Forthcoming	in	Philosophical	Studies The	Property	of	Rationality: A	Guide	to	What	Rationality	Requires? Julian	Fink1 Abstract.	Can	we	employ	the	property	of	rationality in	establishing	what	rationality requires?	According	to	a	central	and	formal	thesis	of	John	Broome's	work	on	rational requirements, the answer is 'no' – at least if we expect a precise answer. In particular,	Broome	argues	that	(i)	the	property	of	full	rationality	(i.e.	whether	or	not you are fully rational) is independent of whether we formulate conditional requirements	of	rationality	as	having	a	wide	or	a	narrow	logical	scope.	That	is,	(ii)	by replacing a wide-scope requirement with a corresponding narrow-scope requirement	(or	vice	versa),	we	do	not	alter	the	situations	in	which	a	person	is	fully rational.	As	a	consequence,	(iii)	the	property	of	full	rationality	is	unable	to	guide	us	in determining	whether	a rational requirement	has	a	wide	or	a	narrow logical scope. We	cannot	resolve	the	wide/narrow	scope	debate	by	appealing	to	a	theory	of	fully rational attitudes. This paper argues that (i), (ii) and (iii) are incorrect. Replacing a widewith	a	corresponding	narrow-scope	requirement (or	vice	versa)	can	alter the set of circumstances in which a person is fully rational. The property of full rationality is therefore not independent of whether we formulate conditional requirements of rationality as having a wide or a narrow logical scope. As a consequence, the property of full rationality can guide us in determining what rationality	requires	–	even	in	cases	where	we	expect	a	precise	answer. 1.	Advancing	the	debate The debate on the content and nature of rational requirements that govern attitudinal	coherence	faces	a	serious	obstacle.2	On	the	one	hand,	most	parties to	the	debate	agree	about	numerous	combinations	of	attitudes3	that	violate	a requirement of rationality. For example, if you hold a pair of contradictory beliefs	or intentions, fail to intend	a	means you	acknowledge	as	necessary to your	ends,	have	no	intention	of	doing	what	you	believe	you	ought	to	do,	hold intransitive	preferences,	or	assign	inconsistent	probabilities	to	states	of	affairs, you	violate	a	requirement	of	rationality. On	the	other	hand,	there	is	no	unified	agreement	on	how	we	should	formulate the requirements that are violated in the above examples. Philosophers disagree about the logical form of rational requirements and, in particular, about	whether those requirements	are	best formulated	as requirements	with 1	Department	of	Philosophy,	University	of	Berne,	Länggassstrasse	49a,	CH-3012	Bern,	Switzerland. 2	I	assume	that	rationality	is	reducible	to	a	particular	kind	of	(structural)	coherence	among	a	person's attitudes (cf. for example Scanlon 2007; Broome	2013). I have argued elsewhere that this kind of coherence can	be cashed	out in terms	of the	possibility	of attitudinal success (Fink	2014	and	ms). However,	we	should	also	acknowledge	a	competing	(and,	it	seems,	increasingly	popular)	conception according	to	which	rationality	consists	in	responding	correctly	to	particular	normative	reasons	(see, for example, Lord 2014a and forthcoming; Kiesewetter 2013). For detailed criticism, see Broome 2007d	and	2013a.	I	have	criticised	versions	of	this	view	in	Fink	(2014	and	ms). 3	Throughout	this	paper,	I	use	'attitude'	to	include	the	lack	of	an	attitude. 2 conditional contents or as conditionals	whose consequents express a rational requirement. Consider	an	illustration	of	this	problem.	Suppose	you	are	akratic:	you	have	no intention	to	X	even	though	you	believe	that	you	ought	to	X.	I	assume	that	you violate a requirement of rationality.4	But which precise requirement do you violate?	How	should	we	formulate	it? The answer to this question is not clear. There are at least two plausible formulations,	both	of	which	do	an	equally	good	job	of	generating	the	violation. According	to	the	first	formulation,	rationality	simply	prohibits	the	combination of	the	two	attitudes.	What	is	required	is	that	you	not	[believe	that	you	ought	to X	and	not	intend	to	X].	Or,	put	in	its	equivalent	material	conditional	form: (W) Necessarily:	rationality	requires	of	you	that	[(you	believe	you ought	to	X)	→	(you	intend	to	X)], where	→ represents	a	material conditional. In (W) 'rationality requires'	has	a wide	conditional	scope:	it	governs	the	entire	material	conditional	'(you	believe you	ought	to	X)	→	(you	intend	to	X)'.	This	guarantees	that	by	believing	that	you ought to X without intending to X, you violate a rational requirement. (The conditional content of the requirement then turns out to be false.) It also guarantees	that	you	can	satisfy	this	requirement	by	either	intending	to	X	or	not believing	that	you	ought	to	X. (The	content	of	the	requirement	then	turns	out to be true.) Accordingly, (W) represents a first prima facie plausible requirement	formulation	that	would	ensure	the	irrationality	of	akrasia. According to the second formulation, 'rationality requires' does not govern a material conditional. Instead, it says that either it is not the case that you believe	that	you	ought	to	X	or	rationality	requires	you	to	intend	to	X.	Or,	again, expressed	with	the	help	of	a	material	conditional: (N) Necessarily: (you believe you ought to X) → [rationality requires	of	you	that	(you	intend	to	X)]. In	(N)	'rationality	requires'	has	a	narrow	conditional	scope:	it	governs	only	the consequent of the	material conditional '(you believe you	ought to	X)	→ (you intend to	X)'. This also ensures that	akrasia is irrational. Your belief that you ought to	X entails that you are rationally required to intend to	X. But, being akratic,	you	do	not	intend	to	X.	Thus,	you	violate	a	requirement.	You	can	satisfy this	requirement	in	only	one	way,	i.e.	by	intending	to	X.	(N)	represents	a	second prima	facie	plausible	formulation	that	would	ensure	the	irrationality	of	akrasia.5 4	Within the recent	debate, see, for	example,	Broome (2013a,	2013b),	Brunero (2013),	and	Coates (2013)	and	Reisner	(2013)	on	the	irrationality	of	akrasia. 5	Here	is	a	third	(but	implausible)	formulation: 3 Which formulation should we prefer: (W) or (N)? Also, which formulation should we employ as a model for stating other conditional requirements of rationality? In the	current	debate, these	are	open	questions.	Good	arguments are presented for and against both (types of) formulations.6	But are these arguments	really	worth	the	effort?	Is	the	question	whether	we	use	(W)or	(N)type	formulations	to	represent	a	rational	requirement	important? A close reading of the current debate suggests that it	might	well be. Indeed, there are good reasons to view the difference between (W)and (N)-type requirements as in some sense fundamental to the nature of rational requirements. For example, the choice between either (W)or (N)-type requirements	is	thought	to	influence	whether	the	requirements	of	rationality	..." (i)	... give	us	genuinely	symmetric	options	regarding	how	we	can satisfy	them	(Schroeder	2004);7 (ii)	... are	prone	to	issue	contradictory	requirements	(Broome	2007a, 2007b,	2013a;	Kolodny	2007b);8 (iii)	... pick	out	necessary	conditions	for	being	fully	rational (Broome	2007b);9 (iv)	... can	guide	the	formation	of	attitudes	(Reisner	2009);10 (v)	... are	apt	for	constituting	standards	for	correct	reasoning (Kolodny	2005,	2007b;	Broome	2013a).11 (N*) Necessarily: (you	do	not intend	to	X)	→ [rationality	requires	of	you	that (you	do not	believe	that	you	ought	to	X)]. (N*)	says	that	not	intending	to	X	suffices	to	put	you	under	a	rational	requirement	not	to	believe	that you ought to X. But this is surely implausible. The absence of an intention to X is certainly not (conclusive)	evidence	of	its	not	being	the	case	that	you	ought	to	X.	I	will	therefore	not	include	(N*)	in my	discussion. 6	See in	particular	Broome (1999,	2004,	2007a,	2007b, and	2013a),	Brunero (2010,	2012), Kolodny (2005,	2007a),	Rippon	(2011),	Schroder	(2004),	Shpall	(2013),	and	Way	(2010,	2011). 7	Suppose	you	believe	you	ought	to	X,	but	you	have	no	intention	of	X-ing.	If	(W)	is	correct,	there	are two	genuinely	symmetrical	options	when	it	comes	to	satisfying	the	requirement.	You	can	intend	to	X or	you	can	be	such	that	you	do	not	believe	that	you	ought	to	X. If (N) is	correct, there is	only	one option,	i.e.	intending	to	X.	Not	believing	that	you	ought	to	X	is	then	not	an	option	when	it	comes	to satisfying the violated requirement.	On the question of symmetry, see Schroeder (2009), Kolodny (2005),	Brunero	(2010,	2012),	Bedke	(2009),	and	Way	(2010). 8	Suppose	you	believe	you	ought	to	X,	and	you	believe	you	ought	to	not-X.	If	(N)	is	correct,	rationality issues	a set	of contradictory requirements	upon	you.	Rationality then requires you to intend to	X, and	it	requires	you	to	intend	to	not-X.	(W)	has	no	such	implication. 9	Suppose	you	hold	only	one	irrational	combination	of	attitudes:	you	believe	you	ought	to	X,	but	you lack	an	intention	to	X.	If	(N)	is	correct,	you	are	rationally	required	to	intend	to	X.	However,	it	is	clear that 'You intend to X' is not strictly a necessary condition for becoming fully rational. There are conceivable	situations	in	which	you	could	also	become	fully	rational	by	dropping	your	belief	that	you ought	to	X.	By	contrast, the	content	of (W)	seems	to	state	a	genuinely	necessary	condition for full rationality.	You	can	be	fully	rational	only	if	(you	intend	to	X	or	do	not	believe	that	you	ought	to	X). 10	(N)-type requirements can guide the formation	of attitudes insofar as they	pick out a particular attitude that rationality requires you to have; (W)-type requirements, by contrast, do	not tell you which	particular	attitude	you	are	required	to	have;	they	leave	you	with	a	set	of	options. 11	For	example,	you	can	reason	(correctly,	it	seems)	from	the	content	of	a	belief	that	you	ought	to	X to	an intention	to	X.	You	cannot	reason,	however, from	the	content	of	an	absent intention	to	X to 4 (vi)	... are	attitude	sensitive	in	their	application	(Broome	2007b;	Lord 2014b).12 The most important difference, however, lies elsewhere. Many philosophers suppose	that	rational	requirements	are	in	some	way	normative	(Kolodny	2007a, 230;	see	Broome	2005;	2013a).	Interpreted	in	a	minimal13	yet	non-trivial	way,14 this is to say that rational requirements entail normative reasons.15	Or,	more precisely: Reasons entailment. Necessarily: if rationality requires you to X, there	is	a	normative	reason	for	you	to	X. Should	we	endorse	this	entailment?	The	difference	between	(W)and	(N)-type requirements is fundamental to answering this question. Consider a logical consequence of conjoining (N) with Reasons entailment. (N) says that, necessarily,	if	you	believe	you	ought	to	X,	then	rationality	requires	you	to	intend to	X.	Reasons	entailment	implies	that,	necessarily,	if	rationality	requires	you	to intend	to	X,	then	there	is	a	normative	reason	for	you	to	intend	to	X.	By	virtue	of transitive	implication,	this	entails: Implication.	Necessarily:	if	you	believe	you	ought	to	X,	then	there	is a	normative	reason	for	you	to	intend	to	X. That	is:	by	adopting	a	belief	that	you	ought	to	X,	you	guarantee	the	existence	of a	normative	reason	to	intend	to	X.	Should	we	accept	Implication? According	to	a	central	finding	in	the	philosophy	of	reasons	and	rationality,	the answer is clearly 'no'. Implication is subject to the so-called 'bootstrapping objection' (Bratman	1987;	Broome	2001;	Piller	2013). It entails that for	any	X (e.g. 'driving drunk', 'becoming a terrorist', etc.) you can create a reason to intend to X simply in virtue of adopting a belief that you ought to X. Put succinctly, Implication licences	the	creation	of	normative	reasons	where	there aren't	any. suspending the belief that you ought to	X, because an absent intention to	X has no content	with which you can reason. (N), unlike (W), seems to capture this fact insofar as	once you	believe you ought	to	X	(and	you	do	not	intend	to	X),	you	can	only	satisfy	(N)	by	forming	an	intention	to	X,	not	by suspending	your	belief	that	you	ought	to	X. 12	If	(N)	is	correct,	then	you	can	trigger	the	application	of	a	requirement	to	intend	to	X	by	believing that	you	ought	to	X.	If	(W)	is	correct,	the	application	of	the	requirement	is	not	in	any	way	sensitive	to whether	or	not	you	believe	that	you	ought	to	X. 13	See	Broome	(2007c,	pp.	162-5)	on	why	this	is	a	minimal	or	'weak'	version	of	the	view	that	rational requirements	are	normative. 14 There is, of course, a trivial sense in which rationality '[...] is automatically normative [...]. Rationality is a system of requirements or rules. It therefore sets up a notion of correctness: following	the	rules	is	correct	according	to	the	rules.	That	by	itself	makes	it	normative	in	one	sense, because	in	one	sense	'normative'	simply	means	to	do	with	norms,	rules	or	correctness.	Any	source	of requirements is normative in this sense. For example, Catholicism is. Catholicism requires you to abstain	from	meat	on	Fridays.	This	is	a	rule,	and	it	is	incorrect	according	to	Catholicism	to	eat	meat on	Fridays.	So	Catholicism	is	normative	in	this	sense'	(Broome	2007c,	p.	162). 15	See	Southwood	(2008)	and	Reisner	(2011)	for	attempts	to	explain	and	defend	this	view. 5 Let	me	illustrate	this	point.	Suppose	you	have	no	normative	reason	to	intend	to kill yourself. Nothing speaks in favour of such an intention. You also do not believe that you ought to kill yourself. Suppose now that, as a result of someone's	spiking	your	coffee	with	a	dangerous	pill,	you	come	to	believe	that you ought to kill yourself. Does this suffice to create a normative reason to intend	to	kill	yourself?	That	is,	can	we	create	a	reason	to	intend	to	X	by	merely adopting	the	view	that	we	ought	to?	Evidently,	the	answer	is	'no'.	A	mere	belief that	you	ought	to	kill	yourself	cannot	'bootstrap'	such	a	reason	into	existence.	It cannot	create	reasons	where	there	are	none.	In	general,	reasons	for	intending to X depend on whether (intending to) X is good or choiceworthy (in the relevant sense). They do not depend on whether one judges X to be good, choiceworthy,	or	obligatory. The consequence of this is plain: Implication states an untenable entailment relation	between	what	you	believe	you	ought	to	do	and	what	reasons	there	are. Since Implication is a logical consequence of conjoining (N) with Reasons Entailment,	at	least	one	of	these	two	propositions	must	be	incorrect	too. Unlike (N), (W)	does	not	give rise to incredible	bootstrapping	when	conjoined with	Reasons	entailment.	Suppose,	necessarily,	there	is	a	normative	reason	for you to satisfy (W). This does	not imply that your	belief that you	ought to kill yourself	entails	a	reason	to	intend	to	kill	yourself.	Instead,	it	implies	that	there must	be	a	reason	to	satisfy	the	following	relation:	either	it	is	not	the	case	that you	believe	that	you	ought	to	kill	yourself	or	you	intend	to	kill	yourself.	This	is	a reason to be ought-belief/intention coherent. It is not a reason to have a particular intention. Hence, accepting (W) and Reasons entailment does not force	one to	embrace	a	kind	of	bootstrapping	of	normative reasons that	goes beyond	a	normative	reason	for	being	coherent. In	sum:	conjoining	(N)	and	Reasons	entailment	entails	Implication.	By	contrast, conjoining (W) and Reasons entailment does not entail Implication. Since Implication represents an unacceptable form of bootstrapping, Reasons entailment does not seem tenable in conjunction with a regime of (N)-type requirements. Thus, in order to advance the debate on the normativity of rational	requirements,	we	first	need	to	settle	the	choice	between	(W)and	(N)type requirements. We need to devise a method that tells us whether 'rationality requires' takes a wide or a narrow logical scope in formulating conditional	requirements	of	rationality. How	can	we	choose	between	(W)	and	(N)?	In	general:	how	can	we	identify	what rationality	requires	and	when	it	requires	something	of	us?	Not	many	systematic approaches have been put forward. Broome, and others, find themselves '... forced	to	appeal	largely	to	our	intuitions'	(Broome	2013a,	p.	150).	However,	in his recent work (2007a, 2007b, 2013), Broome argues against the very possibility	of	a	seemingly	promising	strategy.	I	will	call	it	the	'property	strategy'. 6 Roughly, the property strategy says that we can employ the property of full rationality	in	deciding	what	rationality	requires	of	us	and	when	it	does	so. This strategy has three steps: first, we develop a theory about which combinations	of	attitudes	and	mental	processes	are in/consistent	with	having the	property	of	full	rationality.	Second,	we	determine	whether	(or	which)	(W)or (N)-type requirements are (more) conducive to our theory	of fully rational attitudes.	And finally,	we	choose	between (W)and (N)-type requirements	on the basis of which logical form fits best with our theory of fully rational attitudinal	combinations	and	mental	processes. Broome	views	this	strategy	as	futile.	He	argues	this	as	a	technical	point	(2007a, pp.	363-4;	2013,	p.	134):	as	far	as	the	property	of	full	rationality	is	concerned, (W) and (N) turn	out to be equivalent. I shall call this 'property equivalence'. That	is,	the	combinations	of	attitudes	under	which	you	are	fully	rational	under	a regime	of	(N)-type	requirements	are	identical	to	the	combinations	of	attitudes under	which you are fully rational under a regime	of corresponding (W)-type requirements. Thus, replacing an (N)-type requirement with a (W)-type requirement	(or	vice	versa)	does	not	affect	the	combinations	of	attitudes	that are	consistent	with	full	rationality.	Any	attempt	to	decide	between	(N)	and	(W) by	considering	the	property	of	full	rationality	is	thus	destined	to	fail. However,	Broome's	rejection	of	the	property	strategy	is	too	quick.	In	this	paper, I	will argue that	we should	not dispense	with the	property	of rationality as a guide	in	settling	the	debate	between	(W)and	(N)-type	requirements.	Replacing an	(N)-type	with	a	(W)-type	requirement	can	indeed	alter	the	combinations	of attitudes that are consistent	with having the property of full rationality. This does	not,	of	course,	undermine	Broome's	own	defence	of	the	wide-scope	form of	conditional	requirements	of	rationality.	Yet	it	shows	that	we	should	make	use of the property of rationality in settling the debate on the scope of rational requirements. Part of what makes Broome's argument authoritative is that he tries to establish property equivalence with a formal theorem and a corresponding proof	(2007a,	pp.	369-70;	2007b,	pp.	39-40;	2013a,	p.	148).	Although	Broome's theorem is correct (as I show in § 6), it fails to establish	what he intends to establish, i.e. property	equivalence. In	particular, the theorem is	premised	on the implicit but implausible exclusion of a particular entailment relation that may	hold	between	rational	requirements.	The	theorem	excludes, for instance, the	existence	of	requirements	that	prohibit	intending	that	X	if	one	knows	that	X will	lead	one	to	have	an	attitude	one	is	rationally	required	not	to	have.	So,	while Broome manages to prove property equivalence for a system of rational requirements that excludes such requirements, I will argue that there is no justification for excluding them. Broome is thus unable to sustain his methodological point. There are situations in which we can decide between (W)and (N)-type requirements by considering attitudinal combinations that are fully rational. Thus the property of rationality might help us to make 7 progress on some of the questions that have traditionally been linked to the scope	of	rational	requirements. This paper proceeds as follows. § 2 introduces the semantic framework for rational requirements that Broome employs in	making his equivalence claim. §	3	defines	Broome's	equivalence	claim, i.e.	the	claim	that	the	property	of	full rationality remains unaffected by replacing a (W)-type with an (N)-type requirement	(or	vice	versa).	§	4	and	§	5	advance	an	argument	against	property equivalence.	I	will	put	forward	a	counterexample	according	to	which	one	is	fully rational	under	a (W)-type	requirement,	but	not	so	under	a	corresponding	(N)type requirement. § 6 turns to Broome's formal theorem, which purports to vindicate	property	equivalence.	I	shall	demonstrate	that	Broome's	theorem	fails to	justify	property	equivalence,	with	the	upshot	that	the	property	of	rationality is still available to us as a possible guide in constructing the logical form of rational	requirements.	There	are	situations in	which	the	property	strategy	can determine whether (N)or (W)-type requirements represent rational requirements	correctly,	thereby	helping	us,	for	instance,	to	form	a	correct	view on	whether the bootstrapping objection poses a threat to the normativity of rational	requirements. 2.	The	code	of	rationality How	can	we	decide	whether	(W)or	(N)-type	formulations	correctly	represent	a conditional requirement of rationality? Two things need to be taken into account:	(i)	'rationality	requires'	is	by	and	large	'...	a	philosopher's	phrase	of	art' (Kolodny	2005,	p.	515);	and	(ii) (W)and	(N)-type	requirements	seem	to	differ significantly	with	regard	to	their	logical	properties.	Consequently,	as	a	first	step towards deciding on the correctness of (W)and (N)-type requirements, we need to work towards a semantics of 'rationality requires' (Broome 2007a, p.	361). Broome proposes a general semantic framework for rational requirements (2007a).	His	framework	is in	fact	so	general	that	it	could	be	adopted	for	other systems of requirements, such as morality or prudence (Broome 2007b and 2013a). Nonetheless, Broome employs this framework to render precise key notions concerning rationality and its requirements and to expose the exact difference	between	(W)and	(N)-type	requirements.	He	also	uses	the	semantic framework	in	his	proof	that	(W)and	(N)-type	requirements	are	equivalent	with respect	to	the	property	of	rationality. In	essence,	Broome's framework	rests	on	two	general	stipulations (2007a,	pp. 361-3). First, for every possible world	w, there is a set of propositions that rationality	requires	of	you.	That is,	at	w,	p is	a	member	of the	set	of	required propositions	if	and	only	if,	at	w,	rationality	requires	of	you	that	p.	Second,	there is	a	function	that	relates	worlds	to	sets	of	required	propositions. 8 This	function	is	called	the	'code	of	rationality'	(or	just	'code'	hereafter).	A	code is a	mapping from	worlds to sets of required propositions. A complete code thus	determines for	all	worlds	w and	all propositions	p	whether	or	not	p is a member of the set of required propositions at w. Less technically, a code specifies	what	rationality	requires	of	you	and	when	it	does	so. Broome's general code semantics also allows us to define when a person possesses	the	property	of	full	rationality.	That is,	at	w,	you	are	fully	rational if and	only if,	at	w,	every	proposition	in	w's	set	of	required	propositions	–	call it RP(w)	–	is	true	at	w	(Broome	2007a,	p.	362). In assigning required propositions to worlds, a code will satisfy a variety of constraints.	Some	constraints	will	be	purely	formal.	Since	a	code	is	a	function,	it cannot assign two different sets of required propositions to the same	world. Other constraints	will stem from the logic	of rational requirements.	A correct code	may,	for	example,	satisfy	a	'no-conflict'	constraint,	as	it	exists	in	standard deontic	logic	(Broome	2007a,	p.	365;	2013a,	p.	122).	That	is,	necessarily,	if,	at	w, p is an element of	RP(w), then it is not the case that not-p is an element of RP(w).	Other	constraints	will	be	more	substantive.	I	assume,	for	instance,	that	if, at	w,	you	possess	no	capacity	for	rationality	(i.e.	logical	and	reasoning	abilities), then	RP(w)	will	be	the	empty	set.16 Some constraints	will represent individual requirements. I will thus call them 'individual constraints'. Put roughly, an individual constraint signifies how a code	injects	a	particular	proposition	into	RP(w).	Individual	constraints	allow	us to express precisely	when a code instantiates a	wideand/or a narrow-scope requirement. In principle, a code instantiates a narrow-scope requirement if and only if (NC) describes how a code injects a proposition into the set of required	propositions.	This	description	reads	as	follows: (NC) For	all	w:	(p	∈	w)	→	[q	∈	RP(w)], where	w	represents	a	possible	world,	p	and	q	stand	for	individual	propositional attitudes	of	yours,	∈	reads	as	'is	an	element	of',	and	RP(w)	represents	the	set	of rationally required	propositions at	w. (NC) says that for all possible	worlds in which	p	holds	true,	it	also	holds	true	that	q	is	a	proposition	that	is	required	by rationality. Analogously,	a	code instantiates	a	wide-scope	requirement if	and	only if (WC) describes	how	a	code	injects	a	proposition	into	the	set	of	required	propositions. This	description	reads	as	follows: (WC) For	all	w:	(p→q)	∈	RP(w). 16	I	elaborate	this	point	in	Fink	(2014). 9 (WC) says that it holds for all possible worlds that the truth of the	material conditional	p→q	is	rationally	required	of	you. In	sum,	the	code	semantics	helps	us	to	expose	the	precise	difference	between wideand narrow-scope requirements. (WC)-type requirements require the truth	of	the	material	conditional	p→q	(i.e.	either	(p	and	q),	or	(p	and	not-q),	or (not-p and not-q)). They do so at all possible	worlds. (NC)-type requirements require	the	truth	of	q.	They	do	so	at	all	worlds	in	which	p	holds	true. 3.	Property	equivalence I	now	turn	to	the	claim	that (WC)and	(NC)-type	requirements	are	equivalent when it comes to the property of full rationality. Consider two individual propositional	attitudes,	p	and	q.	Suppose	that	the	conjunction	of	[p	and	not-q] (but neither p nor not-q individually) necessarily results in your violating a rational	requirement.	(As	indicated	in	§	1,	you	could,	for	example,	think	of	p	as standing	for	'You	believe	that	you	ought	to	X'	and	q	as	standing	for	'You	intend that	you	X'.)	Which	individual	constraint	should	we	assign	to	a	code	in	order	to guarantee	this? As	far	as	this	point	is	concerned,	we	have	a	choice:	we	could	assign	either	(WC) or	(NC).	Any	code	that	satisfies	at	least	one	of	these	constraints	will	ensure	that whenever	[p	and	not-q]	is	an	element	of	w,	the	set	of	required	propositions	at w	–	RP(w)	–	will	contain	at	least	one	false	proposition.	But	how	can	we	decide between (WC) and (NC)? That is,	which constraint – (WC) or (NC) – correctly represents	a	conditional	requirement? In answering this question, Broome rejects the strategy of choosing between (WC)	and	(NC)	by	considering	when	one	is	fully	rational.	In Rationality Through Reasoning,	he	emphasises	this	point	as	follows: One putative approach to answering the question about scope will definitely not work.	It	will	do	no	good	to	think	about	the	property	that	corresponds	to	the	source of	requirements	we	are	investigating.	[...]	You	might	think	we	could	start	by	working out implications	wide-scope	and	narrow-scope	requirements	have for the	property of	[full]	rationality.	It	might	turn	out	that	one	gives	a	better	account	of	the	property than	the	other.	But	actually	this	is	not	so.	(Broome	2013a,	pp.	133-4) That is to say: we cannot first define the attitudinal combinations that are in/consistent with having the property of full rationality and then choose between (WC) or (NC) on the basis of which formulation best matches our account of fully rational attitudes. This strategy is untenable, Broome	argues, because	(WC)	and	(NC)	are	too	similar.	(WC)	and	(NC)	are	'property	equivalent' when	it	comes	to	the	property	of	full	rationality: There	is	less	difference	between	[(WC)	and	(NC)]	than	one	might	think.	Perhaps	the most important question a system of rational requirements needs to settle is whether	you	are	[fully]	rational-have	the	property	of	[full]	rationality. It turns	out 10 that the answer to this question is	unaffected by the choice between narrow and wide scope. The proposition that you are rational is the same whichever way a conditional requirement is formulated. Either	way, you are rational at exactly the same	worlds.	(Broome	2007a,	p.	363;	emphasis	added) In sum, the logical form of a conditional requirement is immaterial to the question	of	when	a	person	is	fully	rational.	By	manipulating	a	code	only	to	the effect	that	it	satisfies	(NC)	instead	of	(WC)	(or	vice	versa),	one	does	not	change the	set	of	combinations	of	attitudes	that	are	consistent	with	full	rationality. For	the	sake	of	precision,	let	me	make	this	point	more	formally.	Take	a	code	– R1 – that satisfies (WC) for a pair of propositions p and q. That is to say:	R1 distributes	(p→q)	to	the	set	of	required	propositions	at	all	worlds.	Perform	the following	operation	on	R1.	First,	only	remove	(WC)	from	R1.	Thus	R1	no longer distributes (p→q) to the set of required propositions at all worlds. Second, apply (NC) to	R1. Call the resulting code	R2. So,	R2	distributes	q to the set of required propositions at all worlds where p holds true. Then R1 and R2 are 'property	equivalent'	in	the	following	sense: Property	equivalence.	Necessarily:	at	w,	you	are	fully	rational	under	R1	if	and only	if,	at	w,	you	are	fully	rational	under	R2. 4.	A	counterexample As noted above, Property equivalence has not received much critical attention. 17 This is surprising because its correctness could reduce the significance	of	the	ongoing	wide/narrow	scope	debate.18	To	the	degree	that	'... the	most	important	question	a	system	of	rational	requirements	needs	to	settle is whether you are [fully] rational – have the property of [full] rationality' (Broome	2007a,	p.	363),	Property	equivalence	threatens	the	importance	of	the scope	distinction.19 However, this lack of critical attention is also a mistake, since Property equivalence is incorrect. By changing a code	merely such that it now satisfies (WC) rather than (NC), one can alter the combinations of attitudes that are consistent	with	being	fully	rational.	So,	even	when	we	are	only	concerned	with the	property	of	rationality,	the	question	of	scope	is	highly	significant	after	all. 17	Kolodny	(2007b)	and	Žarnić	(2010)	represent	two	exceptions. 18	Compare,	for	example,	Broome	(1999,	2007a,	2013a),	Brunero	(2010,	2012),	Evers	(2011),	Kolodny (2007b),	Rippon	(2011),	Shpall	(2013),	and	Way	(2010). 19	Niko	Kolodny	emphasises	this	point	very	eloquently: For years now, it has seemed to Broome and to the rest of us, who have been so stimulated	by	his	work, that	there is	a	crucial	difference	between	the	wide	and	narrow scope.	Time	and	again,	Broome	has	urged	us	to	appreciate	this	important	difference,	and by and large we have been convinced. On closer inspection, however, the difference seems	almost	negligible.	(Kolodny	2007b,	p.	375) 11 Consider	first	an	entirely	schematic	counterexample	to	Property	equivalence.20 Compare two codes: RW and RN. Both satisfy two individual constraints: RW satisfies	(WC)	and	(LR).	(LR)	reads	as	follows: (LR) For	all	w:	[q	∈	RP(w)]	→	[r	∈	RP(w)].21 (LR)	constrains	a	code	as	follows:	suppose	that,	at	w,	q	is	among	the	rationally required propositions. Then, at w, r is also among the rationally required propositions. That is, you cannot be rationally required to q without being required	to	r. Correspondingly, RN satisfies (NC) and (LR). RN is thus the result of only one operation performed on RW, namely the replacement of (WC) with (NC). Accordingly, RW and RN fall within the range of Property equivalence. Schematically,	the	situation	is	as	follows: Code	(RW) Code	(RN) (WC)	For	all	w:	(p	→	q)	∈	RP(w). (LR)	For	all	w:	[q	∈	RP(w)]	→ [r	∈	RP(w)]. (NC)	For	all	w:	(p	∈	w)	→	[q	∈	RP(w)]. (LR)	For	all	w:	[q	∈	RP(w)]	→ [r	∈	RP(w)]. Compare RW with RN. According to Property equivalence, the following proposition	should	hold	true:	necessarily,	at	w,	you	are	fully	rational	under	RW	if and	only	if,	at	w,	you	are	fully	rational	under	RN.	But	this	is	not	the	case.	There	is a	possible	situation in	which	you	are fully	rational	under	RW	and	are less than fully	rational	under	RN. Suppose that,	at	w', [p,	q,	and	not-r] signifies	a	conjunction	of	your	attitudes. Under	RN,	you	cannot	be	fully	rational	at	w'.	To	show	this,	conjoin	(NC)	with	p. This	entails	that,	at	w',	q	is	a	required	proposition.	Next,	conjoin	the	fact	that	q is a required proposition with (LR). This entails that, at w', r is a required 20	Kolodny (2007b,	p.	376)	also	presents	an	argument	against	Property	equivalence.	He	argues that Property equivalence fails to hold for 'process requirements', as he puts it. However, Kolodny's counterexample	proves	incorrect.	This	is	shown	in	the	appendix	to	this	paper. 21	I	have	encountered	the	claim	that	(LR)	is	in	tension	with	Broome's	code	semantics.	This	is	because (LR)	fails	to	specify	a	unique	code.	True,	a	code	could	satisfy	(LR)	in	various	ways.	It	could	satisfy	(LR), for example, by virtue of its being necessarily not the case that	q is a required proposition at	w. Alternatively,	a	code	could	satisfy	(LR)	in	virtue	of	the	fact	that	r	is	a	required	proposition	necessarily. This	claim	puzzles	me,	however.	Broome's	(and	my)	aim	is	to	establish	whether	exchanging	widefor narrow-scope	requirements	(or	vice	versa)	can	influence	the	property	of	full	rationality.	To	do	so,	we are	in	fact	forced	to	formulate	constraints	on	codes	that	fail	to	pick	out	a	unique	code.	For	even	by making	a	code	behave in	accordance	with	a	narrow-scope	requirement	(i.e.	constraining	a	code	so that	it	satisfies	(NC)	[i.e.	For	all	w:	(p	∈	w)	→	[q	∈	RP(w)]),	one	does	not	specify	a	unique	code.	As with (LR), a code can satisfy (NC) in different ways, e.g. by ensuring that p is necessarily not an element	of	w	or	by	q's	being	necessarily	required. 12 proposition.	However,	at	w',	not-r	holds	true.	So,	you	cannot	be	fully	rational	at w'	under	RN. This	is	not	so	under	RW,	however.	You	can	be	fully	rational	under	RW	at	w'.	First, (WC)	assigns	p→q	as	a	required	proposition	to	w'.	The	fact	that,	at	w',	both	p and q hold true ensures the truth of p→q. (LR) says that r is a required proposition	at	w'	whenever	q is a required	proposition	at	w'.	However, given what	we	know	of	RW	and	w',	under	RW,	there	is	no	need	to	assume	that	q is	a required	propositions	at	w'.	Also,	there	is	no	need	to	assume	that,	under	RW,	r	is a	required	proposition	at	w'.	So,	under	RW,	you	can	be	fully	rational	at	w'. Of	course,	this	result	requires	two	things.	First,	conjoining	p	and	(WC)	does	not entail	that	q	is	a	required	proposition	via	'factual	detachment'.	Second,	it	is	not the case that	p is a necessary attitude of yours. I take both conditions to be unproblematic. Put	schematically,	'factual	detachment'	licenses	an	inference	from (i)	at	w,	'p→q'	is	a	required	proposition and (ii)	at	w,	p to (iii)	at	w,	q	is	a	required	proposition. If this	were	correct, [p,	q, and	not-r]	would	not	be	consistent	with	being fully rational	under	RW.	At	w',	by conjoining	p and (WC),	q	would turn	out to	be	a required proposition. (LR) would then imply that, at w', r is a required proposition. Ad hypothesis, r is not the case at w'. You would not be fully rational	under	RW. Likewise,	we	need	to	assume	that	p is	not	necessarily true.	Otherwise,	q (and therefore	r)	would	again turn	out to	be	required	under	RW	–	this time	via	not 'factual' but rather 'necessary' detachment (Broome 2013a, p. 123), i.e. a plausible	inference	to	(iii)	from	(i)	and (ii')	at	w,	necessarily	p. As above, [p, q, and not-r] would not be consistent with being fully rational under	RW. It is easy to avoid 'necessary detachment'. We are, of course, entitled to stipulate that	p stands for a non-necessary attitude. That is,	p represents an attitude	of	yours that	you	have	at some	but	not	all	possible	worlds. I assume this	holds	true	for	most,	if	not	all,	attitudes. 13 Likewise,	'factual	detachment'	does	not	pose	a	problem	either.	I	assume	that	it is	invalid.	First,	it	resembles	an	invalid	modal	inference: Necessarily:	[(I	am	unmarried)	→	(I	am	a	bachelor)] and I	am	unmarried. So Necessarily:	I	am	a	bachelor. No doubt, this is incorrect (cf. Rippon 2011, pp. 4-5). 'Factual detachment' is also	philosophically	unattractive.	If	we	were	to	allow	it,	(WC)-codes	would	be	as open to the bootstrapping objection as (NC) ones. I therefore reject 'factual detachment'. The	upshot, then, is this:	p,	q,	and	not-r	are jointly	consistent	with	being fully rational at w' under RW. However, this is not so under RN. There is a combination	of	attitudes	that	permits	full	rationality	under	RW	but	does	not	do so	under	RN.	RW	and	RN	are	not	equivalent	with	respect	to	the	property	of	full rationality.	Property	equivalence	is	incorrect. 5.	Beyond	the	conceptual	result So	far,	I	have	shown	that,	conceptually,	the	choice	between	wideand	narrowscope requirements is not negligible when it comes to the property of full rationality. Replacing a widewith a narrow-scope requirement can logically alter	the	circumstances	in	which	you	are	fully	rational. This is, I believe, an interesting theoretical result. However, it does not yet imply that there is a correct code for	which replacing a	widewith a narrowscope	requirement	will	actually	change	the	circumstances	in	which	you	are	fully rational	under	that	code.	This	depends	on	whether	we	can	find	a	code	for	which either (WC) or (NC), taken together	with (LR), represents a correct individual constraint.	Only	then	can	we	guarantee	that	the	property	of	full	rationality	can actually help us to determine whether (WC) or (NC) represents a rational requirement	correctly. Recall (LR). It says that one required proposition entails another required proposition. However, you might think that required propositions are not related	in	this	way.	Hence,	a	code	that	satisfies	(LR)	cannot	represent	a	correct code	of	rationality. This reaction	would clearly be	ad	hoc. It is not unnatural to constrain a code such that	a required	proposition implies	another required	proposition.	Take	a code	that	injects	a	conjunction	of	beliefs	–	'You	believe	that	a	and	you	believe that	b'	–	into	the	set	of	required	propositions	at	all	worlds.	It	seems	natural	to think	that	this	code	will	also	inject	each	conjunct	–	'You	believe	that	a'	and	'You 14 believe	that	b'	–	into	the	code	of	required	propositions	at	all	worlds.	A	required proposition	may	thus	entail	another	required	proposition. Next, consider a concrete example, where replacing a widewith a narrowscope requirement changes the circumstances in	which you	are fully rational. Suppose,	at	world	w*, (i) you	believe that	you	ought	give	up smoking	and (ii) you	do	not	believe that it is	not the case that you	ought to	give	up smoking. However, (iii) you believe that if you have a conversation with Simon22	(a passionate	smoker	and	a	master	of	persuasion),	you	will	(instantly)	believe	that it is not the case that you ought to give up smoking. Nevertheless, (iv) you intend	to	have	a	conversation	with	Simon. Let	us	construe	a	code	–	RW*	–	that	permits	your	being	fully	rational	at	w*.	RW* may,	for	instance,	satisfy	the	following	(WC)-type	constraint: Wide	ought-belief	consistency.	For	all	w:	[B(O)	→	¬B(¬O)]	∈	RP(w), where	B	stands	for	'You	believe	that',	O	for	'You	ought	to	give	up	smoking',	and ¬ for negation. Expressed informally,	Wide ought-belief consistency says that rationality	requires	you	not	to	have	contradictory	ought-beliefs.	More	formally, it says that, at all possible	worlds, the	material conditional '(you believe you ought	to	give	up	smoking	→	it	is	not	the	case	that	you	believe	that	it	is	not	the case	that	you	ought	to	give	up	smoking)'	is	a	rationally	required	proposition. Wide	ought-belief	consistency	may	constrain	RW*.	RW*	is	a	code	under	which	you can	be	fully	rational	at	w*.	At	w*,	(i)	you	believe	you	ought	to	give	up	smoking, and (ii) you have no belief that it is not the case that you ought to give up smoking. So, at w*, you satisfy the requirement that wide ought-belief consistency	represents. Consider	another	possible	constraint	on	RW*: Safety. For	all	w:	{[¬B(¬O)	∈	RP(w)]	&	B[X→B(¬O)]}	→	[¬I(X)	∈	RP(w)], where	I	stands	for	'You	intend	that',	and	X	stands	for	'You	have	a	conversation with	Simon'.	The	general	idea	behind	Safety	is	that	rationality	requires	you	not to intend	anything	that	you	believe	will	bring	about	a	situation	that	violates	a requirement	of	rationality.	That	is,	suppose	'You	do	not	believe	that	it	is	not	the case that you ought to give up smoking' is a rationally required proposition. Suppose	also	that	you	believe	that	if	you	have	a	conversation	with	Simon,	then you	will	believe	that	it	is	not	the	case	that	you	ought	to	give	up	smoking.	Then, 22	In	other	words:	not	having	a	conversation	with	Simon	is	a	necessary	condition	for	not	coming	to believe	that	it	is	not	the	case	that	you	ought	to	give	up	smoking. 15 as	Safety	expresses, 'You	do	not intend to	have	a	conversation	with	Simon' is also	a	rationally	required	proposition.23 As	with	Wide	ought-belief	consistency,	Safety	may	constrain	RW*.	It	permits	you to	be	fully	rational	at	w*.	This	requires,	of	course,	that	(ii) 'You	do	not	believe that it is not the case that you ought to give up smoking' is not a required proposition	at	w*.	For	if	(ii)	were	a	required	proposition	at	w*,	Safety	would,	in conjunction with (iii) and (iv), entail that RP(w*) contains at least one false proposition	at	w*. However,	we	need	not	assume	that	(ii) is	a	member	of	RP(w*).	First,	as	I	deny factual	detachment,	conjoining	(i)	with	Wide	ought-belief	consistency	does	not imply	that	(ii)	is	required	at	w*.	Second,	I	assume	that,	at	w*,	it	is	not	the	case that (i) is	a	necessary	attitude	of	yours.	This	prevents (ii)'s	being injected into RP(w*)	via	necessary	detachment.24	Safety	can	hence	constrain	R(w*)	too. Moreover, I think	that	Safety is	a	plausible	constraint	on	a	code	of	rationality. Consider an analogy	with	moral requirements. Suppose that racist beliefs are gravely immoral (cf.	Appiah	1990;	Lengbeyer	2004).	Racist	beliefs	are	not	only false	but	also	dispositions	to	act immorally.	Thus, if	r	expresses	racist	content, then	morality	requires	you	not	to	believe	r.	Suppose	now	that	you	believe	that having	a	conversation	with	William	–	a	persuasive	racist	–	will	lead	you	to	form a	cluster	of	racist	beliefs.	It	seems	very	plausible	that	in	this	situation	morality requires	you	not	to intend	to	have	a	conversation	with	William.	Put	generally, morality	requires	you,	among	other	things,	not	to	intend	to	engage	in	behaviour that	will	make	you	gravely	immoral. A	similar	argument	suggests	itself	for	Safety	and	rationality.	Rationality, I	have already	assumed,	aims	at	attitudinal	coherence.	Roughly,	this	is	to	say	(as	I	have argued in	detail in	Author's paper) that rationality aims at ensuring that your attitudes can simultaneously fulfil their 'constitutive aims' (or 'success conditions'). For example, I assume that beliefs aim constitutively at truth, intentions at implementation, and ought-beliefs at both truth and implementation. Suppose now that rationality requires you to abstain from	believing that it is not	the	case	that	you	ought	to	give	up	smoking.	Given	my	account	of	coherence, this	is	the	case	only	if	abstaining	from	having	this	belief	is	pivotal	to	preserving your attitudes' ability simultaneously to fulfil their constitutive aims. Suppose 23	For	the	sake	of	simplicity,	I	have	kept	a	temporal	restriction	on	Safety	implicit.	Suppose	rationality requires	you	not	to	have	a	particular	ought-belief	–	call	it	BO	–	between	December	1 st	and	December 24th. Suppose too that	before	December	1st and	after	December	24th, you	are	not required	not to have	BO.	Then	Safety	implies	a	requirement	not	to	intend	X	if	and	only	if	you	believe	that	[X	will	make you	adopt	BO between	December	1 st and	December	24th]. Suppose you	believe instead that [X	will make you	adopt	BO only before	December	1 st and/or	after	December	24th]. Then, I assume,	Safety does	not	imply	a	rational	requirement	not	to	intend	to	X. 24	Compare	§	4	for	a	brief	discussion	of	'factual'	and	'necessary	detachment'. 16 you	believe,	however,	that	having	a	conversation	with	Simon	will	cause	you	to believe	that it is	not	the	case	that	you	ought	to	give	up	smoking. Intending	to have	a	conversation	with	Simon	therefore	jeopardizes	your	attitudes'	ability	to fulfil their constitutive aims. Rationality thus requires you not to have this intention. In general, as in the	moral example, rationality requires you	not to intend anything you believe will cause you to have an attitude for which it happens	to	be	true	that	rationally	requires	you	not	to	have	it. Here is another brief way to consolidate this point. Having a pair of contradictory intentions is one clear way to be incoherent. You cannot implement	both	intentions.	Thus,	rationality	requires	you	not	to	have	a	pair	of contradictory intentions. However, intending to have a pair of contradictory intentions	is	also	a	distinctive	way	of	being	incoherent.	It	is	to	aim	to	implement something	that	cannot	itself	be	implemented.	This	is	why,	I	assume,	rationality requires	you	not	to	intend	to	have	a	pair	of	contradictory	intentions.	This	lends support	to	viewing	Safety	as	a	plausible	requirement	of	rationality. I	now	return	to	Property	equivalence.	Recall	that	RW*	is	a	code	under	which	you are fully rational at w*. Apply the instructions from Property equivalence: remove	Wide ought-belief consistency from RW* and inject its narrow-scope equivalent (i.e. 'narrow ought-belief consistency') into RW*. Call the resulting code	RN*.	'Narrow	ought-belief	consistency'	reads	as	follows: Narrow	ought-belief	consistency.	For	all	w:	[B(O)	∈	w]	→	[¬B(¬O)	∈	RP(w)]. Narrow	ought-belief	consistency says that	whenever	you	believe	you	ought to give	up	smoking, 'You	do	not	believe that it is	not the	case that	you	ought to give	up	smoking'	is	a	rationally	required	proposition.	In	general,	as	long	as	you believe	something,	rationality	requires	you	not	to	believe	its	negation. In	sum,	RW*	and	RN*	compare	as	follows: Code	(RW*) Code	(RN*) (Wide	ought-belief	consistency) For	all	w:	[B(O)	→	¬B(¬O)]	∈	RP(w). (Safety) For	all	w:	{[¬B(¬O)	∈	RP(w)]	& B[X→B(¬O)]}	→	[¬I(X)	∈	RP(w)]. (Narrow	ought-belief	consistency) For	all	w:	[B(O)	∈	w]	→	[¬B(¬O)	∈	RP(w)]. (Safety) For	all	w:	{[¬B(¬O)	∈	RP(w)]	& B[X→B(¬O)]}	→	[¬I(X)	∈	RP(w)]. Property	equivalence	predicts	that	you	are	fully	rational	under	RW*	if	and	only	if you	are	fully	rational	under	RN*.	However,	w*	shows	this	to	be	incorrect. I	have	already	shown	that	you	are	fully	rational	under	RW*.	However,	this	is	not so	under	RN*.	Recall	w*:	(i)	you	believe	that	you	ought	to	give	up	smoking,	and 17 (ii)	you	do	not	believe	that	it	is	not	the	case	that	you	ought	to	give	up	smoking. Furthermore, (iii)	you	believe	that if	you	have	a	conversation	with	Simon,	you will	believe	that	it is	not	the	case	that	you	ought	to	give	up	smoking.	Also,	(iv) you intend to have a conversation with Simon. Conjoining (i) with Narrow ought-belief	consistency	of	RN* implies	that 'It is	not	the	case	that	you	believe that it is not the case that you ought to give up smoking' is a required proposition	at	w*.	Conjoining	this	with	the	fact	that	(iii)	you	believe	that	[if	you have	a	conversation	with	Simon,	then	you	believe	that	it	is	not	the	case	that	you ought	to	give	up	smoking],	implies,	via	Safety,	that,	at	w*	'It	is	not	the	case	that you intend to have a conversation with Simon' is a required proposition. However, ad hypothesis, at	w*, (iv) you intend to have a conversation with Simon.	So	while,	at	w*,	you	are	fully	rational	under	RW*,	this	is	not	so	under	RN*. Again,	Property equivalence proves incorrect.25	This time, however, it does so for what I take to be a plausible set of codes. This shows that there are situations in which the property of full rationality can actually help us to determine the scope of a conditional requirement of rationality. Wideand narrow-scope requirements differ practically in more respects than Broome suggests. 6.	Broome's	theorem This result is surprising. Broome does not defend Property equivalence in passing. Rather, he attempts to prove Property equivalence by formulating a general	theorem	and	a	corresponding	proof. This final section turns to	Broome's theorem. I argue that it fails to vindicate Property	equivalence.	Though	formally	correct,	the	theorem	neither	represents nor entails	Property equivalence. In fact, the theorem is too	weak to support the	following	two	main	points:	(i)	you	can	replace	a	widewith	a	narrow-scope requirement	(and	vice	versa)	without	changing	the	conditions	under	which	you are fully rational; and (ii) '[...]	we	cannot	decide	between the	wide-scope	and narrow-scope formulations by considering when you have the property of rationality'	(Broome	2007a,	p.	364). 25	Kolodny	(2007b,	p.	375,	n.	6)	claims	that	'Broome	might	have	proved	a	more	general	claim'	than Property	equivalence.	This	is	also	incorrect,	however.	Here	is	Kolodny's	claim: Take	two	codes	of	rationality	according	to	which	(however	different	they	may	otherwise be) the proposition that you are rational is the same. Add a narrow-scope conditional requirement to	one	code	and the	corresponding	wide-scope requirement to the	other. Then	the	proposition	that	you	are	rational	remains	the	same.	(Kolodny	2007b,	p.	375,	n. 6) I	shall	call	this	'addition	equivalence'.	Both	of	my	counterexamples	show	that	addition	equivalence	is incorrect. Let	RN	and	RW	be two codes and assume that: (i) both	pick out the same circumstances under	which	you	are	fully	rational,	and	(ii)	both	contain	Safety.	Add	Wide	ought-belief	consistency	to RW	and	Narrow	ought-belief	consistency	to	RN.	As	I	have	demonstrated	above,	there	is	a	combination of	attitudes	under	which	you	are	fully	rational	under	RW	and	not	so	under	RN. 18 To	see	this,	first	consider	Broome's	theorem26: Theorem.	Let	R1	and	R2	be	two	codes	that	are	the	same	except	that,	for	one pair	of	propositions	p	and	q,	q	∈	R1(w)	for	all	w	at	which	p is	true	(and	this may	not	be	so	for	R2)	whereas	(p	→	q)	∈	R2(w)	for	all	w	(and	this	may	not	be so for R1). Then 'You are [fully] rational' is true under R1 at exactly those worlds	where	it	is	true	under	R2.	(Broome	2007a,	p.	369) To	avoid	confusion,	note	that	R1	and	R2	represent	entire	codes.	R1(w)	and	R2(w) stand for corresponding sets of rationally required propositions. Theorem claims	the	following.	Suppose	two	codes,	R1	and	R2,	differ	only	in	the	following way: for a pair of propositions	p and	q,	R1 satisfies (NC) and	does not satisfy (WC). Analogously, R2 satisfies (WC) and does not satisfy (NC). In all other respects,	R1	and	R2	are	identical.	Then	the	two	codes	pick	out	the	same	set	of worlds	at	which	you	are	fully	rational. Unlike	Property	equivalence,	Theorem is correct.27	It is relatively	easy to show this.	Let	R1	and	R2	differ	in	terms	of	precisely	the	two	properties	that	Theorem assigns	to	R1	and	R2.	That	is:	R1	satisfies	(WC)	and	not	(NC);	R2	satisfies	(NC)	and not	(WC).	In	all	other	respects,	R1	and	R2	are	identical.	This	effectively	turns	the comparison	of	R1	and	R2 into	a	comparison	between	R1*	and	R2*,	where	both codes	only	satisfy	one	constraint:	R1*	only	satisfies (NC)	and	R2*	only	satisfies (WC). Let us compare	R1* and	R2*. Under	R1*,	q is rationally required of you at all worlds	where	p	holds	true,	whereas	under	R2*	(p→	q) is	rationally	required	of you at all worlds. Thus, under both R1* and R2*, you violate a rational requirement (and	are	not fully rational) at	w if and	only if, at	w,	p and	not-q hold true of you. In all other situations, you are fully rational. Consequently, Broome's	Theorem	is	correct. But	why	does this fail to vindicate	Property equivalence?	Recall that	Property equivalence	implies	that	by	replacing	(NC)	with	(WC)	(or	vice	versa)	in	a	code	R1, one creates another code R2, which picks out the same set of worlds (and combinations	of	attitudes)	at	which	you	are	fully	rational	as	that	picked	out	by R1. However, in contrast,	Theorem implies that if	R1 and	R2 differ only in the described way, then R1 and R2 pick out an identical set of worlds (or combination of attitudes) at which you are fully rational. The difference is subtle,	yet	significant. Here	is	when	it	is	significant.	Suppose	you	perform	only	the	following	operation on a code R: you remove (WC) and inject (NC). As a consequence, this may 26	I	cite	the	(2007a)	version	of	the	theorem	because	it	is	explicitly	about	the	code	of	rationality. 27	This	holds	true	despite	an	error in	the	first two	versions	of	his	proof (Broome	2007a,	pp.369-70; 2007b,	pp.	39-40),	which	Broome	successfully	corrected	in	the	latest	formulation	(2013a,	p.	148). 19 entail	that	the	resulting	code,	call	it	R*,	differs	in	ways	that	go	beyond	satisfying (NC)	rather	than	(WC).	It	may	differ	in	another	significant	respect.	By	replacing (WC)	with	(NC),	one	may	indirectly	apply	to	R*	another	constraint	that	does	not apply to R. This further constraint may manipulate the set of required propositions	such	that	it	becomes	possible	for	you	to	be	fully	rational	under	the original	but	not	under	the	resulting	code. The	counterexamples	in	§	4	and	§	5	represent	cases	in	point.	Recall	my	entirely schematic counterexample. In creating RN, I followed the instructions of Property equivalence. I removed (WC) from RW and applied (NC) instead. In doing	so,	however,	I	did	not	create	a	code	that	differs	from	the	original	code	RW with respect to at	most two properties. Instead, I created a code that differs from	RW	with	respect	to	more	than	two	properties.	By	replacing	(NC)	with	(WC), I indirectly injected another constraint – call it (CC) – into RN. (CC) reads as follows: 'For all	w: (p	∈	w)	→ [q	∈ RP(w)]'. But I injected (CC) into RN only indirectly, in virtue of the fact that the constraints on RN are closed under inference	by	modus	ponens.	The	following	table	represents	this	situation: Code	(RW) Code	(RN) (WC)	For	all	w:	(p	→	q)	∈	RP(w). (LR)	For	all	w:	[q	∈	RP(w)]	→	[r	∈	RP(w)]. (NC)	For	all	w:	(p	∈	w)	→	[q	∈	RP(w)]. (LR)	For	all	w:	[q	∈	RP(w)]	→	[r	∈	RP(w)]. (CC)	For	all	w:	(p	∈	w)	→	[r	∈	RP(w)]. I	showed	that	under	RW,	[p,	q,	and	not-r]	is	consistent	with	being	fully	rational, while	this	is	not	so	under	RN.	Replacing	a	(WC)-type	constraint	with	an	(NC)-type constraint can thus make a difference as to which attitudinal combinations count	as	fully	rational. However, Theorem evades this result. It does so by stipulating that the two codes	can	differ	only	with	respect	to	two	particular	constraints.	Yet	RW	and	RN differ	with respect to	more than two	constraints.	As	a	consequence,	Theorem disallows	the	comparison	of	a	(WC)-code	and	an	(NC)-code	if	these	codes	satisfy (LR), i.e.	one	required	proposition	implying	another	required	proposition.	(LR)codes	are	excluded	from	Theorem,	and	this	ensures	that	RW	and	RN	thereby	fall outside the theorem's scope. Hence, Theorem remains immune to my counterexamples. But this immunity	comes	at	a	heavy	cost.	As I	have	argued in	§	5, there is	no good	reason	to	exclude	the	existence	of	(LR)-type	constraints	on	a	code.	In	§	5,	I presented (LR)-type constraints that I find plausible. Also, Broome has not offered any reasons to doubt their existence. This, however, undermines the aim	in	terms	of	which	Broome	advances	his	theorem. 20 Broome advances his theorem in order to demonstrate that '[...] we cannot decide	between	the	wide-scope	and	narrow-scope	formulations	by	considering when	you	have	the	property	of	[full]	rationality'	(2007a,	p.	364).	Under	Property equivalence, this would hold true. By excluding (LR)-type requirements, Theorem	fails	to	support	it. Again,	the	counterexample	in	§	5	shows	this.	Here	is	a	schematic	version	of	it. Suppose	you	believe	you	ought to	A and	you	do	not	believe that it is	not the case	that	you	ought	to	A.	Suppose,	further,	that	you	believe	that	if	you	do	not believe	that it is	not	the	case	that	you	ought	to	A,	then	you	do	not	X.	Yet	you intend	to	X.	Are	you	fully	rational? Suppose the answer is 'yes'. Then, as long as Safety holds, this excludes the correctness	of	Narrow	ought-belief	consistency	(i.e.	if	you	believe	you	ought	to A, then rationality requires	of you that	you	not	believe that it is	not the	case that you ought to A). Narrow ought-belief consistency, in conjunction with Safety, entails that a required proposition fails to hold true of you. Under Narrow	ought-belief	consistency,	you	would	not	be	fully	rational. By	contrast,	suppose	that	the	answer	is	'no'.	Then,	as	long	as	Safety	holds,	Wide ought-belief consistency (i.e. rationality requires you not to [believe that you ought to A] and [believe that it is not the case that you ought to A] simultaneously) cannot be correct, because	Wide ought-belief consistency, in conjunction	with	Safety,	does	not	entail that	any required	proposition fails to hold true of you. Under	Wide ought-belief consistency, you would be fully rational. In sum –	pace Broome – the property of full rationality can help to determine	whether	a	conditional	requirement	takes	a	wide	or	a	narrow	scope. The	property	of	rationality	can	therefore	help	us	to	determine	what	rationality requires. 7.	Conclusion In	the	debate	over	the	logical	form	of	rational	requirements,	it	has	been	argued (most	prominently	by	Broome)	that	the	difference	between	wideand	narrowscope	requirements	is immaterial	to	the	issue	of	when	a	person	possesses	the property of rationality. Suppose we propose a wide-scope requirement of rationality and replace it with its narrow-scope equivalent. This replacement will not	make	any	difference	when it comes to	determining	when	a	person is fully rational under the proposed requirement. There is no combination of attitudes that turns out to be rational under a regime of wide-scope requirements that would not turn out to be rational under a regime of equivalent	narrow-scope	requirements. In	this	paper,	I	show	that	this	is	incorrect.	First,	the	equivalence	claim	cannot	be established	by	Broome's	theorem	and	proof	(see	§	6).	Second,	replacing	a	widewith a narrow-scope requirement (or	vice versa) can	make a difference as to when	a	person	is	fully	rational.	As	I	have	demonstrated	in	§	4	and	§	5,	there	are 21 combinations	of	attitudes	that	are	rational	under	a	wide-scope	requirement	but fail	to	be	so	under	the	same	narrow-scope	requirement.	This	is	the	case	when the introduction	of	a	narrow-scope requirement triggers the	detachment	of	a further	requirement	that	was	not	detachable	under	a	wide-scope	requirement (as § 4 shows for a schematic code of requirements, and § 5	with an actual code). This	result	presents	an	opportunity	for	the	debate	on	rational	requirements.	By following	the	equivalence	claim,	we	were	misled	into	accepting	that	we	cannot overcome the scope debate by examining whether wideor narrow-scope requirements give a better account of the property of rationality. But this position is too	sceptical. In fact, it	deprives	us	of	an important	opportunity to make progress in the scope debate. There are situations in which deciding whether you are fully rational will also determine whether a particular requirement	has	a	wide	or	a	narrow	logical	scope.	So,	by	working	out	when	a person is fully rational,	we can also	make progress on the question of	which logical	form	represents	conditional	requirements	of	rationality. This	does	not	only	mean	progress	for	the	scope	debate.	It	will	also	prove	helpful for	advancing	answers	to	some	of the	most important	questions linked	to	the requirements	of	rationality.	Scope	and	logical	form	decide,	among	other	things, whether rational requirements can explain the correctness of reasoning, can guide our attitude formation, and are apt to serve as sources of normative reasons. Perhaps	most	importantly,	the	scope	of	rational	requirements	decides	whether the so-called bootstrapping objection entails a forceful argument against the normativity of rational requirements. As explained in § 1, to assume that narrow-scope	requirements	are	normative	leads	to	incredible	bootstrapping.	It would licence the spurious fabrication	of normative reasons	where clearly no such	reasons	exist. In	order	to	maintain	a	normative interpretation	of	rational requirements, these requirements	must	have	a	wide logical scope.	Thus,	until we	settle	the	scope	question,	the	consequences	of	the	bootstrapping	objection for the normativity of rational requirements will remain undecided. This underlines why the result of the presented argument is important: if the property	of	rationality	can	help	us	to	resolve	the	scope	debate,	it	will	also	prove useful	for	deciding	whether	or	not	rational	requirements	are	normative. Thus,	research	on	rationality	should	no	longer	ignore	the	property	of	rationality. Indeed,	we	should try to	give	an	account	of the	property	of rationality that is independent of its requirements – an account on the basis of which	we can then determine precisely what rationality requires. 28 28	Of course, this proposal involves a considerable challenge. We need to establish a way to determine	the	property	of rationality	before	we	formulate	the	requirements	of rationality.	That is, we	need to find	a	way to	establish the	degree	of a	person's rationality that	does	not rely	on first establishing which and how many rational requirements that person satisfies or violates. For a constructive	suggestion	on	this	point,	see	Fink	(2014	and	ms). 22 Appendix Kolodny's counterargument. Kolodny (2007b, pp. 375-6) argues that Property equivalence and Theorem do not hold for what he calls 'process requirements'.29	I	argue	that	Kolodny	fails	to	show	this. Consider a simplified version of a narrow-scope conditional requirement, the wide-scope	counterpart	of	which	differs,	according to	Kolodny, in terms	of its conditions	of	violation:30 Necessarily,	if,	at	t1,	you	believe	that	you	ought	to	X,	then	rationality	requires	of you	that,	at	t3,	you	intend	to	X, where time t1 precedes t3. Expressed as a code constraint, this requirement reads	as	follows: (NP)	For	all	w:	Bt1[O(X)]	→	[It3(X)	∈	RP(w)], where	B	stands	for	'you	believe	that',	O	for	'you	ought	to',	and	I	for	'you	intend to'.	The	corresponding	wide-scope	constraint	reads	as	follows: (WP)	For	all	w:	{Bt1	[O(X)]	→	It3(X)}	∈	RP(w). Kolodny thinks that there are situations in	which you are fully rational under (WP),	but	not	so	under	(NP).	His	argument	runs	as	follows	(2007b,	pp.	375-6): suppose that, at t1, you believe that you ought to X without intending to X. However, at t2 (i.e. after t1 and before t3), you abandon your belief that you ought to	X. Furthermore,	at t3, you fail to intend to	X.	Kolodny	argues that in this	situation	you	cannot	be	fully	rational	under	(NP).	Yet	(WP)	does	not	imply this. This	is	not	correct.	It	is	true	that	under	(NP)	you	are	not	entirely	rational.	Since, at t1, you believe that you ought to X, 'At t3, you intend to X' is a required proposition.	But	this	proposition	turns	out	to	be	false.	You	are	not	fully	rational. However,	the	same	holds	for	(WP).	If,	at	t1,	you	believe	that	you	ought	to	X,	and, at	t3,	you	fail	to	intend	to	X,	you	are	also	not	entirely	as	rationality	requires	you to	be,	since	the	required	proposition	'If,	at	t1,	you	believe	you	ought	to	X,	then, at t3, you intend to	X' turns	out to	be false.	This result	holds	despite the fact 29	Note, first, that Kolodny's 'process requirements' are not exactly process requirements: their contents	do	not	represent	a	process,	nor	is	a	process	necessary	for	their	satisfaction	(Fink	2011	and 2012). These requirements	are in fact	diachronic requirements,	where rationality requires	a crosstemporal	relation	among	attitudes. 30	I have slightly adapted Kolodny's formulation. Kolodny's original formulation reads as follows: 'Necessarily,	if	you	believe	at	t	that	you	ought	to	X,	but	you	do	not	intend	at	t	to	X,	then	rationality requires	you	to	form	going	forward	from	t,	on	the	basis	of	the	content	of	your	belief,	the	intention	to X'	(2007b,	pp.	378-9). 23 that, at t2, you	drop	your	belief that you	ought to	X. Thus	Kolodny's	example disproves	neither	Property	equivalence	nor	Theorem. Broome's proof.	Broome (2007a, pp. 369-70) provides us	with a proof for his theorem (see	§	6).	Although	Theorem proves correct,	Broome's	original	proof does	not.	Here	is	why. Consider	only	the	final	part	of	the	proof.	Here,	Broome	tries	to	establish	that, necessarily, if	you	are fully rational	under	R2,	you	are	also fully rational	under R1:31 [T]ake	a	world	w	where	'You	are	rational'	is	true	under	R2.	I	shall	prove	it	is	also true	under	R1.	Since	w	satisfies	all	the	requirements	in	R2(w),	and	R1(w)	contains all the	same	requirements	apart from	the	single	one	that	differs,	w satisfies	all the	requirements	in	R1(w)	apart	from,	possibly,	that	final	one. Because	(p→q)	is	in	R2(w),	and	'You	are	rational'	is	true	at	w	under	R2,	(p→q)	is true	at	w.	Either	p	is	true	at	w	or	it	is	not.	If	it	is,	then	q	is	in	R1(w):	q	is	required at	w according to	R1. And this requirement is satisfied;	q is true at	w because both	p	and	(p→q)	are	true	there.	On	the	other	hand,	if	p	is	not	true	at	w,	there	is no final requirement in R1(w) to be satisfied. Either way, w satisfies all the requirements	in	R1(w).	'You	are	rational'	is	therefore	true	at	w	under	R1. Broome	argues	as	follows:	if	p	is	true	at	w,	and	you	are	fully	rational	under	R2, then	you	also	satisfy	all	requirements	under	R1.	Under	R2, (p→q) is	a	required proposition. At all	p-worlds (p→q) is true if and	only if	q is true. This in turn guarantees	that	you	also	satisfy	all	requirements	under	R1.	At	all	p-worlds,	q	is	a required	proposition	under	R1. What	about	not-p-worlds?	In	those	worlds,	(p→q)	is	true	in	virtue	of	p's	being false.	Hence,	you	are	fully	rational	under	R2.	But	what	about	R1?	Broome	argues that	you	are	also	fully	rational	under	R1.	His	point	is	this:	'if	p is	not	true	at	w, there	is	no	final	requirement	in	R1(w)	to	be	satisfied'.	That	is,	if	p is	false	at	w, then	q	is	not	a	required	proposition. Consequently,	Broome's	proof	relies	on	the	following	principle	of	requirement 'avoidance'.	Described	as	a	constraint	of	a	code,	this	principle	reads	as	follows: Avoidance. Necessarily For all w: {{[p ∈ w] → [q ∈ RP(w)]} &	[¬p	∈	w]}	→	¬[q	∈	RP(w)]. Less technically:	whenever	p implies that rationality requires	you to	q, then if not-p,	you	are	not	required	to	q. Avoidance	has	been	commonly	assumed	to	hold	true	for	requirements	that	are represented	by	a	code	satisfying	(NC)	(see,	for	example,	Broome	2007b,	p.	38; 2013a;	Lord	2011;	Hill	1973;	Schroeder	2004,	2005,	p.	362;	and	Vranas	2008). 31	R1	and	R2	correspond	to	Broome's	Theorem	here. 24 However,	the	logic	of	an	(NC)-code	fails	to	support	Avoidance.	So,	to	the	extent that	it	relies	on	Avoidance,	Broome's	proof	contains	a	mistake. (NC) depicts the following constraint of a code: necessarily, if	w is a	p-world, then	q is a required	proposition at	w. The implication	here is a	material one. This is necessary, inter alia, to support an important aspect of (WC)-type requirements: if (p→q) is a required proposition at w, you can satisfy the corresponding	requirement	by	ensuring	that	'not-p'	holds	at	w.	However,	it	also implies that the logic of the (NC)-type requirements does not support Avoidance. In fact, Avoidance falls foul of the requirements of logic, as it represents the fallacy of denying the antecedent: the fact that p materially implies	that	q	is	a	required	proposition	does	not	imply	that	if	p	is	not	true,	then it	is	not	the	case	that	q	is	a	required	proposition. The following	example shows	why it	would	not	even	be	a	good idea to inject Avoidance into the logic of requirements that (NC) represents. Suppose you believe that you	ought to	drive carefully. Suppose this implies	materially that 'You	to	intend	to	drive	carefully'	is	rationally	required	of	you.	At	some	point	you drop your belief that you ought to drive carefully. This does not suffice to ensure	that	intending	to	drive	carefully	is	no	longer	rationally	required	of	you. For	example: suppose that	you,	at the same time, intend to	arrive	home	safe and	sound,	and	you	believe	that	a	necessary	condition	of	your	doing	so	is	that you	drive	carefully.	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