Mind%the%Is+Ought%Gap1% Forthcoming+in+the+Journal(of(Philosophy( Daniel+J.+Singer+ singerd@phil.upenn.edu+ Penultimate+draft+from+February+2015+–+Please+cite+only+the+published+version+ + Abstract:+ The+isEought+gap+is+Hume's+claim+that+we+can't+get+an+'ought'+from+just+'is's.+Prior+ (1960a)+ showed+ that+ its+ most+ straightEforward+ formulation,+ a+ staple+ of+ introductory+philosophy+classes,+ fails.+Many+authors+attempt+ to+resurrect+ the+ claim+by+restricting+its+domain+syntactically+or+by+reformulating+it+in+terms+of+ models+of+deontic+logic.+But,+those+attempts+prove+to+be+complex,+incomplete,+or+ incorrect.+I+provide+a+simple+reformulation+of+the+isEought+gap+that+closely+fits+ Hume's+ description+ of+ it.+ My+ formulation+ of+ the+ gap+ avoids+ the+ proposed+ counterexamples+from+Prior+and+offers+a+natural+explanation+of+why+they+seem+ compelling.+Moreover,+I+show+that+my+formulation+of+the+gap+is+guaranteed+by+ standard+ semanticses+ of+ normative+ terms,+ which+ provides+ a+ more+ general+ reason+to+accept+it.++ + According+to+Hume,+we+shouldn't+be+able+to+learn+about+how+things+ought+to+be+just+ from+how+things+are.+The+idea+is+often+summed+up+as+"no+ought+from+an+is."+This+is+ the+putative+is0ought(gap.+ A.+N.+Prior+purported+to+gave+several+counterexamples+to+the+isEought+gap,+and+there+ are+many+proposed+modifications+and+defenses+of+the+gap+in+response.2+I+argue+for+a+ new+way+to+understand+the+isEought+gap.+Along+with+Russell+and+Restall,+I+claim+that+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 1The+core+idea+presented+here+was+developed+in+conversations+with+Alex+Silk.+I+am+ extremely+grateful+to+him+for+his+help+on+this.+I+also+want+to+thank+Elisabeth+Camp,+ Allan+Gibbard,+James+M.+Joyce,+Sarah+Moss,+Peter+Railton,+Chandra+Sripada,+ W.+Robert+Thomas,+and+the+University+of+Michigan+Graduate+Student+Working+Group+ for+feedback+on+previous+versions+of+this+work.+ 2+See+Prior,+A.+N.+1960.+"The+Autonomy+of+Ethics."+Australasian(Journal(of(Philosophy+ 38+(3):+199–206.++For+responses,+see+Jackson,+Frank.+1974.+"Defining+the+Autonomy+ of+Ethics."+The(Philosophical(Review+83+(1).+Duke+University+Press+on+behalf+of+ Philosophical+Review:+pp.+88–96,+Pigden,+Charles+R.+1989.+"Logic+and+the+Autonomy+ of+Ethics."+Australasian(Journal(of(Philosophy+67:+127–51,+and+Russell,+Gillian,+and+ Restall,+Greg.+2010.+"Barriers+to+Implication."+In+Hume(on(Is(and(Ought,+edited+by+ Charles+Pigden.+Palgrave+MacMillan.+ the+isEought+gap+is+best+understood+in+terms+of+the+semantics,+rather+than+the+ syntax,+of+arguments.3+Unlike+Russell+and+Restall+though,+I+provide+a+complete+and+ correct+formulation+of+the+isEought+gap+that+offers+a+natural+explanation+of+why+the+ counterexamples+fail+and+stays+true+to+Hume's+original+motivation.+ Introducing%the%Gap% In+Book+III,+Part+I,+Section+I+of+the+Treatise(of(Human(Nature,+Hume+gives+the+first+ statement+of+the+isEought+gap.+He+says:+ In#every#system#of#morality,#which#I#have#hitherto#met#with,#I#have#always#remark'd,#that#the#author# proceeds#for#some#time#in#the#ordinary#ways#of#reasoning,#and#establishes#the#being#of#a#God,#or#makes# observations#concerning#human#affairs;#when#of#a#sudden#I#am#surpriz'd#to#find,#that#instead#of#the#usual# copulations#of#propositions,#is,#and#is#not,#I#meet#with#no#proposition#that#is#not#connected#with#an#ought,# or#an#ought#not.#This#change#is#imperceptible;#but#is#however,#of#the#last#consequence.#For#as#this#ought,# or#ought#not,#expresses#some#new#relation#or#affirmation,#'tis#necessary#that#it#shou'd#be#observ'd#and# explain'd;#and#at#the#same#time#that#a#reason#should#be#given,#for#what#seems#altogether#inconceivable,# how#this#new#relation#can#be#a#deduction#from#others,#which#are#entirely#different#from#it.4# Hume+has+us+imagine+a+hypothetical+interlocutor+seeking+to+give+a+theory+of+ morality.+The+interlocutor+offers+an+argument+from+wholly+nonEnormative+premises+ to+a+conclusion+about+how+things+ought+to+be.+This+inference+of+a+normative+claim+ from+only+descriptive+facts,+Hume+seems+to+be+claiming,+is+problematic+because+"this+ new+relation"+of+normativity+seems+"entirely+different"+from+descriptive+or+ observational+propositions.+What+is+the+case,+the+observational+or+descriptive+facts,+ do+not+seem+to+determine+at+all+how+things+ought+to+be.+This+is+a+rough+first+pass+at+ the+isEought+gap:+ SIMPLE+GAP+No+normative+truth+is+determined+by+any+nonEnormative+truths.5+ SIMPLE+GAP,+if+right,+would+have+it+that+no+collection+of+the+descriptive+facts+is+enough+ to+establish+how+things+ought+to+be.+SIMPLE+GAP,+as+stated,+is+ambiguous+between+an+ epistemic+reading+and+a+metaphysical+reading.+On+the+epistemic+reading,+the+claim+is+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 3+Op.+cit.+ 4+Hume,+David.+1978.+A(Treatise(of(Human(Nature.+Edited+by+L.+A.+SelbyEBigge+and+P.+ H.+Nidditch.+2nd+ed.+Clarendon+Press+;+Oxford+University+Press,+Oxford+:+New+York.+P.+ 469+ 5I+formulate+the+simple+version+of+the+claim+here+in+terms+of+normative+and+nonE normative+truths.+It+is+thus+formulated+to+mirror+Hume's+talk+of+propositions,+which+ I+take+to+be+bearers+of+truthEvalues,+though+the+use+of+'truth'+in+the+claim+is+ unnecessary.+If+for+example,+one+denies+the+possibility+of+normative+truths,+one+may+ substitute+whatever+analogue+of+truth+one+wishes+here+or+simply+formulate+the+ claim+without+any+such+analogue:+"Nothing+normative+is+determined+by+anything+ nonEnormative"+(though+I+take+this+formulation+to+be+less+clear).+ about+what+we+can+properly+infer:+We+cannot+draw+any+conclusions+about+what+ ought+to+be+the+case+just+from+what+is+the+case.+Such+an+argument,+according+to+the+ epistemic+reading,+would+be+invalid.+ Since+Hume+uses+the+gap+to+reject+the+arguments+of+his+contemporaries,+Hume+ seems+to+accept+the+epistemic+reading+of+the+claim.+But,+Hume+doesn't+defend+it+by+ pointing+to+any+formal,+syntactic,+or+conceptual+problems+of+their+arguments.+ Hume's+defense+of+the+gap+is+metaphysical:+it's+about+whether+there+really+is+that+ connection+between+the+descriptive+and+the+normative+that+the+offending+arguments+ need.+The+normative+conclusions+"[express]+some+new+relation+or+affirmation,+'tis+ necessary+that+it+shou'd+be+observ'd+and+explain'd;+and+at+the+same+time+that+a+ reason+should+be+given;+for+what+seems+altogether+inconceivable,+how+this+new+ relation+can+be+a+deduction+from+others,+which+are+entirely+different+from+it,"+he+tells+ us.6+ The+metaphysical+reading+of+SIMPLE+GAP+expresses+this+deeper+disconnection+ between+the+normative+and+the+nonEnormative.+On+the+metaphysical+reading,+what+ is+the+case+normatively+isn't+fixed+by+nonEnormative+facts.+So,+if+there+were+a+creator+ who+set+up+all+of+the+truths,+the+metaphysical+version+of+the+isEought+gap+would+ require+that+the+creator+to+set+the+normative+truths+even+after+all+of+the+nonE normative+truths+were+established.++ As+Hume's+argument+requires,+there+is+a+natural+connection+between+the+two+ versions+of+the+gap+claim.+If+the+metaphysical+claim+is+true,+the+epistemic+claim+ would+be+true+as+well:+one+could+not+properly+argue+from+just+nonEnormative+facts+ to+any+normative+facts+(without+any+bridge+principles+as+premises).+This+is+because+ there+would+be+some+possibilities+not+ruled+out+by+the+premises+that+are+ruled+out+ by+the+conclusion,+so+such+an+argument+would+be+invalid.+Following+Hume,+I'll+ restrict+my+focus+here+to+the+epistemic+reading+of+the+claim,+the+claim+that+we(cannot( properly(reason+from+claims+about+how+things+are+to+a+claim+about+how+things+ought+ to+be.7+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 6+Op.+cit.+p.+468+ 7For+more+on+the+metaphysical+version+of+the+claim,+see+Blackburn,+S.+1971.+"Moral+ Realism."+In+Morality(and(Moral(Reasoning,+edited+by+John+Casey,+101–24.+London,+ Methuen+for+a+discussion+of+the+supervenience+of+the+normative+on+the+nonE normative+and+2013.+"Autonomy+of+Ethics."+In+International(Encyclopedia(of(Ethics.+ Blackwell+Publishing+Ltd+for+remarks+on+how+this+affects+the+metaphysical+claim.+ Problems%with%the%Simple%Conception%of%the%Gap% A.+N.+Prior+showed+that+the+epistemic+reading+of+SIMPLE+GAP+is+false+with+three+ counterexamples:8+ (A)+ 1.! TeaEdrinking+is+common+in+England.+ 2.! Therefore,+either+teaEdrinking+is+common+in+England+or+all+New+ Zealanders+ought+to+be+shot.+ (B)+ 1.! There+is+no+man+over+20ft+high.+ 2.! Therefore,+there+is+no+man+over+20ft+high+who+ought+to+sit+in+an+ordinary+ chair.+ (C)+ 1.! Undertakers+are+church+officers.+ 2.! Therefore,+if+church+officers+ought+to+be+reverent,+undertakers+ought+to+ be+reverent.+ Each+example+consists+of+a+formally+valid+argument+with+nonEnormative+premises+ and+a+normative+conclusion.+They+show+that+the+epistemic+reading+of+SIMPLE+GAP+is+ false:+we+can+properly+reason+from+nonEnormative+premises+to+a+normative+ conclusion.9+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 8+See+Prior,+op.+cit.++I+provide+slightly+modified+versions+of+the+examples+from+Pigden,+ op.+cit.+p.+132,+of+each+of+Prior's+examples.+ 9Though+Prior+did+not+think+of+a+claim+like+SIMPLE+GAP+as+ambiguous+between+the+two+ given+readings,+the+counterexamples+also+show+against+the+metaphysical+reading+of+ the+claim:+since+there+are+valid+arguments+from+nonEnormative+facts+to+some+ normative+facts,+that+means+that+some+nonEnormative+facts+must+fix+some+normative+ facts.+ Prior+also+noted+that+there+seems+to+be+something+deficient+about+each+of+the+ conclusions+of+these+argument,+in+that+they+don't+seem+to+be+actionEguiding+or+ genuinely+normative.+On+that+line,+one+might+attempt+to+avoid+the+worries+by+ identifying+that+deficiency+and+omitting+similarly+deficient+conclusions+from+the+ intended+scope+of+the+isEought+gap.+ Prior+considers+this+move,+but+he+argues+that+it+won't+work+by+showing+how+each+of+ the+conclusions+can+be+used+in+the+context+where+it+does+have+interesting,+possibly+ Some%Attempts%to%Avoid%the%Counterexamples% Several+authors+have+proposed+responses+to+Prior's+worries+for+the+isEought+gap.+A+ popular+move+here+is+to+limit+the+intended+domain+of+the+isEought+gap+to+arguments+ with+sufficiently+simple+normative+conclusions.+The+underlying+idea+is+that+none+of+ Prior's+examples+are+counterexamples+to+the+isEought+gap+because+none+of+them+ entail+a+simple+statement+of+what+ought+to+be+the+case+or+what+we+have+reason+to+do.+ Gibbard,+for+example,+argues+that+it's+commonplace+for+hypothetical+ought+claims+to+ follow+from+descriptive+premises,+and+he+offers+a+restriction+of+the+claim+to+ sufficiently+simple+conclusions,+where+a+normative+conclusion+is+simple+when+its+ main+connective+is+Gibbard's+primitive+subjective+ought.10+ But,+restricting+the+gap+to+only+arguments+with+simple+conclusions+is+both+too+strong+ and+too+weak.+It's+too+strong+because+it+excludes+some+arguments+from+the+purview+ of+the+isEought+gap+that+it+should+not.+For+instance,+it+excludes+an+argument+with+the+ conclusion+"Either+Jane+ought+to+eat+tomato+soup,+or+Ange+ought+to+buy+garlic+ bread."+This+conclusion+isn't+a+simple+normative+sentence+in+Gibbard's+sense.+But+ that+conclusion+tells+us+something+substantive+about+what+ought+to+be+the+case,+and+ the+isEought+gap,+properly+formulated,+ought+to+deny+the+validity+of+arguments+with+ only+nonEnormative+premises+and+that+conclusion.+(Note+that+to+show+that+Gibbard's+ restriction+is+too+strong,+I+need+not+produce+a+valid+argument+from+descriptive+ premises+to+this+conclusion.+Doing+so+would+be+to+pronounce+the+fate+of+the+isEought+ gap,+not+merely+clarify+its+intended+domain.+Rather,+to+show+Gibbard's+restriction+to+ be+too+strong,+I+must+only+show+that+if(there(were(such(an(argument,+it+would+be+a+ counterexample+to+the+isEought+gap.+An+argument+with+only+nonEnormative+ premises+and+the+given+disjunctive+conclusion+would+be+one+that+would+"[express]+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ actionEguiding,+normative+force.+For+example,+we+can+get+the+conclusion+of+the+first+ argument+like+this:+ 1.! Anyone+who+does+what+is+not+common+in+England+ought+to+be+shot;+ 2.! All+New+Zealanders+drink+tea;+ 3.! Therefore+either+teaEdrinking+is+common+in+England+or+all+New+Zealanders+ ought+to+be+shot.+ This+example+shows+that,+contra+the+intuition+that+there's+no+real+force+behind+the+ normative+terms+in+the+conclusion+of+the+first+argument,+it+is+not+always+normatively+ impotent.+So,+we+can't+merely+restrict+the+class+of+conclusions+that+the+isEought+gap+ is+meant+to+apply+to.+Prior+concludes+then+that+there+is+no+gap.+ 10See+Gibbard,+Allan. 2012.+Meaning(and(Normativity.+Oxford+University+Press.+p.+80E 81.+Note+that+Gibbard+does+take+himself+to+be+responding+to+Prior+here.+Rather,+he+is+ considering+some+potential+outs+for+a+puzzle+about+correct+belief.+He+does+conclude+ though+that+"we+can+maintain+...that+no+elementary+ought+follows+analytically+from+ an+is"+(op.+cit.+p.+88),+in+light+of+his+consideration+of+that+puzzle.+ some+new+relation+or+affirmation"+for+which+"'tis+necessary+that+it+shou'd+be+ observ'd+and+explain'd.")+ Thinking+of+the+isEought+gap+as+only+applying+to+arguments+with+simple+normative+ conclusions+is+also+too+weak.+Gillian+Russell+attributes+the+following+example+to+ Gideon+Rosen:11+Suppose+"to+flurg"+means+to+do+something+that+one+ought+not+do+in+ front+of+children.+Then+we+could+deduce+from+"Lauren+is+in+front+of+children."+to+ "Lauren+ought+not+flurg."+The+conclusion+here+is+simple,+in+Gibbard's+sense,+but+it+ also+follows+from+the+nonEnormative+premise.12+So,+modifying+the+domain+of+the+gap+ claim+to+make+it+apply+only+to+simple+normative+sentences+is+too+strong+in+that+it+ doesn't+capture+all+of+the+intended+domain+of+the+isEought+gap,+and+it+is+too+weak+in+ that+it+doesn't+save+the+claim+of+PriorEstyle+counterexamples+like+this+one+from+ Russell.+ Other+authors+have+proposed+modifications+of+the+isEought+gap+claim+that,+like+ Gibbard,+attempt+save+it+by+limiting+its+intended+domain+on+the+basis+of+the+syntax+of+ the+arguments.+In+Prior's+original+essay+about+the+problematic+arguments,+for+ example,+he+notes+that+the+normative+terms+in+his+first+two+examples+appear+not+to+ do+any+normative+work;+in+them,+"the+duty+established+is+not+one+that+we+need+ever+ be+practically+anxious+about."13+Prior+diagnoses+this+as+what+he+calls+"contingent+ vacuousness".+A+term+is+contingently+vacuous+when+it+can+be+replaced+with+a+ grammatical+counterpart+without+sacrificing+the+validity+of+the+argument.+Prior's+ first+two+examples+would+be+still+be+valid+if+'ought'+where+replaced+by+'want',+for+ example.+Prior+fears+that+this+cannot+be+the+feature+that+sets+his+counterexamples+to+ the+isEought+gap+apart+from+other+arguments+though,+because+he+thinks+that+the+ 'ought'+in+his+third+example+is+not+contingently+vacuous.14+ Frank+Jackson+also+considers+examples+like+Prior's+and+diagnoses+them+as+being+ being+ethically(invariant,+a+property+that+is+formally+similar+to+Prior's+contingent+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 11+Gillian+Russell.+2010.+"In+Defence+of+Hume's+Law."+In+Hume(on(Is(and(Ought,+edited+ by+Charles+Pigden.+Palgrave+MacMillan.+P.+145.+ 12One+might+worry+that+stipulating+concepts+like+FLURG+is+illegitimate+and+subject+to+ worries+like+those+surrounding+the+concept+TONK+as+discussed+by+Prior,+Arthur+N.+ 1960.+"The+Runabout+Inference+Ticket."+Analysis+21:+38–39.+In+general,+that+seems+ right,+but+this+particular+case+is+not+worrisome.+FLURG+is+plausibly+quite+similar+to+ everyday+thick+normative+concepts+like+OBNOXIOUS:+being+obnoxious+requires+ satisfying+some+descriptive+criteria,+such+as+being+loud+or+unrelenting,+as+well+as+ being+such+that+one+ought+not+be+that+way.+The+example+of+'flurg'+is+used+since+it's+ easier+to+specify+in+the+stipulated+case+what+exactly+the+descriptive+content+is.+ 13+Prior, A. N. 1960. "The Autonomy of Ethics." Australasian Journal of Philosophy 38 (3): p. 203+ 14+op.+cit.+p.+204E6.+ vacuousness.15+To+avoid+other+potential+counterexamples+to+the+isEought+gap,+ Jackson+proposes+an+intricate+formulation+of+its+domain,+claiming+that+it+permits+ arguments+with+normative+conclusions+only+if+they+are+factualEinvariant,+ethicalE invariant,+or+reducible+to+such+by+synonymy+substitution.16+ Pigden,+following+MacIntyre,+objects+to+Jackson's+method+by+suggesting+that+without+ motivating+such+a+conception+of+the+isEought+gap+by+means+of+a+more+general+ principle,+we+can+expect+nothing+more+than+the+mere,+"perhaps+temporary,+drying+ up+of+counterexamples."17+Pigden+then+attempts+to+provide+a+more+general+ motivation+for+the+isEought+gap,+which+treats+it+as+an+instance+of+the+claim+that+logic+ is+conservative,+i.e.+that+nothing+substantive+can+occur+in+the+conclusion+of+a+ deductively+valid+argument+that+is+not+somehow+contained+in+the+premises.++Pigden+ says+that+we+should+treat+a+logic+as+conservative+when+"A+predicate+or+propositional+ variable+cannot+occur+nonEvacuously+in+the+conclusion+of+a+valid+inference+unless+it+ appears+among+the+premises."+Then,+the+conservativeness+of+our+standard+logics+ vindicates+the+isEought+gap,+according+to+Pigden,+since+it+shows+us+that+we+cannot+ get+an+'ought'+claim+in+the+conclusion+of+a+valid+argument+with+'ought'Efree+premises+ unless+that+'ought'+is+vacuous.18+ Pidgen's+proposal,+like+the+other+proposed+solutions+I+discuss+above,+construes+the+ isEought+gap+as+essentially+making+a+claim+about+when+and+how+certain+words+like+ 'ought'+can+appear+in+an+argument.+As+such,+those+proposals+treat+the+gap+as+ primarily+a+syntactic+or+logical+claim.+This+spells+trouble+for+Pidgen's+approach,+as+he+ notices,+since+he+must+deny+the+possibility+of+an+illuminating+deontic+logic,+since+ such+a+logic+would+treat+some+normative+claims+as+nonEvacuously+introducible+into+a+ conclusion+of+a+valid+argument.19+I+hope+we+can+accept+the+isEought+gap+without+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 15+See+Jackson,+Frank.+1974.+"Defining+the+Autonomy+of+Ethics."+The(Philosophical( Review+83+(1).+Duke+University+Press+on+behalf+of+Philosophical+Review:+pp.+88–96.++ Formally,+an+argument+is+ethically+invariant+when+the+normative+terms+in+it+can+be+ replaced+uniformly+with+any+other+grammatically+appropriate+term+without+ sacrificing+argument+validity+(p.+91).+This+is+a+slightly+different+property+than+Prior's+ contingent+vacuousness;+see+Pigden,+Charles+R.+1989.+"Logic+and+the+Autonomy+of+ Ethics."+Australasian(Journal(of(Philosophy+67:+133E4+for+an+explanation+of+the+ difference+and+discussion+of+it.+When+an+argument+is+ethically+invariant,+its+validity+ is,+in+a+sense,+independent+of+the+ethical+terms.+ 16An+argument+is+ΣEinvariant+when+its+validity+is+independent+of+the+meaning+of+the+ terms+of+type+Σ.++See+op.+cit.+p.+91E3.+ 17+See+Pigden,+op.+cit.+p.+134E5+and+MacIntyre,+Alasdair+C.+1981.+After(Virtue(:(A(Study( in(Moral(Theory.+University+of+Notre+Dame+Press.+p.+54E5.+ 18+Pigden,+Charles+R.+1989.+"Logic+and+the+Autonomy+of+Ethics."+Australasian(Journal( of(Philosophy+67:+127–51.+ 19This+is+because+Pigden+cannot+treat+'ought'+as+a+sentential+operator,+like+deontic+ logics+do,+because+there+would+be+truths+of+deontic+logic+that+contain+'ought'+nonE denying+the+possibility+of+an+informative+deontic+logic,+especially+given+the+progress+ that+has+been+made+by+treating+normative+terms+as+modal+terms+in+linguistics.20+So+ following+Pigden's+and+MacIntyre's+charge,+in+the+next+section,+I+provide+a+ formulation+of+the+isEought+gap+that+flows+from+a+more+general+understanding+of+the+ idea.+I+avoid+the+problems+of+the+approaches+I+mention+above+by+treating+the+isE ought+gap,+not+as+a+syntactic+or+logical+claim,+but+as+a+semantic+claim.+ A%New%Formulation%of%the%Is+Ought%Gap% For+a+more+general+defense+of+the+gap,+we+should+look+more+closely+at+Hume's+ problematic+case+of+the+moral+theorist+who+gives+an+argument+with+solely+nonE normative+premises+to+a+normative+conclusion.+Notice+that+when+we+imagine+this+ case,+we+don't+imagine+that+the+conclusion+is+just+any+normative+claim;+since+she+is+a+ moral+theorist,+we+imagine+Hume's+interlocutor+to+be+defending+a+claim+about+what+ ought+(or+ought+not)+to+be+the+case+in+the+actual+world.+For+this+reason,+the+moral+ theorist+would+not+be+offering+an+argument+like+Prior's+proposed+counterexamples.+ That's+because+the+conclusions+of+those+arguments+don't+offer+any+substantive+ normative+claims+to(someone(who(accepts(the(premises:+Consider+argument+(A),+the+ argument+from+'TeaEdrinking+is+common+in+England'+to+'Either+teaEdrinking+is+ common+in+England+or+all+New+Zealanders+ought+to+be+shot.'+This+would+be+an+odd+ argument+for+a+real+moral+theorist+to+offer.+But,+its+oddness+can't+be+due+to+the+ argument+being+invalid+(because+it+isn't).+Rather,+what's+odd+about+the+argument+is+ that+the+normative+impact+of+the+conclusion+is+irrelevant+to+the+possibilities+being+ reasoned+about.+If+the+premises+are+true,+the+conclusion+doesn't+tell+us+anything+ about+how+things+ought+to+be+in(the(actual(world.+For+that+reason,+(A)+would+not+be+ the+sort+of+argument+Hume's+moral+theorist+would+give+in+defending+his+moral+ theory.+More+generally,+the+point+is+that+when+our+goal+is+to+find+out+what+ought+to+ be+the+case,+like+we+do+in+moral+theorizing,+arguments+to+normative+conclusions+are+ useful+only+insomuch+as+those+arguments+offer+substantive+and+relevant+normative+ constraints+on+the+possibilities+under+consideration.+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ vacuously+and+that+can+be+deduced+from+no+premises+(and+so+any+'ought'Efree+ sentences+as+well),+counter+to+the+way+he+employs+the+conservativeness+of+logic.+ Perhaps+Oφ → ¬O¬φ+(If+it+ought+to+be+the+case+that+φ,+then+it+is+permissible+for+it+to+ be+the+case+that+φ)+is+one+such+example+that+can+deduced+from+any+premises.+ For+another+critique+of+Pigden,+see+Nelson,+Mark+T.+1995.+"Is+It+Always+Fallacious+to+ Derive+Values+from+Facts?"+Argumentation+9+(4).+Springer+Netherlands:+553–62.+ 20See,+for+example,+the+nowEstandard+analysis+of+normative+terms+as+modal+terms+ from+Angelika+Kratzer.++See+Kratzer,+Angelika.+1977.+"What+'Must'+and+'Can'+Must+and+ Can+Mean."+Linguistics(and(Philosophy+1:+337–55+as+well+as+Kratzer,+Angelika.+1991.+ "Modality."+In+Semantics:(An(International(Handbook(of(Contemporary(Research,+ edited+by+A.+von+Stechow+and+D.+Wunderlich,+639–50.+Berlin,+Germany:+de+Gruyter.+ When+we+introduce+and+motivate+the+isEought+gap+claim+in+teaching+contexts,+we+ also+only+consider+arguments+where+the+normativity+in+the+conclusion+is+substantive+ and+relevant+to+the+possibilities+described+by+the+premises.+In+an+introductory+ philosophy+class,+for+example,+we+might+try+to+convince+students+that+there+is+such+a+ gap+by+giving+an+example+of+fallacious+argument+offered+by+disputants+in+a+fight+over+ a+real+moral+issue.+For+example,+we+might+introduce+the+argument+from+"Abortion+ kills+babies"+to+"Abortion+is+wrong"+and+expect+the+students+to+have+the+intuition+ that+the+argument+is+invalid.+We+would+not+try+to+motivate+the+gap+claim+with+an+ argument+where+the+conclusion+was+irrelevant+to+the+premise,+such+as+the+argument+ from+"Abortion+kills+babies"+to+"If+abortion+doesn't+kill+babies,+it+is+wrong."+The+best+ explanation+of+this+is+that+the+gap+claim+is+really+the+idea+that+we(can't(advance(our( normative(inquiry+by+considering+an+argument+from+nonEnormative+premises+to+a+ normative+conclusion,+not+that+there+are+no+valid+arguments+of+that+form.+ My+proposed+formulation+of+the+isEought+gap+takes+these+considerations+seriously+by+ restricting+the+domain+of+isEought+gap+to+arguments+where+the+normativity+in+the+ conclusion+is+relevant+to+the+possibilities+described+by+the+premises.+ ISEOUGHT+GAP+There+are+no+valid+arguments+from+nonEnormative+premises+to+a+ relevantly+normative+conclusion.+ where+a+conclusion+of+an+argument+is+relevantly(normative+when+it+has+substantive+ normative+implications+for+the+possibilities+described+by+the+premises+(assuming+ there+are+some+such+possibilities).+A+more+fleshed+out+account+of+when+a+conclusion+ counts+as+relevantly+normative+is+still+required,+and+below+I'll+give+a+natural+one.+ Before+that+though,+notice+that+none+of+Prior's+proposed+counterexamples+show+ against+the+ISEOUGHT+GAP+formulated+thusly.+Each+of+those+arguments+has+the+ property+that+if+the+premises+are+true+in+the+some+world,+then+the+conclusion+offers+ no+substantive+claim+about+what+ought+to+be+done+in+that+world.+Consider+argument+ (A)+again.+If+we+have+two+moral+theorists+who+both+agree+that+teaEdrinking+is+ common+in+England+but+disagree+about+what+ought+to+be+the+case,+such+as+about+ whether+New+Zealanders+ought+to+be+shot.+Learning+the+conclusion+of+(A)+surely+ won't+help+them+reach+consensus.+The+conclusion+is+only+substantively+normative+in+ possibilities+they+aren't+considering,+namely+ones+in+which+teaEdrinking+isn't+ common+in+England.+A+similar+lesson+applies+to+Prior's+other+examples,+so+none+of+ those+threaten+ISEOUGHT+GAP.+ The%Is+Ought%Gap%in%Normative%Semantics% Hume+gave+us+an+intuitive+motivation+for+ISEOUGHT+GAP.+Here+I+take+the+case+one+step+ further+by+showing+that+ISEOUGHT+GAP,+when+properly+formalized,+should+be+seen+as+a+ theorem+of+normative+semantics.+If+that's+correct,+the+isEought+gap+is+not+subject+to+ Prior's+or+any+other+counterexamples.+To+show+this,+I+assume+that+normative+ sentences/utterances+are+interpreted+with+respect+to+points+of+evaluation+that+ consist+of+(perhaps+among+other+things)+an+ordinary+possible+world+and+a+normative+ standard.+This+is+an+extremely+minimal+assumption+that+allows+me+to+remain+ agnostic+about+interpreting+the+normative+semantics+as+relativist,+contextualist,+or+ invariantist.+ To+see+just+how+minimal+the+assumption+is,+recall+that+on+the+double+indexing+sort+of+ semantics+inherited+from+Stalnaker,+Kaplan,+and+Lewis,+points+of+evaluation+are+ structured+in+terms+of+a+context+that+takes+expressions+into+contents,+and+an+index+ (or+circumstance+of+evaluation)+that+takes+contents+into+extensions.+This+kind+of+ semantics+is+very+general+and+is+meant+to+provide+a+foundation+for+doing+semantics+ of+all+kinds+of+language.+The+double+indexing+semantics+is+often+supplemented+with+ different+elements,+like+times,+places,+worlds,+and+individuals+to+account+for+different+ aspects+and+types+of+language,+like+temporality+and+modality.+To+account+for+ normative+language,+the+double+indexing+picture+is+supplemented+with+a+normative+ standard.+According+to+the+contextualist+about+normative+language,+the+normative+ standard+figures+in+the+context+and+affects+what+proposition+is+expressed.+According+ to+the+relativist,+the+normative+standard+figures+into+the+index+and+affects+the+truth+ value+of+the+proposition+expressed+in+a+context.+According+to+the+invariantist,+the+ normative+standard+is+contained+in+the+structure+of+the+possible+world,+which+is+ itself+standardly+treated+as+a+coordinate+of+the+index.+So,+each+position+admits+the+ very+minimal+apparatus+that+I+need,+that+sentences+are+evaluated+with+respect+to+a+ possible+world+and+a+normative+standard.21+ Here+I+will+show+that+ISEOUGHT+GAP,+properly+conceived+of,+is+a+theorem+of+a+particular+ normative+semantics,+the+one+given+by+Gibbard's+Thinking(How(to(Live.22+This+ particular+semantics+makes+it+easy+to+formalize+ISEOUGHT+GAP,+show+how+it+is+a+ theorem,+and+see+how+to+generalize+these+lessons+to+other+semantics+of+normative+ language+that+meet+the+minimal+assumption.+Gibbard+uses+his+semantics+in+a+defense+ of+an+expressivist+account+of+normative+language,+but+my+use+of+the+framework+is+ completely+orthogonal+to+that+issue.+ On+Gibbard's+semantics,+the+contents+of+sentences+and+utterances+are+modeled+as+ sets+of+pairs,+each+consisting+of+a+possible+world+and+a+complete+plan+for+action+in+ any+hypothetically+possible+scenario.+Then,+like+in+a+standard+possibleEworld+ semantics,+we+model+the+content+of+a+sentence+'P'+with+the+set+of+worldEnorm+pairs+ that+are+compatible+with+P.+The+contents+of+nonEnormative+sentences+like+'Snow+is+ white'+are+represented+as+the+collection+of+worldEnorm+pairs+where+the+world+is+one+ in+which+snow+is+white.+The+semantics+of+'snow+is+white,+or+Mark+ought+to+cook'+is+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 21+The+three+positions+simply+disagree+about+how+best+to+account+for+those+two+ aspects+of+the+semantics.+Also,+in+order+to+distinguish+the+interpretations+of+ normative+sentences+that+differ+in+truth+value,+the+invariantist+will+either+need+to+ allow+impossible+worlds+that+differ+in+which+normative+standard+is+contained+in+the+ world+or+allow+that+the+normative+aspects+of+worlds+are+not+fixed+by+the+nonE normative+aspects.+Many+thanks+to+Alex+Silk+and+Elizabeth+Camp+for+helping+me+to+ clarify+the+flexibility+of+my+proposal+in+this+respect.+ 22+Gibbard,+Allan.+2003.+Thinking(How(to(Live.+Cambridge:+Harvard+University+Press.+ given+by+the+set+of+worldEplan+pairs+where+either+snow+is+white+in+the+world+or+the+ plan+calls+for+Mark+cooking.+ A+sentence+will+be+nonEnormative,+on+this+kind+of+semantics,+when+it+is+normE invariant,+i.e.+if+each+world+in+the+set+is+paired+with+every+possible+plan.+More+ explicitly,+if+W+is+the+collection+of+all+possible+worlds+and+N+is+the+collection+of+all+ complete+plans+for+action,+a+set+of+worldEnorm+pairs+P = {⟨w-, n0⟩}+is+norm0invariant+ iff+(∀w ∈ W)(∃n(⟨w, n⟩ ∈ P) → (∀n ∈ N)(⟨w, n⟩ ∈ P)).23++A+set+of+worldEnorm+pairs+ that+is+normEinvariant+is+compatible+with+all+possible+plans.+Such+a+set+therefore+ doesn't+exclude+any+normative+possibilities,+so+the+sentence+or+utterance+that+it+ represents+must+be+nonEnormative.+ Before+considering+ISEOUGHT+GAP+in+this+semantics,+consider+first+how+to+formalize+ SIMPLE+GAP:+Take+an+argument+from+premises+{P-}+to+conclusion+C.+SIMPLE+GAP+would+ say+this:+If+each+of+the+P-+is+normEinvariant,+then+C+is+normEinvariant.+As+we+should+ expect,+Prior's+(A)+shows+against+this+formulation+of+the+claim.+The+premise,+that+ teaEdrinking+is+common+in+England,+is+normEinvariant,+but+the+conclusion,+that+ either+teaEdrinking+is+common+in+England+or+all+New+Zealanders+ought+to+be+shot,+is+ not.+The+set+of+worldEnorm+pairs+that+represents+the+conclusion+includes+a+pair+ where+there+is+no+tea+and+all+New+Zealanders+ought+to+be+shot,+but+it+doesn't+include+ a+teaEless+world+where+some+New+Zealanders+ought+not+be+shot.+So,+it+is+not+normE invariant,+and+this+worldEnormEstyle+analogue+of+SIMPLE+GAP+fails,+as+expected.+ The+problem+I+diagnosed+with+Prior's+counterexamples+is+that+they+only+make+ substantive+normative+claims+about+worlds+that+are+incompatible+with+the+premises:+ the+normative+aspects+of+the+conclusion+doesn't+tell+us+how+things+ought+to+be+in+the+ worlds+the+argument+is+about.+The+solution+then+is+to+restrict+the+domain+of+the+isE ought+gap+to+arguments+in+which+the+normative+aspect+of+the+conclusion+is+relevant+ to+the+possibilities+being+reasoned+about.+We+can+formalize+this+intuition+in+our+ semantic+framework+easily.+To+decide+whether+the+conclusion+of+an+argument+ makes+a+claim+about+how+things+ought+to+be+in+the+worlds+described+by+the+ premises,+we+decide+whether+the+conclusion+is+normEinvariant+when+restricted+only+ to+the+worlds+compatible+with+the+premises.+In+our+semantics,+when+the+premises+ are+normEinvariant,+deciding+this+is+equivalent+to+deciding+whether+the+conjunction+ of+the+conclusion+and+the+premises+is+normEinvariant.+This+then+is+a+reformulated+ version+of+ISEOUGHT+GAP+in+Gibbard's+semantics:+ WORLDENORM+GAP+If+{P-} ⊢ C,+each+of+{P-}+is+normEinvariant,+and+P: ∧ P< ∧ ...+is+ satisfiable,+then+P: ∧ P< ∧ ...∧ C+is+normEinvariant.+ Intuitively,+WORLDENORM+GAP+tells+us+that+if+the+premises+of+an+argument+are+normE invariant,+then+the+set+of+all+worldEnorm+pairs+compatible+with+the+conclusion+and( the(premises+is+also+normEinvariant.+By+checking+the+conclusion+conjoined+with+the+ premises+for+normEinvariance,+we+restrict+our+attention+to+only+those+worlds+where+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 23This+is+a+restatement+of+the+definition+of+'normEinvariant'+employed+by+Schroeder,+ Mark.+2011.+"Attitudes+and+Epistemics."+(Manuscript).+ the+premises+are+true.+The+condition+that+the+premises+be+satisfiable+is+included+to+ avoid+the+special+case+where+nonEnormEinvariant+claims+follow+trivially+from+ contradictory+premises.+ As+I+claimed,+WORLDENORM+GAP+avoids+Prior's+counterexamples.+Consider+this+one:+ (C)+ 1.! Undertakers+are+church+officers.+ 2.! Therefore,+if+church+officers+ought+to+be+reverent,+undertakers+ought+to+ be+reverent.+ Since+the+argument+is+valid,+the+conclusion+must+be+satisfied+by+at+least+the+same+ worldEnorm+pairs+that+satisfy+the+premise.+Therefore,+once+we+conjoin+the+ conclusion+with+the+premise,+we're+left+with+a+claim+that+is+logically+equivalent+to+the+ premise.+Since+the+premise+is+normEinvariant,+it+follows+that+the+conclusion+ conjoined+with+the+premises+is+also+normEinvariant.+Hence,+that+argument+is+ compatible+with+this+formulation+of+the+isEought+gap.+Prior's+other+supposed+ counterexamples+are+handled+similarly.24+ One+might+worry+about+avoiding+the+counterexamples+to+SIMPLE+GAP+by+limiting+the+ scope+of+the+isEought+gap+to+arguments+from+premises+to+the+conjunction+of+those+ premises+and+the+conclusion.+In+doing+so,+it+ignores+the+possibility+that+normativity+ may+arise+in+a+conclusion+that+is+strictly+weaker+than+the+conjunction+of+the+ premises.+ But+this+is+feature,+not+a+bug.+If+normativity+arises+only+when+the+conclusion+of+an+ argument+is+strictly+weaker+than+the+conjunction+of+the+premises,+no+reasoner+could+ use+that+argument+to+come+to+a+conclusion+about+what+they+ought+to+do.+The+worldE norm+semantics+gives+us+a+natural+framework+for+understanding+why+this+is+so:+ Suppose+Rachel+wants+to+know+whether+she+ought+to+donate+to+charity.+We+can+ represent+Rachel's+mental+state+by+the+collection+of+worldEnorm+pairs+M+compatible+ with+what+she+believes+and+the+norms+she+accepts.+For+Rachel+to+become+decided+on+ whether+she+ought+to+donate,+it+is+for+the+plan+in+each+worldEnorm+pair+in+M+to+call+ for+donating+in+the+(centered)+world+of+the+pair.+So,+if+Rachel+isn't+already+committed+ on+whether+to+donate,+there+must+be+two+worldEnorm+pairs+⟨w:, n:⟩+and+⟨w<, n<⟩+in+ M+such+that+n:+calls+for+donating+in+w:+and+n<+permits+not+donating+in+w<.+Now+ suppose+Rachel+happens+across+a+valid+argument+where+the+premises+are+normE invariant+but+the+conclusion+is+not.+The+only+way+for+Rachel+to+become+committed+to+ donating+in+response+to+that+argument+is+for+her+to+change+her+mental+state+so+that+ one+of+those+two+worldEnorm+pairs+is+removed+from+its+representation.+Could+Rachel+ do+this+as+a+proper+response+to+a+valid+argument?+No:+Since+the+argument+is+valid,+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 24E.g.+the+conjunction+of+'There+is+no+man+over+20ft+high'+with+the+conclusion+that+ 'There+is+no+man+over+20ft+high+who+ought+to+sit+in+an+ordinary+chair'+is+firstEorder+ equivalent+to+'There+is+no+man+over+20ft+high,'+which+is+normEinvariant.+ Rachel+must+either+accept+the+conclusion+or+reject+a+premise.+The+premises+are+ normEinvariant,+so+we+can+think+of+them+as+ordinary+centered+possible+world+ propositions.+Rachel+accepts+them+when+every+world+in+a+worldEnorm+pair+in+M+is+ contained+in+every+premise.+So,+if+Rachel+does+accept+them,+w:+and+w<+must+be+in+ every+premise.+Since+the+premises+are+normEinvariant,+the+premises+must+also+have+ w:+and+w<+paired+with+every+possible+norm,+so+importantly,+⟨w:, n:⟩+and+⟨w<, n<⟩+ must+be+in+every+premise.+But,+since+those+worldEnorm+pairs+satisfy+the+premises+ and+the+argument+is+valid,+they+must+also+satisfy+the+conclusion.+So+when+Rachel+ accepts+the+conclusion,+those+pairs+will+remain+in+her+mental+state,+and+she'll+remain+ uncommitted+about+whether+to+donate.+On+the+other+hand,+if+Rachel+does+not+accept+ the+premises+of+the+argument,+her+mental+state+will+not+change+either.+So+again,+she+ will+remain+uncommitted+about+whether+to+donate.25+ The+key+claim+of+ISEOUGHT+GAP+is+this:+for+arguments+from+nonEnormative+premises+to+ a+normative+conclusion,+none+of+the+genuinely+normative+aspects+of+the+conclusion+ can+be+relevant+to+the+possibilities+described+by+the+premises.+But,+since+a+deductive+ argument+could+only+help+us+learn+something+about+how+things+ought+to+be+ insomuch+as+we+accept+the+premises,+any+potential+normative+guidance+that+could+ be+derived+from+nonEnormative+premises+must+only+apply+in+possibilities+where+the+ premises+fail.+When+we+ignore+those+possibilities+by+restricting+our+attention+only+to+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 25This+proof+works+for+deductive+arguments+because+deduction+is+nonEampliative.+ By+accepting+the+conclusion+of+such+an+argument,+the+reasoner+is+not+committed+to+ anything+she+wasn't+committed+to+before+considering+the+argument.+Suppose+though+ that+our+reasoner+doesn't+respond+properly+to+the+argument+and+does+become+ committed+to+the+premises+or+conclusion+of+the+argument+even+though+she+wasn't+ before.+This+is+an+odd+thing+for+her+to+do,+epistemologically+speaking,+in+response+to+ an+argument,+but+it+would+make+it+possible+that+the+reasoner+would+come+to+a+ decision+about+whether+to+donate+in+response+to+the+argument.+If+the+reasoner+does+ become+committed+about+whether+to+donate+by+accepting+either+a+premise+or+the+ conclusion+of+the+argument,+it+must+be+because+one+of+the+two+worldEnorm+pairs+ ⟨w:, n:⟩+and+⟨w<, n<⟩+is+removed+from+M.+Assuming+that+she+doesn't+learn+anything+ strictly+stronger+than+the+premises+or+the+conclusion,+this+requires+that+the+part+of+ the+argument+she+comes+to+accept+is+false+at+either+w:+or+w<.+But+since+the+parts+of+ the+argument+are+all+silent+about+what+ought+to+be+the+case+at+w:+and+w<+(since+they+ include+those+worlds+paired+with+every+possible+norm),+the+reasoner+still+doesn't+ learn+anything+normative+from+the+argument.+This+means+that+even+if+the+reasoner+ acts+in+what+appears+to+be+an+epistemically+irresponsible+way+in+response+to+the+ argument,+either+by+accepting+a+premise+or+the+conclusion+without+already+having+ been+committed+to+it,+the+information+that+the+reasoner+gains+from+the+argument+is+ nonEnormative.+So,+if+the+reasoner+does+become+committed+about+whether+to+donate+ by+accepting+parts+of+the+argument,+she+does+so+only+because+she+is+already+ committed+to+a+conditional+of+the+form+'If+w:(/<)+is+not+actual,+then+I+ought+(not)+ donate.'+It+is+this+conditional,+which+she+must+already+be+committed+to,+that+must+ play+the+role+of+the+normative+bridge+principle+in+her+reasoning.+ the+possibilities+compatible+with+the+premises,+the+normativity+disappears.+So,+ WORLDENORM+GAP+is+correct+to+effectively+limit+the+scope+of+the+isEought+gap+to+ arguments+from+premises+to+a+conjunction+of+the+premises+with+the+conclusion.+Any+ normativity+present+in+weaker+conclusions+is+deficient+for+reasoning+about+how+ things+ought+to+be+for+the+worlds+described+by+the+premises,+so+it+can+be+ignored+for+ the+purposes+of+understanding+the+gap+claim.+ What+the+above+discussion+brings+out+is+that+the+correctness+of+WORLDENORM+GAP+is+ dependent+on+the+fact+that+for+deductively+valid+arguments,+the+conclusion+is+at+most+ as+strong+as+the+conjunction+of+the+premises.26+This+property+allows+us+to+show+ formally+that+WORLDENORM+GAP+is+guaranteed+by+Gibbard's+semantics.+Proof:+For+some+ valid+argument+to+C+from+{P-},+suppose+that+each+of+{P-}+is+normEinvariant,+P: ∧ P< ∧ ...+ is+satisfiable,+and+{P-} ⊢ C.+Then+since+the+argument+is+valid,+C+must+be+satisfied+by+ every+worldEnorm+pair+that+satisfies+P: ∧ P< ∧ ....+So,+P: ∧ P< ∧ ...∧ C+is+satisfied+by+ every+worldEnorm+pair+that+satisfies+P: ∧ P< ∧ ....+Without+loss+of+generality,+let+⟨w, n⟩+ be+some+worldEnorm+pair+that+satisfies+P: ∧ P< ∧ ...∧ C.+Since+⟨w, n⟩+must+satisfy+each+ of+the+{P-}+and+each+of+the+{P-}+is+normEinvariant,+for+each+{P-}+∀n ∈ N(⟨w, n⟩ ∈ P-).+So+ ∀n ∈ N(⟨w, n⟩ ∈ P: ∧ P< ∧ ... ).+Then+since+every+worldEnorm+pair+that+satisfies+the+ conjunction+of+the+premises+must+satisfy+the+conclusion,+∀n ∈ N(⟨w, n⟩ ∈ P: ∧ P< ∧ ...∧ C).+So+P: ∧ P< ∧ ...∧ C+is+normEinvariant.+ This+proof+can+easily+translated+into+a+proof+of+ISEOUGHT+GAP+in+any+semantics+of+ normative+terms+that+accepts+the+minimal+assumption+that+we+evaluate+normative+ sentences/utterances+in+terms+of+an+ordinary+possible+world+and+normative+ standard.+This+is+done+by+treating+the+possible+world+coordinate+of+evaluation+like+ Gibbard's+world,+treating+the+normative+standard+like+Gibbard's+plan+for+action,+and+ treating+a+sentence+as+nonEnormative+iff+it+is+normEinvariant.+This+last+aspect+of+the+ translation+should+be+nonEcontroversial:+if+a+sentence+being+true+doesn't+exclude+ some+normative+standard+(which+we+can+also+think+of+as+a+normative+"possibility"),+ then+it+can't+put+any+constraints+on+what+ought+to+be+the+case.27+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 26One+might+worry+therefore+that+the+understanding+of+the+gap+claim+that+I+provide+ is+too+restricted+in+that+it+applies+only+to+valid,+nonEampliative+arguments.+One+might+ think+there+is+a+plausible+version+of+the+gap+claim+that+is+meant+to+apply+to+ ampliative+arguments.+But+the+most+general+version+of+this+idea+is+clearly+ implausible,+since+we+could+have+an+ampliative+logic+that+permits+arguments+from+ 'snow+is+white'+to+'Rachel+ought+to+donate+to+charity'.+In+the+case+of+particular+ ampliative+logics,+like+logics+of+enumerative+induction,+something+like+the+isEought+ gap+may+hold.+A+full+understanding+of+those+kinds+of+gap+claims+would+have+to+ proceed+on+an+individual+basis+for+each+logic+though,+which+is+not+a+task+I+will+take+ up+here.+ 27Note+that+this+does+require+rejecting+the+simple+view+that+a+sentence+is+normative+ if+it+contains+normative+terms,+like+'ought',+'should',+or+'reason'.+That+simple+view+is+ certainly+overly+simplistic+though.+'Shoplifting+is+permissible,+or+it+is+not',+for+ example,+should+not+count+as+normative.+That+said,+one+could+accept+the+simplistic+ What+this+shows+is+that+ISEOUGHT+GAP+should+be+seen+as+a+theorem+of+any+plausible+ semantics+of+normative+language.+As+I+argued+above,+ISEOUGHT+GAP+also+fits+our+ intuitive+understanding+of+the+gap+as+described+by+Hume+while+taking+into+account+ the+upshot+of+Prior's+examples+that+the+normativity+must+be+relevant+to+the+ possibilities+being+reasoned+about.+As+such,+we+ought+to+think+that+ISEOUGHT+GAP+both+ captures+and+vindicates+Hume's+idea.+ Comparing%Russell%and%Restall's%Approach% Gillian+Russell+and+Greg+Restall+give+a+different+reformulation+of+the+isEought+gap+ that+avoids+Prior's+counterexamples.28+They+take+the+gap+claim+to+be+an+instance+of+a+ more+general+notion+of+an+implication+barrier.+In+their+terminology,+there+is+an+ implication+barrier+from+one+class+of+sentences+to+another+when+no+sentence+of+the+ second+type+is+implied+by+a+collection+of+sentences+of+the+first+type.+Restall+and+ Russell+provide+a+general+barrier+theorem+that+they+use+to+derive+an+implication+ barrier+from+descriptive+sentences+to+normative+sentences,+under+a+particular+ understanding+of+these+classes+of+sentences+in+their+models+of+deontic+logic.+The+ models+they+use+are+standard+models+consisting+of+a+set+of+worlds+W+and+a+relation+S+ supplemented+with+a+distinguished+actual+world+where+sentences+are+evaluated.+The+ relation+is+one+of+deontic+accessibility,+so+that+if+all+of+the+worlds+accessible+from+the+ actual+world+are+PEworlds,+then+P+is+obligatory.+They+also+assume+that+S+is+transitive,+ euclidean,+serial+and+secondarily+reflexive,+though+not+all+of+these+assumptions+are+ necessary+for+their+proof.+ Their+implication+barrier+theorem+works+in+cases+where+there+is+a+set+of+sentences+ that+are+not+preserved+under+extensions+of+the+models+or+under+changes+of+the+ worlds+related+by+S.+They+take+normative+claims+to+be+such+a+class.+For+example,+ while+it's+impermissible+for+Alice+to+hit+Bob,+it's+permissible+for+Alice+to+hit+Bob+ when+they+are+in+a+boxing+class.+More+formally,+Russell+and+Restall+take+it+that+a+ claim+is+normative+when+its+truthEvalue+is+always+changeable+either+via+model+ extension+or+tinkering+with+S+in+every+deontic+model.+A+claim+is+descriptive+when+it+is+ always+preserved+under+tinkerings+with+S.+It+then+follows+as+an+instance+of+their+ Barrier+Construction+Theorem+that+no+satisfiable+collection+of+descriptive+sentences+ entails+a+normative+one.29++ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ view+and+still+accept+almost+everything+I+say+here.+Their+formulation+of+the+isEought+ gap+would+have+to+be+in+terms+of+nonEtrivial+normative+claims+though.+ 28+For+the+full+details+of+their+proposal,+see+Russell,+Gillian,+and+Greg+Restall.+2010.+ "Barriers+to+Implication."+In+Hume(on(Is(and(Ought,+edited+by+Charles+Pigden.+ Palgrave+MacMillan.+ 29+For+a+more+precise+statement+of+their+result,+see+Russell+and+Restall,+op.+cit.+p.+ 252–7.+ Both+ISEOUGHT+GAP+and+the+formulation+of+the+gap+from+Russell+and+Restall+(2010)+ aim+to+make+sense+of+the+isEought+gap+in+terms+of+the+semantics+of+normative+ language.+There+are+many+important+differences+between+our+approaches+though.+ Russell+and+Restall's+approach+employs+Kripke+models+of+deontic+logic+and+claims+ that+the+class+of+normative+sentences+are+those+that+have+a+certain+feature+with+ respect+to+that+class.+They+treat+the+class+of+descriptive+sentences+similarly.+Their+ stipulated+account+of+normative+sentences+doesn't+seem+to+capture+all+of+the+ sentences+that+we+might+pretheoretically+count+as+normative+though.+Peter+Vranas,+ for+example,+shows+that+the+sentence+'All+citizens+ought+to+vote'+does+not+count+as+ normative+on+their+account.30+Certainly+though,+as+Vranas+continues,+a+hypothetical+ argument+from+descriptive+premises+to+that+conclusion+is+in+the+intended+domain+of+ the+isEought+gap.+This+appears+to+be+a+quite+problematic+result+for+taking+Russell+and+ Restall's+understanding+of+the+isEought+gap+to+be+fully+general.+ The+reason+that+'All+citizens+ought+to+vote'+doesn't+count+as+normative+on+their+ account+is+because+the+sentence+is+captured+in+their+semantics+as+a+universally+ generalized+disjunction.+One+of+the+disjuncts+of+each+disjunction+is+nonEnormative,+ namely+that+the+object+is+a+citizen.+Vranas+shows+that+because+the+disjunction+is+not+ always+unstable+under+both+model+extension+and+tinkering+with+the+accessibility+ relation,+it+violates+their+definition+of+'normative.'+That+said,+their+account+also+ doesn't+count+the+sentence+as+descriptive,+as+it+is+not+always+stable+under+model+ extension+either.+This+shows+that+their+account+of+the+gap+relies+on+an+essentially+ incomplete+notion+of+normativity+-+it+does+not+count+every+sentence+as+either+being+ normative+or+in+the+class+of+sentences+that+shouldn't+entail+the+normative.+ My+account+is+able+to+count+'All+citizens+ought+to+vote'+as+normative,+since+it+is+not+ normEinvariant:+that+all+citizens+ought+to+vote+is+incompatible+with+a+worldEnorm+ pair+where+the+norm+calls+for+some+citizens+not+to+vote.+So,+the+formulation+of+the+ gap+I+provide+would+deny+the+validity+of+nonEtrivial+arguments+to+this+conclusion.+ Moreover,+my+account+will+treat+any+other+normative+claim+similarly:+if+the+claim+ rules+out+any+ways+the+combination+of+the+world+and+norms+could+be,+it+will+not+be+ normEinvariant,+so+there+will+be+no+nonEtrivial+arguments+from+normEinvariant+ premises+to+that+claim.31+ One+benefit+of+Russell+and+Restall's+account+is+that+they+can+state+the+restriction+ given+by+the+isEought+gap+simply:+They+start+by+delineating+two+classes+of+claims,+ ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 30+See+Vranas,+Peter.+2010.+"Comments+on+'Barriers+to+Implication'."+In+Hume(on(Is( and(Ought,+edited+by+Charles+Pigden.+Palgrave+MacMillan.+ 31Notice+though+that+there+is+still+a+class+of+claims+that+contain+normative+terms+that+ my+account+doesn't+count+as+normative,+namely+those+that+are+trivially+true.+These+ include+conceptual+truths,+like+'If+you+ought+not+sit,+you're+not+permitted+to+sit'+but+ also+ordinary+trivialities+with+normative+content+like+'Either+you+ought+to+sit,+or+it's+ not+the+case+that+you+ought+to+sit.'+This+is+a+benefit+of+the+account+though,+as+ certainly,+the+gap+claim+is+not+meant+to+block+inferences+to+these+kinds+of+claims.+ what+they+call+'descriptive'+and+'normative,'+and+then+they+say+that+there+are+no+valid+ arguments+from+sentences+in+the+first+class+to+a+conclusion+in+the+second.+My+ account+must+be+slightly+more+complex:+it+puts+a+restriction+on+what+arguments+are+ possible,+but+that+restriction+is+not+statable+as+a+restriction+that+blocks+arguments+ from+one+predetermined+class+of+sentences+to+another.+My+formulation+says+that+ there+are+no+valid+arguments+from+a+collection+of+nonEnormative+premises+to+a+ relevantly+normative+conclusion.+Which+normative+conclusions+count+as+relevantly+ normative+will+depend+on+what+the+premises+of+the+argument+are.+So+in+any+ particular+case,+the+class+of+sentences+that+cannot+be+derived,+on+my+view,+is+ dependent+on+the+premises+being+used.+So+although+my+account+preserves+our+ standard+complete+account+of+whether+a+sentence+is+normative,+it+cannot+capture+ the+gap+claim+simply+as+a+restriction+on+arguments+from+one+set+of+sentences+to+ another.+ There+is+a+general+reason+to+think+that+no+account+of+the+isEought+gap+could+ formulate+it+as+blocking+arguments+from+one+predetermined+class+of+sentences+to+ another+and+also+cast+every+sentence+as+being+in+exactly+one+of+those+classes.+Take+a+ generalized+version+of+one+of+Prior's+examples:+'P.+Therefore,+P+or+Q.'+where+P+is+in+ the+class+with+"snow+is+white"+and+Q+is+in+the+other+class,+which+contains+the+ paradigmatically+normative+sentences.+For+the+account+to+put+every+sentence+into+ exactly+one+class,+it+must+count+'P+or+Q'+as+in+the+normative+or+in+the+other+one.+If+it's+ normative,+then+'P.+Therefore,+P+or+Q.'+is+a+counterexample+to+the+gap+claim.+If+it's+in+ the+other+class,+then+we+can+generate+a+new+counterexample:+'notEP.+P+or+Q.+ Therefore,+Q.'++So+any+account+of+the+gap+claim+must+suffer+either+the+incompleteness+ disadvantage+that+Russell+and+Restall's+faces+or+the+disadvantage+of+not+treating+the+ isEought+gap+as+blocking+inferences+from+one+fixed+class+to+another.+ By+taking+the+first+horn,+Russell+and+Restall+miss+out+on+capturing+the+full+extent+of+ the+isEought+gap+by+not+classing+some+sentences+as+either+normative+or+descriptive+ (including+some+that+seem+like+they+should+be).+My+formulation+is+a+simple+and+ straightforward+way+to+take+the+second+horn.+In+doing+so,+it+is+able+to+offer+a+ complete+way+to+save+the+gap+that+relies+only+the+minimal+assumption+about+the+ semantics+of+normative+language+discussed+above.+Hume's+dictum,+on+my+account,+ relies+on+only+this+weak+assumption,+and+as+such,+it+is+much+more+secure+than+if+it+ were+to+rely+on+the+more+controversial+semantics+provided+by+deontic+logics+that+ Russell+and+Restall+use.+ A+final+benefit+of+my+approach+over+theirs+is+that+mine+offers+a+natural+explanation+of+ what+goes+wrong+in+Prior's+proposed+counterexamples.+On+the+epistemic+reading,+ the+gap+claim+is+about+whether+we+can+properly+reason+from+nonEnormative+ premises+to+a+normative+conclusion.+According+to+ISEOUGHT+GAP,+the+normativity+in+ the+conclusion+of+an+argument+is+only+a+challenge+to+the+isEought+gap+when+the+ normative+aspects+of+the+conclusion+are+relevant+to+the+possibilities+being+reasoned+ about.+So,+the+isEought+gap+is+not+challenged+by+the+purported+counterexamples+ because+no+reasoner+could+properly+employ+those+arguments+to+reach+a+conclusion+ about+what+ought+to+be+the+case+in+the+situation+they+take+themselves+to+be+in.+ Putting+the+gap+claim+in+terms+of+a+barrier+to+implication,+as+Russell+and+Restall+do,+ does+not+offer+an+analogous+explanation.+ Conclusion% Hume's+isEought+gap+is+a+staple+of+introductory+philosophy+and+logic+classes,+where+ it+is+typically+presented+as+SIMPLE+GAP.+SIMPLE+GAP+is+doomed+by+Prior's+ counterexamples+though.+Others+have+tried+to+save+the+claim+by+syntactically+ restricting+its+intended+domain,+like+Gibbard+who+proposes+that+we+only+view+it+as+a+ limit+on+arguments+to+simple+normative+conclusions.+But+this+move+is+both+too+ strong+and+too+weak.+Instead,+we+should+seek+a+semanticallyEmotivated+ understanding+of+the+gap+claim.+ Russell+and+Restall's+deonticElogicEbased+approach+offers+one+way+to+do+that,+but+as+ Vranas+and+I+show,+it+is+incomplete+and+its+conception+of+normativity+is+overly+ complicated.+I've+introduced+a+simple+way+to+understand+and+defend+the+isEought+ gap+that+saves+Hume's+reasons+for+thinking+there+is+such+a+gap.+My+reformulation+ vindicates+the+gap+claim+and+offers+an+explanation+of+what+goes+wrong+in+Prior's+ cases.+On+my+account,+whether+the+isEought+gap+ought+to+block+a+conclusion+is+ relative+to+the+particular+premises+in+play:+the+isEought+gap+says+that+we+can't+get+ from+nonEnormative+premises+to+conclusions+about+how+things+ought+to+be+in+cases+ where+the+premises+are+true.+ +