Forthcoming	in	American	Philosophical	Quarterly Recent Work in the Epistemology of Understanding Michael	Hannon University	of	Nottingham Abstract The	philosophical	interest	in	the	nature,	value,	and	varieties	of	human	understanding	has	swelled in	recent	years.	This	article	will	provide	an	overview	of	new	research	in	the	epistemology	of understanding,	with	a	particular	focus	on	the	following	questions:	What	is	understanding	and	why should	we	care	about	it?	Is	understanding	reducible	to	knowledge?	Does	it	require	truth,	belief,	or justification?	Can	there	be	lucky	understanding?	Does	it	require	'grasping'	or	some	kind	of	'knowhow'?	This	cluster	of	questions	has	largely	set	the	research	agenda	for	the	study	of	understanding in	epistemology.	This	article	will	conclude	by	discussing	some	varieties	of	understanding	and highlight	directions	for	future	research. Humans	are	naturally	inquisitive	creatures.	As	Aristotle	observed,	"All	men	by	nature	desire	to	know." But	knowledge	is	not	the	only	intellectual	achievement	at	which	humans	aim,	and	it	might	not	be	the most	valuable.	As	Albert	Einstein	once	said,	"Any	fool	can	know;	the	point	is	to	understand."1 It	is	widely	assumed	that	understanding	is	a	valuable	intellectual	achievement;	however,	the	cognitive state	of	understanding	is	itself	poorly	understood.	What	is	understanding?	Why	is	it	valuable?	And	how do	we	achieve	it?	These	questions	are	at	the	forefront	of	recent	work	in	the	epistemology	of understanding.	In	this	article,	I	will	attempt	to	give	a	sense	of	the	range	and	depth	of	this	new	research on	the	nature,	value,	and	varieties	of	human	understanding.	I	will	also	critically	evaluate	some	of	this work. 1	The	Aristotle	quote	is	from	the	opening	line	of	his	Metaphysics.	The	Einstein	quote	can	be	found	in	Christian (1990,	p.	207). 2 Understanding	in	Epistemology The	philosophical	interest	in	understanding	has	swelled	in	recent	years.	In	epistemology,	scholars	have attempted	to	explore	the	nature,	value,	and	varieties	of	understanding	largely	by	comparison	with knowledge.	This	methodology	isn't	surprising.	Knowledge	has	been	a	focal	point	of	modern epistemology,	and	the	language	of	"knowing"	is	closely	related	to	the	language	of	"understanding."	For example,	"knows"	and	"understands"	come	in	the	same	linguistic	forms:	just	as	one	can	know-that, know-how,	know-who,	know-what,	know-where,	know-when,	and	know-why,	one	can	also	understandthat,	understand-how,	understand-who,	and	so	forth	(Kvanvig	2009,	p.	96).	Moreover,	the	terms "knows"	and	"understands"	are	sometimes	interchangeable;	for	instance,	"I	know	that	two	plus	two equals	four"	seems	to	express	the	same	thought	as	"I	understand	that	two	plus	two	equals	four" (Hannon	2019,	p.	223).	Knowing	and	understanding	thus	seem	like	closely	related	cognitive achievements.	According	to	some	scholars,	the	contrast	between	knowing	and	understanding	is superficial	(see	Brogaard	2005). However,	ordinary	parlance	also	points	to	some	important	differences	between	knowing	and understanding.	For	example,	Einstein's	abovementioned	remark	implies	that	understanding	is	a	much greater	cognitive	achievement	than	mere	knowing.	Duncan	Pritchard	echoes	this	idea:	"We	would	surely rather	understand	than	merely	know"	(2010,	p.	74).	Knowledge	and	understanding	are	often	contrasted in	a	way	that	indicates	that	understanding	may	require	a	level	of	intellectual	sophistication	that	is	not necessarily	demanded	by	knowledge.	We	find	additional	support	for	this	idea	by	looking	at	other languages.	As	Alison	Hills	(2016,	pp.	668-9)	reports,	many	languages	draw	a	similar	distinction	between knowing	and	understanding,	including	French: Je	sais	que...	I	know	that	... Je	comprends	que	...	I	understand	that	... Je	sais	pourquoi...	I	know	why... Je	comprends	pourquoi...	I	understand	why... and	German Ich	weiss	dass...	I	know	that... Ich	verstehe	dass...	I	understand	that... 3 Ich	weiss,	warum...	I	know	why	... Ich	verstehe,	warum...	I	understand	why	... The	distinction	between	knowing	and	understanding	can	also	be	found	in	Russian,	Hebrew,	Danish,	and Irish,	amongst	others	languages	(Hills	2016,	p.	668). This	linguistic	data	gives	some	prima	facie	support	to	the	idea	that	knowing	and	understanding	are distinct	states.	Presumably	we	wouldn't	find	this	distinction	in	many	natural	languages	if	knowledge	and understanding	were	simply	interchangeable	or	referred	to	the	same	concept.	This	linguistic	evidence	is not	conclusive,	but	it	is	suggestive. The	comparison	between	understanding	and	knowledge	has	led	philosophers	to	concentrate	their analyses	on	the	following	set	of	questions:	Is	understanding	reducible	to	knowledge?	Does	it	require truth?	Can	there	be	lucky	understanding?	Is	it	transmittable	via	testimony?	Is	it	transparent	in	the	sense that	we	know	when	we	have	achieved	it?	This	cluster	of	questions	has	largely	set	the	research	agenda for	the	study	of	understanding	in	epistemology.	Philosophers	have	sought	to	improve	our	understanding of	understanding	by	comparing	it	with	what	we	know	about	knowledge. Let's	start	with	the	question	whether	understanding	is	reducible	to	knowledge.	This	is	one	of	the	most pressing	questions	in	the	epistemology	of	understanding	because	the	reducibility	of	understanding	to knowledge	would	suggest	that	we	do	not	need	separate	accounts	of	these	epistemic	goods.	Also,	if understanding	were	simply	a	type	of	knowledge,	then	it	would	make	little	sense	to	say	that understanding	should	replace	knowledge	as	the	primary	focus	of	epistemology	(e.g.,	Zagzebski	2001; Kvanvig	2003;	Elgin	2006;	Pritchard	2010).	If,	however,	understanding	were	not	reducible	to	knowledge, then	this	would	threaten	the	justification	for	the	focus	on	knowledge	displayed	in	the	history	of epistemology.	Indeed,	"epistemology"	is	typically	defined	as	the	"theory	of	knowledge,"	and	talk	of knowledge	has	dominated	the	bulk	of	modern	literature	in	epistemology.	Thus,	if	understanding	has	a special	status	or	value	that	knowledge	does	not,	then	philosophers	may	be	accused	of	myopically focusing	their	efforts	on	analyzing	knowledge	at	the	expense	of	greater	intellectual	goods. 4 Is	Understanding	a	Kind	of	Knowledge? Understanding,	like	knowledge,	is	an	intellectual	achievement.	It	is	therefore	unsurprising	that,	on	many accounts,	understanding	is	just	a	type	of	knowledge.	This	has	been	the	dominant	view	in	the	philosophy of	science	and	it	is	also	popular	within	epistemology.	Aristotle	is	perhaps	the	most	prominent	defender of	this	view	(Posterior	Analytics	71b9-11).	He	maintained	that	understanding	is	simply	knowledge	of causes.	More	specifically,	understanding	why	X	is	the	case	is	equivalent	to	knowing	why	X	is	the	case; and	this,	in	turn,	is	equivalent	to	knowing	that	X	because	of	Y.	For	example,	my	understanding	of	why my	eyes	are	watering	is	equivalent	to	my	knowing	why	my	eyes	are	watering,	where	this	is	tantamount to	knowing	that	my	eyes	are	watering	because	(say)	I	am	chopping	onions. In	the	philosophy	of	science,	the	view	that	understanding	is	just	a	type	of	knowledge	has	been	defended by	Peter	Achinstein	(1983),	Wesley	Salmon	(1984),	James	Woodward	(2003),	Peter	Lipton	(2004,	2009), Kareem	Khalifa	(2011,	2012,	2017),	and	Mark	Newman	(2017).	In	epistemology,	it	has	been	taken	up	by Berit	Brogaard	(2005),	Stephen	Grimm	(2006,	2012,	2014),	John	Greco	(2014),	Christoph	Kelp	(2014, 2015,	2017),	Paulina	Sliwa	(2015),	and	Amber	Riaz	(2015),	among	others.	For	simplicity,	I	will	use	the label	"reductionism"	for	the	view	that	understanding	is	a	species	of	knowledge. Others	have	opposed	the	reduction	of	understanding	to	knowledge.	According	to	these	"antireductionists,"	understanding	demands	more	than	knowledge.	Defenders	of	this	view	include	Linda Zagzebski	(2001),	Jonathan	Kvanvig	(2003),	Catherine	Elgin	(2004,	2007,	2009,	2017),	Duncan	Pritchard (2009,	2010),	Alison	Hills	(2016),	Wayne	Riggs	(2009),	Christoph	Baumberger	(2011),	Mikael	Janvid (2012),	Kevin	Morris	(2012),	Yasha	Rohwer	(2014),	Henk	de	Regt	(2015,	2017),	Sabine	Ammon	(2016), Insa	Lawler	(2016),	Daniel	Wilkenfeld	(2017),	and	Finnur	Dellsén	(2017).	These	anti-reductionists	have denied	the	reducibility	of	understanding	to	knowledge	on	various	grounds,	which	I	will	explore	in	a moment.	Let's	first	consider	the	reasons	in	favor	of	reductionism. Why	think	that	understanding	is	just	a	form	of	knowledge?	On	several	accounts,	it	is	because	the conditions	for	understanding	closely	resemble	the	well-known	traditional	conditions	of	knowledge: belief,	justification,	and	truth	(Gettier	1963).	As	Baumberger	and	colleagues	observe,	understanding seems	to	require	individuals	to	"possess	a	representation	of	what	is	understood,"	and	it	is	plausible	that "the	representation	must	in	some	way	be	accepted	by	the	agent"	(Baumberger	et	al.	2017,	p.	6).	Thus, 5 we	end	up	with	a	condition	that	parallels	the	belief	condition	for	knowledge.	Moreover,	it	seems	natural to	say	that	one	lacks	understanding	if	one	is	unable	to	"provide	good	reasons	for	the	representation	that underlies	her	understanding"	(Baumberger	et	al.	2017,	p.	6).	This	parallels	the	justification	condition	for knowledge.	Finally,	it	seems	that	an	individual	lacks	proper	understanding	if	their	representation	does not	fit	the	facts:	one	who	misrepresents	the	world	fails	to	understand	it.	Thus,	understanding	seems	to require	a	truth	condition	(Baumberger	et	al.	2017,	p.	6). These	ideas	are	not	uncontroversial.	In	recent	work,	each	of	these	conditions	has	been	denied	as necessary	for	understanding.	Whether	or	not	understanding	requires	belief,	justification,	or	truth	is	an important	issue	in	epistemology.	If	reductionism	is	true	and	if	knowledge	requires	belief,	justification, and	truth,	then	it	immediately	follows	that	one	cannot	have	understanding	without	each	of	these conditions.	However,	if	it	could	be	shown	that	belief,	justification,	or	truth	is	not	necessary	for understanding,	this	would	entail	that	understanding	is	not	a	species	of	knowledge.	I	will	briefly	consider each	of	these	issues	below. Belief	and	Understanding It	is	widely	accepted	that	you	can	only	know	what	you	believe.	For	example,	if	I	do	not	believe	that	there is	coffee	in	my	cup,	then	I	cannot	know	there	is	coffee	in	my	cup.	Is	the	same	true	for	understanding? Reductionists	must	think	so.2	However,	Wilkenfeld	(2017)	presents	a	case	in	which	an	agent	seems	to understand	why	p	and	yet	does	not	fully	believe	the	explanation	for	why	p.	Here	is	the	case: Challenger:	Richard	is	an	established	and	skilled	scientist	tasked	with	investigating	why	the	Challenger	space shuttle	exploded.	His	investigative	instincts	are	excellent,	and	he	is	immediately	suspicious	of	the	O-Rings' ability	to	operate	at	cold	temperatures.	In	fact,	the	reason	the	Challenger	exploded	was	because	of	O-Ring failure.	Sadly,	before	he	goes	public	he	is	subjected	to	a	deliberate	cover-up,	casting	doubt	on	whether	the O-Rings	failed	in	this	case.	Arbitrarily	large	amounts	of	evidence	can	be	presented	that	there	really	was	no O-Ring	failure,	to	the	point	that	Richard	loses	confidence	in	his	belief	that	the	Challenger	exploded	because of	O-Ring	failure.	He	is	now	only	about	30%	confident	that	the	Challenger	explored	because	of	the	O-Ring failure.	However,	Richard	still	has	a	detailed	model	of	how	O-Ring	failure	would	cause	the	explosion. Moreover,	when	he	pictures	the	explosion,	it	is	often	accompanied	by	the	fleeting	suspicion	that	the	O- 2	Even	some	anti-reductionists	claim	that	understanding	requires	belief	(e.g.	Kvanvig	2003;	Hills	2016;	Pritchard	2009). 6 Rings	might	have	failed.	Richard	is,	in	fact,	the	world's	preeminent	expert	on	the	cause	of	the	Challenger explosion-he	just	fails	to	believe	his	own	conclusions. According	to	Wilkenfeld,	it	seems	right	to	say	that	Richard	understands	why	the	Challenger	exploded even	though	he	does	not	believe	the	correct	explanation.	Wilkenfeld	concludes	that,	unlike	knowledge, understanding	does	not	require	(full)	belief. But	Wilkenfeld's	argument	can	be	challenged	in	at	least	two	ways.	First,	we	may	question	the	purported intuition	that	Richard	understands	why	the	Challenger	exploded.	For	example,	if	I	were	to	simply	ask Richard	why	he	thinks	the	Challenger	exploded,	Richard	would	either	say	he	does	not	understand	why	it exploded	or	he	would	cite	an	incorrect	explanation	for	the	cause	of	the	explosion.	After	all,	Richard	is only	30%	confident	that	the	O-Rings	failure	was	the	cause	of	the	disaster.	Thus,	it	seems	odd	to	say	that Richard	understands	why	the	challenger	exploded	given	that	he	himself	would	not	identify	the	O-Ring failure	as	the	reason	why. Second,	Wilkenfeld's	argument	involves	a	sleight	of	hand.	According	to	the	traditional	view	of knowledge,	belief	is	necessary	in	the	sense	that	one	cannot	know	that	p	without	believing	that	p.	Thus, it	is	impossible	to	know	that	the	Challenger	exploded	without	believing	that	it	exploded.	Now	consider the	analogous	case	of	understanding:	to	understand	that	(or	why)	p,	one	must	believe	that	p.	This	seems uncontroversial.	If	Richard	did	not	believe	that	the	Challenger	exploded,	then	he	would	not	understand that	(or	why)	it	exploded.	In	this	sense,	one	cannot	have	understanding	without	belief. This	illustrates	that	understanding	requires	belief	in	the	very	same	way	that	knowledge	requires	belief: just	as	one	cannot	know	that	p	without	believing	that	p,	one	also	cannot	understand	that	(or	why)	p without	believing	that	p. There	may	be	other	types	of	understanding	that	do	not	require	belief.	For	example,	I	can	understand phlogiston	theory,	or	astrology,	or	creationism	without	believing	any	of	these	theories.	Similarly,	a devout	creationist	may	understand	the	theory	of	evolution	perfectly	well	without	believing	that	it describes	the	origins	of	humanity.	Assuming	the	theory	of	evolution	is	true,	we	would	not	say	that	the creationist	understands	why	humanity	exists	or	has	the	features	it	does	(Wilkenfeld	2017,	p.	319). However,	these	are	cases	in	which	one	who	understands	the	theory	still	believes	that	the	theory	says 7 such-and-such.	Admittedly,	one	may	understand	the	content	of	the	theory	without	believing	it;	in	these cases,	we	understand	the	content	of	a	theory	without	believing	that	the	theory	accurately	represents the	world.	Thus,	the	theory	does	not	enable	one	to	understand	why	the	relevant	phenomenon	occurs. But	if	we	do	not	believe	that	it	accurately	represents	the	world,	then	we	cannot	possibly	understand that	(or	why)	it	accurately	represents	the	world. Taking	another	line	of	argument,	Elgin	(2004)	and	Dellsén	(2017)	say	that	understanding	does	not require	belief,	but	rather	acceptance.	On	L.	J.	Cohen's	(1992)	distinction,	one	believes	that	p	just	in	case one	is	normally	disposed	to	feel	it	true	that	p	(and	false	that	not-p)	when	one	is	attending	to	issues raised	by	p.	By	contrast,	one	accepts	that	p	just	in	case	one	treats	it	as	given	that	p;	that	is,	just	in	case one	"adopts	a	policy	of...including	[p]	among	one's	premises	for	deciding	what	to	do	or	think	in	a particular	context"	(Cohen	1992,	p.	4).	According	to	Dellsén	(2017,	p.	248),	"understanding	something may	merely	involve	treating	certain	propositions	or	theories	as	given	in	the	context	of	explaining something,	as	opposed	to	being	disposed	to	feel	that	the	propositions	or	theories	are	true."	He	provides the	following	case	to	illustrate	this	point: String	Theory:	Carrie	is	a	theoretical	physicist	in	a	nearby	possible	world	(perhaps	this	one)	in	which	string theory	is	true.	Carrie	has	built	her	career	around	using	string	theory	to	explain	various	known	phenomena about	the	natural	world,	and	has	become	one	of	the	world's	leading	contributors	in	the	field	because	of	her unmatched	insight	into	the	theory	and	its	applications.	Moreover,	she	has	adopted	the	policy	of	treating string	theory	as	given	in	her	scientific	endeavors	–	using	it	in	explanations	of	various	natural	phenomena	– and	thus	accepts	string	theory	for	explanatory	purposes.	However,	like	many	other	physicists,	Carrie	has significant	methodological	reservations	about	string	theory	in	its	current	form,	and	therefore	is	not disposed	to	feel	that	string	theory	is	even	approximately	true.	In	other	words,	Carrie	does	not	believe	that string	theory	is	even	approximately	true.	(Dellsén	2017,	p.	249) According	to	Dellsén,	Carrie	understands	the	fundamental	structure	of	her	world	that	string	theory	is meant	to	describe.	Thus,	we	(allegedly)	have	a	case	of	understanding	without	belief. However,	this	is	not	obviously	a	case	of	understanding	without	the	relevant	belief.	What	Carrie understands	is	"the	fundamental	structure	of	her	world	that	string	theory	is	meant	to	describe"	(Dellsén 2017,	p.	249).	But	what	she	fails	to	believe	is	something	different,	namely,	she	doesn't	believe	that string	theory	explains	the	fundamental	structure	of	her	world.	The	object	of	understanding	has	shifted, 8 so	the	counterexample	fails	to	establish	its	point.	Although	this	is	a	case	of	understanding	without	belief, it	is	not	a	clear	case	of	understanding	p	without	believing	p.	Indeed,	it	makes	no	sense	to	say	that	Carrie understands	the	fundamental	structure	of	her	world	that	string	theory	is	meant	to	describe	but	she	does not	believe	the	fundamental	structure	of	her	world	that	string	theory	is	meant	to	describe. Justification	and	Understanding It	is	widely	assumed	that	knowledgeable	beliefs	must	be	arrived	at	in	the	right	way;	for	instance,	a	lucky guess	wouldn't	suffice	for	knowledge,	nor	would	a	belief	based	on	defeated	evidence.	In	these	cases, one	does	not	have	the	right	kind	of	justification	for	knowledge.	Does	understanding,	like	knowledge, require	justification? Hills	(2016)	argues	that	understanding	differs	from	knowledge	because	only	the	former	is	compatible with	defeaters	that	undermine	one's	justification.	Consider	the	following	case: Napoleon:	Suppose	that	you	read	a	history	book	with	many	details	about	Napoleon's	career-that	he	was well-organized,	tactically	astute	and	ruthless,	and	on	that	basis	you	draw	the	conclusion	that	he	was	a	great military	leader.	You	are	completely	right	and	you	are	able	to	explain	why	he	was	a	great	leader.	You	can	also explain	why	similar	figures	(e.g.,	Wellington	and	Marlborough)	were	also	very	good	commanders.	But	now your	history	teacher,	whom	you	regard	as	extremely	trustworthy,	tells	you	that	Napoleon	was	not	a	great leader.	Your	teacher	is	not	basing	this	judgement	on	other	information	or	on	a	different	interpretation	of what	it	takes	to	be	a	great	general:	he	simply	irrationally	dislikes	Napoleon.	You	have	no	idea	about	any	of this,	but	even	so,	you	ignore	your	teacher	and	continue	to	maintain	your	conclusion.	(Hills	2016,	p.	672) In	this	case,	Hills	says	that	you	understand	why	Napoleon	was	a	great	general.	Your	beliefs	are	correct and	you	seem	to	possess	the	abilities	required	for	understanding;	thus,	you	do	understand	why Napoleon	was	a	great	general.	However,	it	seems	incorrect	to	say	that	you	know	why	he	was	a	great general-at	least	according	to	the	standard	account	of	knowledge.	You	have	evidence	that	your conclusion	is	false,	which	undermines	your	justification.	Although	you	choose	to	ignore	the	evidence,	it nonetheless	defeats	your	justification	because	it	is	based	on	seemingly	reliable	testimony.	Thus,	you cannot	know	that	(or	why)	Napoleon	was	a	great	general,	even	though	you	understand	why	he	was.	This allegedly	shows	that	understanding	does	not	require	justification,	or	at	least	the	same	level	of justification	as	knowledge. 9 Hills	assumes	that	we	will	agree	with	her	that	this	is	a	case	of	understanding	without	knowledge	(or justification).	She	writes,	"it	is	natural	to	say	that	you	understand	why	Napoleon	was	a	great	general	in these	examples"	and	"you	plainly	do	not	know	.	.	.	why	Napoleon	was	a	great	general"	(2016,	p.	672).	I wonder	whether	others	will	feel	the	pull	of	Hill's	intuitive	judgment.	For	what	it's	worth,	I	do	not. Indeed,	it	also	seems	natural	to	say	that	you	cannot	possibly	understand	why	Napoleon	was	a	great general	if	you	do	not	know	that	(or	why)	he	was.	As	Hills	herself	acknowledges,	any	sentence	of	the	form "You	understand	why	p	but	you	do	not	know	why	p"	sounds	wrong	(2016,	p.	677).	To	avoid	this objection,	she	says	our	intuitions	about	this	case	ought	to	be	explained	away.	However,	we	may	instead explain	away	the	intuitions	that	drive	Hills	to	claim	that	understanding	is	possible	in	the	absence	of knowledge.	Perhaps	it	makes	more	sense	to	say	that	you	think	you	understand	why	Napoleon	was	a great	general,	while	genuine	understanding	is	not	compatible	with	denying	contrary	evidence	from	an "extremely	trustworthy"	source	of	relevant	information.	Ultimately,	one	wonders	how	much	stock	we should	put	in	these	intuitions.	Nevertheless,	Hills's	argument	is	important	because	it	illustrates	that understanding	may	be	irreducible	to	knowledge,	in	which	case	the	traditional	view	of	understanding	in the	philosophy	of	science	is	mistaken. Finnur	Dellsén	(2017)	also	attempts	to	drive	a	wedge	between	understanding	and	justification	by	using thought	experiments.	He	provides	the	following	hypothetical	case	in	which	an	agent	allegedly	grasps	the explanatory	relations	required	for	understanding	and	yet	fails	to	have	justification: Geometry:	Alice	is	a	struggling	middle-school	student	who	is	yet	to	find	her	true	academic	calling.	Having failed	miserably	at	every	school	assignment	this	year,	Alice	now	encounters	geometry	for	the	first	time	in her	life.	Unbeknownst	to	her,	Alice	has	an	innate	knack	for	geometry	and	therefore	(rather	impressively) succeeds	in	deriving	the	Pythagorean	theorem	using	a	version	of	Pythagoras's	original	proof	without consulting	any	teacher	or	textbook.	However,	from	Alice's	point	of	view,	her	proof	of	the	Pythagorean theorem	is	no	different	than	her	previous	attempts	at	understanding	new	subject	matters	in	school	this year	(all	of	which	were	failures).	So	Alice	has	good	reasons	to	believe	that	this	attempt	at	understanding	a new	subject	matter	in	school	is	a	failure	as	well	as	all	past	attempts	this	year,	and	thus	she	is	not	justified	in believing	that	the	Pythagorean	theorem	is	true	(or	that	the	proof	is	correct).	(Dellsén	2017,	p.	242) According	to	Dellsén,	"Alice	clearly	understands	the	Pythagorean	theorem"	(2017,	p.	243)	despite lacking	justification. 10 We	may	doubt	this	claim	for	a	number	of	reasons.	First,	we	may	simply	doubt	that	Alice	believes	that she	has	derived	the	Pythagorean	theorem.	After	all,	she	is	aware	that	her	proof	"is	no	different	than	her previous	attempts	at	understanding	new	subject	matters	in	school	this	year	(all	of	which	were	failures)." Why,	then,	would	she	believe	that	her	attempt	was	successful?	Alice	may	lack	understanding	simply because	she	lacks	the	relevant	belief.	In	reply,	Dellsén	says	we	may	"suppose	that	Alice	irrationally forms	this	belief	in	spite	of	her	being	aware	of	her	dreadful	track	record"	(2017,	p.	242n8).	But	if	her belief	is	so	irrational,	then	we	may	begin	to	wonder	whether	she	really	has	understanding	(rather	than just	lucky	true	belief).	Elsewhere,	Dellsén	says	"we	could	easily	stipulate	that	Alice,	for	whatever	reason, got	lucky	in	her	attempt	to	prove	the	Pythagorean	theorem	and	that	she	fails	to	construct	similar	proofs in	geometry	on	other	occasions"	(2017,	p.	243n10).	If	this	is	true,	we	might	doubt	that	Alice	exhibits understanding	rather	than	lucky	true	belief. Setting	this	point	aside,	we	may	also	argue	that	Alice	does	have	the	relevant	justification.	Alice	is	able	to derive	the	Pythagorean	theorem	using	a	version	of	Pythagoras's	original	proof	because	she	grasps	the correct	mathematical	relations	between	the	theorem	and	other	geometrical	facts.	Had	she	not	grasped these	relations,	she	would	lack	understanding.	But	the	very	fact	that	she	grasps	these	relations	is	what justifies	her	beliefs	about	the	proof	she	derives.	It	is	the	very	fact	that	she	grasps	these	relations-not the	fact	that	she	grasps	that	she	grasps	them-that	justifies	her	belief.3	Although	Alice's	awareness	of her	bad	track	record	may	undermine	her	justification	to	believe	that	she	grasps	the	correct	relations,	it needn't	defeat	her	justification	for	understanding	the	Pythagorean	theorem. This	does	not	conclusively	show	that	understanding	requires	justification	or	that	understanding	is reducible	to	knowledge.4	However,	I	have	attempted	to	illustrate	that	some	common	arguments	against the	necessity	of	justification	for	understanding	misfire. Lucky	Understanding It	is	commonly	held	that	knowledge	is	incompatible	with	certain	types	of	luck.	For	example,	if	you	come to	believe	that	it's	2pm	on	the	basis	of	a	clock	that	(unbeknownst	to	you)	has	stopped	12	hours	ago, 3	Kvanvig	(2003,	pp.	193-202)	makes	this	point. 4	That	said,	a	number	of	anti-reductionists	also	claim	that	understanding	requires	justification;	for	example,	Kvanvig	(2003,	p. 202),	Elgin	(2009,	p.	323),	and	Pritchard	(2009,	p.	33). 11 then	you	may	truly	and	justifiably	believe	that	it	is	2pm	even	though	you	do	not	know	this	(Russell	1948; Gettier	1963).	Your	belief	is	just	too	lucky	to	qualify	as	knowledge. Is	understanding	also	incompatible	with	luck?	Many	epistemologists	have	sought	to	distinguish	knowing from	understanding	by	arguing	that	understanding	is	compatible	with	certain	forms	of	knowledgeundermining	luck.	In	particular,	understanding	is	often	said	to	be	compatible	with	"environmental	luck." Environmental	luck	occurs	when	a	true	belief	is	acquired	in	an	epistemically	unfavorable	environment	in which	one	could	easily	have	arrived	at	false	beliefs.5	Consider	the	following	scenario: Orwellian	State.	Winston	is	living	in	an	Orwellian	state	in	which	the	government	attempts	to	falsify	the past.	Winston	is	in	a	room	full	of	elaborately	falsified	history	books,	but	he	luckily	picks	up	the	one accurate	book	that	was	not	destroyed.	As	he	reads	the	book,	he	comes	to	believe	many	of	its	true	claims about	the	past.	To	focus	on	one	claim	in	particular,	suppose	Winston	comes	to	believe	that	the	Comanche dominated	the	southern	plains	of	North	America	during	the	eighteenth	century	because	of	their	superior horsemanship.6 Let's	suppose	that	Winston	grasps	this	explanation,	it	makes	sense	to	him,	and	so	forth.	Does	he	now understand	why	the	Comanche	dominated	the	southern	plains	during	this	period?	According	to	Kvanvig (2003),	Pritchard	(2009),	and	Hills	(2016),	it	seems	that	Winston	does	have	understanding.7	After	all, Winston	can	now	correctly	answer	a	wide	range	of	questions	about	the	Comanche	dominance,	he grasps	the	relevant	connections,	and	so	on. But	does	Winston	also	know	why	the	Comanche	dominated	the	southern	plains?	Many	scholars	are tempted	to	say	that	he	does	not.	Winston's	beliefs	might	easily	have	been	mistaken,	and	one	of	the main	lessons	from	the	literature	on	epistemic	luck	is	that	knowledge	requires	a	more	secure	connection to	the	truth:	it	requires	a	non-accidental	connection	between	mind	and	world. 5	This	type	of	luck	is	often	distinguished	from	"intervening	luck"	(or	"Gettier	luck")	in	which	a	person	has	true	beliefs	only	due	to a	lucky	intervention	"between"	the	facts	and	her	cognitive	abilities	(see	Pritchard	2010,	p.	36).	Zagzebski	(2001),	Kvanvig	(2003), and	Hills	(2016)	claim	that	understanding	(but	not	knowledge)	is	compatible	with	both	types	of	luck.	In	contrast,	Pritchard argues	that	understanding	is	only	compatible	with	environmental	luck.	I	will	set	aside	intervening	luck	because	the	intuitions driving	this	debate	are	even	more	controversial	than	the	intuitions	about	environmental	luck.	This	point	is	acknowledged	by both	proponents	(Hills	2016,	p.	672)	and	critics	(Pritchard	2010)	of	the	view	that	understanding	is	compatible	with	intervening luck. 6	This	example	is	from	Grimm	(2014). 7	Zagzebski	(2001),	Morris	(2012),	Rohwer	(2014),	and	Riaz	(2015)	have	also	taken	this	line	of	argument. 12 Hills	(2016,	p.	672)	describes	similar	cases	of	epistemic	luck: Inaccurate	Textbooks.	Your	history	class	has	all	been	given	very	inaccurate	textbooks,	except	for	you.	You read	in	your	textbook	some	details	about	Napoleon's	career:	that	he	was	well-organized,	tactically	astute and	ruthless,	and	on	that	basis	you	draw	the	conclusion	that	he	was	a	great	military	leader.	You	are completely	right	and	you	are	able	to	explain	why	he	was	a	great	leader.	And	you	can	explain	why	similar figures	(Wellington	and	Marlborough	for	instance)	were	also	very	good	commanders. According	to	Hills,	this	example	shows	that	you	do	understand	why	Napoleon	was	a	successful	leader, although	you	do	not	know	this	fact.	Kvanvig	(2003,	pp.	197-8)	and	Pritchard	(2010,	p.	79)	describe similar	examples	that	are	designed	to	show	that	knowledge	is	not	necessary	for	understanding. Although	these	examples	are	just	philosophical	fictions,	they	illustrate	an	important	point.	Our informational	environments	are	increasingly	polluted	with	fake	news,	liars,	and	bullshitters.	We	live	in what	we	might	call	epistemically	hostile	environments.	Consequently,	it	is	important	to	determine	the relationship	between	knowledge,	understanding,	and	environmental	luck.	If	people	like	Kvanvig, Pritchard,	and	Hills	are	correct,	then	epistemically	hostile	environments	may	threaten	our	knowledge without	threatening	our	understanding.	This	is	rather	good	news.	Although	it	may	become	harder	to know	things	in	our	post-truth	era	of	misinformation,	we	may	still	achieve	understanding	as	long	as	we hit	upon	accurate	sources	of	information. However,	it	is	unclear	whether	we	can	distinguish	knowing	from	understanding	by	appealing	to epistemic	luck.	In	particular,	the	claim	that	knowledge	(but	not	understanding)	is	incompatible	with environmental	luck	is	highly	questionable.	Our	intuitions	about	cases	with	the	same	structure	are	flimsy, as	illustrated	by	Hawthorne	(2003),	Gendler	and	Hawthorne	(2005),	and	Sliwa	(2015).	We	can	easily construct	cases	of	environmental	luck	where	it	is	intuitive	to	ascribe	knowledge.	For	example, Hawthorne	(2003,	p.	68-9)	describes	a	scenario	in	which	six	children	are	given	books	where	only	one	of these	books	provides	accurate	information	about	the	capital	of	Austria.	When	asked	"Which	one	of	the schoolchildren	knows	the	capital	of	Austria?",	an	onlooker	who	has	witnessed	the	sequence	of	events will	answer	by	selecting	the	child	whose	book	read	"Vienna"-even	though	that	child	was	only	given	the correct	answer	by	luck.	This	illustrates	that	knowledge,	like	understanding,	is	achievable	in	epistemically hostile	environments,	as	long	as	the	source	of	information	is	good. 13 Further,	Grimm	(2006)	puts	forward	some	cases	against	the	claim	that	understanding	can	be	lucky,	and then	argues	that	the	cases	where	understanding	isn't	undermined	by	luck	are	also	cases	where epistemic	luck	does	not	undermine	knowledge.	He	therefore	provides	an	intuitive	case	that	knowledge and	understanding	seem	to	"sway	together,"	at	least	when	the	details	of	these	cases	are	adequately spelled	out.8 Beyond	the	intuitive	arguments	for	this	view,	there	is	empirical	evidence	that	understanding	and knowledge	are	both	compatible	with	environmental	luck.	Wilkenfeld,	Plunkett,	and	Lombrozo	(2018) experimentally	tested	a	number	of	different	cases	involving	epistemic	luck	and	they	found	no	evidence that	judgments	concerning	knowledge	and	understanding	diverge	as	a	result	of	a	belief's	etiology.9	They write,	"attributions	of	knowledge	and	attributions	of	understanding	involve	comparable	(and	minimal) roles	for	epistemic	luck"	(Wilkenfeld	et	al.	2018,	p.	24).	This	throws	into	doubt	a	crucial	assumption made	by	scholars	who	claim	that	knowledge	is	incompatible	with	environmental	luck. Colaço	et	al.	(2014)	provide	additional	support	for	the	view	that	knowledge	and	understanding	are equally	insensitive	to	epistemic	luck.	They	designed	a	study	to	determine	whether	members	of	the 8	Brogaard	(2005),	Khalifa	(2013a),	and	Greco	(2014)	also	argue	that	understanding	is	incompatible	with	the	same	type	of epistemic	luck	as	knowledge.	In	defense	of	lucky	understanding,	Morris	(2012)	claims	the	intuitions	that	rule	against	lucky understanding	can	be	explained	away.	However,	Sliwa	(2015,	pp.	60–61)	argues	that	sentences	of	the	form	"I	understand	why x,	but	I	don't	know	why	x"	are	infelicitous,	and	there	is	no	obvious	way	to	explain	their	infelicity	by	appealing	to	pragmatic considerations. 9	Here's	a	summary	of	one	of	their	experiments: Participants	were	randomly	assigned	to	read	one	of	four	vignettes,	all	variations	on	the	case	of	Becky	in	the	blacksmith's shop	from	Grimm	(2006).	In	each	vignette,	Becky	sees	John,	a	blacksmith,	strike	a	chestnut	with	a	hammer,	and	sees	the chestnut	explode.	Unbeknownst	to	Becky,	the	anvil	is	hot	enough	to	cause	chestnuts	to	explode	and	John	is	playing	a game	of	timing	his	blows	based	on	when	the	heat	would	cause	each	chestnut	on	his	anvil	to	explode.	In	all	vignettes, Becky	forms	the	belief	that	the	chestnut	exploded	because	it	was	hit	by	the	hammer	.	.	.	In	the	normal	belief	condition, Becky's	belief	is	true.	John	usually	strikes	the	chestnut	just	before	it	would	explode	from	the	heat,	and	he	does	so	as	she is	watching.	In	the	false	belief	condition,	John	times	his	blows	so	that	he	strikes	after	each	chestnut	explodes	due	to	the heat,	and	he	does	this	as	she	is	watching.	Accordingly,	Becky's	belief	that	the	chestnut	exploded	due	to	the	hammer	is false.	The	lucky	environment	condition	follows	Grimm's	blacksmith	example	most	closely:	John	usually	strikes	each chestnut	after	it	explodes	due	to	the	heat.	But,	on	the	one	occasion	Becky	is	watching,	his	timing	is	off	and	his	hammer blow	does	cause	the	chestnut	to	explode.	Thus,	Becky's	belief	is	true,	but	lucky	in	that	she	would	have	formed	a	false belief	based	on	identical	evidence	if	she	had	walked	in	a	moment	earlier	or	later.	Finally,	in	the	veridical	hallucination condition,	John	usually	strikes	the	chestnut	before	it	explodes	due	to	the	heat,	and	does	so	as	Becky	is	watching.	In	this scenario	though,	Becky	accidentally	ingests	a	hallucinogenic	plant	before	entering	John's	shop.	Becky's	hallucinations	just happen	to	correspond	exactly	to	what	she	would	have	seen	if	she	had	not	been	hallucinating	.	.	.	After	reading	one	of these	four	vignettes,	participants	were	randomly	assigned	to	judge	either	Becky's	knowledge	or	her	understanding." (Wilkenfeld	et	al.	2018,	pp.	32-5). Wilkenfeld	and	colleagues	found	no	significant	differences	in	participants'	ratings	of	Becky's	knowledge	and	of	her understanding	in	any	of	the	four	conditions. 14 general	public	will	deny	knowledge	to	the	protagonist	in	fake	barn	cases	of	environmental	luck	(see Goldman	1976).	Contrary	to	philosophical	lore,	Colaço	and	colleagues	find	that	participants	are	willing	to attribute	knowledge	in	fake-barn	cases,	thereby	undercutting	the	widespread	assumption	that environmental	luck	is	incompatible	with	knowledge.	Many	philosophers	have	likewise	claimed	that	fake barn	scenarios	are	compatible	with	knowledge;	e.g.,	Millikan	(1984),	Brogaard	(2005),	Grimm	(2006,	p. 529)	Lycan	(2006,	p.	158),	and	Turri	(2011,	p.	8).	Thus,	it	seems	that	the	fake	barn	intuition	is	not	"clearly enough	correct	for	it	to	be	usable	as	the	premise	of	a	good	argument"	(DeRose	2009,	p.	49). This	casts	doubt	on	the	putative	case	for	understanding's	immunity	to	epistemic	luck.	Although	one	of the	most	common	ways	to	argue	that	understanding	is	different	from	knowing	is	to	claim	that understanding	is	immune	to	the	kind(s)	of	epistemic	luck	that	undermine	knowledge,	it	seems	that people	do	not	differentiate	between	knowing	and	understanding	on	the	basis	of	luck. Truth	and	Understanding What	is	the	relationship	between	understanding	and	the	facts?	This	is	one	of	the	most	hotly	debated questions	in	the	epistemology	of	understanding.	It	is	widely	accepted	that	knowledge	is	"factive"	in	the sense	that	a	belief	amounts	to	knowledge	only	if	the	belief	is	true.	After	all,	you	cannot	know	that	the Titanic	sank	in	1912	if	it	didn't	sink	in	1912.	But	the	relationship	between	understanding	and	truth	is more	complicated. On	the	one	hand,	it	seems	clear	that	understanding	must	somehow	answer	to	the	facts.	You	cannot understand	how	the	Titanic	capsized	if	your	beliefs	about	how	it	capsized	are	false.	On	the	other	hand,	a strictly	factive	conception	of	understanding	may	be	unable	to	do	justice	to	the	cognitive	contributions	of science.	As	Elgin	(2017)	and	de	Regt	(2017)	argue,	scientists	commonly	rely	on	models,	idealizations,	and thought	experiments	that	are	known	not	to	be	true.	For	example,	scientists	purport	to	understand	the behavior	of	actual	gases	by	reference	to	so-called	ideal	gas,	even	though	there	is	no	such	gas.	Elgin	calls these	"felicitous	falsehoods"	and	claims	they	are	often	essential	to	fostering	understanding.10 10	Philosophers	are	deeply	divided	over	the	connection	between	understanding	and	the	facts.	Opponents	of	factivity	include Zagzebski	(2001),	Elgin	(2007,	2009,	2017),	and	Riggs	(2009).	In	contrast,	Lipton	(2004,	2009),	Grimm	(2006,	2010),	Pritchard (2009,	2010),	Strevens	(2013),	Greco	(2014),	Hills	(2016),	Frigg	and	Nguyen	(forthcoming),	Le	Bihan	(forthcoming),	and	Nawar (forthcoming)	claim	that	understanding	is	factive.	Insofar	as	one	thinks	that	understanding	reduces	to	knowledge,	one	must think	that	understanding	is	factive.	If	understanding	is	not	factive,	then	it	cannot	reduce	to	knowledge. 15 Taking	a	middle	path,	Kvanvig	(2003)	maintains	that	understanding	is	compatible	with	some	peripheral beliefs	that	are	false,	while	beliefs	that	are	central	to	one's	understanding	must	be	true.	On	this	view, false	beliefs	will	always	detract	from	one's	understanding:	our	cognitive	situation	would	improve	by removing	falsehoods	from	our	belief	set.	This	is	the	"quasi-factive"	view	of	understanding. It	might	seem	plausible	that	explanations	and	theories	must	at	least	be	approximately	true	to	provide understanding.	However,	Elgin	(2017)	argues	that	scientific	models	involving	highly	unrealistic idealizations	can	enhance	understanding.	Further,	it	seems	possible	to	use	fictions	and	counterfactual scenarios	to	advance	understanding.	Consider	Thomas	Hobbes's	genealogical	account	of	the	political sovereign.	Hobbes	imagines	a	"state	of	nature"	in	which	there	was	no	government,	no	laws,	no civilization,	but	rather	a	war	of	"all	against	all"	where	life	was	"nasty,	brutish,	and	short."	Even	though this	is	philosophical	fantasy,	it	is	used	to	shed	light	on	the	legitimacy	of	political	authority.	We	could make	similar	points	about	Hume's	genealogy	of	justice	and	Rawls's	thought	experiment	involving humans	in	the	"original	position"	behind	a	veil	of	ignorance	(see	Elgin	2017,	p.	29).	These	theorists	were under	no	illusions	that	their	accounts	were	accurate	descriptions	of	human	history.	Yet	these	theories are	intended	to	foster	genuine	understanding	nonetheless. This	illustrates	that	even	central	falsehoods	are	sometimes	compatible	with	understanding.	As	Elgin writes, A	central	element	in	a	second	grader's	view	of	human	descent	may	be	that	humans	descended	from	apes, although,	on	a	more	sophisticated	account,	humans	and	great	apes	descended	from	a	common	hominid ancestor	who	was	not,	strictly	speaking,	an	ape.	Nonetheless,	the	child's	view	displays	some	understanding and	is	certainly	better	than	thinking	that	humans	and	apes	are	not	relatives	of	any	sort.	Likewise,	even though	Copernicus	thought	that	the	Earth	orbits	around	the	sun	in	a	circle	(and	not	in	an	ellipse),	his	theory constitutes	a	major	advance	in	understanding	the	motion	of	the	planets	if	compared	to	Ptolemaic	theories. (2007,	pp.	37-8) This	seems	to	contradict	Kvanvig's	claim	that	we	cannot	understand	a	subject	matter	unless	all	of	the central	propositions	in	a	comprehensive	body	of	information	are	true.	In	some	cases,	divergences	from the	truth	may	be	large	without	undermining	one's	understanding.	Indeed,	Elgin	says	that	divergences from	the	truth	are	often	essential	to	fostering	understanding. 16 It	seems	clear	that	falsehoods	can	produce	understanding.	Elgin	(2017),	Strevens	(2017),	de	Regt	and Gijsbers	(2017),	and	de	Regt	(2017)	argue	that	divergences	from	the	truth	often	foster	understanding	in science.	Recall	the	case	of	the	child	who	believes	that	human	beings	descended	from	apes.	Elgin	writes, the	pattern	exhibited	in	this	case	is	endemic	to	scientific	education.	We	typically	begin	with	rough characterizations	that	properly	orient	us	toward	the	phenomenon,	and	then	refine	the	characterizations	as our	understanding	of	the	science	advances.	Think	of	the	trajectory	from	naïve	folk	physics	through Newtonian	mechanics	to	relativity	and	quantum	mechanics.	(2009,	p.	325) In	a	similar	vein,	Strevens	says:	"many	explanatory	models	contain	idealizations,	that	is,	deliberate falsifications	that	are	generally	considered	not	to	harm	and	even	to	help	their	users	to	understand	why certain	phenomena	occur"	(2017,	p.	37).	Even	theories	that	are	utterly	false	may	be	used	to	understand something.	Thus,	deliberate	falsehoods	clearly	play	a	role	in	helping	scientists	better	understand	the world. It	seems	plausible	that	felicitous	falsehoods	may	be	effective	routes	to	understanding.	A	simplified model	may	even	foster	better	understanding	than	an	explanatory	model	that	contains	no	falsehoods. But	this	idea	is	perfectly	compatible	with	the	factive	view	of	understanding.	To	say	that	felicitous falsehoods	can	yield	understanding	is	a	claim	about	the	route	to	understanding;	it	is	not	a	claim	about what	is	understood	(i.e.,	the	object	of	understanding).	A	false	theory	may	foster	genuine	understanding, but	the	phenomenon	that	is	understood	(or	the	predictions	that	one	is	attempting	to	make)	must	still	be true-or	at	least	approximately	true.	For	example,	the	ideal	gas	law	represents	gas	molecules	as perfectly	elastic	spheres	that	occupy	negligible	space	and	exhibit	no	mutual	attraction.	No	such	gas exists,	but	this	idealization	is	useful	for	scientific	explanation	and	prediction.	It	gives	accurate	predictions regarding	the	behavior	of	the	target	systems	under	certain	conditions	(Mizrahi	2012,	p.	242).	But	the scientists	working	with	the	ideal	gas	law	or	other	idealizations	do	not	necessarily	have	false	beliefs	as	a result.	The	underlying	idea	is	that	idealizations	can	be	an	efficacious	way	to	get	to	further	truths	or	make true	predictions. Thus,	the	effectiveness	of	false	models	or	idealizations	is	no	objection	to	the	factive	view	of understanding.	As	Kelp	(2017)	points	out,	"it	is	simply	not	part	of	the	[factive]	view	that	a	proposition	or theory	can	contribute	to	our	understanding	of	various	scientific	phenomena	only	if	it	is	known	to	be 17 literally	true."	Fidelity	to	the	truth	does	not	imply	that	explanations	adducing	idealizations	are epistemically	unacceptable. We	may	also	grant	that	false	theories	can	be	understood.	In	this	fairly	trivial	sense,	understanding	is compatible	with	falsehood.	But	false	theories	are	themselves	comprised	of	truths,	just	as	fictional worlds	are	teeming	with	facts.	It	is	a	fact	that	Hamlet	was	the	Prince	of	Denmark	in	Shakespeare's	play, just	as	it	is	a	fact	that	Geminis	and	Libras	are	a	great	romantic	match	according	to	astrology.	Thus, understanding	false	theories	still	requires	a	commitment	to	the	truth.	To	understand	a	false	theory	we must	understand	what	is	true	of	the	theory. Must	the	factivists	claim	that	science	is	cognitively	defective	insofar	as	it	relies	on	laws,	models,	and idealizations	that	diverge	from	the	truth?	It	would	be	mistaken	to	saddle	the	defenders	of	factivity	with this	view	(although	Elgin	2004,	p.	113	attributes	it	to	them).	To	say	that	truth	is	mandatory	for understanding	is	not	to	imply	that	our	best	science	"turns	out	to	be	intellectually	dishonest"	(Elgin	2004, p.	113).	Factivists	needn't	regard	felicitous	falsehoods	as	defects.	Rather,	they	can	acknowledge	that felicitous	falsehoods	are	critical	to,	and	indeed	constitutive	of,	the	understanding	delivered	by	science. For	example,	felicitous	falsehoods	may	allow	us	to	achieve	more	understanding	in	cases	where	the vastly	more	complicated	truth	would	impede	understanding.	The	point,	however,	is	that	these falsehoods	are	preferable	to	truth	owing	to	our	cognitive	limitations. In	other	words,	the	examples	adduced	by	the	non-factivists	show	that	felicitous	falsehoods	are instrumentally	valuable.11	Specifically,	they	are	instrumentally	valuable	for	cognitively	limited	creatures like	us.	It	is	because	of	our	cognitive	limitations	that	we	are	sometimes	better	off	with	simplified	models, idealizations,	and	approximations.	These	will	figure	ineliminably	in	the	success	of	science	and	thus	are not	defects.	Indeed,	they	may	be	practically	necessary.	But	from	a	purely	epistemic	point	of	view,	when we	bracket	our	cognitive	shortcomings,	the	factivist	may	be	right	that	our	understanding	of	the	world would	be	enhanced	if	it	contained	only	truths.	Our	predicament	is	that,	from	the	perspective	of	nonideal	inquirers,	the	demand	for	nothing	but	the	truth	may	obstruct	our	epistemic	goals. 11	Le	Bihan	(forthcoming)	makes	a	similar	point. 18 Understanding,	Grasping,	and	Ability As	mentioned	earlier,	a	prominent	view	in	the	philosophy	of	science	is	that	understanding	is	simply knowledge	of	causes.12	According	to	Pritchard	(2010)	and	Hills	(2016),	however,	there	are	some	cases	in which	it	is	intuitive	to	say	that	one	has	knowledge	without	the	corresponding	understanding.	Consider the	following	example: Suppose	that	I	understand	why	my	house	burned	down,	know	why	it	burned	down,	and	also	know	that	it burned	down	because	of	faulty	wiring.	Imagine	further	that	my	young	son	asks	me	why	his	house	burned down	and	I	tell	him.	He	has	no	conception	of	how	faulty	wiring	might	cause	a	fire,	so	we	could	hardly imagine	that	merely	knowing	this	much	suffices	to	afford	him	understanding	of	why	his	house	burned down.	Nevertheless,	he	surely	does	know	that	his	house	burned	down	because	of	faulty	wiring,	and	thus also	knows	why	his	house	burned	down.	(Pritchard	2010,	p.	81) If	Pritchard	is	correct	about	this	case,	it	illustrates	that	one	can	have	knowledge	without	the corresponding	understanding.	Hills	provides	a	similar	example: Suppose	that	you	know	why	giving	money	to	charity	is	right,	namely	because	we	owe	assistance	to	the	very needy.	You	were	told	this	by	your	parents.	You	understand	what	the	statement	means.	You	believe	it	and	it is	true.	You	have	formed	it	in	the	right	way	to	have	knowledge	(by	testimony	from	sources	you	rightly believe	to	be	reliable).	But	you	won't	necessarily	yet	have	the	abilities	to	make	accurate	judgments	about other,	similar	cases-where	you	are	aware	that	your	sacrifice	would	be	more	significant,	or	that	the	needs you	could	meet	are	not	pressing.	And	so	on.	So	you	can	have	knowledge	why	without	cognitive	control,	and so	without	understanding	why.	(Hills	2016,	p.	669) In	both	of	these	cases,	understanding	why	something	is	the	case	seems	to	demand	more	cognitive ability	than	knowing	why	it	is	the	case.13	In	particular,	understanding	seems	to	require	more	than	simply knowing	the	cause	of	p	or	the	reason	why	p.14	For	this	reason,	it	is	widely	assumed	that	understanding	is a	greater	cognitive	achievement	than	knowledge. 12	We	may	use	the	term	'cause'	broadly	to	include	not	just	causes	relations	but	dependency	relations	more	broadly	(see	Kim 1994;	Greco	2014;	Grimm	2014). 13	See	Sliwa	(2015)	for	a	contrary	view. 14	Grimm	(2014)	disagrees	with	Pritchard's	claim	that	the	child	knows	why	his	house	burned	down. 19 These	examples	may	correctly	show	that	understanding-why	is	not	a	form	a	knowing-why,	but	they	do not	illustrate	that	understanding-why	is	irreducible	to	knowledge.	As	Grimm	(2014)	argues, understanding	may	be	a	form	of	non-propositional	knowledge	of	causes.	This	is	compatible	with Pritchard's	and	Hill's	claim	that	understanding	is	not	reducible	to	propositional	knowledge-why.	One might	instead	think	of	understanding	as	a	kind	of	ability	or	know-how	(that	is	not	reducible	to propositional	knowledge).	Thus,	the	argument	by	Pritchard	and	Hills	is	too	narrow	to	establish	the broader	conclusion	that	understanding	is	irreducible	to	any	type	of	knowledge.	At	best,	it	shows	that one	type	of	understanding	is	not	reducible	to	one	type	of	knowledge. Let's	suppose	that	understanding	requires	more	cognitive	ability	than	the	corresponding	knowledge. What	precisely	is	required?	A	widely	accepted	view	if	that	some	kind	of	grasping	is	additionally necessary	for	understanding	(Kitcher	1989;	Kvanvig	2003;	Riggs	2003;	de	Regt	and	Dieks	2005;	Greco 2014;	Kelp	2015;	Grimm	2006,	2016;	de	Regt	2009;	Newman	2012;	Khalifa	2013a;	Hills	2016;	Elgin	2007; 2017;	and	Strevens	2017).	Elgin	says,	"understanding	the	Athenian	victory	involved	more	than	knowing the	various	truths	that	belong	to	a	suitable	tethered	comprehensive,	coherent	account	of	the	matter. The	understander	must	also	grasp	how	the	various	truths	are	related	to	each	other	and	to	other elements	of	the	account"	(2017,	p.	46).	Similarly,	Grimm	maintains	that	understanding	involves	grasping a	"structure"	(2016,	p.	12).	Hills	says	that	understanding	why	p	requires	a	grasp	of	the	reason	why	p (2016,	p.	663).	According	to	Baumberger	and	Brun	(2017),	a	person	S	understands	a	subject	matter	M	by means	of	a	theory	T	to	the	degree	that:	(a)	S	grasps	T;	(b)	S	is	committed	to	T;	(c)	T	answers	to	the	facts; and	(d)	T	of	M	is	justified	for	S.	This	view	is	structurally	similar	to	the	traditional	view	of	knowledge,	but it	also	includes	a	grasping	condition	that	is	absent	in	the	case	of	knowledge. We	can	draw	out	two	general	ideas	from	these	various	views.	First,	we	can	see	that	understanding, unlike	knowledge,	is	not	primarily	concerned	with	a	belief	in	an	individual	proposition.	Rather,	it	is focused	on	what	Boyd	(forthcoming)	calls	"a	mental	representation	of	a	relational	structure."15	Second, we	can	see	it	is	widely	accepted	that	understanding	requires	grasping. Precisely	what	"grasping"	consists	in	is	a	matter	of	debate.	Theorists	have	tended	to	use	the	term	in	an intuitive	and	largely	metaphorical	way;	for	instance,	when	one	"sees"	how	various	bits	of	information 15	Hills	(2016)	argues	that	understanding	is	ultimately	concerned	with	relationships	between	propositions,	whereas	Grimm (2014)	argues	that	grasping	is	a	non-propositional	way	of	knowing.	I	will	leave	open	whether	a	relational	structure	can	be expressed	in	terms	of	propositions. 20 "hang	together."	A	natural	idea	is	that	grasping	is	related	to	coherence	theories	of	justification	(see	Elgin 2004,	2006,	2007;	Kvanvig	2003,	2009;	Riggs	2009;	Carter	and	Gordon	2014).	Kvanvig	characterizes	the central	feature	of	understanding	as	"in	the	neighborhood	of	what	internalist	coherence	theories	say about	justification.	Understanding	requires	the	grasping	of	explanatory	and	other	coherence-making relationships	in	a	large	and	comprehensive	body	of	information"	(2003,	p.	192).	Likewise,	Riggs	suggests that	understanding	"requires	a	deep	appreciation,	grasp	or	awareness	of	how	[the	subject	matter's] parts	fit	together	[and]	what	role	each	one	plays	in	the	context	of	the	whole"	(2003,	p.	217).16 Other	scholars	defend	an	ability-based	account	of	grasping.	Elgin	says,	"to	grasp	a	proposition	or	an account	is	at	least	in	part	to	know-how	to	wield	it	to	further	one's	epistemic	ends"	(2017,	p.	33).	Grimm (2006;	2012;	2014)	defends	the	view	that	to	have	understanding	is	to	have	a	set	of	abilities	or	know-how needed	to	answer	"what	if	things	were	different"	questions.	Khalifa	(2013a)	maintains	that	grasping involves	the	ability	to	reliably	evaluate	explanations.	According	to	Hills	(2016),	grasping	a	relationship between	two	propositions	requires	"cognitive	control,"	which	is	a	set	of	abilities	or	know-how.	These abilities	include:	following	some	explanation	of	why	p	given	by	someone	else;	giving	an	explanation	of why	p	in	your	own	words;	and	drawing	the	conclusion	that	p	(or	that	probably	p)	from	the	information that	q	(Hills	2016,	p.	663).	The	idea	here	is	that	grasping	a	proposition	is	a	matter	of	being	able	to	use the	information	in	some	way,	to	have	it	under	you	control,	and	to	be	able	to	manipulate	it.17 Although	it	is	widely	accepted	that	understanding	requires	grasping,	there	is	no	consensus	about	what such	grasping	amounts	to.18	Strevens	even	claims	that	"To	give	a	philosophical	account	of	grasping would	be	an	extraordinary	thing,"	and	he	makes	no	attempt	to	do	so.	However,	he	does	say	that	"to grasp	a	fact	is	like	knowing	a	fact,	but	it	involves	a	more	intimate	epistemic	acquaintance	with	the	state of	affairs	in	question"	(2017,	p.	41). However,	we	may	wonder	whether	grasping	is	really	anything	other	than	simply	knowing.	When	one "grasps"	a	correct	explanation	for	why	an	event	occurs,	perhaps	one	simply	knows	the	correct 16	Khalifa	(2017)	denies	that	coherence	is	part	of	the	core	conception	of	understanding. 17	Zagzebski	(2001),	Kvanvig	(2003),	de	Regt	and	Dieks	(2005)	and	Newman	(2014)	also	connect	understanding	to	abilities. Sullivan	(2018)	argues	that	the	abilities	constitutive	of	understanding	are	the	same	kind	of	cognitive	abilities	that	we	find	in ordinary	cases	of	knowledge-that	(and	not	the	kind	of	practical	abilities	associated	with	know-how).	Thus,	anti-reductionists cannot	maintain	that	understanding	is	irreducible	to	knowledge-that	by	appealing	to	the	idea	that	understanding	requires know-how. 18	See	Kelp	(2015)	for	an	overview	of	how	grasping-related	conditions	on	understanding	should	be	explicated. 21 explanation.	This	is	perfectly	compatible	with	the	view,	defended	by	Kvanvig	(2003)	and	Elgin	(2017), that	understanding	involves	more	than	knowing	the	various	truths	that	belong	to	a	comprehensive, coherent	account	of	some	topic.	It	may	also	require	that	we	"grasp"	how	these	various	truths	relate	to each	other;	but	this	grasping	may	simply	bottom	out	at	knowing	the	various	causal	relata.	Along	this line,	Riaz	(2015)	argues	that	grasping	is	not	a	distinct	psychological	state	that	accompanies understanding.	To	understand	why	something	is	the	case	is	to	grasp	or	"see"	why	it	is	the	case,	but grasping	and	seeing	are	just	ways	of	knowing.	For	those	tempted	by	this	line	of	thought,	we	could	simply jettison	talk	of	"grasping"	and	give	an	account	of	understanding	in	terms	of	knowing.19 Varieties	of	Understanding For	the	most	part,	the	current	debates	in	epistemology	have	not	so	much	centered	around	proposals	for a	complete	theory	of	understanding	but	rather	on	a	variety	of	hotly	debated	questions,	such	as	whether understanding	requires	belief,	justification,	or	truth,	as	well	as	whether	it	is	compatible	with	certain forms	of	epistemic	luck.20	But	we	might	wonder:	are	there	any	characteristics	of	understanding	that	are widely	accepted?	Can	we	say	anything	about	the	nature	of	understanding	in	general? As	Le	Bihan	(2017,	p.	123)	observes,	understanding	is	commonly	taken	to:	(a)	involve	something	like grasping	connections,	(b)	be	a	cognitive	achievement	due	to	ability,	(c)	come	in	degrees,21	(d)	manifest itself	through	some	abilities	or	know-how	(i.e.,	to	infer,	generalize,	or	answer	"what	if	things	had	been different"	questions),	and	(e)	be	not	easily	transmittable	by	testimony	alone.	Bengson	also	provides	a comprehensive	characterization	of	understanding: To	genuinely	understand	something	is	to	grasp	it	.	.	.	in	such	a	way	that	it	makes	sense	to	you	.	.	.	it	involves genuinely	grasping	some	portion	of	reality,	and	not	simply	enjoying	a	subjective	sense	of	grasping	it	.	.	.	it displays	coherence	.	.	.	it	can	be	or	become	better,	greater,	deeper	.	.	.	it	is	a	praiseworthy	good.	(2017,	p. 19) 19	Lynch	(2019)	thinks	we	should	eschew	talk	of	"grasping." 20	Additional	questions	I	do	not	have	space	to	discuss	include	the	relationship	between	knowledge,	understanding,	and testimony	(see	Hills	2009;	Sliwa	2015;	Hills	2016;	Boyd	2017;	Malfatti	2019;	Croce,	forthcoming),	as	well	as	the	transparency	of understanding	(see	Zagzebski	2001;	Trout	2002;	Pritchard	2010;	Hills	2016;	Grimm	2017). 21	A	few	theorists	have	attempted	to	distinguish	knowledge	from	understanding	on	the	grounds	that	understanding,	but	not knowledge,	comes	in	degrees.	Although	it	is	widely	agreed	that	understanding	comes	in	degrees	(see	Hills	2016:	665),	there	is some	disagreement	over	whether	knowledge	admits	of	degrees.	Kvanvig	(2003)	and	Hills	(2016;	2017)	argue	that	propositional knowledge	does	not	admit	of	degrees,	whereas	Hetherington	(2001)	says	knowledge-that	is	also	gradable.	Brogaard	(2005)	and Riaz	(2015)	argue	that	knowledge-why	is	gradable. 22 As	Bengson	admits,	this	is	not	a	theory	of	understanding	but	rather	a	theory-neutral	description	of	the core	features	of	understanding. In	contrast,	Trout	(2017)	is	deeply	skeptical	that	there	could	be	any	general	characterization	of understanding	as	such.	He	writes, 'Understanding'	may	denote	an	unprincipled	stew	of	states,	processes,	capacities,	and	goals	that	are	only occasionally	present	when	philosophers,	and	ordinary	folks,	apply	the	term	or	concept.	A	unified	account	of understanding	might	be	valuable,	but	understanding	isn't	a	natural	kind	or	defined	by	a	set	of	necessary	and sufficient	conditions.	Any	unity	we	find	in	understanding	comes	not	from	the	involvement	of	common mechanisms	across	diverse	cases,	but	rather	of	messy	cognitive	activities	in	the	common	goal	of	pursuing	the truth.	(2017,	p.	232) Trout	goes	on	to	say	that	work	on	the	nature	of	understanding	is	"half	baked"	and	"in	a	terrible	state" because	scholars	are	unable	to	agree	on	even	the	most	basic	features	of	understanding.	As	my	review	of the	literature	has	shown,	scholars	disagree	about	whether	understanding	requires	truth,	whether	it	is reducible	to	knowledge,	whether	it	is	compatible	with	luck,	whether	it	is	propositional	or	nonpropositional,	and	whether	it	requires	grasping. A	more	fruitful	approach,	then,	is	to	treat	understanding	not	as	a	unified	or	monolithic	thing,	but	instead to	expand	the	senses	of	"understanding"	to	include	a	variety	of	types.	Many	existing	analyses	have	done exactly	this;	in	particular,	it	is	now	common	to	distinguish	between	understanding	why,	understanding how,	understanding	of,	and	understanding	that-perhaps	among	other	types	of	understanding.	This may	make	the	investigation	of	the	nature	and	value	of	understanding	more	tractable.	Instead	of	trying to	find	consensus	about	the	nature	of	understanding	per	se,	it	may	be	better	to	ask	what	types	of understanding	there	are. In	the	recent	philosophical	literature,	it	is	common	to	find	three	distinct	senses	of	'understanding': holistic	understanding,	explanatory	understanding,	and	practical	understanding. Holistic	understanding	is	the	kind	of	understanding	that	one	has	toward	a	subject	matter	or	domain.	It	is sometimes	called	"objectual"	understanding	(Kvanvig	2003,	p.	191).	This	type	of	understanding	is	usually 23 attributed	using	the	verb	"understands"	followed	directly	by	a	noun;	for	example,	"Irena	understands American	history"	and	"Lana	understands	quantum	physics."	Holistic	understanding	requires systematized	knowledge	of	a	comprehensive	body	of	information,	coherence,	and	a	grasp	of	the dependency	relations	among	the	various	items	of	information	within	a	subject	matter.	Elgin	(2017)	and Kvanvig	(2003)	claim	that	holistic	understanding	is	the	"core"	or	"paradigm"	conception	of understanding.	Further,	they	distinguish	holistic	understanding	primarily	from	knowledge	of	individual or	isolated	propositions. Explanatory	understanding,	by	contrast,	is	the	kind	of	understanding	that	one	has	when	one understands	why	something	is	the	case.	For	this	reason,	explanatory	understanding	is	also	often	called "understanding	why."	This	type	of	understanding	is	at	the	center	of	a	lot	of	recent	work	in	epistemology and	the	philosophy	of	science	(see	Baumberger	et	al.	2017	for	an	overview).	Pritchard	(2010),	Hempel (1965),	Kitcher	(1989),	Grimm	(2008),	Khalifa	(2012),	Strevens	(2013),	Hills	(2016),	and	de	Regt	(2017)	all focus	on	explanatory	understanding,	and	Pritchard	and	Hills	say	it	is	the	paradigmatic	form	of understanding. The	focus	of	explanatory	understanding	is	somewhat	narrower	than	holistic	understanding.	Instead	of striving	to	understand	a	subject	matter	or	domain,	explanatory	understanding	is	typically	directed	at	a specific	phenomenon	or	question;	for	instance,	understanding	why	the	earth's	average	temperature	is rising	or	why	the	sky	is	blue. Pritchard	contrasts	explanatory	understanding	with	understanding-that,	which	he	calls	"propositional understanding."	According	to	Pritchard,	explanatory	understanding	usually	isn't	concerned	with propositions	because	"it	is	rare	to	talk	of	understanding	that	p"	(2010,	p.	74).22	However,	it	is	plausible that	understanding	why	p	requires	that	one's	understanding	be	directed	toward	a	set	of	propositions, namely,	those	reasons	as	to	why	p	is	the	case	(see	Hills	2016	and	Boyd	2017).	Thus,	the	contrast between	explanatory	understanding	and	propositional	understanding	is	spurious.	Pritchard's	reasoning does	not	necessarily	speak	against	the	idea	that	explanatory	understanding	is	also	propositional. For	Kvanvig,	the	primary	contrast	is	between	holistic	understanding	and	understanding-that.	Elgin makes	a	similar	point: 22	This	is	actually	false	(see	Hannon	2019,	p.	231n9). 24 There	are	two	obvious	candidates	for	the	bearer	of	epistemic	entitlement:	individual	propositions	and	more comprehensive	bodies	of	information.	I	can	say,	'I	understand	that	the	Comanches	dominated	the	southern plains	of	North	America	in	the	18th	century'.	Or	I	can	say,	'I	understand	the	power	relations	among	the tribes	in	the	southern	plains	in	the	18th	century'.	(2009,	p.	321) Both	Kvanvig	and	Elgin	tend	to	contrast	holistic	understanding	with	a	specific	kind	of	propositional understanding,	namely	understanding-that.	Elgin	goes	on	to	say,	"If	the	primary	unit	of	understanding	is the	proposition,	then	the	difference	between	knowledge	and	understanding	seems	slight"	(see	also Gordon	2012). These	types	of	understanding	may	be	further	contrasted	with	another,	more	neglected	form	of understanding:	understanding	how	to	do	something.	Zagzebski	(2008)	call	this	"understanding-how"	and she	takes	it	to	be	the	paradigmatic	type	of	understanding.	Bengson	(2017)	calls	it	"practical understanding"	and	contrasts	it	with	"theoretical	understanding."	Recent	work	in	epistemology	and	the philosophy	of	science	has	focused	on	theoretical	understanding,	where	the	emphasis	is	on	whether understanding	is	factive,	explanatory,	immune	to	luck,	and	so	forth.	Practical	understanding,	however,	is centrally	concerned	with	skillful	action	and	practical	activity.	As	such,	this	type	of	understanding	is	more closely	tied	to	abilities	(i.e.,	physical	dispositions,	habits,	or	bodily	activities)	than	explanations.	For example,	a	player	who	understands	how	to	catch	a	fly	ball	might	be	unable	to	explain	how	he	can	do this,	and	explanations	seem	inadequate	to	imbue	such	a	skill.	As	any	sports	fan	will	know,	it	is	difficult not	to	notice	the	banality	of	explanations	given	by	top	athletes	in	post-game	TV	interviews.	Even	the best	athletes	are	often	unable	to	describe	the	content	of	their	physical	prowess	without	availing themselves	to	strings	of	clichés	like	"taking	it	one	pitch	at	a	time"	and	"focusing	on	fundamentals."	For this	reason,	philosophers	of	mind,	action	theory,	and	phenomenology	have	tended	to	focus	on questions	concerning	the	embodiment,	automaticity,	and	(non)conceptuality	of	practical	understanding (Bengson	2017). The	distinction	between	theoretical	and	practical	understanding	is	probably	not	exhaustive.	There	may be	other	forms	of	understanding	that	do	not	belong	to	either	category.	To	use	an	example	from	Bengson (2017,	p.	24),	"a	psychoanalyst's	empathetic	understanding	of	a	patient,	or	a	lover's	understanding	of	a beloved,	is	(perhaps)	neither	theoretical	nor	practical."	In	addition	to	empathetic	understanding	(see 25 Hannon,	forthcoming),	there	is	moral	understanding	(Hills	2009),	aesthetic	understanding	(Hills	2017), religious	understanding	(Ellis	2017),	linguistic	understanding	(Longworth	2008),	historical	understanding (Little	2017),	philosophical	understanding	(Graham	2017),	mathematical	understanding	(Lipton	2011), and	scientific	understanding	(de	Regt	2017),	presumably	among	many	others.	Whether	or	not	these	are all	distinct	kinds	of	understanding,	as	opposed	to	merely	different	domains	of	(the	same	type	of) understanding,	is	an	open	question.	In	all	likelihood,	there	are	multiple	types	of	understanding	across different	domains. Concluding	Remarks By	distinguishing	these	varieties	of	understanding,	we	may	better	appreciate	the	nature	and	value	of this	intellectual	achievement	(or	these	intellectual	achievements).	For	example,	it	may	be	that	some forms	of	understanding	are	more	likely	reducible	to	knowledge	than	others.	Khalifa	(2012),	for	instance, argues	that	explanatory	understanding	is	a	form	a	propositional	knowledge,	but	this	is	compatible	with the	claim	that	other	forms	of	understanding	are	not	reducible	to	knowledge.	Further,	it	may	be	that some	forms	of	understanding	are	more	likely	to	be	factive,	immune	to	luck,	and	so	on,	than	others. Distinguishing	various	types	of	understanding	will	allow	us	to	see	which	features	they	have	in	common and	what,	if	anything,	makes	them	different.	Do	they	take	the	same	objects	(e.g.,	theories,	phenomena, etc.)?	Are	some	types	more	valuable	than	others?	Can	some	be	explicated	in	terms	of	others?	We cannot	make	headway	on	these	issues	until	we	appreciate	the	various	senses	of	"understanding." Recent	work	in	the	epistemology	of	understanding	has	shed	light	on	the	nature,	value,	and	varieties	of understanding;	however,	a	variety	of	topics	call	for	more	research.	First,	we	may	reasonably	ask	what these	various	senses	of	understanding	have	in	common.	Is	there	a	way	to	unearth	some	unity	amid	this diversity?	Second,	what	is	the	boundary	between	understanding	and	other	epistemic	states,	such	as knowledge,	imagination,	and	wisdom?	This	question	is	immediately	connected	to	a	third	issue,	namely, epistemic	value.	Are	some	types	of	understanding	more	valuable	than	others?	Are	they	instrumentally or	intrinsically	valuable?	Does	the	value	of	understanding	exceed	the	value	of	knowledge?	Fourth,	is understanding	the	goal	in	inquiry?	According	to	de	Regt	(2017),	understanding	is	the	goal	of	science. Hills	(2009)	claims	that	understanding	is	required	for	an	action	to	have	moral	worth.	Pritchard	(2010) argues	that	inquiry	generally	ought	to	end	at	understanding;	while	Hannon	(2019)	claims	that	ordinary inquiry	ought	to	aim	for	knowledge	rather	than	understanding.	Fifth,	we	may	connect	this	point	about the	aim	of	inquiry	with	the	epistemology	of	education.	According	to	many	epistemologists,	truth	is	the 26 ultimate	goal	of	inquiry.	Outside	of	academic	philosophy,	however,	understanding	is	often	invoked	as the	primary	goal	of	education.	In	general,	we	may	wonder	whether	understanding	is	(or	ought	to	be)	the goal	of	some	inquiries	but	not	others. 27 References Achinstein,	Peter.	1983.	The	Nature	of	Explanation	(Oxford,	UK:	Oxford	University	Press). Ammon,	Sabine.	2016.	"Explaining	Understanding,	Understanding	Knowledge,"	in	Explaining Understanding:	New	Perspectives	from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen	Grimm, Christoph	Baumberger,	and	Sabine	Ammon	(New	York,	NY:	Routledge),	pp.	92-110. Aristotle.	1993.	Posterior	Analytics	(Oxford,	UK:	Oxford	University	Press). Baumberger,	Christoph.	2011.	"Understanding	and	its	Relation	to	Knowledge,"	in	Epistemology: Contexts,	Values,	Disagreement	(Proceedings	of	the	34th	International	Ludwig	Wittgenstein	Symposium), ed.	Christoph	Jäger	and	Winfried	Loeffler	(Germany:	Ontos	Verlag),	pp.	16-18. Baumberger,	Christoph,	Claus	Beisbart,	and	Georg	Brun.	2017.	"What	is	Understanding?	An	Overview	of Recent	Debates	in	Epistemology	and	Philosophy	of	Science,"	in	Explaining	Understanding:	New Perspectives	from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen	Grimm,	Christoph	Baumberger, and	Sabine	Ammon	(New	York,	NY:	Routledge),	pp.	1-34. Baumberger,	Christoph	and	Georg	Brun.	2017.	"Dimensions	of	Objectual	Understanding,"	in	Explaining Understanding:	New	Perspectives	from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen	Grimm, Christoph	Baumberger,	and	Sabine	Ammon	(New	York,	NY:	Routledge),	pp.	165-189. Bengson,	John.	2017.	"The	Unity	of	Understanding,"	in	Making	Sense	of	the	World:	New	Essays	on	the Philosophy	of	Understanding,	ed.	Stephen	Grimm	(New	York,	NY:	Oxford	University	Press),	pp.	15-50. Boyd,	Kenneth.	2017.	"Testifying	Understanding,"	Episteme,	vol.	14,	no.	1,	pp.	103-127. ------.	Forthcoming.	"Environmental	Luck	and	the	Structure	of	Understanding,"	Episteme. Brogaard,	Berit.	2005.	"I	Know,	Therefore	I	Understand,"	Unpublished	manuscript. Carter,	J.	Adam,	and	Emma.	C.	Gordon.	2014.	"Objectual	Understanding	and	the	Value	Problem," American	Philosophical	Quarterly,	vol.	51,	no.	1,	pp.	1-13. Christian,	James	L.	2009.	Philosophy:	An	Introduction	to	the	Art	of	Wondering	(Boston,	MA:	Wadsworth Cengage	Learning). Cohen,	L.	Jonathan.	1992.	An	Essay	on	Belief	and	Acceptance	(Oxford,	UK:	Clarendon	Press). Colaco,	David,	Wesley	Buckwalter,	Stephen	Stich,	and	Edouard	Machery.	2014.	"Epistemic	Intuitions	in Fake-barn	Thought	Experiments,"	Episteme,	vol.	11,	no.2,	pp.	199-212. Croce,	Michel.	Forthcoming.	"Moral	Understanding,	Testimony,	and	Moral	Exemplarity,"	Ethical	Theory and	Moral	Practice. Dellsén,	Finnur.	2017.	"Understanding	without	Justification	or	Belief,"	Ratio,	vol.	30	no.	3,	pp.	239-254. 28 de	Regt,	Henk	2009.	"Understanding	and	Scientific	Explanation,"	in	Scientific	Understanding: Philosophical	Perspectives,	ed.	Henk	de	Regt,	Sabine	Leonelli,	and	Kai	Eiger	(Pittsburgh:	University	of Pittsburgh	Press),	pp.	21-42. -----2015.	"Scientific	Understanding:	Truth	or	Dare?"	Synthese,	vol.	192,	no.	12,	pp.	3781-3797 -----2017.	Understanding	Scientific	Understanding	(New	York,	NY:	Oxford	University	Press). de	Regt,	Henk	and	Dennis	Dieks.	2005.	"A	Contextual	Approach	to	Scientific	Understanding,"	Synthese, vol.	144,	no.	1,	pp.	137-170. de	Regt,	Henk	and	Victor	Gijsbers.	2017.	"How	False	Theories	Can	Yield	Genuine	Understanding,"	in Explaining	Understanding:	New	Perspectives	from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen Grimm,	Christoph	Baumberger,	and	Sabine	Ammon	(New	York,	NY:	Routledge),	pp.	50-75. DeRose,	Keith.	2009.	The	Case	for	Contextualism	(Oxford,	UK:	Oxford	University	Press). Elgin,	Catherine.	2004.	"True	Enough,"	Philosophical	Issues,	vol.	14,	no.	1,	pp.	113-131. -----2006.	"From	Knowledge	to	Understanding,"	in	Epistemology	Futures,	ed.	Stephen	Hetherington (Oxford,	UK:	Oxford	University	Press),	pp.	199-215. -----2007.	"Understanding	and	the	Facts,"	Philosophical	Studies,	vol.	132,	no.	1,	pp.	33-42. -----2009.	"Is	Understanding	Factive?"	in	Epistemic	Value,	ed.	Adrian	Haddock,	Alan	Millar,	and	Duncan Pritchard	(New	York,	NY:	Oxford	University	Press),	pp.	322-330. -----2017.	True	Enough	(Cambridge,	MA:	MIT	Press). Ellis,	Fiona.	2017.	New	Models	of	Religious	Understanding	(Oxford,	UK:	Oxford	University	Press). Frigg,	Roman	and	James	Nguyen.	Forthcoming.	"Mirrors	without	Warnings,"	Synthese. Gendler,	Tamar	and	John	Hawthorne.	2005.	"The	Real	Guide	to	Fake	Barns:	A	Catalogue	of	Gifts	for	Your Epistemic	Enemies,"	Philosophical	Studies,	vol.	124,	no.	3,	pp.	331-352. Gettier,	Edmund.	1963.	"Is	Justified	True	Belief	Knowledge?"	Analysis	vol.	23,	no.	6,	pp.	121-123. Goldman,	Alvin.	1976.	"Discrimination	and	Perceptual	Knowledge,"	Journal	of	Philosophy,	vol.	73,	no.	20, pp.	771-791. Gordon,	Emma	C.	2012.	"Is	there	Propositional	Understanding?"	Logos	and	Episteme,	vol.	3,	no.	2,	pp. 181-192. Graham,	Gordon.	2017.	"Philosophy,	Knowledge,	and	Understanding,"	in	Making	Sense	of	the	World: New	Essays	on	the	Philosophy	of	Understanding,	ed.	Stephen	Grimm	(New	York,	NY:	Oxford	University Press),	pp.	99-116. 29 Greco,	John.	2014.	"Episteme:	Knowledge	and	Understanding,"	in	Virtues	and	Their	Vices,	ed.	Kevin Timpe	and	Craig	Boyd	(New	York,	NY:	Oxford	University	Press),	pp.	285-302. Grimm,	Stephen.	2006.	"Is	Understanding	a	Species	of	Knowledge?"	British	Journal	for	the	Philosophy	of Science,	vol.	57,	no.	3,	pp.	515-535. -----2012.	"The	Value	of	Understanding,"	Philosophy	Compass,	vol.	7,	no.	2,	pp.	103-117. -----2014.	"Understanding	as	Knowledge	of	Causes,"	in	Virtue	Epistemology	Naturalized:	Bridges between	Virtue	Epistemology	and	Philosophy	of	Science,	ed.	Abrol	Fairweather	(Dordrecht:	Springer),	pp. 329-346. -----2016.	"How	Understanding	People	Differs	from	Understanding	the	Natural	World,"	Philosophical Issues,	vol.	26,	no.	1,	pp.	209-225. -----2017.	"Understanding	and	Transparency,"	in	Explaining	Understanding:	New	Perspectives	from Epistemology	and	Philosophy	of	Science,	ed.	Stephen	Grimm,	Christoph	Baumberger,	and	Sabine	Ammon (New	York,	NY:	Routledge),	pp.	212-229. Grimm,	Stephen,	Christoph	Baumberger,	and	Sabine	Ammon.	eds.,	2017.	Explaining	Understanding: New	Perspectives	from	Epistemology	and	Philosophy	of	Science	(New	York,	NY:	Routledge). Hannon,	Michael.	2019.	What's	the	Point	of	Knowledge?	(New	York,	NY:	Oxford	University	Press). -----Forthcoming.	"Empathetic	Understanding	and	Deliberative	Democracy,"	Philosophy	and Phenomenological	Research. Hawthorne,	John.	2003.	Knowledge	and	Lotteries	(Oxford,	UK:	Oxford	University	Press). Hempel,	Carl.	1965.	Aspects	of	Scientific	Explanation	and	Other	Essays	in	the	Philosophy	of	Science	(New York,	NY:	Free	Press). Hetherington,	Stephen.	2001.	Good	Knowledge,	Bad	Knowledge:	On	Two	Dogmas	of	Epistemology (Oxford,	UK:	Oxford	University	Press). Hills,	Alison.	2009.	"Moral	Testimony	and	Moral	Epistemology,"	Ethics,	vol.	120,	no.	1,	pp.	94-127. -----2016.	"Understanding	Why,"	Noûs,	vol.	49,	no.	2,	pp.	661-688. -----2017.	"Aesthetic	Understanding,"	in	Making	Sense	of	the	World:	New	Essays	on	the	Philosophy	of Understanding,	ed.	Stephen	Grimm	(New	York,	NY:	Oxford	University	Press),	pp.	160-176. Janvid,	Mikael.	2012.	"Knowledge	versus	Understanding:	The	Cost	of	Avoiding	Gettier,"	Acta	Analytica vol.	27,	no.	2,	pp.	183-197. 30 Kelp,	Christoph.	2014.	"Knowledge,	Understanding,	and	Virtue,"	in	Virtue	Epistemology	Naturalized: Bridges	between	Virtue	Epistemology	and	Philosophy	of	Science,	ed.	Abrol	Fairweather	(Dordrecht: Springer),	pp.	347-360. -----2015.	"Understanding	Phenomena,"	Synthese,	vol.	192,	no.	12,	pp.	3799-3816. -----2017.	"Towards	a	Knowledge-Based	Account	of	Understanding,"	in	Explaining	Understanding:	New Perspectives	from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen	Grimm,	Christoph	Baumberger, and	Sabine	Ammon	(New	York,	NY:	Routledge),	pp.	251-271. Khalifa,	Kareem.	2011.	"Understanding,	Knowledge,	and	Scientific	Antirealism,"	Grazer	Philosophische Studien,	vol.	83,	no.	1,	pp.	93-112. -----2012.	"Inaugurating	Understanding	or	Repackaging	Explanation?"	Philosophy	of	Science,	vol.	79,	no. 1,	pp.	15-37. -----2013a.	"Understanding,	Grasping,	and	Luck,"	Episteme,	vol.	10,	no.	1,	pp.	1-17. -----2013b.	"Is	Understanding	Explanatory	or	Objectual?"	Synthese,	vol.	190,	no.	6,	pp.	1153-1171. -----2017.	Understanding,	Explanation,	and	Scientific	Knowledge	(Cambridge,	UK:	Cambridge	University Press). Kim,	Jaegwon.	1994.	"Explanatory	Knowledge	and	Metaphysical	Dependence,"	Philosophical	Issues,	vol. 5,	pp.	51-69. Kvanvig,	Jonathan.	2003.	The	Nature	and	Value	of	Knowledge	(Cambridge,	UK:	Cambridge	University Press). -----2009.	"The	Value	of	Understanding,"	in	Epistemic	Value,	ed.	Duncan	Pritchard,	Adrian	Haddock, and	Alan	Millar	(New	York,	NY:	Oxford	University	Press),	pp.	95-111. Kitcher,	Philip.	1989.	"Explanatory	Unification	and	the	Causal	Structure	of	the	World,"	in	Scientific Explanation,	ed.	Philip	Kitcher	and	Wesley	Salmon	(Minneapolis:	University	of	Minnesota	Press),	pp. 410-505. Lawler,	Insa.	2016.	"Reductionism	about	Understanding	Why,"	Proceedings	of	the	Aristotelian	Society, vol.	116,	no.	2,	pp.	229-236. Le	Bihan,	Soazig.	2017.	"Enlightening	Falsehoods:	A	Modal	View	of	Scientific	Understanding,"	in Explaining	Understanding:	New	Perspectives	from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen Grimm,	Christoph	Baumberger,	and	Sabine	Ammon	(New	York,	NY:	Routledge),	pp.	111-136. -----Forthcoming.	"Partial	Truth	versus	Felicitous	Falsehoods,"	Synthese. Lipton,	P.	2004.	Inference	to	the	Best	Explanation	(London:	Routledge). 31 -----2009.	"Understanding	without	Explanation,"	in	Scientific	Understanding:	Philosophical	Perspectives, ed.	Henk	de	Regt,	Sabine	Leonelli,	and	Kai	Eiger	(Pittsburgh:	University	of	Pittsburgh	Press). -----2011.	"Mathematical	Understanding,"	in	Meaning	in	Mathematics,	ed.	John	Polkinghorne	(Oxford, UK:	Oxford	University	Press). Little,	Daniel.	2017.	"Philosophy	of	History,"	in	Stanford	Encyclopedia	of	Philosophy,	ed.	E.	N.	Zalta.	URL	= https://plato.stanford.edu/archives/sum2017/entries/history/. Longworth,	Guy.	2008.	"Linguistic	Understanding	and	Knowledge,"	Noûs,	vol.	42,	no.	1,	pp.	50-79. Lycan,	William.	2006.	"On	the	Gettier	Problem	Problem,"	in	Epistemology	Futures,	ed.	Stephen Hetherington	(Oxford,	UK:	Oxford	University	Press). Lynch,	Michael.	2019.	"Understanding	and	Coming	to	Understand,"	in	Making	Sense	of	the	World:	New Essays	on	the	Philosophy	of	Understanding,	ed.	Stephen	Grimm	(New	York,	NY:	Oxford	University	Press), pp.	195-209. Malfatti,	Federica.	2019.	"Can	Testimony	Generate	Understanding?"	Social	Epistemology,	vol.	33,	no.	6, pp.	477-490. Millikan,	Ruth.	1984.	Thought,	Language,	and	Other	Biological	Categories	(Cambridge,	MA:	MIT	Press). Mizrahi,	Moti.	2012.	"Idealizations	and	Scientific	Understanding,"	Philosophical	Studies,	vol.	160,	no.	2, pp.	237-252. Morris,	Kevin.	2012.	"A	Defense	of	Lucky	Understanding,"	British	Journal	for	the	Philosophy	of	Science, vol.	63,	no.	2,	pp.	357-371. Nawar,	Tamer.	Forthcoming.	"Veritism	Refuted?	Understanding,	Idealizations,	and	the	Facts,"	Synthese. Newman,	Mark.	2012.	"An	Inferential	Model	of	Scientific	Understanding,"	International	Studies	in	the Philosophy	of	Science,	vol.	26,	no.	1,	pp.	1-26. -----2014.	"EMU	and	inference:	what	the	explanatory	model	of	scientific	understanding	ignores," European	Journal	for	Philosophy	of	Science,	vol.	4,	no.	1,	pp.	55-74. -----2017.	"Theoretical	Understanding	in	Science,"	British	Journal	for	the	Philosophy	of	Science,	vol.	68 no.	2,	pp.	571–595. Pritchard,	Duncan.	2010.	"Knowledge	and	Understanding,"	in	The	Nature	and	Value	of	Knowledge:	Three Investigations,	ed.	Duncan	Pritchard,	Alan	Millar,	and	Adrian	Haddock	(New	York,	NY:	Oxford	University Press). -----2009.	"Knowledge,	Understanding	and	Epistemic	Value,"	in	Epistemology,	Royal	Institute	of Philosophy	Supplements,	ed.	Anthony	O'Hear	(Cambridge,	UK:	Cambridge	University	Press),	pp.	19-43. 32 Riaz,	Amber.	2015.	"Moral	Understanding	and	Knowledge,"	Philosophical	Studies,	vol.	172,	no.	1,	pp. 113-128. Riggs,	Wayne.	2003.	"Understanding	'Virtue'	and	the	Virtue	of	Understanding,"	in	Intellectual	Virtue: Perspectives	From	Ethics	and	Epistemology,	ed.	Michael	DePaul	and	Linda	Zagzebski	(Oxford,	UK: Clarendon	Press). -----2009.	"Understanding,	Knowledge,	and	the	Meno	Requirement,"	in	Epistemic	Value,	ed.	Adrian Haddock,	Alan	Millar,	and	Duncan	Pritchard	(New	York,	NY:	Oxford	University	Press),	pp.	331-338. Rohwer,	Yasha.	2014.	"Lucky	Understanding	without	Knowledge,"	Synthese,	vol.	191,	no.	5,	pp.	1-15. Russell,	Bertrand.	1948.	Human	Knowledge:	Its	Scope	and	Limits	(London,	UK:	George	Allen	and	Unwin). Salmon,	Wesley.	1984.	Scientific	Explanation	and	the	Causal	Structure	of	the	World	(Princeton,	NJ: Princeton	University	Press). Sliwa,	Paulina.	2015.	"Understanding	and	Knowing,"	Proceedings	of	the	Aristotelian	Society,	vol.	115,	no. 1,	pp.	57-74. Strevens,	Michael.	2013.	"No	Understanding	without	Explanation,"	Studies	in	History	and	Philosophy	of Science,	vol.	44,	no.	3,	pp.	510-515. -----2017.	"How	Idealizations	Provide	Understanding,"	in	Explaining	Understanding:	New	Perspectives from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen	Grimm,	Christoph	Baumberger,	and	Sabine Ammon	(New	York,	NY:	Routledge),	pp.	37-49. Sullivan,	Emily.	2018.	"Understanding:	not	know-how,"	Philosophical	Studies,	vol.	175,	no.	1,	pp.	221240. Trout,	J.	D.	2002.	"Scientific	Explanation	and	the	Sense	of	Understanding,"	Philosophy	of	Science,	vol.	69, no.	2,	pp.	212-233. -----2017.	"Understanding	and	Fluency,"	in	Making	Sense	of	the	World:	New	Essays	on	the	Philosophy	of Understanding,	ed.	Stephen	Grimm	(New	York,	NY:	Oxford	University	Press),	pp.	233-251. Turri,	John.	2011.	"Manifest	Failure:	The	Gettier	Problem	Solved,"	Philosophers'	Imprint,	vol.	11,	no.	8, pp.	1-11. Wilkenfeld,	Daniel.	2017.	"Understanding	without	Believing,"	in	Explaining	Understanding:	New Perspectives	from	Epistemology	and	Philosophy	of	Science,	ed.	Stephen	Grimm,	Christoph	Baumberger, and	Sabine	Ammon	(New	York,	NY:	Routledge),	pp.	318-334. Wilkenfeld,	Daniel,	David	Plunkett,	and	Tania	Lombrozo.	2016.	"Depth	and	Deference:	When	and	Why We	Attribute	Understanding,"	Philosophical	Studies,	vol.	173,	no.	2,	pp.	373-393. Woodward,	James.	2003.	Making	Things	Happen:	A	Theory	of	Causal	Explanation	(Oxford,	UK:	Oxford University	Press). 33 Zagzebski,	Linda.	2001.	"Recovering	Understanding,"	in	Knowledge,	Truth,	and	Duty:	Essays	on	Epistemic Justification,	Responsibility,	and	Virtue,	ed.	Matthias	Steup	(Oxford,	UK:	Oxford	University	Press),	pp. 235-252. -----2008.	On	Epistemology	(New	York,	NY:	Wadsworth	Cengage	Learning).