INDEFINITELY	DESCENDING	GROUND Einar	Duenger	Bohn University	of	Agder [Forthcoming	in	Reality	and	its	Structure,	edited	by	R.Bliss	&	G.Priest,	OUP.] We	often say that some facts obtain in	virtue	of others, e.g. that semantic facts obtain in virtue of facts about language-use, or that normative facts obtain in virtue	of	descriptive	facts,	or	that	mental	facts	obtain	in	virtue	of	physical	facts. The	question	I'm	interested	in	is:	must	such	in-virtue-of	chains	eventually	end	in some facts that don't obtain in virtue of any other facts? Or can they go on indefinitely	without end?1	In other	words (to be clarified below),	must the invirtue-of	relation	be	well-founded? In	what	follows,	I	argue	that	it	must	not,	and	point	to	some	reasons	for	it even actually not being so. More specifically, in section 1, I introduce	what is perhaps the closest we get to a standard notion of the in-virtue-of relation, namely	a	relation	of	grounding;	in	section	2,	I	argue	that	there	is	no	good	reason to	think	that	this	relation	of	grounding	must	be	well-founded;	and	in	section	3,	I argue	more	directly	that	it's	not	necessarily	well-founded,	and	further	that	there are	reasons	to	think	it's	actually	non-well-founded. 1.	The	standard	notion	of	grounding Everything about in-virtue-of-talk can and has been questioned, but the following is perhaps the closest	we get to a standard underlying notion these days (Rosen, 2010; Bliss & Trogdon 2014; Raven 2015). Saying that a fact obtains	in	virtue	of	some	others	is	to	say	that	the	fact	is	grounded	in	those	other facts.	Such	grounding	is	taken	to	be	a	one-many	relation	between	one	fact	and	a plurality	of	(one	or	more)	facts,	imposing	what	we	might	(with	some	slack)	call	a strict partial order on its domain: 2 no fact even partially grounds itself (irreflexivity);	if	a	fact	p	is	grounded	in	some	facts	qq,	then	no	one	of	qq	is	even partially	grounded in	p (asymmetric); and if a fact	p is grounded in some facts q,rr,	and	q	is	grounded	in	some	facts	ss,	then	p	is	grounded	in	rr,ss	(transitivity). Also,	if	a	fact	p	is	grounded	in	some	facts	qq,	then,	necessarily,	if	qq	obtain,	then	p obtain	(necessitation);	if	a	fact	p	is	grounded	in	some	facts	qq,	then	is	not	the	case that for any r, p is grounded in qq,r (non-monotonicity); and if a fact p is grounded in	some facts	qq, then	qq	metaphysically	explain	p (explanatoriness).3 The	latter	kind	of	metaphysical	explanation	amounts	to	constitutively	explaining what	a	fact	consists	in.	The	underlying	notion	of	grounding	is	a	notion	of	full	as 1	Note	that	there	can	be	infinite	chains	that	are	limited,	but	I	wish	to	talk	about	infinite chains	that	are	unlimited;	I	here	and	throughout	use	the	term	'indefinite'	for	that purpose.	This	should	not	be	confused	with	the	way	'indefinite'	is	sometimes	used	in	the philosophy	of	mathematics,	where	there	is	a	constructional	or	potential	aspect	to	it,	nor should	it	be	confused	with	the	way	'indefinite'	is	sometimes	used	in	debates	over vagueness,	where	there	is	an	aspect	of,	well,	vagueness	to	it. 2	I	thus	adopt	the	so-called	predicate	approach,	not	the	operator	approach.	I	also	assume grounding	to	be	factive. 3	One	might	here	distinguish	between,	on	the	one	hand,	grounding	being	explanation, and	on	the	other	hand,	grounding	backing	explanation.	I	assume	the	former,	unless noted	otherwise. 2 opposed	to	partial	grounding,	where	a	fact	p	is	partially	grounded	in	some	facts qq	iff	there	are	some	facts	rr	such	that	p	is	fully	grounded	in	rr	and	qq	are	among rr; p being fully grounded in rr being our official primitive, but intuitively characterized	as	providing	a	complete	metaphysical	explanation	of	p. I henceforth call this the standard	notion of grounding (SNG). I will not further	discuss	or	defend	SNG	or	any	of	its	abovementioned	features.4	Instead,	I will	here	simply	assume	SNG	in	order	to	argue	against	it	being	necessarily	wellfounded,	in	favor	of	some	reasons	for	it	actually	being	non-well-founded. What is the notion of well-foundedness in play? There has been some ambiguity in the literature with respect to what it is more exactly, but my arguments	below	will	be	directed	at the following	notion identified in	Schaffer (2009, 2010), and made more precise in Dixon (forthcoming) and Rabin & Rabern (forthcoming):5	every non-fundamental fact p is fully grounded in some fundamental	facts	qq,	where	a	fact	q	is	fundamental	iff	there	are	no	facts	rr	such that	q	is	(partially	or	fully)	grounded	in	rr.6	I	henceforth	call	this	notion	of	wellfounded	grounding	WF,	regimented	as	follows: (WF):	∀p(∼Fp→∃qq(Fqq∧qqGp)) where 'qq'	range	over	pluralities	of	(one	or	more)	facts, 'p'	over	single	facts, 'F' expresses	being	fundamental,	and	'G'	expresses	grounding.7	The	question	then	is simply	this:	must	SNG	obey	WF? 2.	Why	believe	grounding	must	be	well-founded? What	are the	arguments for	WF?	There	aren't	many. It	seems	to	be	more	of	an assumed	metaphysical	axiom (or	metaphysical law) supported	by intuition. The underlying intuition is perhaps most forcefully identified and endorsed in Schaffer	(2009:376,	2010:37),	where	he	claims	that	'[t]here	must	be	a	ground	of being.	If	one	thing	exists	only	in	virtue	of	another,	then	there	must	be	something from which the reality of the derivative entities ultimately derives.' Schaffer (2010:62)	further	claims	that	if	there	is	no	ultimate	ground,	then	'[b]eing	would be infinitely deferred, never achieved.' Finally, Schaffer (forthcoming: section 4.5) claims that '[g]rounding	must be	well-founded because a grounded entity inherits	its	reality	from	its	ground,	and	where	there	is	inheritance	there	must	be a	source.'	And	(ibid): 'the	grounded	exists in	virtue	of its	ground.	This is	why	a 4	For	references	to	further	discussions	on	each	of	these	features,	see	Bliss	&	Trogdon (2014)	and	Raven	(2015).	For	a	general	criticism	of	an	overall	notion	of	grounding,	see Wilson	(2014)	and	Koslicki	(2015).	See	also	Dasgupta	(2014a),	where	grounding	is argued	to	be	many-many,	rather	than	one-many. 5	Note	that	the	following	notion	of	well-foundedness	is	not	the	mathematical	(settheoretical)	notion	of	well-foundedness.	The	above	well-foundedness	of	grounding	is	a distinctively	metaphysical	notion.	Note	also	that	this	is	just	one	among	several	notions	of metaphysical	well-foundedness.	Though	I	think	much	of	what	I	go	on	to	say	does	not hinge	on	this	particular	notion,	my	conclusions	should	be	hedged	accordingly. 6	See	Dasgupta	(2014b)	for	some	problems	with	the	above	definition	of	fundamentality. Fortunately,	those	problems	will	not	affect	my	overall	argument	in	this	paper. 7	I	take	'F'	to	be	distributive,	but	see	fn.13,	section	2	below. 3 source of reality is needed, in order for there to be anything to transfer.'8 Cameron	(2008:6)	too	finds	Schaffer's	intuition	appealing	(though	he	ultimately rejects that it must hold in favor of it only most likely actually holding for methodological	reasons):	'if	we	never	reach	a	bottom	level,	then	it	is	hard	to	see why	there	are	any	complex	objects	at	all.'9 The intuition thus seems to be something like this: reality, or being is transferred from the	ground to the	grounded, so	all facts	gain	their	being from their	ground,	so	if	there	is	no	bottom	ground,	there	is	nowhere	from	which	the transfer of being initially comes, nowhere from which to gain being to begin with,	so	SNG	must	obey	WF	on	pain	of	there	not	being	any	(being	to)	facts	at	all.10 Here is one way to make the intuition into an argument for WF: by definition,	something	is	a	fundamental	fact	if	and	only	if	it	has	no	ground;	hence, if there are no fundamental facts, all facts have ground; and if all facts have ground, there	are	no facts;	but	obviously there	are	some facts;	hence there	are some	fundamental	facts.	Let's	call	this	the	argument	for	WF. The argument is valid; the	main question is	why	we should believe the next	to	last	premise:	if	all	facts	have	ground,	there	are	no	facts?	I	for	one	simply don't	feel	the	intuitive	pull	here.11	An	intuition	pump	might	come	by	the	more	or less dynamical metaphors often used to explain the grounding relation: the ground transmits its being to the grounded, the grounded gains, achieves, or derives its being from the ground. So, if there is no bottom ground, there is nothing that can thus transmit being to the grounded, nothing from	which the grounded	can thus	gain, achieve	or	derive its	being.	The	dynamical talk	makes this	sound	somewhat	plausible.	It's	as	if	you	are	to	fill	up	a	swimming	pool	by	the use of a hose: if nothing comes	out of that hose, then	of course the swimming pool	will	not	be	filled	up.	Or,	at	least	in	my	experience,	if	I	don't	at	some	definite point start	writing	my paper, it just	won't be	written. But the problem is that grounding is nothing like such dynamical processes. There is no such definite dynamical	starting	point	of the	grounding	chain.	Grounding is like	a	synchronic, static	mathematical relation (like in arithmetic), not like a	diachronic,	dynamic physical relation (like in thermodynamics, or action theory). Grounding is an explanation	of	what	the	obtaining	of	a	fact	consists	in,	atemporally;	grounding	is not	an	explanation	of	the	causal	history	of	that	fact	(cf.	Fine,	2001,	2012;	Rosen, 2010).	So,	any	intuitive	pull	we	might	feel	from	the	dynamical	metaphors	is	of	no help	in	a	defense	of	SNG	necessarily	obeying	WF. Now,	before	I	look	at	other	ways	to	try	to	defend	the	above	premise	in	the argument for WF, consider the argument that simply drops it: by definition, something is a fundamental fact iff it has no ground; hence, if there are no 8	Thomas	Aquinas'	(1266-8/1993:200-202),	in	his	five	ways	towards	the	necessary existence	of	God,	shares	Schaffer's	intuition	concerning	the	need	for	a	source	of	being.	In general,	there	are	great	similarities	between	Aquinas'	foundationalism	in	his	five	ways and	Schaffer's	foundationalism	with	respect	to	grounding. 9	Note:	Schaffer	doesn't	and	Cameron	might	not	endorse	the	full	package	of	SNG,	but officially	I'm	here	only	interested	in	whether	SNG	in	particular	must	be	well-founded (though	I	do	believe	my	arguments	generalize	to	other	notions	of	grounding	as	well). 10	For	more	on	this	picture	of	transference,	inheritance,	or	source	of	being,	see	Trogdon (ms).	I	treat	the	notions	of	reality	and	being	as	interchangeable,	but	try	to	keep	the notion	of	existence	separate;	though	in	fact	nothing	hinges	on	this	for	present	purposes. 11	And,	in	any	case,	why	believe	my	intuitions	match	deep	metaphysical	truths? 4 fundamental facts, all facts have ground. Now that is a solid conditional argument	for	what	I	henceforth	call	indefinitely	descending	ground: (IDG):	∀p∃qq(qqGp) Given our assumption that G is a strict partial order as per SNG, IDG gives us infinite, non-ending chains of grounding.12	Given some very minor, plausible assumptions, IDG is incompatible with	WF. Proof: assume	WF and ∼Fp. Then, ∃qq(Fqq∧qqGp).	Let	q1	be	one	of	those	qq	and	assume	the	distributivity	of	F.	It then	follows	that	Fq1;	but	by	definition	of	fundamentality,	∀p(∼Fp↔∃ss(ssGp)); hence	∼∃ss(ssGq1);	but	by	IDG,	∃qq(qqGq1);	hence,	contradiction.	Now,	the	minor assumptions	that	fundamentality	is	a	distributive	property	and	the	definition	of fundamentality is here taken for granted (though neither one is beyond dispute13),	so	WF	and	IDG	are	incompatible. Now,	one	way	to	indirectly	defend	the	controversial	premise	in	the	above argument	for	WF	(i.e.	the	premise	that	if	all	facts	have	ground,	there	are	no	facts) is	to	argue	that	IDG	amounts	to	an	appropriately	vicious	infinite	regress.	I	take	it	a benign	infinite	regress	won't	do	(for	example,	it	's	not	a	problem	that	we	have:	's' is	true;	''s'	is	true'	is	true;	'''s'	is	true'	is	true'	is	true;	and	so	on	ad	infinitum).	I	also take	it	a	mere	infinite	regress	won't	do	(for	example,	it's	not	a	problem	that	zero has infinitely	many	successors).	Rather, IDG	must	amount to	an infinite	vicious regress,	and	it	must	be	of	the	appropriate	kind	to	support	the	argument	for	WF. But	what	could	such	an	appropriately	infinite	vicious	regress	be	in	this	case? I can think	of at least two candidates (adapted from	Nolan, 2001;	Bliss, 2013).	The	first	candidate	deals	with	reductive	explanations.	Now, 'reduction' is said	in	many	ways,	but	assume	SNG	is	reductive	in	the	sense	that	if	qqGp,	then	qq explain away p as being in some sense non-real. Given IDG, one would then explain	away facts,	but	never	explain them	away in terms	of something that is not	thus	further	explained	away.	One	might	then	get	the	feeling	that	every	fact	p is somehow explained away, but into nothing, so to speak; that every fact is 'infinitely	deferred,	never	achieved'	(Schaffer,	2010:6314). But,	first,	why	think	grounding	is	thus	explanatorily	reductive?	It	is	not	a common view of grounding (Fine, 2001, 2012; Schaffer, 2009, 2010; Rosen, 2010).	In	fact,	much	initial	motivation	for	appealing	to	grounding	is	to	be	able	to truly	say	that	some	things	obtain	without	thereby	admitting	that	they	are	as	real as	all	other	things	obtaining	(Schaffer,	2009).	For	example,	we	want	to	say	–	truly 12	Cf.	Bliss	(2013);	Tahko	(2014);	Morganti	(forthcoming).	With	G	being	transitive	but failing	irreflexivity,	we	could	have	loops	of	ground;	see	Bliss	(2014).	I'm	not	in	principle opposed	to	such	loops,	but	SNG	is	for	present	purposes	assumed	to	be	irreflexive,	so,	by assumption,	no	loops. 13	If	there	are	fundamental	facts,	but	fundamentality	is	a	collective	property,	things	will look	slightly	different.	Though	that	is	an	interesting	idea,	I	will	ignore	it	in	what	follows since	I	believe	that	there	most	likely	are	no	fundamental	facts.	See	Dasgupta	(2014b)	for criticism	of	the	notion	of	fundamentality. 14	Though	note	that	to	the	extent	one	is	concerned	with	grounding	objects	rather	than facts,	the	notion	of	grounding	seems	to	fail	the	assumption	of	explanatoriness,	in	which case	one	loses	this	particular	defense	of	his	intuition.	One	must	then,	as	e.g.	Schaffer (forthcoming)	does,	appeal	to	a	notion	of	grounding	that	backs	explanation,	without grounding	itself	being	explanation. 5 – that there	are tables	and	chairs,	but	not thereby	admit that tables	and	chairs are	as	fundamental	as	particles.	So,	as	far	as	I	can	tell,	a	proponent	of	IDG	could and	should	simply	reject	that	grounding	is	explanatorily	reductive.	Grounding	is explanatory,	but	non-reductive.15	Grounding	metaphysically	explains	a	given	fact in terms of other facts, but grounding does not thus explain away that fact as somehow	non-real.16 Second,	assume	grounding	is	thus	explanatorily	reductive.	Then	the	above argument, corresponding intuition and supposed vicious regress get things backwards.	By	SNG,	the	grounded	has	its	being	(or	nature,	or	existence)	in	virtue of the ground. But if so, the ground surely cannot have less being than the grounded.	Either the	ground	has the	same	degree	of	being	as the	grounded,	or the	ground	has	more	being	than	the	grounded.	But	then,	as	we	approach	infinity towards	ground,	we	either	stay	with	the	same	degree	of	being,	or	we	approach infinite	being!	In	neither	case	is	being	infinitely	deferred,	never	achieved,	as	per Schaffer's	intuition.	If	anything,	being	is	always	deferred,	but	infinitely	achieved! So, if grounding is reductive,	we're	not explaining facts away	only to	approach nothingness,	but	rather	we're	explaining	facts	away	in	terms	of	other	facts	that have	equal	or	more	being.17 Now,	one	might	object that infinite	being	makes	no	sense, so	at	best	we have an equal degree of being along the grounding chain. But then, as we go down	the	grounding	chain,	being is infinitely	deferred,	never	achieved	because without	WF that equal degree of being is zero! But, of course, that would be begging	the	question. It is	very important	not	to	confuse	various	perspectives	of the	supposed explanatoriness	involved	in	SNG	(cf.	Bliss,	2013;	Morganti,	forthcoming).	Assume IDG,	its	corresponding	chains	of	grounding,	and	the	corresponding	totality	of	all such	chains	of	grounding,	which	I'll	call	the	chains	of	being.18	We	then	have	three questions, what we	might call a local, a regional, and a global question. Local Question (LQ): for any fact p, what grounds p? Regional Question (RQ): what 15	One	might	of	course	still	accept	Rosen's	(2010:123)	principle	that	if	p	reduces	to	qq, then	qqGp,	without	accepting	that	grounding	is	reductive	in	the	above	sense. 16	Note	that	this	latter	notion	of	being	real	is	not	necessarily	Fine's	(2001)	notion	of being	real.	Note	also	that	to	the	extent	that	Fine's	notion	of	being	real	is	taken	as	a	guide (though	no	guarantee)	to	being	fundamental,	Fine's	(2001:26)	definition	of	reduction	is incompatible	with	IDG. 17	See	also	Fine	(2001:27	and	fn.38).	Morganti	(forthcoming)	argues	that	rather	than disappearing	as	per	the	above	intuition,	being	emerges	from	infinite	grounding	chains. Cameron	(2008:10)	too	raises	a	similar	point:	'Why	could	not	everything	get	a	bit	more real	as	we	progress	down	the	chain,	without	anything	being	wholly	real?'	But	his intuition	'rules	this	out',	though,	as	he	himself	points	out,	'this	just	is	the	intuition	that there	must	be	a	fundamental	level.'	Note	that	an	appeal	to	an	analogy	with	causation doesn't	seem	to	help	here:	there	seems	to	be	no	more	to	an	effect	than	what's	in	its cause(s).	In	fact,	since	WF	postulates	unexplained	facts	at	the	bottom,	it	seems	to	me	it's ultimately	WF	that	fails	to	explain	the	being	of	our	facts,	not	IDG.	See	section	3	below. See	also	Tahko	(2014). 18	Recall,	grounding	is	supposed	to	impose	a	partial	order,	not	a	total	order,	so	the chains	of	being	need	not	be	a	single	connected	grounding	chain,	but	can	be	many disconnected	ones. 6 grounds the chain	of grounding	of	p?19	Global	Question	(GQ):	what grounds the chains	of	being?	A	proponent	of	IDG	should	commit	to	answering	LQ,	and	might or might not commit to answering RQ (cf. Dasgupta, 2014b). But should she commit	to	answering	GQ?	No!	Given	SNG+IDG,	GQ	is	incoherent.	First	of	all,	the chains	of	being	is	presumably	a	plurality	of	facts,	not	a	single	fact,	which	is	what it needs to be to be grounded as per SNG. Second, assume the chains of being amount	to	an	all-encompassing	global	fact;	call	it	g.	Then,	by	IDG,	there	are	some facts	that	ground	g;	but,	by	SNG	being	a	strict	partial	order,	those	facts	must	be distinct from g; so g is not an all-encompassing global fact, contradicting the initial assumption. So, we might put it like this: each fact individually has a ground, but all facts taken together (speaking unrestrictedly!) cannot have a ground. One might object that by invoking many-many grounding (as per Dasgupta,	2014a),	one	has	the	logical	resources	to	answer	GQ.	But	note	first	that one	is	then	changing	the	assumptions	of	the	argument,	by	switching	from	SNG	to another	slightly	different	notion	of	grounding,	call	it	SNG*.	Second,	that	might	be the	right	thing	to	do,	perhaps	for	independent	reasons	too,	but,	given	IDG,	it	does not help answering GQ. Assume the chains of being amount to an allencompassing	plural	global	fact;	call	it	gg.	Then,	by	IDG,	there	are	some	facts	that ground	gg;	but,	by	SNG*	being	a	strict	partial	order,	those	facts	must	be	distinct from gg; so gg is not an all-encompassing plural global fact, contradicting the initial	assumption.	So,	this	time,	we	might	put it like	this:	each	fact individually has a ground, but all facts taken collectively (speaking unrestrictedly!) cannot have	a	ground. Neither does it help to invoke Fine's (2012) distinction between being ungrounded and being zero-grounded. We might put the distinction like this: something	is	zero-grounded	iff	it	is	grounded,	but	in	the	empty	collection	of	facts, and	something	is	ungrounded	iff	it	is	not	grounded	at	all.	Now,	SNG	is	assumed	to be explanatory, so	while	being	ungrounded	amounts to	having	no explanation, being zero-grounded amounts to having an explanation, but in terms of the empty	collection	of	facts.	But,	I	say,	a	metaphysical	explanation	of	a	fact	in	terms of the empty collection of facts is no	metaphysical explanation of that fact, at least	not	as	per	SNG.	Saying	that	the	obtaining	of	a	fact	p	consists	in	the	obtaining of	the	empty	collection	of	facts,	is	not	metaphysically	explaining	p	unless	p	is	the empty	fact.	So,	by	trying	to	answer	GQ	by	invoking	zero-ground,	one	either	fails due	to	not	being	appropriately	explanatory,	or	one	must	be	invoking	a	different notion of grounding from SNG.20	So, assuming SNG, invoking Fine's (2012) distinction between being ungrounded and being zero-grounded just does not help,	at least	not	on	pain	of	changing	the	assumptions.	Of	course,	maybe	that	is the	right	thing	to	do	in	the	end,	but	not	for	present	purposes.21 19	Note	that	RQ	is	not	the	question	of	what	grounds	a	grounding	fact.	The	question	of what	grounds	a	grounding	fact	falls	under	LQ. 20	Presumably,	one	could	do	better	with	respect	to	zero-grounding	by	switching	to	an operator	approach	towards	G,	rather	than	our	predicate	approach.	But	then,	again,	one is	moving	away	from	SNG,	which	is	our	present	concern. 21	See	Litland	(forthcoming)	for	some	further	work	on	zero-grounding.	Unfortunately, Litland's	assumptions	are	difference	from	ours	(e.g.	G	is	a	non-factive	operator),	so	his account	does	not	obviously	help	answering	GQ.	Despite	his	insistence	to	the	contrary,	I 7 Admittedly, the above argument is quick, but, whether or not it's too quick,	there	is	another	more	decisive	argument	for	not	invoking	zero-grounding to assist us with respect to GQ: by our present assumptions, it entails necessitism, the	view	that	all	actual facts	are	necessary.22	Assume	the	chains	of being are zero-grounded, i.e. grounded in the empty collection of facts. Then, since the empty collection of facts necessarily exists, by the assumption of necessitation, all actual facts exist necessarily; hence necessitism. But, I claim, necessitism	is	false,	so	the	chains	of	being	are	not	zero-grounded. So, I conclude,	whether grounding is reductive or	not, by IDG, each fact has	a	ground,	and	hence	a	metaphysical	explanation	in	terms	of	some	other	facts, and no fact is thereby lost into nothingness; i.e. no fact is 'infinitely deferred, never achieved'. Given IDG (and SNG, or SNG*), there is no sensible question about what the ground of being as such is; the global question (GQ) of what grounds	the	chains	of	being	themselves	is	incoherent. The	point that	LQ (and	maybe	RQ) is	what	we	want	answered,	with	GQ being	incoherent,	resembles	a	point	made	by	Hume	(1779:IX)	in	his	objection	to cosmological	arguments	for	the	existence	of	God.	According	to	Hume,	if	one	has explained	each	step	in	a	perhaps	infinite	causal	chain,	there	is	nothing	more	to	be explained, and in particular no need to postulate a first cause to explain it all. Now, Pruss (2012:81-82) objects to	Hume by the following example. Consider the	flight	of	a	cannonball	between	12:00	and	12:01,	and	let	pt	be	the	state	of	the cannonball	at	time	t.	Let	p	be	the	conjunction	of	all	pt	such	that	12:00<t<12:01. Then	each	pt	might	explain its	successor	pt+, such	that	each	pt is	explained,	but still,	Pruss	claims,	the	flight	of	the	cannonball	itself	is	not	explained,	so	Hume	is wrong. Is there a similar objection in the vicinity	with respect to IDG?	No. The flight	case	is	misleading	because	there	is	an	external	perspective	on	the	flight	of the	cannonball,	but	there	isn't	any	such	external	perspective	on	all	the	chains	of being (witnessed by GQ being incoherent). So, adapted to our global case of grounding,	I	think	Hume	is	right. The second candidate for a vicious regress in indirect support of the controversial	premise	in	the	argument	for	WF	is	similar	to	the	prior	one	in	terms of reductive explanations, but claims that there is another kind of failure. Whether grounding is reductive or not, the supposed failure can be seen by analogy	with	the	toy	example	of	the	homunculus	theory	of	perception	(Cf.	Nolan, 2001;	Bliss,	2013).	Suppose	someone	attempts to	explain the	perception	of the fact	that	p	as	follows.	There	are	outside	signals	coming	into	the	eye,	received	by	a homunculus	sitting	on	the	inside	of	the	eye,	who	interprets	the	signals	as	being of	the	fact	that	p	before	sending	them	off	to	the	brain.	How	does	the	homunculus so	interpret	the	signals?	Well,	there	is	another	homunculus	sitting	inside	the	first homunculus,	who	interprets	the	signals	as	being	of	the	fact	that	p	before	sending them	off	to	the	first	homunculus.	How	does	the	second	homunculus	so	interpret the signals? Well, there is a third homunculus sitting inside the second homunculus... and	so	on	ad	infinitum.	Obviously,	here	the	supposed	explanation also	fail	to	see	how	Litland's	account	of	zero-grounding	is	metaphysically	explanatory, but	let	that	be	as	it	may. 22	I	owe	this	argument	to	Jon	Litland,	though	of	course	he	is	not	to	blame.	Note	that	the necessitism	in	play	is	not	to	be	confused	with	our	earlier	assumption	of	necessitation. 8 of the perception that p fails; we might plausibly blame the explanation for creating	a	vicious	regress. Now,	the	worry	this	time	is	not	so	much	that	we	explain	away	facts	into nothingness, but that the explanation fails in the sense of having to re-ask the same	question	with respect to the same	kind	of object over and	over again	ad infinitum.	The	explanation	thus	gets	us	nowhere,	so	to	speak.	But	there	is	no	such problem	in	our	case	of	grounding.	IDG	does	not	create	any	such	vicious	regress. If	qqGp,	then,	by	SNG,	qq	provide	a	full	metaphysical	explanation	of	p,	so	there	is no	further	question	about	what	grounds	p.	So,	we	do	get	somewhere.	We	do	of course have the further question of what grounds the facts among qq (not to mention	what	grounds	the	fact	that	qqGp),	and	so	on	ad	infinitum,	but	that	is	not analogous	with the homunculus theory of perception. In the homunculus-case, one has the same content over and over again, but not so in the IDG-case of grounding. To	make the homunculus-case	more analogous to the IDG-case,	we would	have	to	explain	the	perception	that	p	in	terms	of	the	first	homunculus,	but then	explain	this	homunculus	in	terms	of	something	non-homunculus-like,	or	at least something different-hounculus-like and so on ad infinitum. But then the reason for the initial failure in	explanation	has	gone	away.	The	analogy	simply doesn't	hold	up	to	scrutiny. In	general,	we	might	say	that	an	infinite	regress	is	vicious	if	something	we want	to	explain	cannot	be	explained	because	of	the	regress	(Nolan,	2001;	Bliss, 2013),	so, in	the	particular	case	of	grounding, IDG's infinite	regress is	vicious	if something	we	want	to	ground	cannot	be	grounded	because	of	it.	But,	as	we	have just seen, given IDG, it	makes no sense to ask for the ground of the chains of being themselves, i.e. there is	no	"global" fact to	be	grounded,	and	by IDG	each fact	is	grounded,	so	it	is	not	the	case	that	some	fact	cannot	be	grounded	because of	IDG's	regress.23 I conclude that IDG	does	not create	a	vicious regress	of the	appropriate kind, and hence a defense of the controversial premise (that if all facts have ground, there are no facts) based on IDG creating a vicious regress of the appropriate	kind	fails. 3.	Against	grounding	being	well-founded Here	is	what	I	take	to	be	the	best	argument	for	why	SNG	need	not	obey	WF,	i.e. why	it	is	possible	that	SNG	is	true,	but	WF	is	false. First, assume proper parthood is a strict partial order, and that the concrete world U is gunky: every entity in U has a proper part.24	Then U is indefinitely	divisible into	proper	parts, i.e.	unlimitedly	so (so	U	contains	neither extended	nor	unextended	mereological	atoms).	Assume	further	that	for	any	x,	if	x is	part	of	(or	in)	U,	then	the	fact	that	x	exists	is	(at	least	partly)	grounded	in	the fact that its proper parts exist. Then we have in effect a needed case of IDG, contradicting	WF (cf. Rosen, 2010:116). So, if SNG	must obey	WF, then either proper parthood is not a strict partial order or such a gunky scenario is 23	See	also	Schaffer	(forthcoming:section	4.5).	My	arguments	above	amounts	to	a rejection	of	Schaffer's	"transfer	model"	in	the	sense	that	I	argue	there	is	no	need	for	a source	of	being. 24	On	gunk,	see	e.g.	Sider	(1993),	Schaffer	(2003),	and	Arntzenius	(2008). 9 metaphysically	impossible;	but	proper	parthood	is	a	strict	partial	order	and	such a	gunky	scenario	is	metaphysically	possible,	so,	SNG	need	not	obey	WF. Second, assume proper parthood is a strict partial order, and that the concrete world U is junky: every entity in U is a proper part.25	Then U is indefinitely	extendable	along	the	proper	parthood	chains,	i.e.	unlimitedly	so	(so	U contains	no	maximal fusion that is	not a	proper	part).	Assume further that for any	x	and	y	in	U, if	x is	a	proper	part	of	y,	then	the	fact	that	x	exists	is	(at least partly)	grounded	in	the	fact	that	y	exists.26	Then	we	have	in	effect	another	case	of IDG,	contradicting	WF.	So,	if	SNG	must	obey	WF,	then	either	proper	parthood	is not	a	strict	partial	order	or	such	a junky	scenario	is	metaphysically	impossible; but proper parthood is a strict partial order and such a junky scenario is metaphysically	possible	(Bohn,	2009b),	so	SNG	need	not	obey	WF. Finally, assume proper parthood is a strict partial order, and that the concrete	world	U	is	hunky:	every	entity	in	U	both	is	and	has	a	proper	part.27	Then U	is	indefinitely	extendable	and	indefinitely	divisible	along	the	proper	parthood chains	(so	U	contains	neither	a	minimal	nor	a	maximal	entity).	Then,	whichever mereological	direction	a	chain	of	grounding	goes	(though	of	course	it	cannot	go in	both	directions	at	once!),	we	have	in	effect	another	case	of	IDG,	contradicting WF.	So,	if	SNG	must	obey	WF,	then	either	proper	parthood	is	not	a	strict	partial order or such a hunky scenario is metaphysically impossible; but proper parthood is a strict partial order and such a hunky scenario is	metaphysically possible	(Bohn,	2009b,	2012),	so	SNG	need	not	obey	WF. These	three	arguments	seem	very	good	to	me;	in	fact,	they	seem	as	good as	arguments	get	in	philosophy.	Rhetorically:	why	exactly	is	a	gunky,	a	junky	or	a hunky scenario	metaphysically impossible? I know of	no convincing reason to believe	they	are.28,29 Assuming	SNG	appropriately tracks the	mereological	hierarchy	as	above (which is no	minor assumption, but	we only need its	mere possibility here), I conclude	that	the	claim	that	SNG	must	obey	WF	is	simply	false. In	fact,	there	are	even	some	(highly	defeasible!)	reasons	to	believe	that	the concrete	world is	actually hunky.	We are faced	with a general cosmic pattern that	so	far	has	no	clear	end	points	in	sight.	Starting	high	up,	the	universe	is	partly composed	of	clusters	of	galaxies;	the	clusters	of	galaxies	are	partly	composed	of galaxies;	the	galaxies	are	partly	composed	of	solar	systems;	the	solar	systems	are partly	composed	of	planets	and	stars;	the	planets	and	stars	are	partly	composed of various chemicals; the various chemicals are partly composed	of	molecules; the various molecules are partly composed of atoms; the atoms are partly composed of electrons, protons and neutrons; the protons and neutrons are 25	On	junk,	see	Schaffer	(2010)	and	Bohn	(2009a;	2009b;	2012;	ms). 26	See	Schaffer	(2010),	where	this	direction	of	grounding	is	defended.	If	junk	is	possible, Schaffer's	version	of	WF	in	terms	of	priority	monism	fails	to	be	necessarily	true	(Bohn, 2012). 27	On	hunk,	see	Bohn	(2009b;	2012). 28	Arguably,	Sider's	(2011,	2013)	reasons	rest	on	a	too	deflationary	notion	of	modality. 29	In	Bohn	(2009a,	2009b,	2012)	I	argued	that	if	composition	is	not	identity	and	gunk	is possible,	then	junk	is	possible.	I	now	believe	(i)	that	composition	is	identity	and	entails unrestricted	composition	(Bohn,	2009c,	2011,	2014);	(ii)	that	hunk	is	possible,	likely actual,	if	not	necessary;	(iii)	that	plural	comprehension	is	false;	and	(iv)	that	because	of (iii),	(i)	and	(ii)	are	compatible	(Bohn,	ms). 10 partly	composed	of	various	quarks;	the	various	quarks	are	partly	composed	of	... to be continued? Starting low down, the various quarks partly compose the protons and neutrons; the electrons, protons and neutrons partly compose atoms; the atoms partly compose molecules; the molecules partly compose chemicals;	the	chemicals	partly	compose	planets	and	stars;	the	planets	and	stars partly compose solar systems; the solar systems partly compose galaxies; the galaxies partly compose clusters of galaxies; the clusters of galaxies partly compose super-clusters of galaxies; the super-clusters of galaxies partly compose	...	to	be	continued?	Or	perhaps	they	partly	compose	the	universe,	which in turn partly compose a multiverse;30	which in turn partly compose ... to be continued? As	science	has	progressed,	we	have	again	and	again	discovered	that	U	is both	bigger	(cf.	the	development	of	cosmology)	and	smaller	(cf.	the	development of particle physics) than we thought before. Considering that overall cosmic pattern,	we	are	faced	with	some	inductive/abductive	reasons	to	think	there	is	no end	in	either	direction;	dismissing	these	reasons	out	of	hand,	and	especially	on	a priori	grounds,	seems	scientifically	and	theoretically	irresponsible.31 By extrapolation on the above cosmic pattern, we are simply forced to question	whether	U is in fact	open	ended in	both	directions, and,	arguably,	we have some inductive/abductive reason to think it is, no convincing reason to think	it's	not.	First,	arguably,	there	is	neither	a	convincing	a	posteriori	reason	nor a	convincing	a	priori	reason	for	believing	that	the	cosmic	pattern	does	eventually have a stopping point; at least none that cannot be equally well explained as being	our	(hopeful)	theoretical	idealization	rather	than	a	real	existent.32	Second, concerning the junk-direction in particular, there is, again arguably, neither a convincing	a	posteriori	reason	nor	a	convincing	a	priori	reason	to	believe	there	is an	all-encompassing	infinite	whole	rather	than	infinitely	many	bigger	and	bigger wholes.33	Third, concerning the gunk direction in particular, there is, again arguably, neither a convincing a posteriori reason nor a convincing a priori reason	to	believe	there	are	mereological	atoms.34	Rhetorically,	why	think	an	end point	is	anything	but	our	(hopeful)	theoretical	idealization	in	any	case? So,	there	are	some	reasons	to	think	the	concrete	world	is	actually	hunky, not just	merely	possibly so. If so, again	assuming	SNG	appropriately tracks the mereological hierarchy, SNG even actually fails to obey	WF (no matter which direction	a	grounding	chain	goes). Of course, all this leaves open whether there might be fundamentality somewhere	else	in	the	mereological	hierarchy	than	at	the	top	or	at	the	bottom, or	whether there	might be fundamentality in a	way that fails to appropriately 30	Cf.	Carr	(2009). 31	See	also	Schaffer	(2003),	which	provides	a	similar	inductive	argument	for	gunk	in particular.	Note	that,	contra	Sider	(2011,	2013),	the	above	inductive/abductive	reasons are	not	just	a	handful	of	cases	of	unpacking	particles,	but	rather	they	are	based	on	a much	more	general	cosmic	pattern.	Note	also	that	Sider's	(2011,	2013)	other	criticisms of	the	actuality	of	gunk	rest	on	the	assumptions	that	fundamentality	is	an	all-or-nothing matter	and	that	fundamentality	is	well-founded;	both	assumptions	are	rejected	by	our picture	of	SNG+IDG. 32	Of	course,	appealing	to	WF	at	this	point	is	a	non-starter. 33	See	Bohn	(2009b)	and	Carr	(2009). 34	See	e.g.	Arntzenius	(2008). 11 track the	mereological structures	at all.	Raven (forthcoming)	defends	one such alternative, where there can be fundamentality	without a foundation a la	WF. The	core	idea	is	that	fundamentality	amounts	to	ineliminability	from	a	grounding chain,	rather	than	being	a	fact	at	an	end-point	of	it.	As	such,	there	can,	at	least	in one sense, be fundamentality even if the world is hunky. Raven's account is subtle,	and	I	cannot	for	reasons	of	space	adequately	discuss it	here,	but	merely note two things: first, the fundamental is then	not necessarily facts, so	we are beyond SNG, and second, it seems even such a watered-down notion of fundamentality can be indefinitely descending, leaving us with nothing truly fundamental	at	all.35 Life is	short,	with	no	time	to	take	deep	breaths,	so	let's	move	on	to	some	other arguments. As we saw earlier,	WF and IDG are	mutually incompatible, so the proponent	of	WF	must	deny	IDG	(and	proponents	of	IDG	must	deny	WF).	Given that	grounding is	explanatory (as	per	SNG), IDG is	equivalent to	a	statement	of what	we	might	call	the	metaphysical	principle	of	sufficient	reason (MPSR):	every fact	p	has	a	metaphysical	explanation	(see	Guigon,	2014;	cf.	Della	Rocca,	2010). So,	the	proponent	of	WF	must	deny	MPSR	too.	That	should	not	be	too	surprising: WF	postulates	that	there	are	some	facts	that	have	no	ground,	so	by	SNG	neither do	they	have	a	metaphysical	explanation. But consider what we might call the well-founded grounding riddle: assume	WF,	i.e.	that	all	grounding	chains	end	in	some	fundamental,	ungrounded facts. Consider these ungrounded facts. Either they have a metaphysical explanation (as per SNG) or they don't. If they do, they are of course not ungrounded,	in	which	case	grounding	is	not	well-founded	after	all.	If	they	don't, then they	have	no	ground.	But then the	obvious	question	arises:	whence these fundamental	facts?36 Not	being	able to	answer this	question fails to	provide	a	natural	resting point for thought.37	There seems to be at least three kinds of answers. First, Brutalism: the	ungrounded	facts just	don't	have	an	explanation,	and	there is	no explanation for it beyond that. Second, Indefinitism: there are no ungrounded facts	because	every	fact	has	an	indefinitely	descending	ground	in	all	directions, so	the	riddle	never	arises.	Third,	Loopism:	there	are	no	ungrounded	facts	because if you go far enough down any grounding chain you'll end up where you started.38 But	just	like	not	answering	the	above	question	is	no	natural	resting	point for thought, so	Brutalism too is	no	natural resting	point for thought.	This is so because	there	is	no	non-ad	hoc	way	to	draw	the	line	between	facts	that	do	and	do not have a	metaphysical explanation, and drawing an ad	hoc line is surely no 35	Raven	(forthcoming)	does	not	deny	this	second	point. 36	Note	that	this	latter	question	is	what	I	earlier	called	a	local	question	(LQ),	not	a regional	(RQ)	or	a	global	question	(GQ).	It	resembles	the	most	common	objection	to Aquinas'	foundationalism:	if	God	is	the	cause	of	all	things,	what	caused	God? 37	Thanks	to	Ralph	Henk	Vaags. 38	For	a	defense	of	Brutalism,	see	e.g.	Aquinas,	T.	(1266-8/1993);	Schaffer	(2009;	2010; forthcoming);	for	a	defense	of	Loopism,	see	e.g.	Bliss	(2014);	and	for	a	defense	of Indefinitism,	see	e.g.	Bliss	(2013);	Tahko,	(2014);	Morganti	(forthcoming);	not	to mention	the	paper	you	are	currently	reading.	Note	that	where	I	use	'indefinitism',	others use,	misleadingly	in	my	mind,	'infinitism'. 12 natural	resting	point	for	thought	(cf.	Della	Rocca,	2010).39	So,	all	else	being	equal, unless it contradicts our evidence, we should prefer Indefinitism or Loopism over	Brutalism.	Assuming	the	transitivity	of	grounding,	Loopism	contradicts	the irreflexivity of grounding, so assuming SNG, according to which grounding is both transitive and irreflexive, Loopism is out.40	So, unless it contradicts our evidence,	we should prefer Indefinitism over Brutalism. As argued throughout the present paper, all else is equal and Indefinitism doesn't contradict any evidence, so we should prefer Indefinitism over Brutalism. That is, on our picture,	WF is	Brutalism	and IDG is Indefinitism,	so	we	should	prefer IDG	over WF.	We	have	assumed	SNG,	so	we	should	prefer	SNG+IDG	over	SNG+WF. One	might	object	that	there	are	various	alternative	ways	one	might	try	to explain the ungrounded facts, making Brutalism less brute, and thus a more natural	resting	point	for	thought.41	For	example,	one	might	think	it	somehow	lies in	the	essences	of	ungrounded	facts	that	they	are	ungrounded	(Rosen,	2010:128133;	Dasgupta,	forthcoming),	which	thus	might	somehow	explain	them,	but	in	a different	sense	from	grounding.	But	then	again,	I	say,	it	might	just	not	thus	lie	in their essences; we simply don't know what the ungrounded facts are, so we simply	don't	know	what	does	and	does	not	have	an	explanation	in	terms	of	their essences. As far as I can tell, we simply have no convincing reason to believe there	actually	is	such	an	alternative	explanation	of	ungrounded	facts	in	terms	of their	essences. Dasgupta (forthcoming) is perhaps the best attempt at this sort of account, according to	which	both	MPSR	and	WF	are true, but the fundamental facts	are	not	apt for	metaphysical	explanation.	But	the	fact	that	all	and	only	the fundamental truths just happen to necessarily not be apt for metaphysical explanation	is incredible.42	The	idea	that	ungrounded	facts	are	by	their	essence ungrounded	is	an	interesting	idea,	but	I	just	see	no	convincing	reason	to	believe it	is	actually	true,	not	to	mention	to	rest	the	necessity	of	SNG+WF	on	it.	The	same goes, I say, in one admittedly too big sweep, for other ways of trying to alternatively	explain the	ungrounded	(e.g. causally,	or teleologically). So, it still seems	to	me	we	should	prefer	SNG+IDG	over	SNG+WF,	if	not	only	for	theoretical purposes. Note	that	MPSR	is	often	thought	to	entail	necessitism,	the	view	according to which all actual facts are	metaphysically necessary (see Della Rocca, 2010; Dasgupta, forthcoming).	But,	as	shown	in	Guigon	(2014),	neccessitism	is in fact no implication of MPSR as such, so necessitism is neither here nor there for SNG+IDG	as	such. Here	is	a	related	methodological	argument	for	SNG+IDG	over	SNG+WF:	all else	being	equal,	a	theory	that	respects	MPSR	is	better	than	a	theory	that	violates MPSR; there is no particular reason to think that WF is true; there is no particular reason to think that IDG is false; and IDG respects MPSR, but WF 39	On	this	point,	among	others,	it	is	worth	comparing	Brutalism	to	Epistemic Foundationalism,	but,	unfortunately,	I	have	no	space	to	do	so	here.	Thanks	to	Jonathan Schaffer	and	an	anonymous	referee	for	this	volume	for	raising	this	question. 40	I	don't	want	to	rule	out	Loopism	as	such,	but	only	for	present	purposes,	where	we	are assuming	SNG.	Maybe	the	mental	is	grounded	in	the	physical,	but	the	physical	in	turn	is grounded	in	the	mental.	I	find	such	a	picture	of	Loopism	well	worth	exploring. 41	Thanks	to	Jon	Litland,	Alex	Skiles	and	Kelly	Trogdon	for	pushing	me	on	this. 42	Thanks	to	Mike	Raven. 13 violates	MPSR; so the theory of SNG+IDG is an overall better theory than the theory	of	SNG+WF.	Therefore, to the	extent	we	should	prefer the	better	of two theories,	we	should	prefer	SNG+IDG	over	SNG+WF.43 The	first	premise	is	not	claiming	that	MPSR	is	true,	just	that	it	is	better	to not violate it unless one has a good reason to. In short, neutrality and non-ad hocness are theoretical	virtues.	The	second	and third	premise is	basically	what this	whole	section	2	of	the	paper	has	been	defending.	The	fourth	premise	is	as	we have seen provable: IDG is logically equivalent	with	MPSR, and	WF is logically incompatible	with	IDG,	so	WF	is	also	incompatible	with	MPSR.44 Most generally, the proponent of WF faces the problem of having to explain	a	non-ad	hoc	restriction	on	MPSR,	which	is	no	easy	task	(cf.	Della	Rocca, 2010).	The	proponent	of	IDG	faces	no	such	problem;	and,	at	least	for	theoretical purposes,	to	the	extent	SNG	doesn't	need	to	restrict	MPSR,	it	shouldn't;	it	doesn't need to, so it shouldn't. The latter is just good old scientific and theoretical practice. Now, contra my methodological arguments above, Cameron (2008) argues that SNG+WF is theoretically better than SNG+IDG because SNG+WF provides a more unified theory than SNG+IDG: by WF there are some fundamental	facts	in	terms	of	which	all	others	are	metaphysically	explained,	but by	IEG	there	is	not;	and	a	more	unified	theory	is	better	than	a	less	unified	theory. But,	why	believe	that	there	is	more	theoretical	unity	with	fundamental	facts	than without?	First,	by	going	far	enough	down	the	grounding	chains,	there	could	be	as much unity without fundamental facts as with. Second, the fundamental facts might	come	in	separate	pluralities	having	little	or	nothing	in	common,	in	which case	there	could	be	as	much	disunity	with	fundamental	facts	as	without.	That	is, there	is	a	big	difference	between	saying	that	some	fundamental	facts	ground	all else and saying that all non-fundamental facts are grounded in some fundamental	facts.	The	former	might	bring	about	more	unity,	but	the	latter	need not.	I	have	construed	things	in	terms	of	the	latter,	not	the	former.	Why	think	the former	is	the	case?	As	far	as	I	can	tell,	SNG+WF	thus	need	not	provide	any	more theoretical	unity	than	SNG+IDG.45 Bibliography Aquinas,	T.	(1266-8/1993).	Selected	Philosophical	Writings.	Oxford University	Press. Arntzenius,	F.	(2008).	Gunk,	Topology	and	Measure.	Oxford	Studies	in Metaphysics,	vol.4.	Oxford	University	Press. Bliss,	R.	(2013).	Viciousness	and	the	structure	of	reality.	Philosophical Studies	166,	pp.399-418. - ----------	(2014).	Viciousness	and	circles	of	ground.	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