRecipe1,orNES,CASandCEA,ifsheusesRecipe2.

That’s thegoodnews for theoctopropositionalist.Thebadnewsis thatoneof these twowaysofproceeding canbealmost immedi-atelydiscounted.InordertobeabletouseRecipe2,itwouldfirstbe

10. In practice it is obviously not necessary to constructNAA andCES state-mentsusingthemethodscontainedinRecipes1and2,sinceuncontroversialexamplesofsuchstatementsareeasilyfound,suchas(1)and(2).Therulesusedtoconstructthesestatements—namely,Rules4,5,9and10—arethere-foreofmuchlessinterestandimportancethantheremainingrules—Rules1,2,3,6,7and8.

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analyticity,makingAnalyticityEntailsNecessitytrue(andoctopropo-sitionalismfalse)bybrutedefinitionalfiat.13

Importantly, Kant did notargueforAnalyticityEntailsApriorityorAnalyticityEntailsNecessitybyproposingatrivializingdefinitionofanalyticity. Indefininganalyticity,he focusedspecificallyonaffirma-tivepredicate-subjectstatementsoftheformR(s).Inhiswords,‟Ana-lyticjudgmentssaynothinginthepredicateexceptwhatwasactuallythoughtalready in theconceptof thesubject, thoughnotsoclearlynorwiththesameconsciousness”(2004,16).Thatis,R(s)isanalyticforKantiffRiscontainedintheconceptofs.Thischaracterizationofanalyticitydoesn’tmakeittrueby definitionthatanalyticstatementsarenecessaryand/ora priori.Andso,atleastforKant,AnalyticityEntailsApriorityandAnalyticityEntailsNecessitydonotthemselves qualify as analytic judgements. (One can’t discover that an analytic statementmustbenecessaryorthatitmustbea priorijustbyunpackingKant’sdefinitionof‘analytic’.)

Why thendoesKant thinkAnalyticityEntailsApriority andAna-lyticityEntailsNecessityaretrue,ifnotbecausetheyareanalyticallytrue?InarguingforAnalyticityEntailsApriority,hewrites,‟[I]t would beabsurdtogroundananalyticjudgmentonexperience,sinceIdonot need to gobeyondmy concept at all in order to formulate thejudgment,andthereforeneednotestimonyfromexperienceforthat”(1998,B11).Hereheismakingthefollowingtacitassumption:

K1. The meaning (and thus the full truth-conditionalimport) of a concept, or of a thought, is accessible to a priori reflection.

If R(s)isanalytic,thenK1impliesthata priori reflectionwillbeabletodetectthatthisisso(i.e.,a priorireflectionwillbeabletodetectthatthepredicate,R,iscontainedintheideaofthesubject,s),fromwhichit follows that a priorireflectionwillbeabletodeterminethatR(s) is

13. See(Casullo,1992)foracritiqueofothertrivializingdefinitionsofanalyticity,asgivenbyQuinton(1963)andSwinburne(1975).

TodothisIwillbeginbyarguingforacertainpositionregardingtheproperframingoftheanalytic/syntheticdistinction.

3. On the analytic/synthetic distinction

Theanalytic/syntheticdistinctionwascoinedbyKant,whotookthefollowingpairofdoctrinestobetrue:

Analyticity Entails Apriority: All analytic statements are a priori.

Analyticity Entails Necessity: All analytic statements arenecessary.

Ifeitherofthesedoctrinesisindeedtrue,thenoctopropositionalismisfalse(forAnalyticityEntailsApriorityimpliesthatneitherNEAnorCEAstatementsexist,whileAnalyticityEntailsNecessityimpliesthatneitherCAAnorCEAstatementsexist).OnewayofarguingforAn-alyticityEntailsApriorityor forAnalyticityEntailsNecessity, andofthereby arguing againstoctopropositionalism,wouldbebyadoptingwhatIwillcallatrivializing definitionofanalyticity.BythisImeanadef-initionwhichbuildsthenotionofapriorityand/orofnecessity directly into the notion of analyticity, thereby, ineffect,making itanalytic thatoctopropositionalism is false.Forexample,Kripkeprovidesa trivial-izingdefinitionwhenhewrites:12

[L]et’s make it a matter of stipulation that an analyticstatement is, in some sense, true by virtue of its meanings and true in all possible words by virtue of its meaning.(Kripke,1980,39,myitalics.)

Thisisatrivializingdefinitionbecauseitbuildsthenotionofnecessity(i.e.,ofbeingtrue inallpossibleworlds)directly into thenotionof

12. Kripkelateracknowledgesthatanalyticitymightinsteadbedefinedinawaythat enables certain contingent statements, like (6), to count as ‟analytic”(1980,122n).

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AnSyn1:Astatementis"analytic”iffitistrueinvirtueofmeaningalone.Otherwiseitis"synthetic”.

AnSyn1isimprecise.Threeambiguitiesthatneedresolvingarethese:1.AnSyn1mentionsastatement’sbeing‟true”invirtueofmeaning

alone.Butisthetruth-valueinquestionthestatement’struth-valueinthe actual world(theworldweinhabitandexperience)oritstruth-val-ue at all possible worlds?14Dependingontheanswer,AnSyn1unpacksintoeitherAnSyn2orAnSyn3:

AnSyn2:Astatementis"analytic” iffit isactuallytrueinvirtueofmeaningalone.Otherwiseitis“synthetic”.

AnSyn3:Astatementis“analytic”iffitisnecessarilytrue(i.e., true in all possible worlds) in virtue of meaningalone.Otherwiseitis“synthetic”.

NoticethatAnSyn3isatrivializingdefinition,foritdefinesanalyticityas a subspecies of necessity. If Kant had intended the analytic/syn-thetic distinction tobeunderstood along the linesofAnSyn3, thenhewouldn’thaveneededtorelyonK1andK2inordertoargueforAnalyticityEntailsNecessity.Thisbeingso,wemustendorseAnSyn2,not AnSyn3, if we are to honor Kant’s usage of the terms ‘analytic’ and‘synthetic’.

2.Kripke’sandPutnam’sexamplesaresometimestakenasshowingthattherearetwokindsofmeaningassociatedwithastatement,thesebeing:(i)anarrow meaningthatisfullyaccessibletoa priorireflectionbutwhich sometimes falls short of determining a statement’s truth-value at a possible world; and (ii) a wide meaning that is sometimes inaccessibletoa priorireflection,butwhichisfullycapable,allbyitself,ofdeterminingastatement’s truth-valueatapossibleworld(Brown,2016).AnSyn2(likeAnSyn1,fromwhichitisdescended)mentionsthe‟meaning”associatedwithastatement,butwithoutspecifyingwhich

14. G.Russell(2008,41,52–57)notesthesameambiguity.

true.K1thereforeimpliesthatanyanalytic judgementwillbeknow-able a priori,justasAnalyticityEntailsAprioritysays.

Kant’s argument forAnalyticityEntailsNecessity ismore compli-cated.ItdependsonK1togetherwithK2:

K2.Apriorityentailsnecessity.

TogetherK1andK2supportAnalyticityEntailsNecessity:forsinceK1impliesthatanalyticstatementsmustbea prioriwhileK2impliesthata prioristatementsmustbenecessary,theyjointlyimplythatallanalyticstatementsmustbenecessary,justasAnalyticityEntailsNecessitysays.(WhydoesKantthinkK2istrue?Theanswerdoesn’treallymatterformy purposes, but Kant’s thoughtwas that judgements about neces-sitycouldnotbeempiricalandmustthereforebetriggeredbyjudge-mentsaboutapriority.Forexample,hewrites:"Experienceteachesus,tobesure, thatsomethingisconstitutedthusandso,butnot that itcouldnotbeotherwise.[Thus]ifastatementisthoughtalongwithitsnecessity,itisana priori judgment”[1998,B3].)

K1 andK2 are substantive, non-trivial, synthetic doctrines aboutthe relationbetweenmeaning, rationality andpossibility.This is re-vealedbythefactthatreceivedopinionnowadaysisthattheyarefalse.Bothwereacceptedasself-evidentlycorrectbyphilosophersfortwocenturiesaftertheCritique of Pure Reason’spublication,until—touni-versal astonishment—Putnam (1973) demolished K1 with his TwinEarththoughtexperimentandKripke(1980)demolishedK2withhisarguments in Naming and Necessity.MorewillbesaidaboutPutnam’sandKripke’s resultsbelow.Fornow, the importantpoint is just thatKant,innocentashewasofPutnam’sandKripke’sideas,tookbothK1andK2tobetrue,andit isforthisreason—andnotbecauseofanytrivializingdefinitionalstipulationonhispart—thatheendorsedbothAnalyticityEntailsApriorityandAnalyticityEntailsNecessity.

With thispoint inmind, let’s turn to thequestionas tohow theanalyticity/syntheticitydistinctionshouldbeframed.Itistraditionallyframedasfollows:

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Allanalytical judgments restentirelyon the lawofcon-tradiction…. For since the predicate of an affirmativeanalyticaljudgmentisalreadythoughtbeforehandintheconceptofthesubject,itcannotbedeniedofthatsubjectwithoutcontradiction.(2004,17)

AndsoitappearsthatKantwouldhaveusprecisifyAnSyn5asfollows:

AnSyn6:Astatementis“analytic”iffitsbeingactuallytrueisdeducible,viaLNC,fromitswidemeaningalone.Oth-erwiseitis“synthetic”.

However,Kant isbeinga littlecarelesshere.Supposep iscontradic-tory. LNC allows us to infer, on this basis, that p is false. But LNCdoesn’tallowustogetfromthefalsityofptotheconclusionthat¬p is (analytically)true.Thisstepinsteadrequirestheuseofanotherfunda-mental law of thought — namely, the Law of the Excluded Middle (LEM),theprinciplethateverystatementiseithertrueorfalse.LEMis justasimportantasLNCwithinthedeductionof¬p.MakingthisexplicitbringsustoAnSyn7:

AnSyn7:Astatementis“analytic”iffitsbeingactuallytrueisdeducible,viaLNCandLEM, from itswidemeaningalone.Otherwiseitis“synthetic”.

InKant’s timebothLNCandLEMwereuncontroversial.Nowadays,however, LEM is denied by constructivists and LNC by paraconsis-tentists, andsoAnSyn7 restsonassumptionsaboutdeductive logicthatarevigorouslycontested.Fortunately,wecanframetheanalytic/synthetic distinction in a way which avoids these controversial as-sumptionsaboutthefoundationalprinciplesoflogicbysimplyremain-ing silentastowhichprinciplesasounddeductivelogicwilluse—asfollows:

AnSyn8:Astatementis“analytic”iffitsbeingactuallytrue

kindofmeaningisrelevant—narroworwide.Itcanthereforebepre-cisifiedtoyieldeitherAnSyn4orAnSyn5:

AnSyn4: A statement is "analytic” iff it is actually truein virtue of its narrow meaning alone. Otherwise it is“synthetic”.

AnSyn5:Astatementis“analytic”iffitisactuallytrueinvir-tue of its widemeaningalone.Otherwiseitis“synthetic”.

AccordingtoAnSyn4,thekindof“meaning”relevanttoanalyticityisnarrowmeaning,whichjust is thekindofmeaningaccessibletoa pri-ori reflection.Thisturnsanalyticityintoasubspeciesofapriorityasamatterofdefinitionalstipulation,makingAnalyticityEntailsAprioritytrivial.Thus,AnSyn4is(likeAnSyn3)atrivializingdefinition.If,whenKantframedtheanalytic/syntheticdistinction,hehadhadsomethinglikeAnSyn4 inmind, thenhewouldnothaveneeded to relyonK1toargue forAnalyticityEntailsApriority. Indeed, it isperfectlyclearthat he can’t havehadAnSyn4inmind,sincetheideathatstatementshavea"narrowmeaning”inadditiontotheirwidemeaningoccurredtophilosophersonlyafterKripke’sandPutnam’sdiscoveries(andre-mainscontroversialevennow).ItwouldbeanachronistictoattributetoKantanythingsimilartoAnSyn4.Andso,ifwearetorespectKant’susageoftheterms‘analytic’and‘synthetic’,weshouldchooseAnSyn5inpreferencetoAnSyn4.15

3.AnSyn5(likeAnSyn1andAnSyn2,fromwhichitisdescended)speaks of a statement being true in virtue of meaning alone.Howpre-ciselyaretheitalicizedpartsofthisstatementtobeunderstood?ForKant,theansweristhatastatementisananalytictruthifitcanbelogi-callydeducedbywhathecallsthe‟LawofContradiction”—thisbeingtheprinciple,nowmorecommonlyknownastheLaw of Non-Contra-diction(LNC),that all contradictions are false.Forinstance,hewrites:

15. If the notion of ‟narrowcontent” isultimately incoherent (Stalnaker, 1989,1990,2008;Wilson,1995),thenthisprovidesanother,evenquickerreasontooptforAnSyn5.

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whichfundamentallawsofthoughtaresound,ityieldstheresultthat(8)isanalytic.

Theproblemissimplythatthisclassificationappearsincorrect.Theessential point here has been made many times down the ages — by Aristotle (Metaphysics,IV,4),Leibniz(1973,93),Carroll(1895),Frege(1964,15)andRussell(1912,72),amongothers:viz.,logiccan’tliftitselfbyitsownbootstraps;itcan’tvalidateitsownfoundationalprinciplesexceptonpainofviciouscircularity.17Alllogicalanalysispresupposescertainfoundationallawsofthought,suchasLNC,LEMandmodus po-nens,andthesearethereforenotthemselvessusceptibleofbeinglogi-callyproved.Statements, like(8),thatassertthesoundnessoftheselawsofthoughtarehence“pre-analytic”.Theirtruthmustbeassumedbeforewecanevenbegintomakesenseoftherebeingsuchthingsas‟analytictruths”inthefirstplace.Sincetheyarepre-analytic,theyarenotanalytic,whichmakesthemsynthetic.

Iffurtherevidenceiswantedforthinking(8)shouldbeclassifiedassynthetic, itcanbeobtainedbynoticing that (8)seemstofit thebillperfectlyforbeingaKantiana priorisynthetictruth.Is(8)know-able a priori?Itwouldcertainlyseemso,fordeductivelogicisasourceof a prioriknowledgeifanythingis,anddeductivelogicassumesthetruthof(8).(If(8)werefalse,thendeductivelogic—whetherclassical,constructiveorparaconsistent—couldnotbetrustedtoyieldtruecon-clusionsfromtruepremises.)Thisbeingso,(8)’sstatusasana priori truthmustbeatleastassecureasthea prioristatusofanydeductivelyprovedresult—whichis tosay,assecureascouldeverbe.Buthowcan(8)bea priori,givenitcannotbelogicallyprovedwithoutbeggingthe question? Kant held that a priori synthetic truths areknownviaa special kind of deduction—a transcendental deduction — that draws onrational insightsintothelimitsofpossibleexperienceandimagi-nation.AccordingtoKant,ϕ will be a prioriandyetsynthetic ifϕ is notprovablebylogic(i.e.,itisnotanalytic)butiftherationalmindcanrecognizeofitselfthatitisincapableofcoherentlyperceivingor

17. Foramorerecentdiscussion,see(Boghossian, 1997, 339, 345–350).

isdeducible,via sound logicalprinciples, from itswidemeaningalone.Otherwiseitis“synthetic”.

AnSyn8hasthevirtueoflettingtwoquestionsbeseparated.Thefirstquestionishowanalyticityshouldbedefined.AnSyn8followsKant’sleadbydefining analyticity in termsofwhat canbededucedusingsoundprinciplesof logic.Thesecondquestionconcernswhatthese“soundprinciplesoflogic”are.AnSyn8referstosuchprincipleswithoutspecifyingtheiridentity.Thereisthereforeroomforclassicallogicians,constructivists and paraconsistentists to agree in acceptingAnSyn8evenwhiledivergingradicallyintheiranswerstothesecondquestion.

Aproblemremains.Consider(8):

(8) At least one of the following logical principles issound:LEM,LNCormodus ponens.

(8)makes an exceedingly modest claim about the foundations of log-ic—a claimsomodest itwillbeacceptednotonlyby classical logi-cians,butalsobyconstructivistsandparaconsistentists.Constructiv-istsrepudiateLEMandparaconsistentistsrepudiateLNC,butitwouldbeavery rare logician indeedwhowouldrepudiatenot justoneofthesefundamentallawsofthought,butallofthem,fora“logic”thatendorsedneitherLEMnorLNCnormodusponenswouldbesoweakastobeinferentiallyuseless.16Becauseallreputablelogicsassumeatleastoneoftheseprinciples,thetruthof(8)istriviallyprovableinallsuchlogics,bysimplyinvokingthelawsthemselves—theverylawswhose truth is in question. Such a proof is obviouslyworthless forpersuasivepurposes,sinceitpresupposeswhatisbeingproved,butAnSyn8 doesn’t prohibit viciously circular deductions. For this rea-son,whenAnSyn8iscombinedwithanyremotelytenableviewabout

16. IntheunlikelyeventofacoherentandusefulnewlogicbeingproposedthatdisclaimedLNCand LEMand modus ponens, my overall point would still stand, sinceIcouldsimplyfurtherweaken(8)byaddingtothedisjunctionaprin-ciplethatthenewlogicrelieson.

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laws that “it seemstomeanattempt to jumpoutofone’sownskinagainstwhichIcandonomorethanurgentlywarnthem”(1964,15).

Inordertocapturetheideathat(8)issyntheticratherthananalytic,we needmerelymodify AnSyn8 by including a prohibition against question-begging logical deductions.TheresultisAnSyn9:

AnSyn9:Astatementis“analytic”iffitsbeingactuallytrueisdeducible,vianon-question-begginguseofsoundlogi-calprinciples,fromitswidemeaningalone.Otherwiseitis“synthetic”.

AnSyn9hasthefollowingimportantvirtues:

1.Itisfullyconsistentwiththetraditionalformulationoftheanalytic/syntheticdistinction—namely,AnSyn1—be-causeitismerelyadisambiguatedversionofAnSyn1.

2. For reasons just explained, it disambiguates AnSyn1in a way that appears to honor Kant’s linguistic inten-tions. Since Kant both coined the analytic/syntheticdistinction and made groundbreaking use of it in hisownhugely influentialphilosophical system,onecouldbreakusagewithKant anduse the terms ‘analytic’ and‘synthetic’ at cross-purposes to him only at the priceof introducing unwonted muddle and confusion into philosophicallanguage.

IwillnowattempttoshowthateachofRecipe1’srawingredientsexists.MyargumentswillassumethatAnSyn9isanadequateformu-lationoftheanalytic/syntheticdistinction.

4. Why NAS statements exist

KantreputedlyshowedlongagothatNASstatements(whichareneces-sary, a priori andsynthetic)exist.Heprovidedmanyexamples,includ-ing(4).Mattersmightjustbeleftthere.ButsomeofKant’sexamples

conceivinganystateofaffairs thatwould falsifyorcontradictϕ. (8)fulfillsthiscondition.Wefindthattherationalmindcanonlycoher-ently imagine,experienceandconceive theworldasconforming tosuch lawsof thoughtasLNC,LEMandmodus ponens.Fromthiswedrawtheconclusionthattheworldwecognizeandexperiencemustitselfbesuchaworld—i.e.,aworldwhere(8)istrue.Inotherwords,therationalmindfindsitself imprisonedincertainwaysofthinking,imagining and experiencing, with logic being, so to speak, the sci-encethatstudiesthebarsofitsprison.Anyworldthatarationalmindcoherentlyimaginesorexperiencesmust,forthisreason,beaworldwherethewaysofthinkingthatlogicdescribesholdgood,whichistosay,aworldwhere(8)istrue.Thisisatranscendentaldeduction:therationalmindshows(8)tobeana prioritruthbyreflectingonitsowninabilitytoimagineorconceiveacounterexampleto(8).

Thisidea—thatthelawsofthoughtareknownviaatranscendentaldeduction—wasnotexplicitlydefendedbyKant,butwasdefended bySchopenhauer:

ItisbymeansofakindofreflectionwhichIaminclinedtocallReason’sself-examination,thatweknowthat[thelawsofthought,includingtheLNCandLEM]expresstheconditionsofallthinking,andthereforehavethesecon-ditionsfortheirreason.For,bythefruitlessnessofitsen-deavors to think in opposition to these laws, our Reason acknowledges themtobe theconditionsofallpossiblethinking:we thenfindout, that it is just as impossibleto think in opposition to them, as it is to move the mem-bers of our body in a contrary direction to their joints. (1974,128)

Fregealsogesturesatthetranscendentalnatureof(8)when,afternot-ingthatthelawsofthoughtcannotbeprovedbylogicwithoutcircu-larity, he writes of people who would question the soundness of these

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describedbydeductivelogic,andso,inpart,by(8).AsWittgensteinput it, ‟Thetruthis,wecouldnotevensay of an ‘unlogical’ world how itwouldlook”(1922,§3.031).Invirtueofthemindhavingtheseimagi-nativelimits,(8)mustbetrue,notjustintheworldweexperience,butalsoineveryworldarationalmindcancoherentlyconceiveorimag-ine — making it not just actually true but also necessarilytrue.

Finally,is(8)analyticorsynthetic?WesawabovethatAnSyn9im-pliesit issynthetic.Wealsosawthattherearevariouspowerfulrea-sonstothinkthisisthecorrectclassification.Viz.,(8)’struthmustbeassumedbeforewecanmakesenseoftherebeinganysuchthingsasanalytictruthsinthefirstplace,fromwhichitfollowsthat(8)ispre-analytic(andthussynthetic).Moreover,ourknowledgethat(8)istrueappearstohaveatranscendentalsource,justaswouldbeexpectedifit were Kantian a priorisyntheticknowledge.

Inshort,(8)appearstobenecessary,a prioriandsynthetic—mak-ingitaNASstatement.

5. Why NEA statements exist

ForanexampleofanNEAstatement,weneedlooknofurtherthan(5):

(5)WaterisH2O.

That(5)isempiricalisobvious:‘water’isanameforthetransparentliquidthatfillsthelakes,riversandoceansonEarth.ThissubstancemightconceivablyhaveturnedouttobesomethingotherthanH2Owhensubjectedtoempirical,scientificanalysis.

That(5)isnecessarywasshownbyKripke.‘Water’isarigiddesig-nator:itrefers,ineverypossibleworld,towhateversubstanceitreferstoactually. ‘H2O’islikewisearigiddesignator:itrefersineverypos-sibleworldtosamplesofacertaintypeofmolecule,composedofoneoxygenatomandtwohydrogenatoms.Givenboth‘water’and‘H2O’are rigid designators, and given that, as an empiricalmatter of fact,they actuallyrefertothesamesubstance,itfollowsthattheyco-referineverypossibleworld—i.e.,necessarily.

havestoodthetestoftimepoorly(e.g.,hisclaimthatdeterminismisa prioriandnecessary),andnoneofhisexamplesisuncontroversial.

Inmyview,(4)isaplausibleexampleofaNASstatement.Ontheone hand, (4)’s denial (namely, ‘Causation doesn’t exist’) is prettyclearlynon-contradictory,making(4)synthetic.Butontheotherhand,italsoseemsthatwecannotcognizeorimagineaworldexceptashav-ingacausalstructure,making(4)necessaryanda priori.18

However,although(4)arguablymakesauseful“ExhibitB”fortheoctopropositionalist,acompelling“ExhibitA”isstillwanted.The“Ex-hibitA”Ihaveinmindisalreadyfamiliar—namely,(8):

(8) At least one of the following logical principles issound:LEM,LNCormodus ponens.

Is(8)a priori?Theanswerisaffirmative,forreasonsexplainedabove.Torecap:(8)’sstatusasana prioritruthmustbeatleastassecureasthea prioristatusofanydeductivelyprovedresult(i.e.,assecureascouldbe),sincedeductivelogic(whetherclassicalornon-classical)assumesthetruthof(8).

Is(8)necessary?(8)couldfailtobenecessaryonlyifitwerepossiblefor(8)tobefalse,butdeductivelogicisourguidewhenwejudgewhatispossibleandimpossible,and(8)makesanextraordinarilymodestclaimaboutthefoundationsofdeductivelogicitself.Inattemptingtoimagineaworldwhere(8)isfalse,wewouldbeattemptingtoimaginea world where deductive logic doesn’t work, and the idea of there being sucha(logically)possibleworldisanoxymoron.Wecannotimaginesuchaworld,becauseourimaginativecapabilitieshavelimits—limits

18. Whynecessary?Because, inHume’swords, “It is an establishedmaxim inmetaphysics,Thatwhateverthemindclearlyconceives,includestheideaofpossibleexistence,orinotherwords,thatnothingweimagineisabsolutelyimpossible.We can form the ideaof a goldenmountain, and from thenceconcludethatsuchamountainmayactuallyexist.Wecanformnoideaofamountainwithoutavalley,andthereforeregarditas impossible”(Hume,2000,§1.2.2).Inshort,causation’sexistenceisnecessarybecauseconceivabil-ityandinconceivabilityareourguidetopossibilityandimpossibility(Chalm-ers,2002)andbecausewecan’tconceiveofitsnon-existence.

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impliesthat‘WaterisH2O’isanalytic,thewidemeaningof‘water’be-ingenoughtodetermineallbyitselfthat‘WaterisH2O’isactuallytrue(and, indeed, not only actually true, but necessarilytrue).19

Chiefamongthereasonswhyoctopropositionalismappearsprima facie implausible is becausemost philosophers remember Kant’s fa-mousargumentagainsttheexistenceofanalyticempiricalstatements:viz.,ifastatementistrueinvirtueofmeaningalone,thena priori re-flectionwillbeabletodetectthatthisisthecase,sothatanalyticityentailsapriority.ThisargumentwithersinthefaceofPutnam’sdem-onstration that ‟meanings ain’t in the head” (Rey, 2016, §4.2). It as-sumesthatthemeaningsofone’swords,andtheirtruth-conditionalimport, areaccessible toa priori rational reflection (K1, above).ThemainlessonfromTwinEarthisthatthisassumptioniswrong.OscarandToscarmeandifferentthingswhentheysay“water”,buttheyarepsychologicallyidenticalandsothefactsaboutwhattheirownwordsmeanarecognitivelyinaccessibletothem.(IfOscarcouldaccessthefulltruth-conditionalcontentofhiswordsviarationalreflection,then(5)would,sinceitisanecessarytruth,alsobeana prioritruth,whichitobviouslyisn’t.)

6. Why CAA statements exist

Asmentioned in§1,prospectiveexamplesofCAAstatements—i.e.,statements that are contingent, a priori and analytic—include bothKripke’s(6)andKaplan’s(7):

(6) The Standard Meter Bar is one meter long, if anythingis.

(7)Iamherenow.

19. More generally, any statement of the form R(D)=R(E) will be of type NEA, where:(i)D and Eareapairofnon-rigiddefinitedescriptions(like‘themorn-ingstar’and‘theeveningstar’)that,asanempiricallydiscoverablematteroffact,designatethesamethingintheactualworld;(ii)R(x) rigidly designates whatever is actually designatedby thedefinitedescription,x; and (iii) x=y returns at world wiffx and y designate the same thing in w.

Finally, is (5)analyticorsynthetic?AnSyn9 implies that it isana-lytic,forreasonsIwillexplainbyreferencetoPutnam’s‟TwinEarth”thought experiment. It involves two people—Oscar, who inhabitsEarth,andToscar,whoinhabitsanotherplanet,TwinEarth.Bothuse‘water’torigidlydesignatethesubstancethatisactuallythedominanttransparentliquidontheirownhomeplanet.InOscar’scasethisliq-uidisH2O.InToscar’scaseitisadifferentchemicalcompound,‘XYZ’,which is, however, superficially indistinguishable from H2O. Oscarand Toscar aremolecule-for-molecule doppelgängers of each other,andhence indistinguishablewith regards to their internalpsycholo-gies.ButPutnampointsoutthattheirpsychologicalsimilaritydoesn’tstop them meaning radically different things when they say, ‟WaterisH2O.”Giventhat ‘water’ isarigiddesignator,thestatementOscarmakeswhenheuttersthissentenceisanecessarytruth,extensionallyandtruth-conditionallyequivalentto‘H2OisH2O’.ThestatementTos-carmakesisinsteadanecessaryfalsehood,equivalentto‘XYZisH2O’.Putnam infers,on thisbasis, that semanticexternalism is true—i.e.,that “‘meanings’justain’tinthehead!”(1973,704,hisitalics).Thatis,thepropositionanutteranceexpressespotentiallydependsnotonlyontheinternalpsychologyofthepersonwhomakestheutterance,butalsoonrelevant factsabout thesurroundingenvironment—suchaswhetherthelocalwaterystuffisH2O,orXYZ.

As mentioned above, philosophers sometimes distinguish wide meaning from narrow.Widemeaningisthekindofmeaningthat‟ain’tinthehead”,whilenarrowmeaningisakindofmeaningthatisinthehead.Onthiswayoftellingthestory,whenOscarandToscareachsay,“WaterisH2O”,theirwordshavedifferent wide meanings while sharing the samenarrowmeaning.WemayputthepointbysayingthatOscarandToscarmakedifferentstatements—statementstruth-conditional-lyequivalentto‘WaterisH2O’and‘TwaterisH2O’respectively—butthatthesetwostatementsareperfectlyalikewithrespecttotheircog-nitivelyaccessible‟narrowcontent”.

RecallthataccordingtoAnSyn9astatementisanalyticifitsbeingactuallytrueisdeduciblefromitswide meaning.Thisbeingso,AnSyn9

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actually (if not necessarily) true by virtue of meaning (both its narrow meaninganditswidemeaning)alone.21

TheoctopropositionalistneedsonlyoneexampleofaCAAstate-ment,butin(6)and(7)shehastwo.22

7. Concluding remarks

Myargumentsof§2showedoctopropositionalismmustbetrueifNAS,CAAandNEAstatementsexist,andmyargumentsof§4–6showedthateachofthesethreetypesofpropositionsdoesindeedexist.Myconclusion:octopropositionalismistrue.

Inordertorejectoctopropositionalism,onemusteither:(i)denythesoundnessof thetrumpingrulesdescribedin§2;or(ii)denyofboth(4)and(8) that theyareNASstatements;or(iii)denythat(5)is anNEAstatement;or (iv)denyofboth (6) and (7) that theyareCAAstatements.Option (i) appearshopeless.Options (ii), (iii) and(iv)wouldalmostcertainlyinvolvedenyingthatAnSyn9adequatelycharacterizestheanalytic/syntheticdistinction.ButonwhatgroundsmightAnSyn9bechallenged?Notonthegroundsthatitisinconsis-tentwiththetraditionalformulationoftheanalytic/syntheticdistinc-tion—namely,AnSyn1—becauseAnSyn9isobtainedfromAnSyn1bydisambiguation.NoronthegroundsthatindisambiguatingAnSyn1Ihave failedtorespecthistoricalusage,because inderivingAnySyn9fromAnSyn1IhaveusedKantasmyguide,andKantisthecanonicalhistoricalsource.

InarguingforoctopropositionalismIhavereliedontheideathat

21. Kripke(1980,122n)himselfacknowledgesthata prioricontingencieslike(6)mightbecountedasanalytic.

22. More generally, any statement of the form F(D)∨(R(D)=D) will be of type CAA,where:(i)Dissomenon-rigiddefinitedescriptionthatpicksoutitsref-erentbydescribinganaccidentalpropertyofthereferent(like‘theinventorofbifocals’);(ii)F(D)returnsTRUEatworldwiffD fails to designate anything in w; (iii) R(D) rigidly designates whatever is actually designated by D; and (iv) x=yreturnsTRUEatworldw iffx and y designate the same thing in w.SimilarexamplesofCAAstatementscanbemanufacturedonthemodelof‘Itisrainingifitisactuallyraining’(aspointedouttomebyananonymousreviewer).

Thereareverystronggroundsforthinkingboth(6)and(7)areCAAstatements.Thecaseforholding(7)tobeaCAAstatement—asarticu-latedbyKaplan(1977)andG.Russell(2008)—isstraightforward.(7)iscontingentbecausealthoughitisactually true that I am here now, counterfactuallyImightnothavebeen:Icouldhavebeensomewhereelsenow, instead. (7) isa prioribecausemererational reflectionsuf-fices toestablish that ‘Iamherenow’ is (actually) true,andnopos-sibleexperiencecoulddisconfirmthisclaim.20Finally,(7)isanalyticbecause themeanings (bothwide andnarrow) of the terms ‘I’, ‘am’,‘here’ and ‘now’ suffice by themselves to determine that (7) is actu-ally (albeit not necessarily)true.(Thedefinitionof‘here’issuchthatinmymouthitrigidlydesignatesthespatiallocationwhereIactually am now,sothat intheactualworld, ifnot inotherpossibleworlds,theexpressions‘here’and‘whereIamnow’mustco-refer.)

Next,(6).Let’smakeitamatterofdefinitionalstipulationthat‘onemeter’isarigiddesignatorthatdenotestheactuallengthoftheStan-dardMeterBar.Withthisstipulationinplace,itisclearthat(6)iscon-tingent.Thereare,forexample,possibleworldswhereintheStandardMeterBaris,say,twice as long asitisintheactualworld,whichistosay, two meterslong.(6)willbefalseinsuchcounterfactualworldsde-spitebeingtrueintheactualworld.That(6)isa prioriisalsoobvious.Mereconsiderationoftheforegoingdefinitionof‘onemeter’sufficesto establish that if the StandardMeter Bar exists, then it isactually (ifperhapsnotcounterfactually)onemeterlong,andthusthat(6)isactually(ifnotalwayscounterfactually)true.(Oneneedn’tempiricallymeasurethelengthoftheactualBartodetermineitslengthinmeters,theBar’slengthbeingitselftheultimatearbiterandreferencepointforallsuchmeasurements.)Finally,AnSyn9 implies that(6) isanalytic:forgiventhatwecandeducethat(6)isactuallytruebymerelycon-templatingtheabovedefinitionof‘onemeter’,itisobviousthat(6)is

20.ThisassumesthatDescarteswasrightandthatonecanknowa priori that the ‘I’ exists. IfDescarteswaswrong—i.e., ifonecanknowonlyviaempiricalintrospectionthatthe‘I’exists—then(7)’sstatusasaCAAstatementcanbepreservedbyaddingareference-failureclause,asfollows:‘EitherIdon’texist,orIamherenow’.

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haveshownthatRecipe1canbeusedtoconstructlogically compound statements belonging in the NAA, NES, CAS, CEA and CEScategories.Whichofthesecategoriescanalsobefilledwithatomic statements (not manufactured using the trumping rules)?23 Third, octopropositional-ismimpliesthatmetaphysical,epistemicandsemanticentailmentarenotreliableguidestoeachother(asexplainedin§1).Foranytwoofthesethreekindsofentailment,whatarethepreciseconditionsunderwhichonecancomeapartfromtheother?Fourth,thedichotomybe-tween truths that are knowable a priori and knowable empiricallycanbeturnedintoatrichotomybyalsorecognizingtruthsthatareunknow-able (aplausibleexamplebeingGoldbach’sconjecture).24 This gives rise to twelvemodalcategories, rather thantheeight.Doall twelvehave members?25 Fifth, G. Russell (2008, 56) and Juhl and Loomis(2010,219)haverecentlyproposedrivalwaysofconstruingtheanalyt-ic/syntheticdistinction.Whataretherelativevirtuesanddis-virtuesoftheirproposalsascomparedwithAnSyn9?

Thesequestionsaretopicsforfuturework.26

References

Boghossian,P.A.(1997).Analyticity.InB.Hale&C.Wright(Eds.),A Companion to the Philosophy of Language(331–368).Blackwell.

Brown, C. (2016). NarrowMental Content. In E.N. Zalta (Ed.),The Stanford Encyclopedia of Philosophy (Summer2016).MetaphysicsRe-searchLab,StanfordUniversity.Retrievedfromhttps://plato.stan-ford.edu/archives/sum2016/entries/content-narrow/.

Burge,T.(1988).IndividualismandSelf-Knowledge.Journal of Philoso-phy,85(11),649–663.

23. ThemostdifficultcategoriestofillwithatomicstatementsappeartobeNES and CEA.

24. See(Swinburne,1975,184,188).

25. Simpleextensionstoargumentsinthispaperyieldanaffirmativeanswer.

26.Manythanks to theanonymousreviewers for theirnumerousconstructivesuggestions.ThankstootoCarolynMason,TarnSomervellFletcherandMi-chael-JohnTurp.

KripkeandPutnam’sdiscoveriesshow—contrarytowhatKantimag-ined possible—that analytic statements can be empirical (i.e., thatAnalyticityEntailsApriorityisfalse)andcontingent(i.e.,thatAnalyti-cityEntailsNecessityisfalse).AnopponentofoctopropositionalismmightbetemptedtoinsistthatAnalyticityEntailsApriorityandAna-lyticityEntailsNecessityarenotupfornegotiation,andtodealwithpurported Kripkean and Putnamian counterexamples to AnalyticityEntailsApriorityandAnalyticityEntailsNecessity (e.g., (5)and(6))by adopting a trivializingconstrualoftheanalytic/syntheticdistinction,likeAnSyn3and/orAnSyn4.ToborrowalinefromBertrandRussell(1919, 72), this is an approachwith ‟many advantages; they are the sameastheadvantagesoftheftoverhonesttoil”.Ifoneredefinesana-lyticitytomakeitamatterofbrutedefinitionalstipulationthatno“an-alytic”statementcanbecontingentorempirical,then,ofcourse,onegets the result that Analyticity Entails Apriority and Analyticity En-tailsNecessityaretrueandthatoctopropositionalism(soconceived)isfalse.Bythesametoken,ornithologistsmighthavesavedthetheorythatallswansarewhitewhentheymettheirfirstblackswanbyrede-fining‘swan’tomeanwhatwasformerlymeantby‘whiteswan’.Surely,we should register Kripke’s and Putnam’s groundbreaking discover-ies aboutpossibility andmeaningby saying thatAnalyticityEntailsApriorityandAnalyticityEntailsNecessityhaveturnedouttobefalse, notbymovingthegoalpostsandredefining‘analyticity’tomakeAna-lyticityEntailsApriorityandAnalyticityEntailsNecessitycomeoutastriviallytrue.Ifwearetoavoidmutilatingthemeaningsoftheterms‘analytic’and‘synthetic’andintroducingunwontedequivocationsintothelanguage,thenwemustrespectKant’susage.Andasdiscussedin§3,itappearsclearthatforKantitwas notamatterofbrutedefinitionalstipulation that all analytic statementsmustbea priori, or that they mustbenecessary.

Myargumentsinthispaperraiseseveralquestions.First,epistemictwo-dimensional semanticsprovidesaunifiedexplanationofneces-sityandapriority(Chalmers,2004).CanitbemergedwithAnSyn9toyieldaunifiedexplanationofall threemodaldistinctions?Second,I

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