Humean	laws	and	(nested)	counterfactuals Penultimate	version,	forthcoming	in	Philosophical	Quarterly Authors: Siegfried	Jaag:	Heinrich-Heine-Universität	Düsseldorf Christian	Loew:	Universität	zu	Köln Abstract: Humean	reductionism	about	laws	of	nature	is	the	view	that	the	laws	reduce	to	the	total distribution	of	non-modal	or	categorical	properties	in	spacetime.	A	worry	about	Humean reductionism	is	that	it	cannot	motivate	the	characteristic	modal	resilience	of	laws	under counterfactual suppositions and that it thus generates wrong verdicts about certain nested	counterfactuals.	In	this	paper,	we	defend	Humean	reductionism	by	motivating	an account	of	the	modal	resilience	of	Humean	laws	that	gets	nested	counterfactuals	right. 1.	Introduction Humean	reductionism	about	laws	of	nature	is	the	view	that	the	laws	reduce	to	facts about	the	Humean	Mosaic,	i.e.,	the	total	distribution	of	non-modal	or	categorical properties	in	spacetime.	David	Lewis's	influential	best	systems	account	(BSA)	aims	to achieve	this	reduction	by	analyzing	laws	of	nature	as	efficient	summaries	of	what actually	happens.1	The	so-analyzed	laws	then	provide	a	foundation	for	reducing	all other	natural	modalities,	including	nomological	possibility	and	necessity, counterfactuals,	causation,	and	dispositions. An	important	worry	about	the	Humean	BSA	is	that	it	cannot	fully	account	for	the resilience	of	the	laws	of	nature	under	counterfactual	suppositions.	It	is	plausible	that the	laws	(typically)	still	would	be	true	under	counterfactual	suppositions	that	are logically	consistent	with	them.	For	instance,	lots	of	things	would	be	different	if	the	Sun were	further	away	from	the	Earth.	But	we	think	that	the	laws	of	nature	would	be	true, 1	Other	proponents	of	a	best	systems	account	include	Beebee	(2000),	Hall	(2015),	and	Loewer (1996).	Anti-Humeans	about	laws,	by	contrast,	hold	that	the	laws	of	nature	are	identified	with or	'grounded	in'	genuinely	modal	entities,	such	as	instantiations	of	an	irreducible	higher-order necessitation	relation	(Armstrong	1983),	primitive	laws	(Maudlin	2007),	fundamental	potencies (Bird	2007),	or	primitive	subjunctive	facts	(Lange	2009a). 2 regardless	of	the	Sun's	position.	This	resilience	allows	the	laws	to	underwrite counterfactuals.	Since	the	laws	would	still	be	true	if	the	Sun	were	further	away	from	the Earth,	we	can	use	them	to	infer	what	else	would	be	the	case	given	this	counterfactual supposition.2	Humeans,	however,	arguably	cannot	motivate	why	the	laws	are	resilient under	nested	counterfactual	suppositions	such	as	"had	there	been	nothing	but	a	lone electron,	then	had	there	been	more	electrons	than	one,	the	force	between	any	two electrons	would	have	accorded	with	Coulomb's	law"	(Lange	2009a:	54	and	Hall manuscript;	cf.	Carroll	1994:	ch.	3).	The	worry	is	that	Humeanism	generates	the	wrong verdicts	about	this	and	similar	counterfactuals	and	so	cannot	fully	explain	the	laws' modal	resilience. In	this	paper,	we	defend	Humean	reductionism	by	providing	a	Humean motivation	of	the	modal	resilience	of	laws	that	also	applies	to	nested	counterfactuals. We	argue	that	holding	fixed	the	actual	laws	under	(nested)	counterfactual	suppositions serves	the	Humean	goal	of	inferring	truths	about	the	actual	world.	Our	argument	in	the paper	is	part	of	a	larger	defense	of	Humeanism.	A	general	challenge	for	Humeans	is	to explain	why	we	use	modal	notions,	such	as	dispositions,	causation,	and	counterfactuals, in	the	way	we	do.	After	all,	Humeans	deny	that	there	are	any	fundamental	modal	facts, and	so	the	point	of	employing	these	notions	cannot	be	to	describe	any	distinctive metaphysical	structure.	Our	paper	partly	answers	this	challenge	by	providing	a Humean-friendly	motivation	for	why	we	use	counterfactuals. Our	plan	for	the	rest	of	the	paper	is	as	follows:	In	§2,	we	outline	Humean reductionism	about	laws	of	nature.	In	§3,	we	explain	the	worry	that	Humean	theories cannot	fully	account	for	the	laws'	modal	resilience	since	they	yield	the	wrong	verdicts about	certain	nested	counterfactuals.	In	§4,	we	argue	that	Humeans	cannot	simply	set aside	the	relevant	nested	counterfactuals.	In	§5,	we	meet	Lange's	challenge	by	providing an	independent	Humean	motivation	for	adopting	a	semantics	of	counterfactuals	that holds	the	laws	fixed	under	counterfactual	suppositions.	We	then	show	that	this motivation	extends	naturally	to	nested	counterfactuals. 2	Most	philosophers,	Humeans	and	anti-Humeans	alike,	hold	that	laws	of	nature	are	more fundamental	than	counterfactuals	such	that	the	nomic	facts	help	fix	the	world's	counterfactual structure.	But	see	Lange	(2009a)	for	an	argument	that	the	world's	counterfactual	structure	fixes the	laws.	Some	dispositionalists	about	laws	of	nature	also	hold	that	counterfactuals	are	more fundamental	or	at	least	ontologically	on	a	par	with	the	laws	(see,	e.g.,	Bird	2007:	64). 3 2.	Humean	reductionism	about	laws	of	nature Setting	the	stage	for	our	account	of	the	modal	resilience	of	Humean	laws	requires reviewing	the	central	ingredients	of	Humean	reductionism.	We	will	focus	on	David Lewis's	version	since	he	is	the	most	influential	advocate	of	Humean	reductionism. Lewis's	central	thesis	is	"Humean	Supervenience,"	i.e., [...]	the	neo-Humean	thesis	that	every	contingent	truth	about	a	world-law,	dependency hypothesis,	or	what	you	will-holds	somehow	in	virtue	of	that	world's	total	history	of manifest	matters	of	particular	fact.	Same	history,	same	everything.	(Lewis	1981:	20) The	"world's	total	history	of	manifest	matters	of	particular	fact"	is	usually	referred	to	as the	'Humean	Mosaic'.	All	there	fundamentally	is,	according	to	Lewis,	is	this	global distribution	of	perfectly	natural	intrinsic	properties	at	spacetime	points	(or	their	pointsized	occupants),	such	as	determinate	masses,	charges,	and	spins.	The	Humean	aspect	of this	view	is	that	these	property	instantiations	are	freely	recombinable:	A	property instantiation	has	no	modal	implications	for	its	neighborhood.	Lewis	aims	to	show	that this	sparse	amodal	fundamental	structure	suffices	to	determine	(or	ground)	all	truths about	the	world,	including	all	modal	truths.3 Lewis's	best	systems	account	(BSA)	of	laws	of	nature	plays	a	central	role	in	this reductive	program	(see	Lewis	1973,	1983,	1994).	According	to	this	account,	what makes	a	fact	p	a	law	is	that	it	is	a	contingent	universal	generalization	belonging	to	the best	systems	about	the	Humean	mosaic.	Here	is	Lewis's	classical	formulation	of	the view: [A]	contingent	generalization	is	a	law	of	nature	if	and	only	if	it	appears	as	a	theorem (or	axiom)	in	each	of	the	true	deductive	systems	that	achieves	a	best	combination	of simplicity	and	strength.	(Lewis	1973:	73) The	idea	roughly	is	that	a	systematization	is	best	when	it	provides	as	much	information as	possible	about	the	actual	Humean	mosaic	in	as	simple	a	way	as	possible.	If	such systematizations	are	formulated	as	axiomatized	(deductively-closed)	theories	in	a 3	Humean	Supervenience	as	stated	above	arguably	requires	some	amendments.	See,	for example,	Dorr	&	Hawthorne	(2013)	for	refinements	of	the	recombination	claim	and	Weatherson (2015)	for	discussion	of	(vectorial)	magnitudes. 4 language	whose	predicates	refer	to	perfectly	natural	properties,	then	the	contingent universal	generalizations	therein	are	identified	with	the	laws.4 Lewis's	account	of	laws	provides	the	foundation	for	a	Humean	reduction	of	all other	natural	modalities.	Best	systems	laws	determine	nomological	necessity	and possibility	and	help	fix	the	world's	counterfactual	structure	(Lewis	1973,	1986c).	Lewis then	gives	a	counterfactual	account	of	causation	(Lewis	1986a)	which,	in	turn,	figures prominently	in	his	causal	account	of	explanation	(Lewis	1986b).	Dispositions,	finally, are	accounted	for	via	a	counterfactual	cum	causal	analysis	(Lewis	1997).	But	can Humean	reductionism	provide	an	adequate	account	of	laws? 3.	The	problem	of	nested	counterfactuals A	plausible	principle	about	laws	is	that	they	(at	least	typically)	are	resilient	under counterfactual	suppositions	that	are	logically	consistent	with	them.	Let	us	call	this proposition	'counterfactual	resilience'	(CR). (CR) The	laws	of	nature	(at	least	typically)	would	still	have	been	true	under counterfactual	suppositions	that	are	logically	consistent	with	them.5 CR	captures	the	idea	that	the	laws	'support'	counterfactuals.	If	it	is	a	law	that	'all	Fs	are Gs,'	then	if	some	x	that	actually	is	a	non-F	had	been	an	F,	it	also	would	have	been	a	G. This	fact	follows	from	the	resilience	of	the	laws	under	the	counterfactual	supposition that	the	distribution	of	Fs	is	different.	If	we	counterfactually	suppose	that	x	is	an	F	and the	law	that	'all	Fs	are	Gs'	remains	true	under	this	supposition,	then	it	follows	that	x	is also	a	G. CR	needs	to	be	distinguished	from	a	stronger	principle	that	may	be	dubbed 'counterfactual	hyper-resilience',	i.e.,	the	claim	that	not	only	the	laws'	truth	is	held	fixed under	counterfactual	suppositions	but	also	their	lawhood	(see	Carroll	1994	and	Lange 2009a).	A	prima	facie	attractive	feature	of	counterfactual	hyper-resilience	is	that	it would	entail	(and	so	perhaps	explain)	CR.	However,	as	we	will	demonstrate	below,	we 4	Lewis	(1994)	gives	an	analogous	account	of	chances.	Chances	are	fixed	by	their	fit	with	the frequencies	in	the	mosaic.	Roughly	put,	a	system	that	assigns	the	actual	history	of	events	a higher	chance	of	happening	has	a	better	fit	than	one	that	assigns	it	a	lower	chance. 5	See	Lange	(2009a:	sec.	1)	for	discussion	of	various	subtleties	concerning	CR,	including	how	it relates	to	nested	counterfactual	suppositions. 5 can	account	for	CR	without	adopting	this	principle.	In	the	following,	unless	we	explicitly say	otherwise,	if	we	talk	about	the	counterfactual	resilience	of	laws	or	holding	the	laws fixed,	we	mean	'holding	the	truth	of	the	laws	fixed',	not	'holding	the	lawfulness	of	the laws	fixed'. Counterfactuals	are	notoriously	context	sensitive,	and	there	might	be	contexts	in which	we	do	not	hold	the	laws	fixed.	In	such	contexts,	we	could	truthfully	assert	that	the laws	would	have	been	false	if	certain	facts	that	are	logically	consistent	with	them	had been	the	case.6	But	it	nonetheless	is	highly	plausible	that	the	laws	are	resilient	in standard	contexts.	Moreover,	this	resilience	is	a	characteristic	feature	of	the	laws	that distinguishes	them	from	non-laws.	Thus,	capturing	the	laws'	characteristic	modal resilience	is	a	desideratum	of	a	theory	of	laws. Can	a	Humean	theory	of	laws	explain	why	the	laws	of	nature	have	this characteristic	modal	resilience?	Humeans	can	build	the	resilience	of	laws	into	their preferred	semantics	of	counterfactuals.	Take	a	standard,	possible	worlds	semantics	of counterfactuals.	Roughly	put,	a	non-vacuous	counterfactual	A	□→	C	is	true	iff	all	Aworlds	that	are	closest	to	the	actual	world	are	C-worlds	(see	Lewis	1973).	Humeans	can then	make	it	a	requirement	on	closeness	that	the	laws	of	the	actual	world	are	still	true.7 For	example,	to	evaluate	the	counterfactual	'if	there	had	only	been	a	lone	electron,	then Coulomb's	law	still	would	have	been	true',	we	go	to	worlds	in	which	there	is	only	one electron	and	the	actual	laws	hold	true.	CR	would	then	be	directly	built	into	the	Humean semantics	of	counterfactuals.8 But	there	is	a	worry	that	a	Humean	account	of	laws	cannot	motivate	why	we	hold the	laws	fixed	under	counterfactual	suppositions.	According	to	Lewis's	BSA,	the	laws	of nature	are	mere	patterns	in	the	distribution	of	non-modal	properties	and	so	are metaphysically	no	different	from	other	facts	about	the	Humean	mosaic.	Hence,	the 6	Lange	(2009a)	argues	that	the	laws	are	held	fixed	under	counterfactual	suppositions	that	are logically	consistent	with	them	in	all	contexts.	But	see	Demarest	(2012)	and	Hall	(2011)	for criticism	of	Lange's	account	based	on	the	context	sensitivity	of	counterfactuals. 7	CR	is	usually	also	built	into	the	'altered	states'	semantics	of	counterfactuals,	an	alternative	to possible	worlds	semantics	(see	Maudlin	2007:	21–34	and	Paul	and	Hall	2013:	47–53). 8	Lewis's	(1986c)	own	preferred	semantics	for	counterfactuals	allows	small	violations	of	the laws	of	nature	(so-called	"small	miracles")	to	account	for	the	time	asymmetry	of	counterfactual dependence.	Lewis,	however,	argues	that	these	violations	are	extremely	small	and	localized such	that	the	laws	can,	for	the	most	part,	be	treated	as	if	they	are	resilient	under	counterfactual suppositions.	Dorr	(2016)	argues	that	we	should	hold	the	laws	completely	fixed	and	accept	that if	determinism	is	true,	the	past	depends,	at	least	to	some	small	degree,	on	the	future	(see	also Albert	2015:	ch.	2	and	Loewer	2012). 6 resilience	of	laws	under	counterfactual	suppositions	cannot	be	grounded	in	any	special metaphysical	status	of	the	laws.	Why	then	is	it	built	into	our	semantics	of counterfactuals	that	the	laws	are	typically	held	fixed	but	not	other	facts	(cf.	Armstrong 1983:	69	and	Lange	2009a:	55)?	Why	do	we	not	hold	fixed,	e.g.,	that	the	actual	world contains	wombats?9 Humeans	have	provided	some	reasons	for	why	best	system	laws	are	(typically) held	fixed	under	counterfactual	suppositions	that	are	logically	consistent	with	them. The	laws,	according	to	the	BSA,	are	especially	important	facts	about	a	world	since (unlike	facts	about	wombats)	they	are	part	of	the	best	systematizations	of	the	total distribution	of	categorical	properties.	Moreover,	when	evaluating	counterfactuals,	it makes	sense	to	hold	fixed	especially	important	facts	about	a	world.	Hence,	we	have reason	for	holding	fixed	the	laws	when	we	evaluate	counterfactuals.	As	Lewis	(1973: 75)	points	out:	"It	makes	a	big	difference	to	the	character	of	a	world	which generalizations	enjoy	the	status	of	lawhood	there.	Therefore,	similarity	and	difference of	worlds	in	respect	of	their	laws	is	an	important	respect	of	similarity	and	difference, contributing	weightily	to	overall	similarity	and	difference.''10	Let	us	call	this	account, according	to	which	the	laws	are	held	fixed	under	counterfactual	suppositions	simply qua	being	part	of	the	best	systems,	the	'received	Humean	view'. Unfortunately,	the	received	Humean	view	cannot	explain	why	we	hold	the	actual laws	fixed	under	nested	counterfactual	suppositions.	Lange	(2009a:	54)	offers	the following	example:	"Had	there	been	nothing	but	a	lone	electron,	then	had	there	been more	electrons	than	one,	the	force	between	any	two	would	have	accorded	with Coulomb's	law."	This	counterfactual	appears	to	be	true.	And	its	truth	is	evidence	that the	counterfactual	resilience	of	laws	also	extends	to	nested	counterfactual	suppositions. It	is	natural	to	think	that	if	the	laws	remain	true	under	simple	counterfactual suppositions,	then	they	also	remain	true	if	we	add	yet	further	counterfactual suppositions.	So,	the	same	reasons	we	have	for	thinking	that	CR	is	true	for	simple 9	See	Wilson	(2013:	657).	Some	anti-Humean	accounts	also	lack	a	worked-out	story	of	why	the laws	are	counterfactually	resilient.	Whatever	metaphysical	features	the	laws	are	supposed	to	be or	be	grounded	in,	we	can	always	ask	why	we	hold	these	features	fixed	under	counterfactual suppositions	and	not	others.	For	example,	Tweedale	(1984:	185–186)	complains	that	it	is	not clear	how	Armstrong's	(1983)	theory	of	laws	of	nature	can	account	for	the	laws'	modal resilience. 10	See	also	Roberts	(2009:	S504).	Wilson	(2013)	also	suggests	this	account	on	behalf	of	the Humean. 7 counterfactuals	also	seem	to	suggest	that	it	is	true	for	counterfactuals	with	nested suppositions.	But	now	Humeans	seem	to	be	in	trouble. Lange	argues	that	Humean	accounts	cannot	accommodate	the	laws'	resilience under	nested	counterfactual	suppositions.	According	to	the	received	Humean	view,	a nested	counterfactual	of	the	form	A	□→	(B	□→	C)	is	true	at	the	actual	world	iff	(B	□→	C) is	true	at	all	A-worlds	that	are	closest	to	the	actual	world.	Consider	Lange's counterfactual	about	the	lone	electron	from	the	previous	paragraph.	The	closest possible	world	to	the	actual	world	in	which	the	first	antecedent	is	true	is	a	lone-electron world,	wl.	(Let	us	assume,	for	simplicity,	that	there	is	a	unique	such	a	world.)	However, even	if	the	actual	laws	are	still	true	in	wl,	its	best	systematizations	arguably	do	not include	most	actual	laws.	These	systematizations	may	include	that	there	is	a	single (inertially	moving)	particle,	but	they	surely	will	not	contain	Coulomb's	law.	According	to the	above	rationale,	Coulomb's	law	is	then	not	among	the	important	features	of	wl. Hence,	there	is	no	reason	why	in	the	closest	world,	wm,	to	wl	in	which	there	is	more	than one	electron,	these	electrons	should	exert	forces	according	to	Coulomb's	law.	Therefore, the	above	nested	counterfactual	appears	to	come	out	as	false	on	the	received	Humean view.	And,	conversely,	analogous	reasoning	shows	that	certain	nested	counterfactuals that	are	intuitively	false	threaten	to	come	out	true	(see	Hall	manuscript	for	an	example). The	lone-electron	world,	wl,	also	illustrates	that	Humean	theories	of	laws	entail that	there	are	nomologically	possible	worlds	in	which	the	actual	laws	are	true	but	are not	laws.	Maudlin	(2007)	uses	cases	like	these	to	object	to	the	BSA	on	the	grounds	that it	violates	the	condition	that	a	law	is	a	law	in	all	of	its	models.	However,	it	is	doubtful that	this	condition	is	an	independently	motivated	desideratum	for	a	theory	of	laws.	So, without	additional	arguments	for	this	principle,	Maudlin's	worry	seems	to	beg	the question	against	the	Humean	(see	Lange	2009b,	Healey	2008,	and	Schwarz	2012). Lange's	considerations	regarding	nested	counterfactuals	can	be	seen	as	providing	such an	argument. Nested	counterfactuals	are	problematic	for	Humeans	because	according	to	best systems	accounts	what	facts	deserve	law-status	is	sensitive	to	the	overall	distribution	of non-nomic	properties.	Which	facts	are	included	in	a	world's	best	systematizations changes	given	drastic	enough	changes	in	its	non-nomic	properties.	The	worry	about nested	counterfactuals	then	arises	as	follows:	Take	a	counterfactual	supposition	that	is consistent	with	the	actual	laws	but	where	the	closest	possible	world	in	which	it	is	true 8 differs	from	the	actual	world	enough	such	that	the	actual	laws	are	not	part	of	its	best systematizations.	According	to	the	BSA,	the	actual	laws	are	then	not	laws	in	this counterfactual	world.	If	we	then	consider	a	second,	nested	counterfactual	supposition, the	received	Humean	view	tells	us	to	hold	the	laws	of	this	counterfactual	world	fixed rather	than	the	laws	of	the	actual	world.	Hence,	we	arrive	at	the	wrong	verdicts	for nested	counterfactuals,	such	as	Lange's	example.11	(You	may	think	that	nested counterfactuals	are	too	baroque	to	play	a	role	in	ordinary	and	scientific	reasoning. However,	as	we	will	show	in	the	next	section,	such	counterfactuals	are	quite	pervasive and,	in	fact,	central	to	the	Humean	project	of	reducing	natural	modality.) Anti-Humeans	avoid	this	problem.	They	deny	that	the	laws	are	in	this	way sensitive	to	the	overall	distribution	of	non-nomic	properties,	and	so	their	laws	do	not exhibit	this	kind	of	modal	fragility.	For	example,	Armstrong	(1983)	identifies	the	laws with	higher-order	facts	about	the	instantiation	of	the	nomic	necessitation	relation	that are	insensitive	to	alterations	in	the	non-nomic	facts	(at	least	if	we	set	Armstrong's Aristotelianism	aside).	Maudlin	(2007)	regards	laws	as	sui	generis	entities	over	and above	the	pattern	of	their	instances.	Dispositional	essentialists,	such	as	Bird	(2007),	also seem	to	avoid	the	problem	since	they	regard	the	laws	as	metaphysically	necessary	and thus	a	fortiori	modally	resilient.	Finally,	Lange	(2009a)	elevates	the	resiliency	of	laws under	nested	counterfactual	suppositions	to	the	defining	feature	of	lawhood.	So,	the problem	is	distinctive	to	Humean	reductionism. Nested	counterfactuals	of	the	kind	Lange	points	to	confront	Humeans	with	an uncomfortable	choice	between,	on	the	one	hand,	not	being	able	to	capture	our	intuitive judgments	about	the	relevant	counterfactuals	and,	on	the	other	hand,	adopting	an account	of	counterfactuals	that	is,	by	Humean	lights,	ill-motivated.	Here	is	why:	Suppose Humeans	adopt	a	semantics	of	counterfactuals	that	builds	the	laws'	resilience	under nested	counterfactual	suppositions	in	by	fiat.	Lange	anticipates	this	maneuver: [Y]ou	might	consider	extending	the	requirement	that	the	actual	laws	still	be	true	in	the closest	p-world	(if	p	is	logically	consistent	with	the	actual	laws)	to	require	additionally that	the	actual	laws	still	be	true	in	the	closest	q-world	to	the	closest	p-world	to	the	actual 11	Several	Humeans	have	proposed	modifications	of	Lewis's	BSA	(see	Cohen	&	Callender	2009, Dorst	2018,	Hall	2015,	Hicks	2018,	Jaag	and	Loew	2018,	Loewer	2007).	These	accounts, however,	maintain	that	the	laws	are	sensitive	to	the	distribution	of	non-modal	property instantiations,	and	so	are	equally	susceptible	to	Lange's	objection. 9 world	(as	long	as	p	is	logically	consistent	with	the	actual	laws	and	q	is,	too).	(Lange 2009a:	55;	see	also	Hall	manuscript) Let	us	call	this	additional	requirement	the	'resilience	rule'	since	building	it	into	the semantics	of	counterfactuals	guarantees	the	modal	resilience	of	the	laws	of	nature.	The resilience	rule	adjusts	the	similarity	metric	that	is	used	to	judge	the	closeness	of	worlds such	that	the	laws	are	not	only	true	in	the	closest	p-world	to	the	actual	world,	but	also	in the	closest	q-world	to	the	closest	p-world	to	the	actual	world.	Adopting	this	semantic rule	would,	thus,	secure	the	intuitively	correct	truth	values	for	nested	counterfactuals. For	instance,	Lange's	counterfactual	about	the	lone	electron	is	guaranteed	to	come	out true	because	Coulomb's	law	is	now	held	fixed	even	under	the	nested	counterfactual supposition	of	further	electrons. The	resilience	rule,	however,	is	at	odds	with	the	received	Humean	view	of	why we	hold	the	laws	fixed	under	counterfactual	suppositions.	Lange	continues	the	above quote	as	follows: But	this	is	an	unattractive	option.	If	the	closest	p-world's	laws	differ	from	the	actual laws,	as	the	Best	System	Account	entails	for	the	closest	lone-electron	world,	then	surely the	closest	p-world's	laws	(rather	than	the	actual	laws)	should	influence	which	q-worlds count	as	closest	to	the	closest	p-world.	(ibid.:	55) The	original	Humean	reason	for	holding	the	actual	laws	fixed	when	evaluating	simple counterfactuals	was	that	the	laws	are	particularly	important	features	of	the	actual	world due	to	figuring	in	its	best	systematizations.	But	then	in	a	counterfactual	world	where	the actual	laws	are	not	part	of	its	best	systematization,	the	actual	laws	are	no	longer important	features.	So,	it	then	seems,	by	Humean	lights,	unmotivated	to	hold	the	laws fixed	under	any	further	counterfactual	suppositions.	Hence,	a	semantics	that	contains the	resilience	rule	(or	a	similar	device	for	ensuring	the	correct	verdicts	for	nested counterfactuals)	is	at	odds	with	the	received	Humean	motivation	for	CR.12 12	In	her	discussion	of	Carroll's	(1994)	mirror	argument,	Beebee	(2000:	591–592)	seems	to concede	that	when	we	entertain	counterfactual	suppositions	within	a	counterfactual	world,	ws, the	Humean	is	bound	to	hold	the	laws	of	ws	fixed	rather	than	the	laws	of	the	actual	world. However,	in	§5	below	we	argue	that	there	are	principled	Humean	reasons	to	hold	the	actual laws	fixed	under	such	suppositions.	Our	account	thereby	provides	new	resources	against Carroll's	anti-Humean	argument,	though	we	will	leave	exploring	them	for	another	occasion. 10 It	is	important	to	keep	separate	two	distinct	challenges	that	nested counterfactuals	raise	for	Humean	accounts	of	laws.	The	first	challenge	is	to	provide	a semantics	of	counterfactuals	that	yields	the	correct	truth	values	for	nested counterfactuals,	including	Lange's	lone-electron	example.	Lange	shows	that	Humeans cannot	rely	on	the	received	way	of	evaluating	counterfactuals	because	it	yields	incorrect verdicts	given	a	Humean	BSA	of	laws.	So,	the	challenge	for	Humeans	is	to	provide	an alternative.	However,	Humeans	additionally	face	a	second,	deeper	challenge. The	second	challenge	is	to	show	that	a	semantics	of	counterfactuals	that	yields the	correct	results	for	nested	counterfactuals	is	motivated	in	light	of	a	Humean metaphysics.	Lange	concedes	that	Humeans	can	meet	the	first	challenge	by	adopting	the resilience	rule.	However,	he	maintains	that	such	a	fix	would	be	merely	cosmetic.	It allows	Humeans	to	correctly	model	our	counterfactual	judgments,	but	it	leaves completely	unmotivated	why	we	use	counterfactuals	in	this	way.	Lange	argues	that	this second	challenge	is	truly	devastating	for	a	Humean	theory	of	laws	because	it	means	that it	cannot	explain	the	role	laws	play	in	counterfactual	reasoning. Our	goal	in	this	paper	is	to	respond	to	the	second	challenge.	We	will	show	that	an account	of	counterfactuals	that	holds	the	actual	laws	fixed	both	under	simple	and	nested counterfactual	suppositions	has,	pace	Lange,	a	Humean	motivation.	In	fact,	we	will argue	that	such	a	semantics	goes	particularly	well	with	Humeanism	about	laws.	For simplicity,	we	will	accept	Lange's	suggestion	that	the	right	way	of	amending	the Humean	semantics	of	counterfactuals	is	to	add	the	resilience	rule.	However,	nothing about	our	account	hinges	on	this	assumption.	In	whatever	way	Humeans	ensure	that laws	are	held	fixed	under	nested	counterfactuals	suppositions,	they	need	to	motivate why	it	makes	sense,	given	a	Humean	metaphysics	of	laws,	to	evaluate	counterfactuals	in this	way.	We	will	provide	such	a	motivation	in	§5. You	may	worry	that	our	reply	to	Lange's	worry	is	incomplete	as	long	as	we	have not	provided	a	semantics	of	counterfactuals	that	meets	the	first	challenge.	Defending such	a	semantics	would	go	beyond	the	scope	of	the	current	paper.	Our	account, however,	is	highly	interesting	even	without	a	worked-out	formal	semantics	to accompany	it:	First,	it	would	be	pointless	for	Humeans	to	develop	such	a	semantics	as long	as	it	has	not	been	shown	that	it	can	be	motivated	on	Humean	grounds.	In	fact, Lange's	challenge	is	precisely	that	merely	providing	a	new	semantics	does	not	address 11 the	deeper	underlying	problem.	Our	goal	is	to	address	this	deeper	problem,	and	so	pave the	way	for	a	full	Humean	account	of	counterfactuals. Second,	there	is	reason	to	be	optimistic	that	Humeans	can	provide	a	suitable semantics	that	captures	our	judgments	about	nested	counterfactuals.	Lange's	proposal to	adopt	a	resilience	rule	naturally	extends	the	received	Humean	view	by	adjusting	the standards	for	similarity	between	possible	worlds.	However,	Humeans	who	would	like	to maintain	the	original	similarity	metric	can	adopt	an	even	more	conservative	strategy. Hall	(manuscript)	proposes	to	simply	restrict	the	sphere	of	possible	worlds	that	are considered	when	evaluating	counterfactual	suppositions	that	are	logically	consistent with	the	actual	laws	to	worlds	that	are	nomologically	possible	relative	to	the	actual world.	Hence,	only	worlds	in	which	the	actual	laws	are	true	are	candidates	for	the closest	possible	world	in	which	the	supposition	is	true.	Like	Lange's	resilience	rule,	this amendment	ensures	that	the	laws	are	held	fixed	across	both	nested	and	simple counterfactuals.	For	example,	Lange's	lone-electron	counterfactual	comes	out	true according	to	this	proposal.	If	we	consider	only	worlds	compatible	with	the	laws	of	the actual	world,	then	if	we	go	to	the	most	similar	world	to	the	actual	world	in	which	there is	only	one	electron,	the	closest	world	to	that	world	in	which	there	are	more	electrons	is still	one	in	which	Coulomb's	law	is	true.	At	the	same	time,	this	proposal	leaves	the machinery	of	the	received	semantics	untouched	and	merely	restricts	the	sphere	of possible	worlds.13 Third,	Humeans	who	want	to	maintain	all	aspects	of	the	received	semantics	have an	even	more	conservative	strategy	available.	They	can	argue	that	counterfactuals	such as	Lange's	lone-electron	example	are	strictly	false,	but	that	there	are	pragmatic	reasons for	asserting	them.	According	to	this	proposal,	our	intuitive	judgments	mistake	the pragmatic	assertability	of	these	counterfactuals	for	their	literal	truth.	This	proposal then	still	needs	to	show	how	the	relevant	pragmatic	aspects	of	our	counterfactual reasoning	are	motivated	in	light	of	a	Humean	metaphysics.	Humeans	who	are	attracted 13	This	list	of	Humean	moves	is	not	exhaustive.	Humeans	who	think	that	Humean	Supervenience is	only	contingently	true	might	hold	that	Lange's	nested	counterfactual	is	true	by	arguing	that the	closest	possible	lone-electron	world	is	an	anti-Humean	world	in	which	Coulomb's	law	still	is a	law.	A	different	proposal,	due	to	Bhogal	(forthcoming),	invokes	metaphysically	impossible worlds.	Bhogal	argues	that	nested	counterfactuals	such	as	Lange's	come	out	true	because	the closest	possible	lone-electron	world	is	a	(by	Humean	lights)	metaphysically	impossible	world	in which	Coulomb's	law	remains	a	law	despite	not	being	part	of	the	best	systems.	Thanks	to [omitted]	for	discussion. 12 to	his	pragmatic	approach	can	understand	our	proposal	in	§5	as	an	account	of	why	the relevant	nested	counterfactuals	are	assertable	despite	being	literally	false.	Before	we turn	to	our	positive	account,	however,	we	want	to	address	why	it	is	important	for Humeans	to	capture	our	judgments	about	nested	counterfactuals	in	the	first	place. 4.	The	importance	of	nested	counterfactuals Humeans	have	argued,	in	other	contexts,	that	some	of	our	intuitions	about	laws	issue from	an	incorrect	picture	of	laws	and	so	are	unreliable	(see	Beebee	(2000)	against governing-conceptions	of	laws).	Could	Humeans	employ	a	similar	strategy	to	argue	that our	judgments	about	nested	counterfactuals,	or	at	least	those	that	are	problematic	for Humeans,	can	be	set	aside	when	developing	a	theory	of	laws?	In	this	section,	we	will show	that	Humeans	cannot	ignore	nested	counterfactual	when	constructing	a	theory	of laws. Nested	counterfactuals	are	important	for	at	least	two	reasons.	First,	nested counterfactuals	reveal	features	of	counterfactual	relations	that	arguably	play	an important	role	in	science.	For	example,	Woodward's	(2003)	influential	theory	takes causal	explanations	in	the	sciences	to	exhibit	patterns	of	counterfactual	dependence.	A characteristic	feature	of	the	relevant	counterfactuals	is	stability,	that	is,	the	relevant counterfactuals	still	need	to	be	true	given	(at	least	some)	changes	in	the	background conditions	(Woodward	2007:	77).	Consider	the	following	counterfactual	about	a	spring: 'If	the	spring's	extension	were	different,	then	the	restoring	force	would	be	different	in accordance	with	Hooke's	law.'	For	this	counterfactual	to	be	stable,	it	still	needs	to	hold given	a	range	of	changes	in	the	background	conditions,	such	as	certain	changes	in	the spring's	temperature	or	location. Nested	counterfactuals	are	the	most	natural	tools	for	capturing	this	stability.	For the	counterfactual	about	the	spring	to	be	stable	under	changes	in	temperature,	the following	counterfactual	needs	to	be	true:	'If	the	spring's	temperature	were	somewhat different,	then	if	its	extension	were	different,	the	restoring	force	still	would	accord	with Hooke's	law.'	So,	if	something	along	the	lines	of	Woodward's	account	of	explanation	is correct,	nested	counterfactuals	are	relevant	for	scientific	explanations. Second,	nested	counterfactuals	are	essential	for	the	Humean	project	of	reducing all	modalities	to	fundamentally	non-modal	facts.	Counterfactuals	play	an	important	role in	this	reduction:	Humeans	analyze	counterfactuals	in	terms	of	best	system	laws;	use 13 the	so-analyzed	counterfactuals	to	analyze	causation	(Lewis	1986a);	and	then,	in	turn, appeal	to	causation	in	their	analyses	of	explanation	(Lewis	1986b)	and	dispositions (Lewis	1997).	So,	causation,	explanation,	and	dispositions	for	Humeans	ultimately presuppose	counterfactuals.	Nested	counterfactuals	then	are	important	for	the	Humean project	because	if	causation,	explanation,	and	dispositions	presuppose	counterfactuals, then	any	counterfactual	claim	about	these	phenomena	involves	a	nested	counterfactual. Let	us	exemplarily	work	through	the	case	of	causation.	Assume,	for	simplicity, that	a	simple	counterfactual	analysis	of	causation	is	correct:	an	event	c	causes	a	distinct event	e	iff	had	c	not	occurred,	then	e	would	not	have	occurred.	Now,	we	do	not	just make	claims	about	which	events	actually	cause	which	other	events.	We	also	often	make claims	about	which	events	would	have	caused	which	other	events	if	certain	things	had been	different.	For	example,	we	might	want	to	say:	'If	I	had	thrown	a	stone	at	the window,	my	stone	throw	would	have	caused	the	window	to	shatter.'	Or,	we	might	be interested	in	whether	some	causal	relation	still	would	have	held	if	certain	things	had been	different	(see	Lewis	1986:	186),	say	whether	it	is	true	that:	'If	there	had	been	more wind,	then	my	stone	throw	still	would	have	caused	the	window	to	shatter.'	If	a counterfactual	analysis	of	causation	is	true,	then	unpacking	these	claims	involves	nested counterfactuals.	For	example,	plugging	the	simple	counterfactual	analysis	into	the consequent	of	the	first	counterfactual	yields:	'If	I	had	thrown	a	stone	at	the	window, then	if	I	had	not	thrown	the	stone,	the	window	would	not	have	shattered.'	So, counterfactuals	about	causal	relations,	given	the	counterfactual	analysis	of	causation, are	implicit	claims	about	nested	counterfactuals. In	fact,	nested	counterfactuals	are	relevant	even	if	causation	is	not	analyzed counterfactually.	Counterfactuals,	at	the	very	minimum,	are	often	evidence	for	causal relations.	So,	nested	counterfactuals	are	important	for	getting	a	grip	on	what	causal relations	would	have	held	in	counterfactual	circumstances.	And,	for	analogous	reasons, nested	counterfactuals	are	relevant	whenever	we	entertain	counterfactuals	about explanation	and	dispositions	because	these	latter	phenomena,	like	causation,	are	closely 14 related	to	counterfactuals.14	So,	Humeans	cannot	simply	dismiss	all	nested counterfactuals	as	irrelevant.15 Could	Humeans	concede	that	some	nested	counterfactuals	are	important	but deny	the	importance	of	those	nested	counterfactuals	for	which	the	received	Humean view	arguably	returns	the	wrong	verdicts?	Recall	Lange's	example:	"Had	there	been nothing	but	a	lone	electron,	then	had	there	been	more	electrons	than	one,	the	force between	any	two	would	have	accorded	with	Coulomb's	law"	(Lange	2009a:	54). Humeans	might	argue	that	counterfactuals	of	this	kind	will	rarely	play	a	role	in	scientific practice	(cf.	Hall	manuscript;	but	see	our	discussion	in	§5	below). Many	counterfactuals	that	are	just	as	problematic	for	Humeans	as	Lange's example,	however,	seem	clearly	relevant	for	science.	Consider	the	following	claims about	causation,	dispositions,	and	explanation: 'Had	there	been	nothing	but	a	lone	electron,	the	absence	of	external	forces	would have	caused	it	to	move	inertially.' 'Had	there	been	nothing	but	a	lone	electron,	the	absence	of	external	forces	would have	explained	its	inertial	motion.' 'Had	there	been	nothing	but	a	lone	electron,	then	it	would	have	been	disposed	to attract	other	electrons	in	accordance	with	Coulomb's	law.' Investigating	the	causal,	explanatory,	and	dispositional	features	of	electrons	is	of	clear interest	to	science.	So,	it	is	hard	to	see	how	these	claims	could	be	dismissed	as 14	Cf.	Lange	(2009a:	fn.	23	and	fn.	25,	194–196).	Lewis's	counterfactual	cum	causal	analysis	ties dispositions	even	more	directly	to	nested	counterfactuals.	Here	is	Lewis's	"unlovely	mouthful" (Lewis	1997:	157):	"Something	x	is	disposed	at	time	t	to	give	response	r	to	stimulus	s	iff,	for some	intrinsic	property	B	that	x	has	at	t,	for	some	time	t'	after	t,	if	x	were	to	undergo	stimulus	s at	time	t	and	retain	property	B	until	t',	s	and	x's	having	of	B	would	jointly	be	an	x-complete	cause of	x's	giving	response	r"	(ibid.).	Lewis's	counterfactual	analysis	of	causation	entails	that	the consequent	of	the	above	counterfactual	already	presupposes	a	counterfactual	claim.	So,	we	get the	following	nested	counterfactual:	'If	x	were	to	undergo	stimulus	s	at	time	t	and	retain property	B	until	t',	then	if	s	and	x's	having	of	B	had	not	occurred	jointly,	x's	giving	response	r would	not	have	occurred.' 15	Could	Humeans	try	to	rephrase	all	nested	counterfactuals	as	non-nested	counterfactuals	with complex	antecedents?	This	strategy	will	not	work,	or	at	least	not	always.	For	example,	the nested	counterfactual	'If	I	had	thrown	a	stone	at	the	window,	then	if	I	had	not	thrown	the	stone, the	window	would	not	have	shattered'	clearly	is	not	equivalent	to	the	counterfactual	'If	had thrown	a	stone	and	I	had	not	thrown	a	stone,	then	the	window	would	not	have	shattered'.	See Lange	(2009a:	22–23)	for	a	similar	example. 15 unimportant.	Moreover,	each	claim	carries	a	commitment	to	some	nested counterfactual.	For	example,	the	first	claim	is	closely	related	to	the	nested counterfactual:	'If	there	had	been	nothing	but	a	lone	electron,	then	if	there	had	been external	forces	acting	on	it,	it	would	not	have	moved	inertially.' These	counterfactuals	are	as	problematic	for	a	Humean	account	of	laws	as Lange's	original	example.	For	example,	the	nested	counterfactual	in	the	previous paragraph	is	plausibly	true.	However,	in	a	world	whose	history	consists	only	of	a	single electron,	there	is	no	guarantee	that	the	actual	force	laws	will	be	part	of	its	best systematization.	In	this	case,	the	counterfactual	will	likely	come	out	as	false	according	to the	received	Humean	view.	But	if	Humeans	cannot	account	for	these	types	of	nested counterfactuals,	then	Lange's	challenge	has	not	been	met. In	sum,	Humeans	cannot	just	ignore	the	nested	counterfactuals	that	the	received Humean	view	gets	wrong.	They	either	need	to	motivate	an	alternative	semantics	of counterfactuals	that	incorporates	the	resilience	of	laws	under	nested	counterfactual suppositions,	or	they	need	to	offer	an	error-theory	that	'explains	away'	our	judgments about	the	problematic	nested	counterfactuals.	In	the	rest	of	the	paper,	we	will	spell	out a	Humean	motivation	for	an	alternative	semantics	that	gets	nested	counterfactuals	right (though	we	will	also	briefly	discuss	the	possibility	of	an	error-theory). 5.	Motivating	why	Humean	laws	are	counterfactually	resilient In	this	section,	we	present	a	motivation	for	holding	the	laws	fixed	in	counterfactual reasoning	that	goes	naturally	with	a	Humean	account	of	laws.	Moreover,	we	will	show that	this	motivation	extends	to	nested	counterfactuals	and	so	provides	Humeans	with the	resources	to	capture	the	kinds	of	counterfactuals	that	Lange	has	identified	as problematic. The	following	type	of	counterfactual	reasoning	plays	an	important	role	in science:	Suppose	you	want	to	predict	the	future	evolution	of	some	system,	such	as	a rock.	How	the	rock	will	behave	depends	not	only	on	its	intrinsic	properties	and immediate	environment.	It	also	depends,	for	example,	on	gravitational	and electromagnetic	forces	from	distant	bodies.	If	you	knew	the	complete	state	of	the	world and	had	unlimited	computational	resources,	you	could	use	the	laws	of	nature	to	infer the	rock's	behavior	with	complete	certainty.	But	in	practice	you	never	have	such complete	knowledge,	nor	would	you	have	the	computational	resources	to	utilize	it.	So, 16 making	predictions	about	systems	by	applying	the	laws	of	nature	to	the	world's complete	state	is	beyond	your	capabilities. But	there	are	other	predictions	that	you	can	use	the	laws	to	make.	You	can predict,	for	example,	how	the	rock	would	behave	if	it	were	the	only	object	in	the universe;	or,	how	it	would	behave	if	the	only	outside	force	acting	on	it	were	the	Earth's gravitation;	or,	perhaps	how	it	would	behave	if	it	were	acted	on	by	both	the	Earth's gravitation	and	the	gravitational	force	from	homogeneously	distributed	distant	galaxies but	nothing	else.	In	other	words,	we	can	use	the	laws	to	infer	how	the	rock	would behave	in	certain	non-actual	circumstances.	These	types	of	inferences	involve counterfactuals,	rather	than	indicative	conditionals,	since	we	apply	the	laws	to circumstances	that	are	known	not	to	obtain.	Entertaining	these	counterfactual suppositions	presents	us	with	simplified	scenarios	that	leave	out	physical	details	that prevent	us	from	applying	the	laws	to	the	actual	circumstances. Our	best	candidates	for	the	fundamental	physical	laws	are	such	that	applying	the laws	to	counterfactual	circumstances	in	this	way	often	yields	(approximately)	true predictions	about	actual	systems	(see	Hicks	2018	and	[author]).	For	example,	you	can make	approximately	true	predictions	about	the	evolution	of	your	rock	by	supposing, contrary	to	fact,	that	it	is	isolated	from	most	distant	going	ons.	Adam	Elga	makes	this point	in	the	following	passage: [W]hen	it	comes	to	the	rough	behavior	of	your	rock,	you	can	often	treat	it	as	if	it	were isolated	from	distant	influences.	Note	the	qualifications,	though.	Your	rock	isn't	really isolated	from	distant	influences.	For	example,	the	exact	microscopic	trajectories	of	the rock's	molecules	are	sensitive	to	goings-on	in	the	next	room,	due	to	gravitational	effects. But	who	cares	about	the	exact	trajectories	of	rock	molecules?	When	it	comes	to	getting around	in	the	world,	the	rough	macroscopic	behavior	of	rocks	is	much	more	important. (Elga	2007:	109;	italics	in	the	original) Note	Elga's	emphasis	on	the	counterfactual	nature	of	this	inference.	In	reality,	there	are numerous	distant	forces	acting	on	the	rock.	These	forces,	however,	typically	do	not make	a	difference	to	the	macroscopic	behavior	of	systems	such	as	rocks.	So,	we	often can	make	(approximately)	true	predictions	about	a	rock's	macroscopic	behavior	by 17 counterfactually	supposing	that	it	is	not	acted	on	by	such	forces.16	In	doing	so,	we consider	a	simplified,	counterfactual	model	of	the	rock	that	is	tailored	to	our	epistemic limitations	and	computational	resources.	So,	counterfactuals	help	creatures	like	us,	who have	only	limited	knowledge	at	their	disposal,	to	infer	(approximate)	actual	truths. As	Frisch	(2014:	62–66)	points	out,	physicists	almost	never	apply	the	laws	to complete	models	that	include	every	physical	detail	of	a	system	since	such	models	would be	much	too	complex.	The	type	of	counterfactual	reasoning	just	sketched	thus	is pervasive	in	science.	We	are	not	saying	that	all	counterfactual	reasoning	is	aimed	at inferring	actual	truths.	When	we	ask,	e.g.,	what	would	be	the	case	if	Denmark	were	ruled by	beavers	or	if	kangaroos	had	no	tails,	it	is	not	clear	that	we	aim	to	make	predictions about	the	actual	world.	However,	we	contend	that	getting	at	actual	truths	is	at	least	one important	goal	of	counterfactual	reasoning. This	role	of	counterfactual	reasoning	motivates	a	Humean	account	of	the	modal resilience	of	laws	that	is	different	from	the	received	Humean	view.	We	can	explain	the laws'	modal	resilience	by	the	utility	of	applying	the	actual	laws	to	counterfactual circumstances	for	the	purpose	of	getting	at	actual	truths.	Our	goal	is	to	predict	how	an actual	physical	system	will	evolve	in	the	actual	circumstances.	The	best	tool	for	making such	predictions	are	the	actual	laws.	But	our	limited	capabilities	prevent	us	from applying	the	laws	to	the	exact	actual	circumstances.	So,	we	instead	apply	the	actual	laws to	counterfactual	circumstances	that	figure	as	epistemically	more	tractable	proxies.	Our best	candidates	for	the	physical	laws	allow	us	to	often	still	arrive	at	(approximately) true	predictions	in	this	way	because	these	laws	are	such	that	for	many	physical	systems the	exact	physical	details	do	not	matter	for	their	rough,	macroscopic	behavior.17 At	the	heart	of	Humeanism	is	the	claim	that	the	world	fundamentally	is exhausted	by	the	distribution	of	perfectly	natural,	categorical	properties	throughout spacetime.	Laws	of	nature,	hence,	do	not	and	cannot	describe	any	genuine	modal 16	For	some	physical	systems,	including	chaotic	systems,	their	behavior	is	sensitive	to	the	exact physical	details.	But	for	many	systems	this	is	not	the	case	and	for	these	systems	we	can	make (approximately)	true	inferences	from	counterfactual	circumstances. 17	Bhogal	(forthcoming)	provides	a	Humean	reason	for	applying	the	actual	laws	to counterfactual	circumstances	that,	though	less	pragmatic,	is	similar	in	spirit	to	our	own.	He argues	that	considering	alternative	situations	that	are	consistent	with	the	actual	laws	can	help us	better	understand	the	laws	by	drawing	out	their	implications.	Bhogal	shows	how	his	account helps	with	the	problem	of	nested	counterfactuals	as	well	as	other	important	problems	for Humean	reductionism	about	laws.	We	address	how	our	own	account	bears	on	these	other problems	elsewhere	(see	[omitted]). 18 aspects	of	reality.	Humeans,	instead,	maintain	that	laws	provide	efficient	summaries	of actual	goings	on	that	"will	serve	you	well,	or	reasonably	well,	or	as	well	as	possible,	in making	your	way	about	in	the	world"	(Albert	2015:	23;	see	also	Beebee	2000:	547).	In other	words,	the	ultimate	purpose	of	laws	of	nature	for	Humeans	is	to	facilitate	the efficient	derivation	of	actual	truths.	Our	motivation	of	the	modal	resilience	of	laws derives	from	this	overarching	Humean	goal.	Holding	the	laws	fixed	in	counterfactual reasoning	helps	creatures	like	us	to	infer	(approximate)	actual	truths.	So,	the counterfactual	resilience	of	laws	of	nature	is	motivated	by	the	arch-Humean	goal	of inferring	(approximate)	truths	about	the	Humean	mosaic.18	Our	proposed	Humean motivation	for	the	laws'	modal	resilience	extends	naturally	to	nested	counterfactuals and	so	answers	Lange's	objection.	Nested	counterfactual	suppositions,	just	like	simple counterfactual	suppositions,	facilitate	inferring	actual	truths.	Simple	counterfactuals allow	us	to	use	the	laws	to	infer	(approximate)	truths	about	actual	systems	from incomplete	information	about	these	systems.	The	role	of	nested	counterfactuals	is	more indirect.	Suppose	you	want	to	predict	how	an	electron	will	behave.	As	pointed	out above,	it	would	be	vastly	too	complex	to	apply	the	laws	to	the	complete	current	state	of the	world.	Instead,	you	apply	the	laws	to	a	simplified	model	that	contains	only	the electron	and	(perhaps)	the	gravitational	force	of	the	Earth,	leaving	out	many	other forces	that	also	act	on	the	electron.	How	can	you	be	confident	that	the	predictions	you derive	from	this	simplified,	counterfactual	model	hold	true	for	the	actual	electron? Nested	counterfactuals	help	justify	the	relevant	predictions.	First,	since	our knowledge	not	only	of	the	electron's	surroundings	but	also	of	the	state	of	the	electron itself	is	imprecise,	we	cannot	reliably	infer	anything	from	the	simplified	model	if	the resulting	predictions	are	extremely	sensitive	to	the	electron's	initial	state.	So,	within	the counterfactual	supposition	that	the	electron	is	isolated,	we	need	to	test	what	impact	its exact	initial	state	has	on	the	predicted	behavior.	We	test	for	this	insensitivity	by 18	This	motivation	also	provides	new	resources	for	answering	another	challenge	against Humean	accounts	of	laws.	Hall	(2015)	worries	that	if	laws	of	nature	are	merely	efficient summaries	of	the	total	distribution	of	non-modal	properties	(as	Humeans	think),	then	it	is puzzling	why	science	posits	laws	that	cover	a	wide	range	of	non-actual	circumstances.	This worry	is	about	'modal	latitude'.	It	concerns	the	information	content	of	the	laws,	viz.,	why	they also	cover	non-actual	circumstances.	So,	it	is	different	from	the	question	in	this	paper,	which	is why	the	laws	are	resilient	under	counterfactual	suppositions.	However,	in	[omitted]	we	argue that	'modal	latitude'	also	is	a	by-product	of	the	laws'	allowing	us	to	infer	(approximate)	truths given	our	epistemic	situation	as	limited	creatures. 19 considering	nested	counterfactuals	of	the	form:	'If	there	had	been	only	a	single	electron, then	if	its	exact	position	had	been	x,	it	would	(still)	behave	this	way.'	Only	if	its	behavior is	relatively	insensitive	to	its	initial	position,	can	we	trust	our	simplified	model	to	make approximately	correct	predictions.	In	the	ideal	case,	the	behavior	of	the	electron	in	the simplified	model	will	depend	continuously	on	its	initial	conditions	such	that	small errors	about	its	initial	position	only	lead	to	small	errors	in	predictions	about	its behavior.	Nested	counterfactuals	allow	us	to	test	whether	this	is	the	case	for	our simplified	model. Second,	nested	counterfactuals	justify	that	omitting	certain	factors	from	our models	is	legitimate.	How	do	we	know	that	our	simplified,	counterfactual	model	makes approximately	true	predictions	about	the	behavior	of	the	electron	despite	leaving	out various	distant	objects?	An	obvious	way	is	to	suppose	the	presence	of	some	distant objects	and	use	the	laws	to	infer	what	difference	they	would	make	to	the	electron's behavior.	If	such	distant	objects	make	little	or	no	difference,	then	we	have	reason	to trust	the	predictions	of	the	original,	simplified	model.	We	will	thus	consider	nested counterfactuals	of	the	form:	'If	there	were	only	a	single	electron	e	and	the	gravitational influence	from	the	Earth,	then	if	some	distant	object	x	were	present,	e	would	(still) behave	like	this.'	So,	nested	counterfactuals	play	a	crucial	role	in	justifying	the application	of	simplified	models	to	actual	systems. In	fact,	Lange's	counterfactual	"[h]ad	there	been	nothing	but	a	lone	electron,	then had	there	been	more	electrons	than	one,	the	force	between	any	two	would	have accorded	with	Coulomb's	law"	(Lange	2009a:	54)	can	be	understood	as	serving	this purpose.	Suppose	we	use	a	counterfactual	model	that	represents	a	certain	actual electron	as	the	only	particle	there	is.	Lange's	nested	counterfactual	then	becomes relevant	for	justifying	inferences	about	the	electron	that	we	draw	from	this counterfactual	model.	We	might,	for	example,	suppose	the	presence	of	other	electrons in	our	counterfactual	model	and	use	the	actual	laws,	including	Coulomb's	law,	to determine	how	the	resulting	forces	would	alter	the	electron's	behavior.	In	doing	so,	we hold	the	actual	laws	fixed	in	order	to	determine	how	sensitive	the	model's	predictions are	to	changes	in	the	background	conditions,	such	as	the	presence	of	further	electrons. Adding	further	charged	particle	to	the	model	will,	in	accordance	with	Coulomb's	law, make	some	difference	to	the	electron's	behavior.	However,	depending	on	the	distance and	charge	of	the	additional	particles,	this	difference	may	be	negligible	for	predicting 20 the	electron's	approximate	behavior.	Considering	nested	counterfactuals	like	Lange's then	teaches	us	to	what	extent	we	can	ignore	the	presence	of	other	particles	and	so trust	the	predictions	of	our	simplified	model. We	then	have	a	principled	Humean	motivation	for	holding	the	actual	laws	fixed under	both	simple	and	nested	counterfactual	suppositions.	With	regard	to	Lange's example,	it	then	follows	that	when	we	suppose	the	presence	of	further	electrons	in	the second	counterfactual	supposition,	we	still	hold	fixed	Coulomb's	law.	So,	pace	Lange, building	the	fixity	of	the	actual	laws	into	our	semantics	of	counterfactuals	has	a perfectly	good	Humean	motivation.	Holding	the	actual	laws	fixed	allows	us	to	make	and justify	inferences	about	actual	systems.	Moreover,	this	Humean	motivation	for	holding the	actual	laws	of	nature	fixed	is	completely	neutral	with	regard	to	how	this	constraint is	formally	implemented	in	the	semantics	(or	pragmatics)	of	counterfactuals	(see	our discussion	at	the	end	of	§3). This	motivation	for	the	modal	resilience	of	laws	and	the	resulting	account	of (nested)	counterfactuals	fits	well	with	the	general	Humean	outlook	on	modality. Humeans	hold	that	reality	has	no	fundamental	modal	structure.	So,	the	import	of counterfactual	reasoning	cannot	be	to	map	out	any	genuine	modal	structure	of	reality. Instead,	on	our	Humean	view,	the	primary	purpose	of	investigating	counterfactual situations	and	counterfactually	altering	them	is	inferring	truths	about	the	actual	world. And	this	purpose	is	best	served	by	holding	the	actual	laws	fixed	under	both	simple	and nested	counterfactual	suppositions.	So,	the	utility	of	applying	the	actual	laws	to counterfactual	circumstances	for	inferring	actual	truths	explains	why	the	laws	are	held fixed	under	counterfactual	suppositions.19 Before	closing,	we	want	to	briefly	discuss	an	alternative	Humean	reaction	toward the	above	described	role	of	nested	counterfactuals	in	scientific	reasoning.	Defenders	of the	received	Humean	view	might	put	forward	an	error-theory	about	nested 19	Our	account	also	addresses	Lange's	(2009a:	55)	worry	about	counterfactuals	such	as	"Had there	been	nothing	in	the	universe's	history	except	for	two	electrons,	then	Coulomb's	law	would still	have	been	true."	Lange	(ibid.)	worries	that	Humeans	cannot	supply	a	"scientific	explanation of	the	truth	of	Coulomb's	law"	in	such	a	world	because	Coulomb's	law,	though	true,	is	not	a	law according	to	Humeans	(due	to	being	not	part	of	its	best	systematizations).	On	our	Humean account	of	counterfactuals,	this	explanatory	request	does	not	even	arise.	Counterfactual suppositions	are	not	windows	into	distant	worlds	whose	features	we	then	seek	to	explain.	They are	mere	tools	that	we	us	to	infer	truths	about	the	actual	world,	and	so	we	do	not	have	to scientifically	explain	any	of	their	aspects. 21 counterfactuals	that	come	out	wrong	according	to	their	view.	We	have	argued	that scientists	use	counterfactual	suppositions	about	worlds	that	contain,	for	example,	only	a lonely	electron	to	facilitate	inferences	about	actual	electrons	that	are	isolated	from certain	aspects	of	their	environment.	But	Humeans	might	argue	instead	that	what scientists	are	actually	stipulating	in	these	counterfactuals	is	not	that	only	a	single electron	exists	but	that	some	electron	is,	contrary	to	fact,	completely	isolated	from	its environment.	Thus,	the	nested	counterfactual	scientists	are	really	interested	in	is	not Lange's	but	instead:	"If	an	electron	had	been	completely	isolated	from	its	environment, then	if	there	had	been	another	electron	in	its	vicinity,	they	would	have	behaved	in accordance	with	Coulomb's	law." This	difference	in	the	content	of	the	relevant	counterfactuals	matters.	While Lange's	counterfactual	about	the	lone	electron	comes	out	false	according	to	the	received Humean	view,	the	alternative	counterfactual	about	an	isolated	electron	arguably	comes out	true.	After	all,	the	closest	possible	world	to	the	actual	world	in	which	some	electron is	fully	isolated	from	its	environment	plausibly	still	includes	Coulomb's	law	in	its	best systematization.	At	the	same	time,	counterfactuals	about	fully	isolated	electrons plausibly	could	play	the	same	role	in	facilitating	inferences	about	actual	systems	as counterfactuals	about	lone	electrons.	These	counterfactuals	could	be	used	to	justify predictions	derived	from	models	that	leave	out	certain	aspects	of	the	environment. Humeans	could	then	maintain	the	received	view	of	counterfactuals	and	argue	that	we mistakenly	regard	counterfactuals	such	as	Lange's	as	true	because	we	confuse	them with	similar	counterfactuals	about	isolated	systems. We	are	not	in	principle	averse	to	this	more	conservative	Humean	approach	to the	challenge	posed	by	nested	counterfactuals.	Nonetheless,	we	prefer	revising	the received	Humean	view	of	counterfactuals	to	guarantee	the	resilience	of	laws	under nested	counterfactual	suppositions.	First,	the	above	error-theory	is	not	very	plausible.	It is	extremely	natural	that	when	scientists	construct	simplified	models	that	ignore	all external	influences	on,	for	example,	an	electron	they	do	indeed	stipulate	that	this electron	is	all	there	is.	Such	a	lonely	electron	model,	after	all,	is	much	simpler	to construct	than	a	model	in	which	the	electron	is	still	embedded	in	an	environment	like ours	but	where	this	environment	has	no	influence	on	its	behavior.	In	many	cases,	it	is far	from	obvious	what	a	model	that	satisfies	these	latter	constraints	and	in	which,	in addition,	the	actual	laws	are	true	would	even	look	like. 22 And,	second,	not	all	scientifically-relevant	nested	counterfactual	can	be	easily reinterpreted	as	concerning	isolated	systems.	For	example,	consider	the	following	two counterfactuals	about	the	universe	as	a	whole: 'If	the	initial	mass-energy	of	the	universe	had	been	twice	as	high,	its	increased mass-energy	would	have	caused	the	universe	to	expand	at	a	different	rate	(or	not to	expand	at	all).' 'If	the	initial	mass-energy	of	the	universe	had	been	twice	as	high,	its	increased mass-energy	would	have	explained	why	the	universe	had	expanded	at	a	different rate	(or	not	expanded	at	all).' These	counterfactuals	appear	to	be	true.	Moreover,	both	claims	are	closely	related	to nested	counterfactuals.	For	example,	the	first	claim	is	closely	related	to	the	nested counterfactual:	'If	the	initial	mass-energy	of	the	universe	had	been	twice	as	high,	then had	there	been	only	half	of	this	mass-energy,	the	universe	would	have	expanded	at	its actual	rate.' It	is	doubtful	whether	the	received	Humean	view	can	account	for	our	judgments about	these	counterfactuals.	The	closest	possible	world	in	which	the	mass-energy	of	the universe	is	twice	as	high	may	well	be	one	in	which	the	Big	Bang	never	happened.	The pattern	of	non-nomic	facts	in	such	a	world	would	then	be	drastically	different.	As	a consequence,	many	actual	laws	may	not	be	part	of	this	world's	best	systematization.	But then	the	actual	laws	of	nature,	according	to	the	received	Humean	view,	may	not	be	true under	the	nested	counterfactual	supposition,	and	so	there	is	no	guarantee	that	the counterfactual	will	be	assigned	the	correct	truth	value.20	At	the	same	time,	it	is	hard	to see	what	alternative	nested	counterfactuals	scientists	might	have	in	mind	when entertaining	the	above	considerations.	By	contrast,	a	revised	Humean	account	of 20	Some	Humeans	hold	that	the	universe's	initial	macrostate	is	a	law	of	nature	(see	Albert	2015 and	Loewer	2012;	but	see	Earman	2006).	The	above	counterfactuals	would	then	not	be counterexamples	to	CR	because	the	supposition	that	the	initial	mass-energy	of	the	universe	is twice	as	high	would	be	logically	inconsistent	with	the	actual	laws.	However,	there	may	be similar	counterexamples	where	the	universe,	while	having	the	same	initial	macrostate,	has	a highly	atypical	initial	microstate	that	leads	to	a	vastly	different	distribution	of	matter.	Moreover, Humeans	would	still	have	to	explain	the	(at	least	apparent)	truth	of	the	counterfactuals	even	if they	turn	out	to	be	counter-nomic. 23 counterfactuals	that	holds	the	actual	laws	fixed	under	all	counterfactual	suppositions delivers	the	correct	truth	values	for	these	kinds	of	counterfactuals. 6.	Conclusion We	have	shown	that	Humeans	can	account	for	the	modal	resilience	of	laws	of	nature. According	to	Humeans,	the	primary	purpose	of	(nested)	counterfactual	suppositions	is to	help	us	infer	actual	truths.	Holding	the	actual	laws	of	nature	fixed	under	both	simple and	nested	counterfactual	suppositions	allows	us	to	use	them	for	this	very	purpose. This	Humean	take	on	counterfactuals	and	natural	modality	contrasts	sharply	with	that of	most	anti-Humeans.	For	anti-Humeans	like	Lange,	counterfactual	latch	on	to	some fundamental	aspect	of	reality.	Humeans,	by	contrast,	hold	that	counterfactuals	are merely	effective	means	for	getting	at	non-modal	truths.	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