The	Epistemic	Function	of	Higher-Order	Evidence Declan	Smithies Draft	chapter	for	Propositional	and	Doxastic	Justification, Edited	by	Paul	Silva	and	Luis	Oliveira	(Routledge,	Forthcoming). Imagine you're a solo pilot flying a small plane in Arizona.1	You're wondering whether to take a scenic detour via the Grand Canyon en route to your final destination. You know how far you can fly on a full tank and how much fuel remains in	the	tank.	You	also	know	the	distance	from	here	to	the	Grand	Canyon and from there to your final destination. But you need to do some mental arithmetic	in	order	to	calculate	whether	you	have	enough	fuel	to	safely	complete the journey. You perform the calculation correctly and deduce that you have enough	fuel.	On	that	basis,	you	decide	to	take	the	detour.	So	far,	so	good! Moments later,	however, you	acquire	worrying	new	evidence that	you	are suffering from	hypoxia – an oxygen deficit that impairs cognitive functioning in ways	that	often	remain	undetectable	to	the	victim.	You	know	about	the	dangers	of hypoxia:	pilots	have	crashed	and	died	as	a	result	of	bad	decisions	made	under	its influence. You know there is a serious risk of hypoxia	when the altitude is high enough	and	the	cabin	pressure is low	enough.	Moreover,	your	control	panel	says you're	now in the	danger zone.	As it	happens, this evidence is	misleading, since there	is	a	malfunction	in	the	barometer	that	measures	cabin	pressure.	The	truth	is that	you're	at	no	risk	of	hypoxia,	although	there's	no	way	you	can	know	this. Should you now reconsider your decision to take the scenic detour once you	acquire	this	new	evidence?	Intuitively,	you	should.	Consider	the	steadfast	pilot who	decides	to	stick	with	his	original	plan.	This	decision	seems	grossly	irrational. After all, the pilot has no way of knowing that the new evidence of hypoxia is misleading.	Moreover,	this	evidence	makes	it	likely	that	he	is	cognitively	impaired in ways that dispose him to	make elementary	mistakes in calculation. It seems reckless	to	ignore	this	possibility	in	dogmatically	maintaining	his	original	plan.	We know	there	is	no	risk	of	hypoxia,	of	course,	and	so	we	can	be	assured	that	the	pilot will	arrive	safely.	But	any	pilot	who	routinely	makes	such	decisions	in	the	face	of evidence	of	hypoxia	is	putting	their	own	life	in	serious	danger. The irrationality of the decision reflects the irrationality of the belief on which	it	is	based.	In	general,	it	is	rationally	permissible	to	believe	that	p	only	if	it's rationally	permissible	to	act	on	the	premise	that	p.	And	yet	it's	no	longer	rationally permissible	to	act	on	the	premise	that	you	have	enough	fuel	when	you	acquire	the new	evidence that you're	hypoxic.	Hence, it's	no longer rationally	permissible to believe	that	you	have	enough	fuel.	This	means	that	you	cannot	know	whether	you have	enough	fuel,	since	it's	rationally	permissible	to	believe	that	p,	and	to	act	on 1	This	example	is	adapted	from	Elga	(2008,	2013)	and	Christensen	(2010). 2 the premise that p, whenever you know that p.2	Previously, however, you knew that you	had enough fuel by competently	deducing this conclusion from	known premises. Therefore, you must lose this knowledge when you acquire the new evidence	that	you	are	hypoxic. This	much	is	intuitively	compelling	but	theoretically	puzzling.	Why	should the	evidence	that	you	are	hypoxic	destroy	your	knowledge	that	you	have	enough fuel?	It	is	extremely	plausible	that	it	does,	but	it	is	not	easy	to	explain	how	it	does. After	all,	the	evidence	that	you	are	hypoxic	doesn't	bear	directly	on	the	question	of whether	you	have	enough fuel: it isn't	evidence that	you	don't	have	enough fuel. But then how exactly does this new evidence undermine the rationality of believing	that	you	have	enough	fuel	and	thereby	destroy	your	knowledge? This is one instance of a more general question about the epistemic function	of	higher-order	evidence.	In	this	context,	higher-order	evidence	is	defined as	evidence	about	whether	your	beliefs	are	responsive to	your	evidence.	Suppose you know that p on the basis of evidence e, but then you subsequently acquire misleading higher-order evidence h that your belief is not responsive to your evidence.	How	does	this	higher-order	evidence	h	destroy	your	knowledge	that	p? And	why	is	it	now	rationally	impermissible	for	you	to	retain	your	belief	that	p	on the	basis	of	your	first-order	evidence	e? This	chapter	provides	a	critical	overview	of	several influential	proposals in the literature on higher-order evidence. I start by criticizing explanations that appeal to evidential defeat (§1), epistemic conflicts (§2), and unreasonable knowledge (§3). Next, I propose an alternative explanation that appeals to a combination	of	improper	basing	(§4)	and	non-ideal	rationality	(§5).	I	conclude	by summarizing	my	reasons	for	preferring	this	explanation	to	the	alternatives	(§6). 1. Evidential	Defeat Richard Feldman (2005) argues that higher-order evidence functions as an evidential defeater: it	undermines	knowledge	by	defeating	evidence.	For	example, the	higher-order	evidence	that	you	are	hypoxic	undermines	your	knowledge	that you have enough fuel by defeating your first-order evidence for this conclusion. You	lose	your	knowledge	because	your	total	body	of	evidence	no	longer	supports this	conclusion. The challenge is to explain why the higher-order evidence that you are hypoxic defeats your first-order evidence that you have enough fuel. As we've already noted, your higher-order evidence doesn't provide evidence against this conclusion,	since	hypoxia	by	itself	makes	it	no	more	or	less	probable	that	you	have enough	fuel.	But	then	how	can	it	defeat	your	evidence	for	this	conclusion? John	Pollock (1986)	draws	an influential	distinction	between two	kinds	of defeaters. First, and	most obviously, there are rebutting defeaters, which reduce 2	Hawthorne	and	Stanley	(2008)	endorse	both	directions	of	this	knowledge-action principle – that is, it's rationally permissible to act on the premise that	p if and only	if	you	know	that	p	–	but	the	opposite	direction	is	more	controversial. 3 your	overall	degree	of	evidential	support for	a	conclusion	by	giving	you	evidence against the conclusion.	Crucially, though, not all defeaters	work this	way.	There are also undercutting defeaters, which reduce your overall degree of evidential support	for	a	conclusion	without	giving	you	evidence	against	your	conclusion.	As Pollock	writes,	"Such	defeaters	attack	the	connection	between	the	reason	and	the conclusion	rather	than	attacking	the	conclusion	itself"	(1986:	196). Consider a textbook example: the fact that the	wall looks red is evidence that	that	it	is	red,	although	this	evidential	connection	can	be	undercut	by	further evidence that the wall is bathed in red light. This is no evidence against the conclusion	that	the	wall	is	red,	since	the	lighting	by	itself	makes	it	no	more	or	less probable that the wall is red. As I'll explain, however, it reduces the degree to which	your	sensory	evidence	supports	this	conclusion. Under normal circumstances, the most probable explanation of why the wall looks	red is that it is	red.	Hence, the	evidence	that	the	wall looks	red	raises the	probability	that	it	is	red.	Given	the	further	evidence	that	the	wall	is	bathed	in the	red	lighting,	however,	this	is	no	longer	the	most	probable	explanation.	In	these abnormal lighting	conditions, the	wall looks red	whatever color it is.	Hence, the evidence that the	wall looks red under red lighting doesn't raise the probability that	the	wall	is	red.	Putting	these	points	together,	the	probability	that	the	wall	is red	given	that	it looks	red	under	red	lighting	is less	than	the	probability	that	the wall	is	red	given	only	that	it	looks	red.	In	this	way,	the	evidence	about	the	lighting reduces	the	degree	to	which	your	sensory	evidence	supports	this	conclusion.	This is presumably what Pollock intends when he says that undercutting defeaters "attack the connection" between the evidence and the conclusion, rather than attacking	the	conclusion	itself. Now	let's	revisit	the	hypoxia	example:	how	does	the	evidence	that	you	are hypoxic defeat your evidence that you have enough fuel? It's not a rebutting defeater,	of course,	but	not	all	defeaters are rebutting	defeaters. Is it	perhaps	an undercutting defeater that reduces the degree to which your evidence supports this conclusion? I'll argue that it isn't, since the evidence that you're hypoxic makes	no	difference	to	your	overall	degree	of	evidential	support	for	the	conclusion that	you	have	enough	fuel.	There	is	no	sense	in	which	your	higher-order	evidence defeats	the	evidential	support	provided	by	your	first-order	evidence. The	key	point	is	that	the	conclusion	that	you	have	enough	fuel	is	entailed	by known	premises	about	the	distance	of	the journey	and	the	amount	of fuel in	the tank.	Entailment	is	monotonic:	we	cannot	undermine	an	entailment	from	premises to conclusion by adding new premises. In particular, we cannot undermine the entailment from	premises to	conclusion	by	adding	the	premise	that	you	botched the	deduction	as a result	of	hypoxia.	The	expanded set	of	premises continues to entail	the	conclusion	that	you	have	enough	fuel. Moreover, entailment is the strongest kind of evidential support relation. Arguments come in varying degrees of strength: the stronger an argument, the higher	the	probability	that	its	conclusion	is	true	given	that	its	premises	are	true.	A deductively	valid	argument	is	the	strongest	kind	of	argument,	since	it	is	not	merely 4 improbable	but	impossible	that	the	conclusion	is	false	when	the	premises	are	true. This is the limiting case in which the probability of the conclusion given the premises is 1. Since the premises of a deductively valid argument entail its conclusion,	the	probability	of	the	conclusion	can	be	no	less	than	the	probability	of the	conjunction	of the	premises.	Thus,	deductively	valid	arguments	preserve	not only	truth	from	premises	to	conclusion,	but	also	degrees	of	evidential	support.3 Before you acquire the evidence of hypoxia, your premises about the distance of the journey and the amount of fuel remaining are highly probable given	your	evidence.	Indeed,	the	probability	of	the	conjunction	of	these	premises is high enough that you can know the conclusion by deduction from these premises. Since your premises entail the conclusion, the probability of the conclusion	is	no	less	than	the	probability	of	the	conjunction	of	the	premises. What changes	when you acquire the new evidence that you are hypoxic? Now	you	have	evidence	that	you	are	cognitively	impaired	in	ways	that	dispose	you to botch the reasoning from your premises to your conclusion. As we've seen, however, this doesn't undermine the entailment from premises to conclusion. Moreover,	this	doesn't	affect	the	evidential	probability	of	the	premises	themselves. The strength of your evidence for these premises remains unchanged. After all, hypoxia	doesn't	cause	you	to	hallucinate	the	readings	on	your	control	panel	or	to invent	new	estimates	of	the	distance	to	your	destination.	Rather,	the	point	of	the example	is	that	it	impairs	your	capacity	to	acquire	knowledge	by	deduction. Since the	evidence	of	hypoxia	doesn't change the	evidential	probability	of the	premises,	it	doesn't	change	the	evidential	probability	of	the	conclusion	either. Hence,	acquiring	this	new	evidence	does	nothing	to	reduce	the	probability	of	your conclusion.	I	conclude	that	the	evidence	of	hypoxia	is	no	evidential	defeater	at	all, since	it	doesn't	reduce	the	overall	degree	of	evidential	support	for	your	conclusion. All evidential defeaters, whether or not they are evidence against a conclusion, reduce the degree to which your total evidence supports a conclusion.	We can articulate	this	as	a	probabilistic	constraint	on	evidential	defeat: A Probabilistic Constraint on Evidential Defeat: If	d defeats the evidential support that	e	provides for	h, then the	probability that	h given	e and	d is less	than	the	probability	that	h	given	e	alone.4 The higher-order evidence that you are hypoxic doesn't satisfy this probabilistic constraint, since the evidential probability that you have enough fuel remains unchanged	when	you	receive	this	new	evidence. Some	may	be	tempted	to	block	this	objection	by	rejecting	the	probabilistic conception	of	evidential	support	on	which	it	depends.	In	response,	however,	this 3	See	Skyrms	(1966:	Ch.	2)	for	a	compelling	articulation	of	this	point.	In	the	text,	I assume	regularity	–	that	is,	impossible	scenarios	have	zero	probability. 4	Compare	Kotzen's	thesis	that	defeaters	are	credence	lowering:	"D	is	a	defeater	for the	evidence	that	E	provides	for	H	just	in	case	p	(H	|	E	∧	D)	<	p	(H	|	E)"	(2019:	15). 5 comes	at	too	high	a	cost.	As	we've	seen,	the	probabilistic	framework	is	designed	to capture	the	important	insight	that	arguments	come	in	varying	degrees	of	strength. Deductively	valid	arguments	provide	the	strongest	possible	degree	of	support	for	a conclusion,	since	the	premises	entail	the	conclusion,	rather	than	merely	raising	the probability	of	the	conclusion.	My	objection	exploits	this	intuitive	point	about	the strength of deductive arguments, which is captured most naturally in a probabilistic	framework. To be clear, I am not questioning the intuitive datum that higher-order evidence of hypoxia destroys your knowledge that you have enough fuel. Moreover,	I	have	no	complaint	about	the	practice	of	articulating	this	datum	using the language	of 'defeat' so long	as	we	are	careful to recognize that this is	not	an explanation	of	the	datum	but	merely	a	restatement	of	the	datum	to	be	explained. The	challenge	that	remains is to	explain	why this	higher-order	evidence	destroys your	knowledge. In this	section, I've	argued	that the	evidence	of	hypoxia	doesn't undermine	your	knowledge	by	reducing	your	overall	degree	of	evidential	support for	the	conclusion	that	you	have	enough	fuel.	Some	other	explanation	is	needed. 2. Epistemic	Conflicts David Christensen (2007, 2010a) argues that higher-order evidence destroys knowledge by creating epistemic conflicts. Misleading higher-order evidence is "rationally toxic" in the sense that it forces you to violate one of the following epistemic	ideals: (1) Respecting	your	first-order	evidence. (2) Respecting	your	higher-order	evidence. (3) Meta-coherence, i.e. coherently integrating your first-order beliefs with your	higher-order	beliefs. In the hypoxia case, for example, you cannot respect all your evidence while coherently integrating your first-order and higher-order beliefs. Your first-order evidence supports the	belief that you	have enough fuel,	while your	higher-order evidence supports the higher-order belief that this first-order belief is probably based on bad reasoning. And yet this combination of beliefs seems dubiously coherent. As Christensen writes, "the rationality of first-order beliefs cannot in general	be	divorced from	the	rationality	of	certain	second-order	beliefs that	bear on	the	epistemic	status	of	those	first-order	beliefs"	(2007:	18). Christensen	argues	that	the	rationally	optimal	way	of	resolving	this	conflict is	to	violate	the	epistemic	ideal	of	respecting	your	evidence.	Rather	than	believing what your evidence supports – namely, that you	have enough fuel – you should instead remain	agnostic.	Hence,	epistemic rationality requires that	you "bracket" your first-order evidence in the sense that you refrain from believing what it supports.	On this view, your knowledge that you have enough fuel is destroyed when you acquire the evidence that you are hypoxic because it is no longer epistemically	rational	to	believe	what	your	evidence	supports. 6 There is something puzzling about this proposal. How can epistemic rationality require you to refrain from believing what your evidence supports? According to evidentialism in epistemology, epistemic rationality is simply a matter of proportioning your beliefs to your evidence.5	On this view, epistemic rationality	never requires	or	even	permits	you to "bracket"	any	of	your	evidence. On	the	contrary,	it	imposes	a	requirement	of	total	evidence,	which	says	you	should always	take	all	of	your	evidence	into	account	in	deciding	what	to	believe. Christensen's	proposal	can	be	understood	as	a	form	of	bifurcationism	about epistemic rationality.6	On this view, the structural requirements of coherence, including meta-coherence, are distinct from and irreducible to the structural requirement	of	respecting	your	evidence.	Moreover,	these	requirements	can	come into	conflict	when	you	have	misleading	higher-order	evidence	about	your	response to your first-order evidence, since your total evidence supports	meta-incoherent beliefs.	Christensen's	proposal	is	that	the	rationally	optimal	way	of	resolving	these conflicting requirements is to maintain meta-coherence in response to your higher-order	evidence	by	disrespecting	your	first-order	evidence. I argue	elsewhere that	we should	prefer a	unified conception	of epistemic rationality,	according	to	which	the	structural	requirements	of	coherence	are	built into the structure	of the	evidential support relation (Smithies, forthcoming).	For example, we can build in requirements of logical or probabilistic coherence by endorsing	a	probabilistic	conception	of	the	evidential	support	relation,	according to	which degrees of evidential support are evidential probabilities. Similarly, we can	build	in	a	meta-coherence	requirement	by	endorsing	structural	constraints	on higher-order	probabilities,	such	as	the	following: Probabilistic	Accessibilism:	Necessarily,	if	the	evidential	probability	that	p	is n,	then	it	is	evidentially	certain	that	the	evidential	probability	that	p	is	n.7 On this	unified conception	of epistemic rationality, there is	no	distinction to	be drawn between the substantive requirement to respect your evidence and the structural	requirement	to	be	coherent.	There	is	just	one	evidentialist	requirement that incorporates both substantive and structural dimensions – that is, to 5	See	Feldman	and	Conee	(1985)	for	a	classic	defense	of	evidentialism. 6	Compare	Worsnip (2018) for a similar view. See Smithies (forthcoming) for a detailed	critical	discussion	of several	different forms	of	bifurcationism, including those	defended	by	Christensen	and	Worsnip. 7	Christensen (2010b)	and	Elga (2013) reject	probabilistic	accessibilism in favor	of rational reflection	principles, but these	higher-order constraints are too	weak to prohibit	instances	of	epistemic	akrasia	in	which	you	are	certain	that	your	credence is	irrational,	although	you	are	agnostic	about	whether	it	is	too	high	or	too	low.	In Smithies (2019:	Ch. 10), I defend	probabilistic accessibilism	against the	objection that	it	is	"immodest"	by	appealing	to	the	distinction	between	ideal	and	non-ideal standards	of	epistemic	rationality	drawn	in	§5	below. 7 proportion	your	beliefs	to	your	evidence	in	the	sense	that	your	beliefs	cohere	with substantive	facts	about	your	evidence	in	accordance	with	structural	facts	about	the evidential	support	relation.	These	structural	constraints	on	the	evidential	support relation	guarantee	that	your	evidence	never	supports	an	incoherent	set	of	beliefs. Occam's razor prohibits	multiplying requirements of epistemic rationality beyond necessity.	Why then	might someone endorse bifurcationism? The usual answer is that bifurcationism is supported by reflection on examples. In the hypoxia	case,	for	example,	your	evidence	seems	to	support	the	following	beliefs: (1) I	have	enough	fuel. (2) But	my	belief	that	I	have	enough	fuel is	probably	based	on	bad	reasoning, since	I	am	cognitively	impaired	as	a	result	of	hypoxia. (3) Therefore,	my	belief that I	have	enough	fuel is	probably	not	supported	by good	evidence. And yet this combination of beliefs violates the meta-coherence requirement, since it is always irrational to	hold	a	belief	while also	believing that it is	neither based	on	nor	supported	by	good	evidence.	Hence,	the	substantive	requirement	to respect your evidence seems to conflict in this case with the structural requirement	of	meta-coherence. As	we've seen,	however,	we	can	build the requirement	of	meta-coherence into the structure of the evidential support relation. Given probabilistic accessibilism, for example, you cannot have misleading higher-order evidence about what your evidence supports, since the facts about what your evidence supports are always	made	certain	by	your	evidence.	On this view, your	evidence never supports a	meta-incoherent combination	of	beliefs of the form, 'p and	my evidence	probably	doesn't	support	p'.	Hence,	respecting	your	evidence	guarantees that	you	are	also	meta-coherent. Now,	of	course,	you	can	have	misleading	higher-order	evidence	about	your response to	your	evidence,	although	you	can	never	have	misleading	higher-order evidence about what your evidence supports. This is because facts about your response	to	your	evidence,	unlike	facts	about	what	your	evidence	supports,	are	not made	certain	by	your	evidence.	As	a	general	rule,	the	argument	from	(2)	to	(3)	is inductively	strong,	since	beliefs	based	on	bad	reasoning	are	not	usually	supported by good evidence. In your own case, however, the inference from (2) to (3) is blocked when your higher-order evidence is misleading. In such cases, your evidence	supports	believing	(1)	and	(2)	but	not	(3). Moreover, believing (1) and (2) is not incoherent in the same way as believing (1) and (3). It's always irrational to believe that p while believing that your	evidence	doesn't support	p.	This	combination	of	beliefs is self-defeating:	by your own lights, you should abandon your belief that p, since you think it is unsupported	by	your	evidence.	In	contrast,	it's	not	always	irrational	to	believe	that p while believing that your belief is not properly based on supporting evidence. Indeed, this	can	be	a	perfectly	rational	response	to	misleading	evidence	that	you 8 believe	the	right	thing	for	the	wrong	reasons.	It	is	not	self-defeating	in	such	cases to conclude that your belief is supported by good evidence, although it is not properly	based	on	good	evidence. To illustrate the point, consider a practical analogy. Suppose a wealthy philanthropist	receives	public	acclaim	for	donating	large	sums	of	money	to	charity. He	knows	he	is	doing	the	right	thing,	but	he	suspects	he	is	doing	it	for	the	wrong reasons	because	he	has	misleading	evidence	that	he	is	selfishly	motivated.	So	long as this evidence is misleading, his action may be rationally responsive to good moral	reasons.	The	same	applies	to	someone	who	knows	that	he	believes	what	his evidence supports, although	he suspects his belief is held for the	wrong reasons because	he	has	misleading	evidence	that	he	is	motivated	by	wishful	thinking.	Once again, his belief may be rationally responsive to good evidence so long as this higher-order	evidence	is	misleading.	In	such	cases,	there	is	nothing	self-defeating about	doubting	the	reasoning	on	which	your	beliefs	and	actions	are	based. Admittedly, there is something	unusual about an	evidential situation that supports	the	following	line	of	argument: (4) It's certain that	my evidence supports the conclusion that I have enough fuel. (5) But	my	belief	that	I	have	enough	fuel	is	probably	based	on	bad	reasoning. (6) So	I	probably	got	lucky,	since	bad	reasoning	led	me	to	form	a	belief	that	is supported	by	the	evidence. In	the	absence	of	strong	evidence, it's irrational to	believe in lucky	coincidences. After	all,	the	prior	probability	of	such	a	coincidence	is	very	low.	In	the	presence	of strong	evidence,	however,	the	posterior	probability	of	a	coincidence	may	be	high. There	is	nothing	in	principle	to	rule	out	the	possibility	that	your	evidence	supports the conclusion that a lucky coincidence has occurred. Otherwise, no one could find	out	when	they	win	the	lottery.	The	hypoxia	example	is	another	case	in	point, since	your	evidence	supports	the	conclusion	that	you	got	lucky. Does this license dogmatism in response to higher-order evidence? Consider	our steadfast	pilot	who	maintains	his	belief that	he	has enough fuel in the face	of the	higher-order	evidence that	he is	hypoxic.	Suppose that instead	of simply ignoring this higher-order evidence, he concludes that he	must have got lucky, since	his	belief is supported	by evidence although it is	probably	based	on bad reasoning. Intuitively, this compounds his irrationality. It was already irrational for	him	to	retain the first-order	belief that	he	has	enough fuel	and	the problem	is	exacerbated	when	he	doubles	down	by	retaining	the	higher-order	belief that his evidence supports this conclusion. Our steadfast pilot maintains metacoherence	at	the	cost	of	both	first-order	and	higher-order	dogmatism. I	agree	the	steadfast	pilot	is	irrational,	but	this	just	shows	that	our	original problem	arises	at	multiple levels.	At level	one,	the	problem	is	to	explain	why	the pilot	cannot	rationally	believe	that	he	has	enough	fuel	when	his	evidence	supports this	conclusion.	At the level two, the	problem is to	explain	why the	pilot	cannot 9 rationally believe that his evidence supports this conclusion when his evidence also	supports	this	higher-order	conclusion.	And	so	on	as	we	ascend	the	hierarchy. I'll	propose	my	own	solution	to	this	problem	in	due	course.	My	goal	in	this	section is merely to argue that we cannot solve it by arguing that the pilot's evidence supports incoherent beliefs. There are general theoretical reasons to doubt that your evidence can ever support incoherent beliefs and there are more specific reasons	to	doubt	that	the	pilot's	evidence	supports	incoherent	beliefs.	We	need	to look	elsewhere	to	explain	why	it	is	irrational	for	the	steadfast	pilot	to	retain	beliefs that	are	nevertheless	supported	by	his	evidence. 3. Unreasonable	Knowledge Maria	Lasonen-Aarnio	(2010,	2020)	argues	that	the	steadfast	pilot	has	unreasonable knowledge.8	On this	view, the	pilot	can retain	his	knowledge that	he	has	enough fuel	even in	the face	of	misleading	higher-order	evidence	that	he is	hypoxic.	The problem is that his belief is unreasonable because it manifests a more general disposition to be unresponsive to evidence in other cases. And yet this needn't undermine	his	knowledge	so	long	as	he	responds	appropriately	to	all	the	evidence that	he	actually	has.	Thus,	reasonable	belief	is	not	necessary	for	knowledge. What	is	it	for	a	belief	to	be	reasonable?	Lasonen-Aarnio	writes: Reasonableness is at least largely a matter of managing one's beliefs through the adoption of policies that are generally knowledge conducive, thereby manifesting dispositions to know and avoid false belief across a wide	range	of	normal	cases.	(2010:	2) The steadfast pilot is unreasonable because he fails to	manifest dispositions are generally	conducive to	knowledge	– that is,	dispositions to	know	and	avoid false belief	across	a	wide	range	of	normal	cases. In	particular,	he is	disposed	to ignore higher-order	evidence	that	his	beliefs	are	based	on	bad	reasoning	not	only	in	the "good	case"	in	which	his	higher-order	evidence	is	misleading	but	also	in	the	"bad case"	in	which	it	is	accurate.	Since	the	actual	case	is	a	good	case,	his	belief	is	not only	true,	but	also	supported	by	his	evidence.	Nevertheless,	it	is	held	dogmatically in a	way that	disposes	him to retain	beliefs in	bad cases that are	both false and unsupported	by	evidence. In	short,	the	steadfast	pilot	is	unreasonable	because	he	manifests	a	general disposition	that	leads	him	astray	in	other	cases.	And	yet	this	leaves	his	knowledge intact	so	long	as	the	disposition	doesn't	lead	him	astray	in	this	case.	He	retains	his knowledge	because	his	true	belief	remains	as	safe	from	error,	and	as	responsive	to his	first-order	evidence,	as	it	was	before	he	acquired	the	higher-order	evidence	of hypoxia.	Since	he	had	knowledge	beforehand,	he	retains	his	knowledge	in	the	face of	his	new	higher-order	evidence,	despite	the	fact	that	his	belief	is	unreasonable. 8	Lasonen-Aarnio	(2010)	focuses	on	standard	examples	of	undercutting	defeat,	but she	extends	her	proposal	to	higher-order	evidence	in	Lasonen-Aarnio	(2020). 10 It's worth noting that the same proposal applies at multiple levels. Presumably,	the	steadfast	pilot	can	retain	not	only	his	first-order	knowledge	that he	has	enough	fuel,	but	also	his	higher-order	knowledge	that	his	evidence	supports this conclusion.	Moreover, given the	misleading evidence that he is hypoxic, he can rationally conclude from these known premises that he probably got lucky, since his cognitive impairment didn't lead him astray on this occasion. The problem	with	his	first-order	and	higher-order	beliefs	is	that	they	are	unreasonable because	they	manifest	more	general	dispositions	to	go	awry	in	bad	cases	in	which his higher-order evidence is accurate. But this has no tendency to undermine either	the	pilot's	first-order	knowledge	or	his	higher-order	knowledge. I'll	now	raise	three	objections	to	this	proposal.	First,	it	fails	to	vindicate	all our	intuitions	about	the	hypoxia	case.	It	vindicates	the	intuition	that	the	steadfast pilot	is	unreasonable,	but	not	the	intuition	that	he	loses	knowledge.	Is	it	plausible that	the	steadfast	pilot	retains	his	first-order	knowledge	that	he	has	enough	fuel	as well	as	his	higher-order	knowledge	that	his	evidence	supports	this	conclusion?	Is	it plausible that he can	use this knowledge, together	with	his	misleading evidence that	he	is	hypoxic,	to	infer	that	he	probably	got	lucky	on	this	occasion?	To	many, myself	included,	these	verdicts	are	strongly	counterintuitive. Lasonen-Aarnio	proposes	to	explain	away	conflicting	intuitions	by	appeal	to the	error theory that	we tend to	conflate reasonableness	and	knowledge. I agree that our intuitions about this case, and	many others, are guided by the implicit assumption	that	only	reasonable	beliefs	can	be	knowledge.	This	explains	why	we find	it	so	natural	to	make	the	inference	from	the	premise	that	someone's	belief	is unreasonable to the conclusion that they lack knowledge. Given the intuitive plausibility	of	this	assumption,	however,	why	suppose	it	is	mistaken?	To	my	mind, the	error	theory	should	be	regarded	as	a	last	resort:	all	else	being	equal,	we	should prefer	an	epistemological	theory	that	vindicates	our	intuitive	reactions. Second, there are general theoretical grounds for doubting that you can acquire	knowledge	by	manifesting	unreasonable	dispositions.	To	know	that	p,	it's not	enough	that	you	truly	believe	that	p;	your	belief	must	be	reliable	in	the	sense that it manifests a more general disposition to have true beliefs. Similarly, to rationally	or	justifiably	believe	that	p,	it's	not	enough	that	your	belief	is	supported by	good	evidence;	it	must	be	properly	based	on	good	evidence	in	the	sense	that	it manifests a	more general disposition to	have	beliefs that are supported	by good evidence. Hence, knowledge requires manifesting good dispositions that are reliably responsive to evidence and truth. When your beliefs manifest unreasonable dispositions, however, they are not reliable enough to constitute knowledge. Presumably, this is why it remains so intuitively plausible that only reasonable beliefs can be knowledge. This is not just a brute intuition with no theoretical support. It is supported by the theoretical consideration that knowledge	must	be	reliably	responsive	to	evidence	and	truth. Lasonen-Aarnio sympathetically	discusses the simple externalist view that knowledge	is	true	belief	that	is	safe from	error in	the	sense	that	it	couldn't	easily have	been	false.	But	the	case	of	mathematical	knowledge	suggests	that	this	view	is 11 too	simple:	I	cannot	know	that	Fermat's	Last	Theorem	is	true	by	means	of	wishful thinking, although there is	no	danger that	my	belief is false, since its content is necessarily	true.	Arguably,	this	is	because	my	safe	belief	is	based	on	manifesting	an unsafe disposition: one that could easily yield false beliefs in other cases. This supports the	claim	that	a	belief is	knowledge	only if it is reasonable in	the	sense that	it	manifests	a	more	generally	reliable	disposition.9 Third, there are theoretical costs involved in rejecting the principle that only	reasonable	beliefs	can	be	knowledge.	Knowledge	is	valuable.	If	we	allow	that knowledge	can	be	unreasonable,	however,	then	we	risk	devaluing	knowledge.	So, for	example,	knowledge	is	often	thought	to	set	a	normative	standard	of	correctness for	belief	and	action:	if	you	know	that	p,	then	you	are	right	to	believe	that	p,	and	to act	on	the	premise	that	p,	and	so	you	cannot	legitimately	be	blamed	for	doing	so. And	yet the	steadfast	pilot is	blameworthy for	acting	on	the	premise that	he	has enough fuel: his mother can be justly angry that he acted so recklessly. As Lasonen-Aarnio	acknowledges,	"Subjects	who	retain	knowledge	in	defeat	cases	are genuinely	criticisable"	(2010:	15).	The	problem	is	that	we	cannot	maintain	that	the steadfast pilot retains his knowledge, while also acknowledging his culpability, unless	we abandon these plausible connections between knowledge, permission, and blameworthiness. But this devalues knowledge in ways that should be unattractive	to	anyone,	especially	to	proponents	of	knowledge-first	epistemology. In conclusion, we need to explain not only how evidence of hypoxia can make your beliefs unreasonable, but also how it can destroy your knowledge. Although Lasonen-Aarnio's proposal fails to explain this datum, it contains an important	grain	of	truth,	which	will	figure	prominently	in	the	discussion	to	follow. To	explain	how	higher-order	evidence	destroys	your	knowledge,	we	need	to	invoke facts	about	the	reliability	of	your	doxastic	dispositions. 4. Improper	Basing My	own	explanation	of	how	higher-order	evidence	destroys	first-order	knowledge appeals	to	improper	basing.10	On	this	view,	the	higher-order	evidence	that	you	are hypoxic doesn't defeat your first-order evidence that you have enough fuel, but merely prevents you from properly basing your beliefs on this evidence. This explains why you lose your knowledge that you have enough fuel when you acquire	the	higher-order	evidence	that	you	are	hypoxic.	Only	justified	beliefs	can be	knowledge	and	a	belief	is	justified	only	if	it	is	properly	based	on	good	evidence. 9	See	Sosa	(2003)	for	a	defense	of	this	claim.	In	Smithies	(2019:	Ch.	11),	I	argue	for similar	conclusions	about	justification	based	on	the	problem	of	the	speckled	hen: justified	belief	requires	exercising	a	disposition	that	is	reliably	responsive	to	what your	evidence	supports. 10	Compare	Smithies	(2015;	2019:	Ch.	10).	Van	Wietmarschen	(2013)	adopts	a	similar line	on	peer	disagreement,	although	his	explanation	of	how	higher-order	evidence undermines	proper	basing	diverges	from	mine. 12 We can articulate the point in terms of the familiar distinction between propositional and doxastic senses of epistemic justification, rationality, or warrant.11	A belief is propositionally justified when its propositional content is supported by good evidence, whereas a belief is doxastically justified when the belief	is	held	in	a	way	that	is	properly	based	on	good	evidence.	Thus,	proper	basing is the relation	between	a	belief and	a	body	of supporting	evidence that converts propositional justification into doxastic justification. The higher-order evidence that	you	are	hypoxic	doesn't	undermine	your	propositional	justification	to	believe that	you	have	enough	fuel	by	defeating	your	evidence	for	this	conclusion.	Rather, it	undermines	your	doxastic justification	by	preventing	you	from	properly	basing your belief on this evidence. In a slogan, higher-order evidence is a doxastic defeater,	rather	than	a	propositional	defeater. What	does it take for	a	belief to	be	properly	based	on	good	evidence? It's not	enough	that	my	belief	is	based	on	good	evidence	that	happens	to	support	my beliefs.	My belief	must also	manifest a	more general disposition that is reliably sensitive	to	differences	in	what	my	evidence	supports.	If	I'm	disposed	to	retain	my belief	even	if	my	evidence	changes	in	ways	that	no	longer	support	the	belief,	then it is not properly based on the evidence. My belief is properly based on the evidence only if it manifests a more general disposition to believe what the evidence	supports.12 Dogmatic beliefs violate this condition. Consider	my belief that drinking red	wine	is	good	for	my	health.	Let's	assume	that	while	the	evidence	for	this	claim is	somewhat	mixed,	the	evidence	in	its	favor	outweighs	the	evidence	against,	and that	the	supporting	evidence	is	strong	enough	to	justify	belief.	Although	I'm	aware of	all	this	evidence,	the	problem	is	that	I	hold	my	belief	dogmatically	in	a	way	that makes	me	relatively	insensitive	to	changes	in	what	my	evidence	supports.	I	am	not disposed	to	respond	to	changes	in	what	my	evidence	supports	with	corresponding changes	in	what	I	believe.	I	will	remain	unmoved,	for	example,	if	I	learn	about	new studies casting doubt on the health benefits of drinking red wine. Intuitively, I don't	know	that	drinking	wine	is	good	for	me,	even	if	my	belief	is	true	and	based on good evidence. The problem is that my belief is not properly based on my evidence,	since	it	manifests	a	disposition	that	is	insufficiently	sensitive	to	changes in	what	my	evidence	supports. I	suggest	that	the	same	is	true	of	the	steadfast	pilot.	He	doesn't	know	that he has enough fuel, despite the fact that his belief is true and based on good 11 This distinction is usually traced back to Firth (1978), although it is now ubiquitous	in	the	literature	on	epistemic	justification. 12	In	Smithies	(2019:	Ch.	11),	I	use	the	problem	of	the	speckled	hen	to	motivate	this constraint on proper basing. More specifically, I argue that a belief is properly based on supporting evidence only if it	manifests a	more general disposition to form beliefs that are safe from the absence of evidential support.	On this view, doxastic	justification	requires	safety	from	the	absence	of	propositional	justification just	as	knowledge	requires	safety	from	error.	I	don't	rely	on	this	proposal	here. 13 evidence,	because	it	is	not	properly	based	on	his	evidence.	The	intuitive	problem	is that	his	belief is	held	dogmatically,	which	means	it is	not	sufficiently	sensitive	to changes in	what	his	evidence	supports.	We	can	see this	by	comparing the "good case"	in	which	his	higher-order	evidence	is	misleading	with	the	"bad	case"	in	which his	higher-order	evidence	is	accurate. Let's	set	aside	modally	remote	cases	in	which	the	steadfast	pilot	is	actually suffering from hypoxia, since this dramatically alters his capacity for reasoning. Instead, let's	consider	more	quotidian	cases in	which	his	reasoning	capacities	are held	constant.	Since	his	capacities	are	fallible,	there	are	cases	much	closer	to	home in	which	he	makes	routine	errors in	calculation	through	the	defective	exercise	of those	very	capacities.	Let's	consider	a	bad	case	in	which	he	makes	a	routine	error and	his	co-pilot	points	out	the	mistake.	If	he	is	disposed	to	remain	steadfast	in	the face	of	evidence	that	he	is	hypoxic,	then	he	will	be	equally	disposed	to	ignore	his co-pilot	and	stick	to	his	guns.	Moreover,	both	cases	manifest	the	same	disposition to	dogmatically	retain	beliefs	in	the	face	of	higher-order	evidence	that	those	beliefs are	based	on	bad	reasoning. As	we	saw	in	§3,	Lasonen-Aarnio	makes	similar	points in	arguing	that	the steadfast	pilot is	unreasonable in retaining	his	belief that	he	has	enough fuel. In contrast,	my goal here is to argue that his belief is doxastically unjustified, and hence not a case of knowledge, since it is not properly based on supporting evidence.	In	the	good	case,	his	belief	is	true	and	supported	by	evidence;	but	in	the bad	case, it is false	and	unsupported	by	evidence.	So,	even in the	good	case, the steadfast	pilot	doesn't	have	knowledge,	since	his	belief	manifests	a	disposition	that is not sufficiently sensitive to changes in what his evidence supports. After all, there are close cases in	which	exercising the same	disposition leads	him to	hold false	beliefs	in	the	absence	of	evidential	support. We	can	apply	the	same	reasoning	one	level	up	to	explain	why	the	steadfast pilot cannot have higher-order knowledge or justified belief about his own epistemic	situation.	Suppose	he	believes	not	only	that	he	has	enough	fuel	but	also that his evidence supports this conclusion. Although this higher-order belief is true and supported by conclusive evidence, it is not properly based on this evidence.	After	all,	the	steadfast	pilot	is	disposed	to	believe	exactly	the	same	thing in the bad case in	which	his higher-order belief is false and	unsupported	by	his evidence.	So,	even	in	the	good	case,	he	doesn't	know	that	his	evidence	supports	his conclusion,	since	his	belief	manifests	a	disposition	that	is	not	sufficiently	sensitive to	changes	in	what	his	evidence	supports. I am not claiming that that the steadfast pilot loses knowledge when he acquires	the	higher-order	evidence	that	he	is	hypoxic.	Indeed,	there	is	something deeply puzzling about this suggestion.13 What changes when he acquires the evidence that he is hypoxic? There is no relevant change in what his evidence supports, since it continues to support the conclusion that he has enough fuel. Moreover,	there	is	no	relevant	change	in	his	responsiveness	to	his	evidence,	since 13	Lasonen-Aarnio	(2010:	3-8)	raises	a	version	of	this	puzzle. 14 acquiring	the	higher-order	evidence	makes	no	difference	to	the	basis	on	which	his belief is held. But then how can it be that acquiring this higher-order evidence destroys	his	knowledge? My	answer	is	that	the	steadfast	pilot	doesn't	lose	knowledge,	since	he	never had knowledge to begin with. You cannot acquire knowledge by manifesting dogmatic dispositions that are insensitive to changes in what your evidence supports.	In	contrast,	the	conciliatory	pilot	loses	knowledge	when	he	acquires	the misleading	higher-order evidence	because	he responds	by abandoning	his	belief. There	can	be	no	knowledge	without	belief.	More	importantly,	however,	knowledge sometimes	requires	being	disposed	to	abandon	belief	in	response	to	new	evidence. The conciliatory pilot has knowledge before acquiring the evidence that he is hypoxic only because he is disposed to respond to this new evidence by abandoning	his	belief.	The	conciliatory	pilot	is	more	reliably	sensitive	to	evidence than	the	steadfast	pilot	because	he	is	not	disposed	in	bad	cases	to	ignore	accurate higher-order	evidence	that	he	has	made	a	mistake. I	don't	claim	that	it's	impossible	in	principle	to	retain	knowledge	in	the	face of	misleading	higher-order	evidence,	but	merely	that	it's	impossible	in	practice	for creatures like us. I see no reason to rule out the	metaphysical possibility of an ideally rational agent who is perfectly sensitive to what her evidence supports. Because	she	is	perfectly	sensitive	to	her	evidence,	she	can	remain	steadfast	in	good cases	without running the risk of remaining steadfast in bad cases in	which	her reasoning	dispositions	are	held	constant.14	And	yet this is	beyond	the	capacity	of any	normal	human	agent,	since	we	are	only	imperfectly	sensitive	to	our	evidence. Any human who remains steadfast in good cases thereby manifests some disposition	to	remain	steadfast	in	bad	cases	too. There	is	a	more	general	moral	to	be	drawn	here.	There	are	cases in	which your evidence supports a conclusion, and	gives you	propositional justification to believe it, although you are psychologically incapable of forming a doxastically justified	belief	that	is	properly	based	on	your	evidence.	We	should	therefore	reject the	doxastic	constraint	on	propositional	justification	stated	below: The	Doxastic	Constraint:	Necessarily,	you	have	propositional	justification	to believe	that	p	only	if	you	have	the	psychological	capacity	to	believe	that	p	in a	way	that	is	doxastically	justified.15 There are independent reasons to reject the doxastic constraint. Suppose you're given a reason-distorting drug that renders you temporarily incapable of responding rationally to your evidence.	Whatever doxastic attitudes you adopt, they	are	guaranteed	to	be	doxastically	unjustified.	It	seems	absurd	to	suppose	that 14	I	don't	claim	that	an ideally	rational	agent	must	be immune	from	hypoxia.	But we	can	ignore	bad	cases	in	which	she	suffers	from	hypoxia,	since	this	changes	her reasoning	dispositions	in	ways	that	make	them	less	than	ideally	rational. 15	Proponents	of	the	Doxastic	Constraint	include	Goldman	(1979)	and	Turri	(2010). 15 merely ingesting this drug undermines your propositional justification to adopt any	doxastic	attitude	at	all.	There is	always	some	doxastic	attitude	that	you	have propositional	justification	to	hold	towards	any	given	proposition.	If	your	evidence is	not	strong	enough	to	justify	either	belief	or	disbelief,	then	you	have	justification to	remain	agnostic	by	default.	Even	so,	there	is	no	guarantee	that	you	are	always psychologically capable of forming a doxastic attitude that is properly based on what your evidence supports. After all, you might just have ingested a reasondistorting	drug. The	natural	thing	to	say	about	the	reason-distorting	drug	is	that	it	impairs your epistemic rationality. It prevents you from properly basing your beliefs on your	evidence	and	thereby	converting	your	propositional	justification	into	doxastic justification. If there are doxastic constraints on propositional justification, however, then	we cannot say this.	We	must say instead that ingesting the drug somehow	changes	what	you	have	propositional	justification	to	believe.	But	this	is hard to reconcile with the evidentialist thesis that you have propositional justification to	believe	whatever is sufficiently supported	by	your	evidence, since ingesting the drug doesn't change what your evidence is or what it supports. Moreover,	it	loses	sight	of	the	intuitive	idea	that	ingesting	the	drug	compromises your epistemic rationality by preventing you from responding appropriately to your	evidence. On	a	plausible	version	of	evidentialism,	there	are	no	doxastic	constraints	on propositional justification. What your evidence supports is one thing, but it's another issue	entirely	whether	or	not	you're	capable	of responding	appropriately by	forming	beliefs	that	are	not	only	supported	by	your	evidence,	but	also	properly based on your evidence.	One theoretical cost of conflating these questions is to obscure	the	epistemic	function	of	higher-order	evidence. 5. Non-Ideal	Rationality Any plausible account of the epistemic function of higher-order evidence must explain	two	intuitive	data	points	about	the	hypoxia	example: (1) The	Negative	Datum:	You	cannot	know	or	rationally	believe	that	you	have enough	fuel	given	higher-order	evidence	that	you're	hypoxic (2) The	Positive	Datum:	You	are	rationally	required	to	withhold	belief	that	you have	enough	fuel	given	higher-order	evidence	that	you're	hypoxic. I explained the negative datum in §4, but this is not yet to explain the positive datum. After all, a reason-distorting drug might prevent you from rationally believing what your evidence supports without thereby imposing any rational requirement	to	refrain	from	believing	what	your	evidence	supports.	Indeed,	there is something puzzling about the very idea of such a requirement. According to evidentialism,	epistemic	rationality	is	simply	a	matter	of	proportioning	your	beliefs to	your	evidence.	So	how	can	epistemic	rationality	ever	require	you	to	refrain	from believing	what	your	evidence	supports? 16 To	answer	this	question,	we	need	a	distinction	between	ideal	and	non-ideal standards of epistemic rationality. 16 By ideal standards, epistemic rationality always requires respecting your evidence. This is an epistemic ideal that sometimes	falls	beyond	our	limited	human	capacities:	we	are	not	always	capable	of rationally	following	our	evidence	where	it	leads.	Moreover,	we	know	this	–	at	any rate, we should know this – since we all have compelling evidence of our own cognitive limitations. By non-ideal standards, in contrast, epistemic rationality sometimes	requires	responding	to	such	evidence	by	adopting	policies	that	diverge from the epistemic ideal. In particular,	we are sometimes required by non-ideal standards to "bracket" our first-order evidence when we have higher-order evidence	that	we	cannot	reliably	follow	our	first-order	evidence	where	it	leads. This	is	what	happens	in	the	hypoxia	example.	When	you	acquire	the	higherorder	evidence	that	you	cannot	respond	rationally	to	your	first-order	evidence,	you are	required	to	"bracket"	this	evidence	and	refrain	from	believing	what	it	supports –	namely,	that	you	have	enough	fuel.	Given	evidence	of	cognitive	impairment,	the sensible strategy is to become agnostic, rather than trying to believe	what your evidence	supports.	On	this	view,	the	epistemic	function	of	higher-order	evidence	is not	to	defeat	your	first-order	evidence	and	thereby	to	affect	which	conclusions	are supported by your total evidence. Rather, it determines	which response to your evidence	is	required	by	non-ideal	standards	of	epistemic	rationality. This is an instance	of a	much	more	general	point. It	doesn't always	make sense to try to	do	what	you	know	would	be	best if	only	you	succeed in	doing it. After	all,	you	sometimes	know	–	or	have	good	evidence	–	that	your	attempt	to	do the	best thing	may	not succeed. In such cases, trying to	do the	best thing	often risks	a	worse	outcome	than	would	be	achieved	by	settling	for	second	best.	Hence, what is	best	by ideal	standards is	not	always	what is	best	by	non-ideal	standards that	take	into	account	your	evidence	about	your	own	limitations. We	can	articulate	this	general	point	more	precisely	within	the	framework	of rule consequentialism,	which	evaluates	rules	by	their	expected	consequences.	We can	evaluate	rules	in	a	way	that	is	sensitive	to	the	distinction	between	following	a rule	and	merely	trying	to	follow	a	rule.	Following	a	rule	is	a	kind	of	achievement: merely	trying	to	the	follow	the	rule	doesn't	guarantee	that	you	will	succeed.	When you have evidence that you might fail, the expected consequences of trying to follow a rule can diverge from those of successfully following the rule. In such cases,	the	best	rule	to	follow	is	not	always	the	best	rule	to	try	to	follow.17 Consider	Professor	Procrastinate	who is invited	to	review	a	book.18	He	has three	options	available,	which	are	listed	below	in	rank	order	from	best	to	worst: (1) Accept	the	invitation	and	complete	the	review	on	time. (2) Decline	the	invitation. 16	Compare	Smithies	(2015;	2019:	Ch.	10;	forthcoming)	for	this	distinction. 17	Compare	Lasonen-Aarnio	(2010:	14-15)	and	Schoenfield	(2015:	650-3). 18	The	example	is	from	Jackson	and	Pargetter	(1986). 17 (3) Accept	the	invitation	and	fail	to	complete	the	review	on	time. Which option should he take? There is no single answer to this question, since deontic	modals	in	ordinary	language	are	highly	context-sensitive.	There	is	a	sense in	which	he	should	accept	the	invitation	and	complete	the	review	on	time,	since	he knows	this	is	the	best	possible	outcome.	But	he	also	knows	(or	has	good	evidence) that	he	won't	complete	the	review	on	time:	if	he	tries	to	achieve	the	best	outcome, then	he	is	more	likely	to	bring	about	the	worst	outcome.19	Hence,	there	is	a	sense in	which	he	should	decline	the	invitation.	Rather	than	trying	to	do	what	is	best,	it makes	more	sense	to	settle for	second	best.	By ideal	standards,	he	should	accept the invitation	and	complete	the	review	on	time,	whereas	by	non-ideal	standards, he	should	decline. We	can	capture	this	distinction	in	the	framework	of	rule-consequentialism. Rule	(1)	is	the	best	rule	to	follow,	but	it	is	not	the	best	rule	to	try	to	follow.	After all, the expected consequence of trying to follow	Rule (1) is that he	will end up following	Rule	(3)	instead.	The	expected	consequence	of	trying	to	follow	Rule	(2), however,	is	that	he	will	succeed.	And	there	is	greater	expected	value	in	following Rule (2) than	Rule (3).	Hence, there is	greater	expected	value in trying to follow Rule (2) than Rule (1), despite the fact that there is greater expected value in successfully following	Rule (1) than	Rule (2).	This is	why ideal standards require following	Rule	(1),	although	non-ideal	standards	require	following	Rule	(2). When	we're evaluating epistemic rules, we're concerned solely with their expected	epistemic	consequences.	And	when	we're	evaluating	them	for	epistemic rationality,	we're	specifically	concerned	with	their	expected	consequences	for	how well you succeed in proportioning your beliefs to your evidence. 20 From an evidentialist perspective, the best rule to follow is the evidentialist rule, "Always proportion	your	beliefs	to	your	evidence!"	By	ideal	standards,	epistemic	rationality always	requires	following	the	evidentialist	rule. Since we are not perfectly rational agents, however, we are not always capable of following the evidentialist rule.	Moreover, this is not always the best rule to try to follow when you have evidence that you may fail. There may be greater expected epistemic value in trying to follow some alternative rule, since you are likely to	manifest	more evidence-sensitive dispositions by adopting this alternative	strategy.	In	such	cases,	trying	to	follow	the	evidentialist	rule	is	a	kind	of self-sabotage:	it's	a	counterproductive	strategy	for	maximizing	your	responsiveness 19	As	far	as	I	can	discern,	it	makes	no	difference	whether	his	evidence	is	misleading. Perhaps	there	are	contexts	in	which	our	intuitions	about	what	people	ought	to	do track	their	actual	tendencies,	rather	than	their	evidence	about	them,	but	there	are also	contexts	in	which	it	is	their	evidence	that	matters. 20 In contrast, Lasonen-Aarnio (2010) is concerned with expected epistemic consequences	for	knowledge,	while	Schoenfield	(2015)	is	concerned	with	expected accuracy,	whereas I am	concerned	with	expected	epistemic rationality construed as	responsiveness	to	evidence. 18 to evidence. This is why you are sometimes required by non-ideal standards of epistemic	rationality	to	refrain	from	believing	what	your	evidence	supports. Now	let's	apply	this	distinction	to	the	hypoxia	example.	When	you	receive the	higher-order	evidence	that	you	are	hypoxic,	you	have	three	options: (1) Steadfastness:	Maintain your first-order belief that you have enough fuel and also your higher-order belief that your evidence supports this conclusion. (2) Level Splitting:	Maintain	your	first-order	belief	that	you	have	enough	fuel, but abandon your higher-order belief that your evidence supports this conclusion. (3) Conciliation:	Abandon	your	first-order	belief	that	you	have	enough	fuel	and also	your	higher-order	belief	that	your	evidence	supports	this	conclusion. Which	option	should	you	take?	Again,	there	is	no	single	answer	this	question.	By ideal standards, you should follow Steadfastness, since this is the best rule to follow: the expected consequence of successfully following this rule is that your beliefs are proportioned to your evidence. By	non-ideal standards, however, you should	follow	Conciliation,	since	this	is	the	best	rule	to	try	to	follow.	As	I'll	explain, there is greater expected epistemic value in trying to follow Conciliation than either	Steadfastness	or	Level	Splitting.21 The	expected	consequence	of	trying	to	follow	Steadfastness	is	that	you	will be like the steadfast pilot.22	As	we saw in	§4, the steadfast	pilot cannot	know	or rationally believe that he has enough fuel whether or not he has higher-order evidence	that	he	is	hypoxic.	This	is	because	his	belief	is	held	dogmatically	in	a	way that is insufficiently sensitive to changes in what his evidence supports. He is disposed	to	maintain	his	belief	when	he	acquires	the	higher-order	evidence	that	it is	based	on	bad	reasoning.	And	he	is	disposed	to	maintain	his	belief	not	only	in	the good case in	which his higher-order evidence is	misleading, but also in the bad case	in	which	his	higher-order	evidence	is	accurate.	Dogmatic	beliefs	of	this	kind are	not	rational	enough	to	constitute	knowledge. In contrast, the expected consequence of trying to follow Conciliation is that	you	will	be	like	the	conciliatory	pilot.	The	conciliatory	pilot	rationally	believes and	knows	that	he	has	enough	fuel	before	acquiring	the	higher-order	evidence	that he	is	hypoxic,	so	long	as	he	is	disposed	to	become	agnostic	when	he	acquires	this higher-order	evidence.	Hence, there is	greater	expected	epistemic	value in	trying to follow Conciliation than Steadfastness: this strategy increases your expected degree	of	epistemic	rationality	by	making	your	beliefs	more	sensitive	to	changes	in 21	Schoenfield	(2015:	652)	gives	a	different	argument	for	the	same	conclusion. 22	Similarly,	the	expected	consequence	of	trying	to	follow	Level	Splitting	is	that	you will	be	like	the	steadfast	pilot	at	level	one	and	the	conciliatory	pilot	at	level	two. 19 what	your	evidence	supports.	This	is	why	you	are	required	by	non-ideal	standards of epistemic rationality to become agnostic when you acquire the higher-order evidence	that	you	are	hypoxic. In	this	way,	we	can	explain	the	positive	datum	as well	as	the	negative	datum. In	summary,	the	epistemic	function	of	higher-order	evidence	is	not	only	to prevent	you	from	responding	properly	to	your	evidence	in	the	way	that	is	required by ideal standards	of	epistemic	rationality. It	also	affects	which	response to	your evidence is required by non-ideal standards of epistemic rationality that are sensitive	to	your	evidence	about	your	cognitive	limitations. 6. Conclusions Let me conclude by summarizing the reasons for preferring my account of the epistemic	function	of	higher-order	evidence	to	the	alternatives	discussed	earlier	in this	chapter. First,	my	view	explains	the intuitive	datum	that	you	lose	knowledge	when you	acquire the	higher-order	evidence that you	are	hypoxic. In this respect, it is preferable to the	unreasonable knowledge view.	What this view	gets right is that the	steadfast	pilot	manifests	bad	dispositions	when	he	retains	his	belief	in	the	face of	misleading	higher-order	evidence.	What	it	gets	wrong	is	that	manifesting	these bad dispositions is compatible	with knowledge. The steadfast pilot doesn't have knowledge because his dispositions are not sufficiently sensitive to changes in what	his	evidence	supports.	It's	possible	in	principle	for	ideally	rational	agents	to retain knowledge in the face of misleading higher-order evidence, but this is impossible	in	practice	for	non-ideal	agents	like	us. Second, my view explains this intuitive datum without distorting the structure	of	the	evidential	support	relation	in	ways	that	compromise	the	objective constraints	imposed	by	logic	and	probability	theory.	In	this	respect,	it	is	preferable to the	evidential defeat	view.	What this	view	gets right is that	your	knowledge is destroyed	when	you	acquire	the	higher-order	evidence	that	you	are	hypoxic.	What it gets wrong is that this is to be explained by a change in	what your evidence supports. My view explains how you can lose your knowledge of a conclusion without losing your evidential support for that conclusion. Misleading higherorder evidence can prevent you from	properly basing your beliefs on	what your total	evidence	supports. Third, my view explains this intuitive datum without any bifurcation between substantive and structural requirements	of epistemic rationality. In this respect,	it	is	preferable	to	the	epistemic	conflict	view.	What	this	view	gets	right	is that	epistemic	rationality	somehow	requires	"bracketing"	your	first-order	evidence when	you	have	misleading	higher-order	evidence.	What	is	gets	wrong	is	that	this	is because your total evidence supports incoherent beliefs. On the contrary, it is because	misleading	higher-order	evidence	prevents	non-ideal	agents	from	properly basing	their	beliefs	on	their	evidence.	As	a	result, they	are	required	by	non-ideal standards of epistemic rationality to manage their cognitive limitations by adopting	policies	that	deviate	from	the	epistemic	ideal	of	respecting	the	evidence. 20 The	"rationally	toxic"	nature	of	higher-order	evidence	is	best	explained	in	terms	of a distinction between ideal and non-ideal requirements of epistemic rationality, rather than a distinction between substantive and structural requirements of epistemic	rationality. In conclusion, my proposal accommodates the intuitive data about the epistemic function	of	higher-order	evidence	with	minimal theoretical	mutilation. We	can	explain	why	you	should	conciliate	in	response	to	misleading	higher-order evidence	without	abandoning	evidentialism	or	compromising	the	objective	logical and	probabilistic constraints	on the	evidential support relation.	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