(Forthcoming	in	Synthese.) The	Nature	of	Doubt	and	a	New	Puzzle	about	Belief,	Doubt,	and	Confidence by	Andrew	Moon [Word	Count:	9148] Abstract. In	this	paper,	I	present	and	defend	a	novel	account	of	doubt. In	§1,	I	make some	preliminary	observations	about	the	nature	of	doubt. In	§2,	I	introduce	a	new puzzle	about	the	relationship	between	three	psychological	states:	doubt,	belief,	and confidence. I	present	this	puzzle	because	my	account	of	doubt	emerges	as	a	possible solution	to	it. Lastly,	in	§3,	I	elaborate	on	and	defend	my	account	of	doubt. Roughly, one	has	doubt	if	and	only	if	one	believes	one	might	be	wrong;	I	argue	that	this	is superior	to	the	account	that	says	that	one	has	doubt	if	and	only	if	one	has	less	than the	highest	degree	of	confidence.	[Word	Count:	115] Keywords:	Doubt,	Confidence,	Belief,	Credence Introduction In	this	paper,	I	present	and	defend	a	novel	account	of	doubt. My	method	will primarily	contain	two	parts:	1)	a	careful	consideration	of	how	we	use	doubt ascriptions	in	ordinary	language	and	2)	an	appeal	to	intuitions	about	the	presence or	absence	of	doubt	in	various	examples	and	counterexamples. As	far	as	I	am	aware, no	one	has	attempted	to	present	and	defend	a	rigorous	account	of	doubt	using	these standard	procedures	in	contemporary	analytic	philosophy.1	Given	the	importance	of doubt	in	philosophy,	it	is	surprising	that	it	has	not	received	more	attention	by contemporary	analytic	philosophers. In	§1,	I	present	linguistic	data	about	'doubt'	to	help	block	potential obfuscations,	identify	the	type	of	doubt	that	will	be	the	focus	of	the	paper,	and	make some	preliminary	observations	about	the	nature	of	doubt. In	§2,	I	introduce	a	new 1	This	is	not	to	say	that	no	one	has	attempted	to	define	'doubt'. For	a	helpful	discussion	and	critique of	the	views	of	doubt	of	Russell,	Pierce,	and	others,	see	Peels	(ms). None	of	those	philosophers employ	the	standard	procedures	in	analytic	philosophy	that	I	mention	above. 2 puzzle	about	belief,	doubt,	and	confidence. My	account	of	doubt	emerges	as	a solution	to	this	puzzle. Lastly,	in	§3,	I	explain	and	defend	my	account	of	doubt. Roughly,	one	has	doubt	if	and	only	if	one	believes	one	might	be	wrong. I	argue	that this	is	superior	to	the	account	that	says	that	one	has	doubt	if	and	only	if	one	has	less than	the	highest	degree	of	confidence. 1.	Preliminary	Remarks	About	Doubt The	word	'doubt'	comes	in	different	forms	of	speech.2	First,	'doubt'	can	be	used	as	a count	noun. As	such,	an	article	can	precede	it	or	an	's'	can	come	at	its	end. For example, 1) "The	incident	raised	many	doubts	about	Fred's	integrity." 2) "I	have	serious	doubts	about	the	value	of	this	project." 3) "I	don't	have	a	doubt	about	it!" Most	of	this	paper	will	not	directly	be	about	doubts. However,	I'll	explain	three accounts	of	doubts	to	help	narrow	in	on	the	sense	of	'doubt'	that	will	be	my	focus. Here	is	the	first	account: Doubts1:	S	has	doubts	about	whether	p	if	and	only	if	S	has	reasons	to	not believe	p. Someone	who	asserted	(1)	or	(2)	could	be	asked,	"Well,	what	are	they? Share	with me	your	doubts."	The	person	would	then	be	expected	to	share	her	reasons	for	being disinclined	to	believe	that	Fred	has	integrity	or	that	the	project	lacks	value. A 2	Not	all	types	of	doubt	ascriptions	will	be	explored. I	will	focus	on	those	doubt	ascriptions	that	will be	necessary	for	the	reader	to	grasp	the	sense	of	'doubt'	in	which	I	am	interested. For	an	exploration of	more	doubt	ascriptions,	see	Peels	(ms). 3 natural	way	to	counter	(3)	would	be	to	say,	"Well	you	should! What	about	X	and	Y?" Such	a	person	would	be	raising	doubts,	which	would	be	reasons	X	and	Y. Second,	Daniel	Howard-Snyder	(2013)	identifies	doubts	with	the appearances	of	reasons. He	writes, For	one	to	have	doubts	about	whether	p-note	the	"s"-is	for	one	to	have what	appear	to	one	to	be	grounds	to	believe	not-p	and,	as	a	result,	for	one	to be	at	least	somewhat	inclined	to	disbelieve	p	(359).3 We	can	draw	out	the	following	account: Doubts2:	S	has	doubts	about	whether	p	if	and	only	if	S	has	appearances	of reasons	to	not	believe	p. Suppose	someone	gives	me	considerations	against	believing	p	that	are,	in	fact,	not really	reasons	at	all. However,	they	appear	to	me	to	be	reasons. It	seems	that	I would	still	have	doubts	about	whether	p. (Some	might	think	that	one	has	reasons	if and	only	if	one	appears	to	have	reasons.4	Then	Doubts1	and	Doubts2	are	equivalent.) The	third	account	is Doubts3:	S	has	doubts	about	whether	p	if	and	only	if	S	has	conscious occurrences	of	doubt	about	whether	p. Though	Doubts3	might	appear	circular,	the	'doubt'	in	the	right-hand	side	is	a	mass noun,	which	will	be	discussed	shortly.	(Unlike	count	nouns,	an	article	cannot 3	A	minor	criticism	of	Howard-Snyder's	suggestion	is	that	the	doubt	need	not	incline	one	to	disbelieve p	(i.e.,	believe	~p);	it	need	only	incline	the	person	to	not	believe	p. For	example,	some	doubts	might come	in	the	form	of	undercutting	defeaters. To	use	Pollock's	well-known	example,	suppose	some widgets	look	red	and	I	come	to	believe	they	are. I	then	learn	that	they	have	red	lights	shining	on them. Then	I	do	not	gain	a	reason	to	disbelieve	that	they	are	red,	but	only	to	not	believe	that	they	are red. I	would	then	have	a	doubt	about	whether	they	are	red. This	correction	is	accounted	for	in Doubts2. 4	Consider	that	internalists	think	that	my	demon	world	twin	and	I	are	evidentially	identical;	this supports	the	claim	that	the	reasons	one	appears	to	have	are	the	reasons	one	has,	and	vice	versa. 4 precede	a	mass	noun	and	an	's'	cannot	come	at	its	end;	typically,	they	can	take	a 'much'	or	'little'	in	front	of	them.)	For	now,	I	will	say	that	Doubts3	comes	closer	to capturing	what	someone	is	expressing	when	she	says, 4) "I've	been	having	a	lot	of	doubts	lately." The	speaker	is	not	necessarily	saying	that	she	has	many	reasons	to	not	believe. She might	only	have	one	such	reason,	and	it	has	been	causing	her	to	have	many experiences	of	doubt	throughout	the	week.5 From	this	discussion,	I	am	inclined	to	think	that	there	are	two	concepts	of doubts. The	first	is	closely	tied	to	reasons,	as	suggested	by	Doubts1	and	Doubts2, although	the	two	accounts	might	differ	as	to	exactly	how. Settling	such	a	dispute would	require	settling	how	reasons	and	the	appearance	of	reasons	relate,	which	is beyond	the	scope	of	this	paper. However,	note	that	either	account	will	make	natural a	corresponding	account	of	varying	strengths	of	one's	doubts. One	can	have	very strong	doubts	about	whether	p,	or	just	weak	doubts	about	it. The	strength	of	one's doubts	will	vary	with	the	strength	of	one's	reasons	(if	Doubts1	is	true)	or	with	the appearance	of	the	strength	of	one's	reasons	(if	Doubts2	is	true).6 The	second	concept	of	doubts	is	expressed	by	Doubts3	and	is	tied	to	the concept	expressed	by	the	mass	noun	form	of	'doubt',	which	I	turn	to	in	the	next paragraph. The	strength	of	these	doubts	will	vary	with	the	strength	of	feeling associated	with	the	conscious	occurrences	of	doubt. Suppose	the	person	who	utters (4)	is	kept	up	at	night	because	the	conscious	occurrences	of	doubt	come	with 5	Cf.	Schellenberg	(2005,	p.	95). 6	I	am	thankful	to	a	referee	of	this	journal,	whose	comments	led	me	to	develop	these	points	about how	the	strength	of	one's	doubts	could	come	in	degrees. 5 intensely	strong	feelings. It	would	be	natural	to	say	that	she	has	strong	doubts,	even if	she	only	had	very	weak	reason	to	have	doubt. There	is	much	more	to	explore about	doubts,	but	I	will	say	that	the	sense	of	'doubt'	I	am	concerned	with	is	one	that is	not	so	closely	tied	to	reasons. Consider, 5) "Fred	doubts	that	Sally	will	arrive	on	time." 6) "Fred	is	in	doubt	about	whether	Sally	will	arrive	on	time."7 7) "Fred	has	some	doubt	that	Sally	will	arrive	on	time." (5)	uses	a	verb	form	of	'doubt',	and	(6)	and	(7)	both	use	a	mass	noun	form.8	Each	of these	sentences	attributes	a	mental	state	to	Fred,	but	they	do	not	ascribe	a	mental state	that	is	closely	tied	to	reasons.9	For	example,	Fred's	doubt	that	Sally	will	arrive on	time	might	not	be	related	to	reasons	at	all;	his	doubt	might	be	caused	solely	by his	jealousy	of	her. It	is	not	obvious	that	(5)–(7)	attribute	a	single	mental	state. Daniel	HowardSnyder	(2013,	359)	has	noted	that	verb	forms	of	'doubt',	like	(5),	indicate	at	least	a strong	inclination	to	disbelieve;	and	sentences	like	(6)	indicate	more	on-the-fence suspension	of	judgment. If	Fred	suspends	judgment	about	whether	Sally	will	arrive on	time,	then	saying,	"I	doubt	that	she	will	arrive	on	time,"	would	be	false,	but	"I	am in	doubt	about	whether	she	will	arrive	on	time"	would	be	true. On	the	other	hand,	if Fred	thinks	that	Sally	will	not	arrive	on	time,	it	might	be	correct	for	him	to	say,	"I 7	Thanks	to	John	Schellenberg	for	drawing	my	attention	to	this	sort	of	ascription. It	is	also	Daniel Howard-Snyder's	(2013)	focus. 8	Thanks	to	Brent	Braga	and	Andrew	Melnyk	for	helping	me	see	the	fruitfulness	of	distinguishing verb	and	noun	doubt	ascriptions. 9	Consider	also,	"It	is	doubtful	that	Sally	will	arrive	on	time,"	which	uses	an	adjectival	form	of	'doubt'. It	seems	to	express	that	there	are	reasons	to	doubt	that	Sally	will	arrive	on	time. This	is	the	sense	of 'doubt'	that	I	am	putting	aside	for	this	paper. Thanks	to	Adam	Auch	for	helpful	discussion. 6 doubt	that	she	will	arrive	on	time"	but	incorrect	to	say,	"I	am	in	doubt	about whether	she	will	arrive	on	time."10 Is	there	anything	that	unites	(5)–(7)? Yes. Consider, 8) "Fred	has	much	doubt	that	Sally	will	arrive	on	time." 9) "Fred	has	little	doubt	that	Sally	will	arrive	on	time." We	see	with	(8)	and	(9)	that	degrees	of	doubt	can	be	ascribed	by	a	mass	noun	form of	'doubt'.11	What	unites	(5)	and	(6)	is	that	they	both	attribute	some	doubt;	(5) attributes	a	high	degree	of	doubt,12	and	(6)	attributes	only	a	moderate	degree	of doubt. The	mental	state	attributed	by	(7),	some	doubt,	is	what	is	common	to	all	of these	different	doubt	attributions,	and	so	it	is	the	mental	state	that	will	be	the	focus of	this	paper.13 Having	clarified	the	type	of	doubt	I	am	interested	in,	I	will	end	this	section	by making	two	observations	about	the	nature	of	doubt. The	first	is	that	belief	is compatible	with	doubt.14	Someone	might	question	this	observation	for	two	reasons. First,	conjuncts	in	sentences	of	the	form, 10) "Fred	believes	that	it	will	rain	tomorrow,	and	he	doubts	that	it	will	rain tomorrow" 10	Thanks	to	Philip	Swenson	for	helpful	conversation	about	these	examples. 11	It	is	not	always	the	case	that	if	one	can	have	much	or	little	of	X,	then	X	comes	in	degrees. One	can have	much	or	little	gold,	but	gold	does	not	come	in	degrees. However,	this	inference	is	plausible	in the	case	of	mental	states:	if	one	can	have	much	or	little	of	mental	state	X,	then	X	comes	in	degrees. For	example,	it	is	plausible	to	infer	from	the	fact	that	we	can	have	much	or	little	desire,	much	or	little hope,	and	much	or	little	happiness,	to	the	conclusion	that	these	mental	states	come	in	degrees. So, this	inference	is	plausible	in	the	case	of	doubt. 12	It	is	interesting	that,	even	with	modifiers,	verb	forms	of	'doubt'	resist	expressing	low	degrees	of doubt. One	can	say,	"I	highly	doubt	that	p",	but	it	is	very	awkward	to	say,	"I	lowly	doubt	that	p"	and still	at	least	a	little	awkward	to	say,	"I	doubt,	a	little	bit,	that	p." 13	Degree	of	doubt	will	be	discussed	more	in	§3.2	and	should	be	distinguished	from	the	degree	of strength	of	one's	doubts,	which	I	discussed	earlier	in	this	section. 14	Contra	Schellenberg's	(2005,	96). 7 seem	to	clash,	which	indicates	that	they	are	inconsistent. Second,	according	to	some dispositionalist	accounts	of	belief,	if	one	believes	that	p,	then	one	has	the	tendency to	consciously	affirm	that	p	when	asked	whether	p.15	We	could	extend	this	point	to doubt:	if	one	doubts	that	p,	then	one	does	not	have	the	tendency	to	consciously affirm	p	when	asked	whether	p. Hence,	the	two	states	are	incompatible. My	reply	to	these	objections	is	to	concede	that	belief	is	incompatible	with	the degree	of	doubt	attributed	by	verb	forms	of	'doubt'	(as	in	(10)),	but	then	say	that belief	is	still	compatible	with	some	doubt.16	Consider	that 11) "Fred	believes	that	it	will	rain	tomorrow,	although	he	has	a	little	bit	of	doubt that	it	will." 12) "Fred	believes	that	it	will	rain	tomorrow,	although	he	has	some	doubt	that	it will." are	consistent. Not	only	are	they	possibly	true;	it	also	seems	that	Fred	could rationally	believe	and	rationally	have	some	(or	a	little)	doubt.17 Regarding	the	second	objection,	I	will	grant	that	the	verb	form	of	'doubt' expresses	a	high	degree	of	doubt,	which	comes	with	a	tendency	that	conflicts	with	a tendency	of	belief. But	this	is	no	reason	to	think	that	a	very	low	degree	of	doubt	that p	comes	with	the	tendency	to	not	consciously	affirm	p	when	asked	whether	p. We learn	from	both	arguments	the	value	of	noting	when	we	are	using	verb	or	mass noun	doubt	ascriptions	since	they	may	attribute	different	degrees	of	doubt.18	(Note 15	Cf.	Cohen (1992), Alston (1996), Schwitzgebel (2002), and Smithies (2012). 16	Thanks	to	Daniel	Howard-Snyder	and	John	Turri	for	helpful	discussion	here. 17	Hawthorne,	John,	et.al.	(2016,	1395)	provide	a	similar	argument	to	show	that	belief	is	a	weak attitude	(that	is,	the	norms	of	belief	are	weaker	than	the	norms	of	assertion). 18	Note	that	the	infinitive	form	also	indicates	a	high	degree	of	doubt. If	I	say,	"Fred	has	reason	to doubt	that	Sally	will	arrive	on	time"	or	"Fred	is	inclined	to	doubt	that	Sally	will	arrive	on	time,"	I 8 that	I	could	have	run	versions	of	both	objections	with	"is	in	doubt	about	whether" rather	than	the	verb	form	of	'doubt',	and	also	replied	to	them	in	the	same	way.) My	second	observation	is	that	doubt,	like	belief,	can	be	either	conscious	or unconscious. My	belief	that	2+2=4	is	currently	conscious;	but	I	continue	to	believe	it unconsciously,	even	when	I	am	asleep. This	same	distinction	applies	to	doubt. A theist	might	consider	some	argument	from	evil	and	begin	to	have	some	doubt	that God	exists. At	that	moment,	her	doubt	is	conscious. Later	throughout	the	day,	the doubt	might	only	be	in	the	back	of	her	mind,	i.e.,	it	might	be	unconscious.	(Consider also	that	if	the	doubt	has	become	conscious	a	few	times	throughout	the	day,	she could	correctly	say,	"I've	been	having	some	doubts	about	belief	in	God."	This	is	in accord	with	Doubts3.) Note	also	the	distinction	between	unconscious	doubt	and	the	disposition	to doubt. The	former	is	doubt	one	actually	has;	the	latter	is	just	an	inclination	to	doubt in	certain	circumstances. A	theist	who	initially	had	no	doubt	about	her	theism	might come	to	have	a	newly	formed	doubt	when	questioned. Such	a	theist	might	have	a disposition	to	doubt	but	no	unconscious	doubt;	she	might	have	not	had	any	doubt	at all	before	she	was	questioned.19 2.	The	Puzzle convey	that	Fred	has	reason	to	believe	that	Sally	will	not	arrive	on	time,	or	that	Fred	is	inclined	to believe	that	Sally	won't	arrive	on	time. Thanks	to	Matt	Duncan	and	Hayoung	Shin	for	helpful conversation. 19	This	follows	Audi's	(1994)	distinction	between	dispositional	beliefs	and	dispositions	to	believe. 9 In	§2.1,	I	lay	out	my	puzzle	about	belief,	doubt,	and	confidence. In	§2.2,	I	discuss four	ways	of	responding	to	the	puzzle. In	§3,	I	present	my	account	of	doubt	as	a solution	to	the	puzzle. 2.1.	The	Puzzle My	puzzle	takes	the	form	of	three	propositions	that	seem	plausible	but	are	jointly inconsistent. Here	is	the	first: A:	Many	ordinary,	unreflective	beliefs,	such	as	those	referred	to	in	the classroom	scenario,	are	held	without	accompanying	doubt. The	classroom	scenario	is	as	follows: Classroom	Scenario:	It	is	an	ordinary	day	and	you	are	going	to	teach	your class. Unlike	many	epistemological	scenarios,	there	are	no	bizarre	twists	in this	one. As	you	walk	into	your	classroom,	you	are	unreflectively	forming	all sorts	of	ordinary	beliefs,	such	as	the	beliefs	that	my	chair	is	tilted	diagonally, attendance	is	pretty	good	today,	and	the	class	clown	is	here. Plausibly,	these	beliefs	are	formed	and	held	without	corresponding	doubt. As	we consider	this	ordinary	scenario,	it	seems	that	you	do	not	also	have	some	doubt	that my	chair	is	tilted	diagonally	or	some	doubt	that	attendance	is	good	today	or	some doubt	that	the	class	clown	is	here. You	just	form	the	beliefs	without	doubt,	and	that's it. In	describing	this	scenario,	I	intend	to	describe	what	happens	to	most	of	us	when we	walk	into	a	classroom. Now,	you	could	form	some	doubt	about	these	propositions. The	student	who looks	like	the	class	clown	could	say	with	a	serious	look	on	his	face,	"I'm	actually	the 10 twin	brother	from	out	of	town."	This	might	cause	you	to	have	a	tiny	bit	of	doubt	that he	is	the	class	clown. But,	in	my	scenario,	no	student	says	any	such	thing;	as	I	said, the	scenario	is	completely	ordinary. And	(A)	is	about	whether	there	is	doubt,	not about	whether	there	could	be	doubt. So,	in	these	ordinary	scenarios	that	we	daily find	ourselves	in,	many	of	our	unreflective	beliefs	are	formed	without	doubt. Here	is	the	second	proposition: B:	S	has	some	doubt	that	p	if	S	has	a	doxastic	attitude	toward	p	and	does	not have	the	highest	degree	of	confidence	that	p	(i.e.,	does	not	have	a	degree	of confidence	that	p	that	is	1).20 (B)	is	a	very	natural	way	to	view	the	relationship	between	confidence	and	doubt. Indeed,	adding	an	'only	if'	would	make	(B)	a	complete	analysis	of	doubt,	but	I'll	stick with	the	weaker	'if',	since	that	will	be	sufficient	for	my	puzzle. As	I	understand	the	term	'doxastic	attitude',	S	has	a	doxastic	attitude	toward p	if	and	only	if	S	believes,	withholds,	disbelieves,	or	has	some	degree	of	confidence toward	p. One	way	to	not	have	the	highest	degree	of	confidence	that	p	is	to	not	have formed	any	doxastic	attitude	toward	p. Most	adults,	even	if	educated,	have	never formed	a	doxastic	attitude	toward	the	proposition	that	actualism	is	true. They neither	have	the	highest	degree	of	confidence	toward	it,	nor	do	they	have	any	doubt about	it. But	if	one	does	form	a	doxastic	attitude	toward	p,	and	if	one	does	not	have a	degree	of	confidence	of	1	toward	p,	then	it	seems	to	follow	that	one	has	at	least	a little	doubt	that	p. So,	if	I	currently	do	not	have	a	degree	of	confidence	of	1	that 20	It	is	part	of	standard	probability	theory	to	assign	the	number	1	to	the	highest	degree	of	confidence that	p	(when	one	is	certain	that	p)	and	the	number	0	to	the	lowest	degree	of	confidence	that	p	(when one	is	certain	that	~p)	and	the	numbers	in	between	0	and	1	to	the	varying	degrees	of	confidence	in between. I	am	assuming	here	that	there	is	a	highest	degree	of	confidence. 11 actualism	is	true	after	forming	a	doxastic	attitude	toward	that	proposition,	then	it seems	that	I	must	have	some	doubt	about	it. These	considerations	support	(B). Linguistic	evidence	also	supports	(B).21	Suppose	I	said, 13) "I'm	not	completely	confident	that	p,	but	I	have	no	doubt	that	p."22 (13)	seems	inconsistent. This	is	evidence	that	the	first	conjunct	entails	the	denial	of the	second,	which	would	be	expected	if	(B)	were	true. Or	consider	the	following dialogue: Victoria:	Are	you	completely	confident	that	p? Danny:	No,	I'm	not	completely	confident	that	p. Victoria:	So	you	have	some	doubt	that	p? Danny:	I	didn't	say	that. I	also	don't	have	any	doubt	that	p. Victoria	should	be	confused	because	the	absence	of	complete	confidence	seems	to entail	the	presence	of	doubt. These	linguistic	considerations	also	support	(B). Here	is	the	third	proposition: C:	Many	ordinary,	unreflective	beliefs,	such	as	those	referred	to	in	the classroom	scenario,	are	not	held	with	the	highest	degree	of	confidence	(do not	have	degree	of	confidence	1). Some	philosophers	think	that	we	have	a	degree	of	confidence	1	toward	only	a	small set	of	propositions	–	propositions	such	as	I	exist	or	I	am	thinking	–	a	set	that	would exclude	the	ordinary,	unreflective	beliefs	mentioned	in	(A). This	is	motivated	by 21	Thanks	to	Jon	Matheson	for	help	in	formulating	the	following	considerations. 22	Earl	Conee	has	objected	that	'complete	confidence'	does	not	indicate	the	highest	degree	of confidence. I	disagree. However,	notice	that	we	could	replace	(13)	with	"I	have	less	than	the	highest degree	of	confidence	that	p,	but	I	have	no	doubt	that	p."	This	also	seems	inconsistent. However,	since we	are	less	likely	to	talk	this	way	in	ordinary	language,	I	will	stick	to	"complete	confidence"	talk. Thanks	to	Jeremy	Fantl	for	this	helpful	suggestion	for	how	to	respond	to	Earl	Conee 12 betting	behavior	tests	for	degrees	of	confidence. Consider	the	following	quote	by Richard	Jeffrey: how	momentous	it	may	be	to	assign	probability	1	to	a	hypothesis. It	means you'd	stake	your	all	on	its	truth,	if	it's	the	sort	of	hypothesis	you	can	stake things	on. To	assign	100%	probability	to	success	of	an	undertaking	is	to think	it	advantageous	to	stake	your	life	upon	it	in	exchange	for	any	petty benefit	(1992:	pp.	1–2). I	take	it	that	many	ordinary,	unreflective	beliefs	do	not	meet	this	test. Furthermore,	even	apart	from	betting	behavior	tests,	it	just	seems	possible that	you	could	have	a	higher	degree	of	confidence	toward	those	propositions. For suppose	I	paused,	took	a	more	careful	look	at	the	class,	and	formed	the	belief,	"Yes, this	is	definitely	a	good	showing	today."	I	then	take	roll	and	check	my	attendance sheet,	noticing	that	this	is	the	best	attendance	I've	had	all	semester. It	seems	that,	in this	process,	my	degree	of	confidence	that	attendance	is	good	today	would	have increased. So,	(C)	seems	well	supported.23 Our	puzzle	is	complete:	(B)	and	(C)	together	entail	the	denial	of	(A). Each	at least	seems	plausible. How	should	we	respond? 2.2.	Four	Ways	of	Responding	to	the	Puzzle The	first	way	is	to	say	that	the	inconsistency	is	merely	apparent. At	least	one	of	the terms	–	perhaps	'doubt'	or	'confidence'	–	means	different	things	in	at	least	two	of	the 23	Clarke	(2013)	and	Greco	(2015)	have	recently	argued	that,	given	some	assumptions,	belief	just	is credence	1	(in	certain	contexts). It	is	not	obvious	how	relevant	their	work	is	to	(C). Greco	(2015, 180)	says	he	is	using	'belief'	in	a	technically	defined	sense,	and	he	seems	to	take	Clarke	to	be	doing the	same. On	the	other	hand,	I	intend	to	mean	by	'belief'	what	it	means	in	ordinary	English. Furthermore,	Clarke	does	not	mean	by	"belief	to	degree	1"	anything	that	entails	certainty	(2013,	11), whereas	my	discussion	is	about	the	highest	degree	of	confidence	(or	certainty). Lastly,	nothing	they say	counts	against	my	argument	that	it	seems	that	my	degree	of	confidence	could	increase,	and therefore,	my	initial	confidence	was	not	the	highest	degree	of	confidence. 13 sentences.24	This	response,	what	I	call	the	'equivocation	response',	is	how	we	would respond	to	the	following	"puzzle": 14) Aristotle	went	to	the	bank. 15) If	Aristotle	went	to	the	bank,	then	he	is	beside	water. 16) Aristotle	is	inside	a	building	with	no	water	nearby. There	is	a	plausible	scenario	where	each	of	(14)–(16)	seem	true,	and	yet	(14)	and (15)	seem	to	entail	the	denial	of	(16). The	response	is	obvious:	'bank'	is	ambiguous, and	its	different	meanings	are	expressed	in	at	least	two	of	the	sentences. The equivocation	response	has	also	been	used	in	more	serious	philosophical	contexts. For	example,	Keith	DeRose	(1995)	has	famously	argued	that	we	mean	different things	by	'knows'	in	the	sentences	comprising	the	premises	of	a	plausible	skeptical argument	and	a	sentence	expressing	an	ordinary	knowledge	claim. So,	one	might claim	that	there	is	some	ambiguity	or	context-sensitivity	in	(A)–(C). The	problem	is	that	there	is	no	good	reason	to	think	that	'doubt,'	'belief,'	or 'confidence'	have	different	meanings	in	(A)–(C).25	It	is	obvious	that	'bank'	is ambiguous,	and	standard	tests	confirm	it. For	example,	consider	the	conjunction reduction	test.26	Two	sentences	with	the	purportedly	ambiguous	term	are	conjoined, but	also	shortened,	so	that	the	term	only	appears	once;	if	the	sentences	are zeugmatic	(i.e.,	have	a	certain	type	of	ridiculousness),	then	the	term	is	ambiguous. For	example,	if	we	conjoin	the	sentences,	"Bill	waded	in	the	bank"	and	"Bill 24	Thanks	to	Neil	Sinhababu	and	Matthew	McGrath	for	pushing	me	to	address	this	point. 25	Thanks	to	a	referee	of	this	journal	for	encouraging	me	to	discuss	my	reply	to	the	equivocation response	more	thoroughly. 26	For	more	discussion	of	this	test,	see	§4.1	of	Sennet	(2016),	as	well	as	the	rest	of	§4	and	the references	therein,	for	more	ambiguity	tests. Thanks	to	Peter	van	Elswyk	and	Daniel	Rubio	for discussion. 14 withdrew	money	from	the	bank,"	the	resulting	sentence,	"Bill	waded	in,	and withdrew	money	from,	the	bank"	is	zeugmatic. Now,	we	already	knew	that	'bank'	is ambiguous,	but	there	does	not	seem	to	be	any	test,	including	the	conjunction reduction	test,	that	would	show	that	any	of	'doubt,'	'belief,'	or	'confidence,'	is ambiguous. Perhaps	they	are	merely	context	sensitive,	like	'I,'	or	'you,'	or	'tall.'	DeRose (2009)	gives	reasons	for	thinking	that	'knows'	is	context	sensitive. Very	briefly, suppose	there	is	much	at	stake	for	Fred	regarding	whether	the	bank	is	closed	on Saturday;	nothing	is	at	stake	for	Sally. After	hearing	a	bystander	say,	"The	bank	is closed	on	Saturday,"	it	seems	that	Sally	could	correctly	say,	"The	bystander	knows that	the	bank	is	closed	on	Saturday,"	but	also	that	Fred	could	correctly	say,	"The bystander	doesn't	know	that	the	bank	is	closed	on	Saturday."	This	is	evidence	that 'knows'	means	different	things	in	the	different	contexts. Now,	notice	that	we	have no	similar	reasons	for	thinking	that	'doubt'	or	'confidence'	is	context	sensitive. Suppose	S	has	much	at	stake	regarding	whether	Sally	will	arrive	on	time,	and	T	does not. It	seems	that	this	will	make	no	difference	to	whether	S	or	T	correctly	asserts that	Fred	has	some	doubt	that	Sally	will	arrive	on	time. Now,	perhaps	'doubt'	is sensitive	to	some	other	feature	of	the	attributor's	context,	but	it	is	far	from	obvious what	that	might	be. Admittedly,	my	being	unable	to	think	of	ways	to	vindicate	the	equivocation response	does	not	prove	that	it	has	no	vindication. However,	at	this	point,	I	leave	it up	to	an	actual	equivocation	responder	to	come	up	with	one. In	the	meantime,	I	am inclined	to	just	think	that	(A)–(C)	are	more	straightforwardly	like 15 17) Socrates	was	a	man 18) If	Socrates	was	a	man,	then	he	was	mortal 19) Socrates	was	not	mortal than	like	(14)–(16). And	just	as	we	should	reject	(19),	we	should	reject	one	of	(A)– (C). So,	I	now	move	on	to	finding	the	best	candidate	for	rejection.27 Consider	(A),	that	many	ordinary	unreflective	beliefs,	such	as	those	in	the classroom	scenario,	are	formed	without	doubt. Here	are	two	possible	objections	to the	claim	that	there	is	no	doubt	in	the	classroom	scenario. First,	one	could	claim that	there	is	doubt,	but	it	is	unconscious. As	such,	it	is	not	a	salient	feature	of	the scenario,	and	so	our	intuitions	are	not	sensitive	to	it. Second,	one	could	claim	that there	is	doubt,	but	our	intuitions	are	misled	by	imprecision	in	language. Suppose that	after	I	have	finished	drinking	a	glass	of	lemonade,	there	are	still	little	drops	left at	the	bottom. You	ask,	"Is	there	any	lemonade	in	the	cup?"	I	say,	"No,	there	is	no lemonade."	This	sentence	seems	correct	to	say. But	of	course,	there	might	still	be little	drops	of	lemonade	left. Similarly,	although	it	seems	correct	to	say	about	the classroom	scenario,	"There	is	no	doubt	toward	those	propositions,"	perhaps	this	is compatible	with	there	still	being	some	doubt.28 Neither	objection	is	convincing. In	the	lemonade	case,	one	can	focus	on	the relevant	proposition	that	there	is	no	lemonade	left	by	just	focusing	on	the	sentence, "There	is	absolutely	and	literally,	not	even	a	tiny	bit,	of	lemonade	left."	That	sentence does	clearly	express	the	proposition	there	is	no	lemonade	left,	and	that	sentence 27	I	revisit	the	equivocation	response	near	the	end	of	§3.1. 28	This	second	objection	and	my	response	are	motivated	by	Peter	Unger	(1975,	63–87). The	first objection	arose	in	conversations	about	the	puzzle. 16 seems	false	because	there	are	the	little	drops	left. On	the	other	hand,	the	sentence, "When	you	walked	into	the	classroom,	you	had	absolutely	and	literally	no	doubt	that the	class	clown	is	here"	still	seems	true. You	just	believed	that	the	class	clown	is	here, but	there	really	was	no	accompanying	doubt	that	he	was	there. What	about	the	claim	that	you	have	unconscious	doubt? The	intuition	that there	is	no	doubt,	whether	conscious	or	unconscious,	is	made	clearer	if	we	consider what	a	bit	of	doubt	would	have	been	like. If	someone	told	you	that	the	class	clown has	a	visiting	twin	in	town,	it	seems	that	you	might	then	come	to	have	some	doubt. It seems	that	your	doubt	would	be	newly	formed,	not	an	unconscious	doubt	rising	to consciousness. These	intuitions	support	the	claim	that	you	never	had	any	doubt	in the	first	place. So,	upon	examination,	(A)	still	seems	plausible. Consider	(C),	that	many	ordinary	unreflective	beliefs,	such	as	those	referred to	in	the	classroom	scenario,	are	not	held	with	the	highest	degree	of	confidence. Above,	I	considered	two	reasons	for	accepting	(C). First,	I	appealed	to	a	betting behavior	test:	I	would	not	be	willing	to	bet	my	life,	for	a	petty	benefit,	on	the	truth	of one	of	those	propositions. One	might	point	out	that	there	are	strong	objections	to betting	behavior	tests	being	accurate	measures	of	our	degrees	of	confidence.29	That discussion	would	take	us	too	far	astray. I	will	just	note	that	it	is	one	way	of attacking	the	first	reason	in	favor	of	(C)	that	I	find	promising. My	own	reason	for accepting	(C)	is	the	second	one:	plausibly,	one's	degree	of	confidence	in	those propositions	could	possibly	increase;	therefore,	the	ordinary	beliefs	are	not	held with	the	highest	confidence. 29	See	Plantinga	(1993,	118–119),	Foley	(1993,	150–153),	and	especially	Erikkson	and	Hajek	(2007). 17 The	fourth	possible	solution	is	to	reject	(B),	that	S	has	some	doubt	that	p	if	S has	a	doxastic	attitude	toward	p	and	does	not	have	the	highest	degree	of	confidence that	p. Here	is	one	possible	way	to	argue	against	(B). Suppose	Danny	considers	the proposition	that	someone	will	score	a	home	run	next	season. (Call	this	proposition 'H'.) He	considers	that	in	the	history	of	baseball,	there	have	always	been	many	home runs	each	season. He	says,	"I	have	no	doubt	that	someone	will	score	a	home	run next	season."	It	seems	that	Danny	has	no	doubt	that	H. However,	Danny	then reflects	on	the	fact	that	the	objective	probability	of	H	is	still	less	than	100%. If	his degree	of	confidence	matches	the	objective	probability	(following	David	Lewis' (1981)	principal	principle),	then	it	will	be	slightly	(very	slightly)	less	than	1. In	this case,	one	might	argue,	he	has	less	than	complete	confidence	in	H,	but	he	doesn't have	any	doubt	that	H.30 Though	I	will	ultimately	argue	that	(B)	is	false,	I	do	not	think	that	this	is	a sufficient	reason	to	reject	(B). At	the	beginning,	when	Danny	has	no	doubt	and	has not	considered	the	objective	probability,	he	also	has	100%	confidence. Again,	to	say that	Danny	has	no	doubt	that	H	but	confidence	of	less	than	100%	seems inconsistent. (Here	I	am	appealing	to	the	intuitions	that	supported	the	linguistic evidence	that	I	initially	used	to	support	B.)	Or	consider	the	following	dialogue: Danny:	"I	have	no	doubt	that	someone	will	score	a	home	run," Victoria:	"So	you	are	100%	confident	that	someone	will	score	a	home	run?" Danny:	"No,	I	didn't	say	that. I	am	less	than	100%	confident." 30	Thanks	to	Matthew	McGrath	for	this	sort	of	case. Scott	Edgar	has	pointed	out	to	me	a	similar	case, according	to	which	many	scientists	say	that	certain	scientific	theories	–	say,	the	theory	of	evolution	– should	be	held	without	any	doubt. However,	they	would	not	ascribe	100%	confidence	toward	the theory. What	I	say	about	the	baseball	case	will	apply	to	these	science	cases. 18 The	last	statement	sounds	very	much	like	a	statement	of	doubt,	and	Danny's statements	together	seem	inconsistent. Now	at	the	later	moment,	when	Danny	considers	that	the	objective probability	is	less	than	100%,	his	confidence	might	be	slightly	(very	slightly)	less than	1. But	then	he	would	come	to	have	a	tiny	(very	tiny)	bit	of	doubt	as	well. If Danny	said,	"Yes,	I	have	almost	100%	confidence	that	H. I	am	99.9999999% confident	that	H. But	I	am	not	100%	confident	that	H,"	then	it	seems	to	follow	that he	has	at	least	a	little	bit	of	doubt	that	H. An	alternative	possibility	is	that	at	the	later	moment,	the	objective probability	of	H	is	so	high	that	Danny's	degree	of	confidence	is	not	actually	less	than 1	because	his	degree	of	confidence,	given	the	limits	of	his	human	mind,	is	not sufficiently	fine-grained	to	match	it;	he	cannot	have	99.9999999%	confidence. But then	it	seems	correct	that	he	has	no	doubt. So,	there	is	still	no	counterexample. In summary,	the	intuitions	behind	the	earlier	linguistic	evidence	I	gave	in	support	of (B)	seem	to	neutralize	the	evidence	this	sort	of	potential	counterexample	could provide. So,	this	case	against	(B)	is	at	best	inconclusive. 3.	Solution	to	the	Puzzle	and	a	New	Account	of	Doubt 3.1	Solution	to	the	Puzzle My	solution	rejects	(B)	and	appeals	to	my	account	of	doubt. As	a	first approximation,	it	states, Doubt1:	S	has	some	doubt	that	p	if	and	only	if	S	believes	that	it's	possible	that ~p. 19 (Note	that	this	is	different	from	Doubts1,	from	§1.)	Although	Doubt1	will	require	a minor	adjustment,	it	represents	the	core	of	my	account	of	doubt	and	is	why	I	believe (B)	is	false. It	should	be	clear	how	Doubt1	supports	(A)	by	explaining	the	intuitions that	there	is	no	doubt	in	the	classroom	scenario:	one	has	not	come	to	believe	that	my chair	might	not	be	tilted	diagonally,	that	attendance	might	not	be	pretty	good	today, and	that	the	class	clown	might	not	actually	be	here. (You	would	believe	that	last proposition	if	you	believed	that	the	class	clown	has	a	twin	brother	in	town.)	So, Doubt1	explains	why	the	unreflective	beliefs	that	my	chair	is	tilted	diagonally, attendance	is	pretty	good	today,	and	the	class	clown	is	here	could	be	propositions that	you	have	a	doxastic	attitude	toward,	but	toward	which	you	have	no	degree	of doubt. Doubt1	is	also	compatible	with	(C). Although	Doubt1	determines	that	the beliefs	in	the	classroom	scenario	are	without	doubt,	it	does	not	determine	that	you have	the	highest	degree	of	confidence. Doubt1	is	incompatible	with	(B). As	I	just	said	in	the	discussion	of	(A),	Doubt1 determines	that	you	do	not	have	doubt	in	the	classroom	scenario. On	the	other hand,	according	to	(B),	S	has	some	doubt	that	p	if	S	has	a	doxastic	attitude	toward	p and	does	not	have	the	highest	degree	of	confidence	that	p. In	the	classroom scenario,	you	do	have	a	doxastic	attitude	toward	the	relevant	propositions	but	do not	have	the	highest	degree	of	confidence	toward	them;	you	thereby	instantiate	the antecedent	of	(B). So,	(B)	determines	that	you	do	have	doubt	in	the	classroom scenario. Hence,	Doubt1	and	(B)	are	incompatible;	they	conflict	in	their determination	of	whether	you	have	doubt	in	the	classroom	scenario. And 20 intuitively,	Doubt1	has	the	correct	verdict;	hence,	the	classroom	scenario	is	a	direct counterexample	to	(B).31 But	what	about	the	linguistic	evidence	in	favor	of	(B)? Recall	the	sentence, 13)	"I'm	not	completely	confident	that	p,	but	I	have	no	doubt	that	p." and	the	earlier	dialogue: Victoria:	Are	you	completely	confident	that	p? Danny:	No,	I'm	not	completely	confident	that	p. Victoria:	So	you	have	some	doubt	that	p? Danny:	I	didn't	say	that. I	also	don't	have	any	doubt	that	p. In	cases	in	which	one	makes	a	claim	about	one's	degree	of	doubt	or	confidence,	one's belief	is	not	unreflective. Since	Danny	is	an	ordinary	human	being,	if	he	knowingly claims	that	he	is	not	completely	confident	that	p,	then	he	has	formed	the	belief	that	p might	be	false. According	to	Doubt1,	it	follows	that	he	does	have	doubt,	which explains	the	seeming	inconsistency	in	both	(13)	and	also	the	sentences	in	the dialogue.	(B)	seems	natural	and	plausible	because	we	are	not	used	to	thinking	about unreflective	cases. So,	Doubt1	both	explains	the	intuitions	in	my	classroom	scenario and	also	undercuts	the	evidence	in	favor	of	(B). The	puzzle	is	solved.32 Some	have	objected	that	there	is	still	a	meaning	of	'doubt',	according	to	which (B)	is	true. Such	people	embrace	the	equivocation	response	and	say	that	on	one meaning	of	'doubt'	–	one	which	I	favor	–	you	don't	have	doubt	in	the	classroom 31	Thanks	to	Daniel	Howard-Snyder	for	conversation	that	helped	clarify	the	reasoning	in	this paragraph. 32	One	might	be	concerned	by	my	use	of	first	person	ascriptions	instead	of	the	third	person. But	note that	it	does	not	always	seem	inconsistent	to	say	of	the	person	in	the	classroom	scenario,	"S/he	is	not completely	confident	that	the	class	clown	is	there,	but	s/he	has	no	doubt	that	he's	there."	Cases	of unreflectively	formed	belief,	such	as	the	classroom	scenario,	are	just	those	cases	where	such statements	can	be	true. 21 scenario;	but	on	another	meaning	of	'doubt'	–	where	'doubt'	means	has	a	doxastic attitude	but	not	the	highest	degree	of	confidence	–	you	do	have	doubt. Then	both	(A) and	(B)	could	come	out	true. Perhaps	the	puzzle	can	be	solved	this	way. My	reply	is	simply	to	emphasize	that	the	classroom	scenario	is	a counterexample	to	the	claim	that	'doubt'	means	has	a	doxastic	attitude	but	not	the highest	degree	of	confidence. Imagine	someone	who	resisted	Gettier's	(1963)	cases by	saying, "Well,	I	admit	that	there	is	a	meaning	of	'knows'	according	to	which	Jones does	not	know	that	the	man	who	will	get	the	job	has	ten	coins	in	his	pocket. Fortunately,	there	is	another	meaning	of	'knows'	–	where	'knows'	just	means justified,	true	belief	–	according	to	which	Jones	does	know	that	proposition." Gettier	should	reply	by	emphasizing	that	his	scenario	is	a	counterexample	to	that definition	of	knowledge;	hence,	'knows'	does	not	mean	justified,	true	belief. So,	just as	this	is	not	a	good	objection	in	the	case	of	'knows'	and	Gettier	cases,	it	is	not	a	good objection	in	the	case	of	'doubt'	and	my	classroom	scenario.33 Before	moving	on	to	a	more	detailed	explanation	and	defense	of	Doubt1,	I	will emphasize	that	even	if	it	is	false,	I	have	raised	a	novel	puzzle	about	belief, confidence,	and	doubt. The	remaining	options	are	to	find	an	alternative	way	of rejecting	(B),	to	reject	(A),	to	reject	(C)	or	to	take	the	equivocation	response. In	my presentations	of	the	puzzle	to	various	audiences,	I	have	found	a	diversity	of	opinions on	which	is	the	best	option.	(Many	of	the	suggested	reasons	for	the	different	options 33	One	could	stipulatively	define	'doubt'	to	mean	has	a	doxastic	attitude	but	not	the	highest	confidence, just	as	one	could	stipulatively	define	'knows'	to	mean	justified	true	belief. Then	there	would	be	a meaning	of	'doubt'	according	to	which	(B)	is	true. But	then	we	would	no	longer	be	talking	about doubt,	just	as	we	would	no	longer	be	talking	about	knowledge. 22 have	been	explored	above.)	It	is	therefore	at	least	not	obvious	what	the	best	solution is,	and	exploration	of	the	different	options	will	likely	lead	to	further	insight	into	the nature	of	doubt. Hence,	I	believe	that	this	puzzle	is	worthy	of	further	consideration, even	if	my	proposed	solution	to	it	is	incorrect. 3.2	Explanation	of	Doubt1	and	Response	to	Objections My	preliminary	account	of	doubt	is Doubt1:	S	has	some	doubt	that	p	if	and	only	if	S	believes	that	~p	is	possible. The	sense	of	'possible'	employed	is	epistemic	possibility. It	has	been	well-discussed in	contemporary	philosophy	and	we	are	quite	familiar	with	it	in	ordinary	life.34	I	am leaving	my	home	when	I	am	suddenly	struck	with	the	possibility	that	I	left	the	stove on. I	go	back	inside	to	check	because	I	believe	that	it	is	possible	that	I	left	it	on. This is	obviously	not	metaphysical	possibility;	my	believing	that	there	is	a	possible	world in	which	I	left	the	stove	on	is	no	reason	to	worry. Note	that	which	propositions	are epistemically	possible	depend	on	individuals'	information	states. It	might	still	be possible	for	me	that	the	stove	is	on,	but	for	Sean,	who	is	still	at	home,	this	is	not	a possibility. It	is	an	open	possibility	for	Fred	that	Sally	still	loves	him,	but	not	for Jenny,	in	whom	Sally	has	confided. It	is	possible	for	Adam	that	26x23≠598,	but	not for	Dainis,	who	has	ruled	out	that	option	with	a	calculator.35 34	See,	for	example,	DeRose	(1991),	Stanley	(2005),	Huemer	(2007),	Yalcin	(2007),	and	Dougherty	& Rysiew	(2009);	as	well	as	the	essays	in	Egan	&	Weatherson	(2011). 35	These	examples	should	make	clear	that	epistemic	possibility	is	distinct	from	other	types	of possibility,	according	to	which	possibility	(or	possible	truth)	is	a	property	of	propositions	and	not dependent	on	individuals'	information	states. Most	accounts	of	metaphysical	possibility	are	like	this, as	are	accounts	of	possibility	depending	on	statistical,	frequentist,	or	logical	accounts	of	probability. On	these	accounts,	truths	like	26x23=598	are	all	necessarily	true,	independent	of	any	individual's information	state. 23 I	intend	for	these	examples	to	be	the	primary	means	of	grasping	the	sense	of 'possible'	I	intend	to	employ. Now,	here	are	potential	analyses	of	epistemic possibility: (Possibility1)	p	is	epistemically	possible	for	S	if	and	only	if	what	S	knows	does not,	in	a	manner	that	is	obvious	to	S,	entail	~p.36 (Possibility2)	p	is	epistemically	possible	for	S	if	and	only	if	S's	evidence	does not,	in	a	manner	that	is	obvious	to	S,	entail	~p.37 I	am	not	committed	to	either	of	these	analyses	of	epistemic	possibility;	I	state	them to	aid	the	reader	in	grasping	the	relevant	concept	of	possibility	that	is	expressed	in ordinary	English	(as	in	my	above	examples),	and	that	is	employed	in	Doubt1. Someone	might	object	that	the	above	analyses	of	epistemic	possibility	are open	to	the	following	objection	by	Seth	Yalcin	(2011). Suppose	Fido	walks	into	the room	and	heels	by	Yalcin's	chair.38	Yalcin	occasionally	tosses	Fido	a	bone	at	dinner, but	not	usually. When	you	ask	Yalcin	why	Fido	is	sitting	there,	he	responds,	"Fido thinks	I	might	give	him	a	bone."	Yalcin	then	writes, Unless	you	have	a	particular	theory	of	epistemic	modals,	I	doubt	you	would flinch	at	this	remark. But	what	exactly	am	I	saying? Does	my	remark	in	part mean...	that	Fido	believes	that	it	is	left	open	by	what	he	knows	that	I	will	give him	a	bone? This	is	a	bit	much	(308). 36	This	is	derived	from	Stanley	(2005,	128). For	other	knowledge-based	accounts,	see	DeRose	(1991) and	Huemer	(2007). Epistemic	logicians	also	commonly	define	epistemic	possibility	in	terms	of knowledge. See	also	the	influential	Kratzer	(1977). 37	This	evidence-based	account	is	derived	from	Dougherty	and	Rysiew	(2009,	127). 38 Fido	also	appears	in	a	similar	example	in	Yalcin	(2007,	997). 24 Similarly,	it	is	implausible	that	Fido	believes	that	what	he	knows	does	not,	in	a manner	obvious	to	him,	entail	that	he	won't	get	food. In	reply,	one	need	not	explicitly	believe	that	the	components	of	the	right	side of	an	analysis	obtains	each	time	one	believes	the	left	side	obtains. Suppose	that	S knows	that	p	if	and	only	if	S	has	an	ungettiered,	justified,	true	belief	that	p. Still, Fred	might	believe	that	S	knows	that	p	without	also	believing	that	S	has	an ungettiered,	justified,	true	belief	that	p;	Fred	might	not	have	any	grasp	of	what	it	is to	be	ungettiered. Similarly,	someone	might	believe	that	~p	is	epistemically possible	without	forming	an	explicit	belief	that	the	components	of	the	analysans	of Possibility1	or	Possibility2	obtain.39 There	are	many	complicated	issues	that	arise	in	discussions	of	epistemic possibility,	issues	that	I	cannot	resolve	in	this	paper. Yet,	our	intuitions	about	the cases	are	clear	enough. In	the	classroom	scenario,	it	seems	that	you	do	not	form	the belief	that	attendance	might	not	be	good. And	in	the	above	scenario,	I	do	form	the belief	that	I	might	have	left	the	stove	on. Doubt1	entails	that	this	belief	is	necessary and	sufficient	for	me	to	have	doubt	that	I	left	the	stove	on. This	should	be	sufficient for	understanding	Doubt1. I	will	now	list	some	of	Doubt1's	virtues. First,	a	natural	extension	of	Doubt1 explains	how	doubt	comes	in	degrees. To	have	some	doubt	that	p	simpliciter,	one needs	only	the	belief	that	it	is	epistemically	possible	that	~p. But	sometimes,	we also	believe	that	~p	is	very	probable	or	that	~p	is	very	improbable. The	degree	of 39	Thanks	to	Hud	Hudson	and	Daniel	Howard-Snyder	for	helpful	conversation. Nothing	I	say	here requires	that	Yalcin's	own	view,	credal	expressivism,	is	false,	but	only	that	this	particular	criticism that	Yalcin	makes	fails. For	a	brief	discussion	of	credal	expressivism	and	its	application	to	this	paper, see	the	next	footnote. 25 one's	doubt	that	p	will	just	be	the	degree	of	epistemic	probability	one	believes	~p	to have. So,	if	one	believes	that	there's	a	very	small	probability	that	one's	lottery	ticket will	not	lose,	then	one	has	only	a	very	small	degree	of	doubt	that	it	will	lose. If	one thinks	it's	very	likely	that	the	Cubs	will	not	win	the	World	Series	in	the	following year,	then	the	person	highly	doubts	(or	has	much	doubt)	that	the	Cubs	will	win. Doubt1	also	explains	why	only	more-complex	beings	have	doubt. Consider that	some	simple-minded	animals	(and	perhaps	more-complex	insects)	might plausibly	be	said	to	be	guided	by	simple	beliefs	and	desires. Peter	Carruthers (2006)	has	argued	that	bees	have	very	simple	beliefs	which	guide	their	behavior. Even	if	we	do	not	go	as	far	as	Carruthers,	there	will	be	some	degree	of	complexity	in an	organism	at	which	we	will	be	willing	to	ascribe	belief	and	desire	to	it. Having such	a	minimally	complex	organism	in	mind,	we	can	ask	whether	that	organism	is the	sort	of	being	that	can	doubt. Intuitively,	doubt	is	the	wrong	sort	of	thing	to ascribe	to	such	a	being. Suppose	that	a	bee	(or	a	slightly	more	complex	organism)	is guided	by	simple	beliefs	about	its	environment	as	it	navigates	itself	through	the	air; intuitively,	the	bee	will	not	also	have	doubt. My	point	here	illustrates	dramatically the	point	I	was	making	with	the	classroom	scenario. It	is	one	thing	to	form	simple, unreflective	beliefs;	doubt	requires	something	more	reflective. This	"something more	reflective"	is	revealed	by	Doubt1:	doubt	requires	belief	about	what's	possible, and	only	more	complex	minds	can	have	that.40 40	According	to	credal	expressivism,	to	believe	that	~p	is	possible	is	to	have	a	nonzero	credence	that ~p. If	this	is	true,	then	the	additional	complexity	that	is	missing	in	the	classroom	scenario	is	as follows. You	do	believe	that	attendance	is	good. But	you	have	not	formed	any	degree	of	credence toward	the	proposition	that	attendance	is	not	good. In	other	words,	you	will	have	formed	a	doxastic attitude	toward	a	proposition	without	having	formed	an	attitude	toward	its	negation. That additional	complexity	is	required	for	you	to	have	doubt	that	attendance	is	good. 26 Now,	one	does	not	need	a	very	complex	mind	to	have	doubt. If	S	can competently	say	something	like,	"Oh,	I	might	be	wrong	about	that,"	then	this sentence	would	express	S's	belief	that	~p	is	possible. Insofar	as	small	children	can have	such	beliefs,	they	can	have	doubt. And	to	the	extent	to	which	it	seems	that more-complex	animals	could	have	such	beliefs,	it	seems	that	they	can	also	have doubt. Suppose	it	looks	like	a	chimpanzee	is	tentatively	approaching	another creature. Insofar	as	it	seems	that	the	chimpanzee	believes	that	this	creature	might not	be	a	friend,	it	also	seems	she	has	doubt	that	this	creature	is	a	friend.41 But	could	a	very	small	child	have	varying	degrees	of	doubt? Plausibly,	it	takes less	sophistication	to	believe	might-p	than,	for	example,	to	believe	it's	very	likely-p. Suppose	a	child	believes	that	mommy	might	be	home	but	doesn't	believe	that	she's very	likely	home	or	that	she's	very	unlikely	home	and	so	on. It	seems	that,	on	my view,	such	a	child	could	have	an	all-or-nothing	doubt	that	p	but	no	degree	of	doubt. But	isn't	it	implausible	that	such	a	child	wouldn't	have	varying	degrees	of	doubt?42 Admittedly,	my	view	does	imply	that	this	child	doesn't	have	degrees	of	doubt. However,	I	distinguish	between	doubt's	coming	in	degrees,	and	the	strength	of	the doubt	coming	in	degrees. The	degree	of	doubt	that	p	is	the	degree	of	epistemic probability	that	~p	is	believed	to	have. In	accord	with	what	I	said	about	Doubts3	in §1,	the	degree	of	the	strength	of	doubt	is	the	degree	of	the	strength	of	feeling associated	with	conscious	occurrences	of	the	doubt. I	believe	that	our	inclination	to 41	Note	that	Doubt1	does	not	require	that	for	one	to	have	doubt	that	p,	one	must	believe	that	it	is possible	that	p	is	false. The	concepts	of	falsity	and	truth	do	seem	to	be	a	bit	more	difficult	to	grasp, and	I	do	not	want	to	say	that	a	grasp	of	either	of	those	concepts	is	required	for	doubt. Thanks	to Chris	Tweedt	for	the	objection	that	led	to	this	clarification. 42	Thanks	to	a	referee	of	this	journal	for	pressing	this	objection,	which	helped	me	to	think	more clearly	about	my	account	of	degrees	of	doubt. 27 think	that	the	small	child's	doubt	comes	in	degrees	can	be	explained	by	our	thinking that	the	strength	of	the	feeling	of	the	doubt	comes	in	degrees. But	let	us	now	consider	whether	the	child's	doubt	itself	might	come	in degrees. I	might	attribute	a	high	degree	of	doubt	to	Sally	with	the	following sentences,	"Sally	highly	doubts	that	p"	or	"Sally	has	much	doubt	that	p,"	or	a	low degree	of	doubt	with	this	sentence,	"Sally	has	little	doubt	that	p."	When	we	move away	from	talking	about	the	degree	of	strength	of	the	feeling	of	the	doubt,	to	the degree	of	the	doubt	itself,	it	does	seem	to	be	something	a	little	more	sophisticated. If	Sally	highly	doubts	that	p,	then	it	seems	she	thinks	it's	very	likely	that	~p,	and	if Sally	has	little	doubt	that	p,	then	it	seems	she	thinks	it's	very	unlikely	that	~p. So,	I believe	it	is	plausible	that	the	small	child	does	not	have	varying	degrees	of	doubt,	so long	as	we	can	still	say	that	the	strengths	of	the	feeling	of	her	doubt	comes	in degrees.43 3.3	Responses	to	Even	More	Objections 43	A	referee	has	offered	the	following	challenging	objection. There	are	various	properties	associated with	doubt:	"hesitancy,	inhibition,	anxiety,	curiosity,	unwillingness	to	assert,	unwillingness	to	stake values	upon,	and	perhaps	a	handful	of	other	phenomenal/dispositional	properties."	Couldn't	a	child exhibit	varying	degrees	of	these	properties,	and	hence,	have	varying	degrees	of	doubt,	even	if	she doesn't	believe	it's	likely	that	~p,	it's	very	likely	that	~p,	and	so	on? In	response,	I	say	'no'. If	the degree	of	the	property	is	not	had	in	virtue	of	believing	something	like	it's	very	likely	that	~p,	then	it	is implausible	that	the	child	has	a	degree	of	doubt. For	example,	suppose	a	child	is	very	unwilling	to assert	that	p,	but	not	in	virtue	of	believing	it's	very	unlikely	that	~p;	it	is	because	the	child	simply doesn't	like	asserting	things. Then	it	is	implausible	that	the	child	has	a	high	degree	of	doubt	that	p, despite	being	very	unwilling	to	assert	that	p. I	would	say	similar	things	about	the	other	properties	in the	referee's	list	of	properties. But	perhaps	the	referee	holds	to	a	dispositionalist	account	of	doubt,	according	to	which having	a	high	degree	of	doubt	just	is	having	a	high	degree	of	enough	of	the	properties	in	that	list. Perhaps	such	an	account	could	be	developed	along	the	lines	of	the	dispositionalist	account	of	belief held	by	Schwitzgebel	(2002). But	if	the	referee	says	that,	then	it	would	also	be	natural	for	the	referee to	accept	a	dispositionalist	account	of	belief,	where	believing	that	it's	very	likely	that	~p	is	also identical	to	having	a	high	degree	of	enough	of	the	properties	in	the	list. Then	it	is	still	impossible	to have	a	high	degree	of	doubt	that	p	without	believing	it's	very	likely	that	~p. Thanks	to	Liz	Jackson	for helpful	discussion	about	these	points. 28 I	now	respond	to	two	more	potential	counterexamples	that	require	very	detailed responses. Those	who	are	not	interested	in	these	objections	can	skip	to	the	next section,	§3.4,	with	little	interruption	in	the	overall	dialectic. One	might	object	to	Doubt1	with	the	following	counterexample. Suppose	an atheist	is	certain	that	God	does	not	exist;	she	believes	there	is	a	100%	probability that	God	does	not	exist. In	virtue	of	this	belief,	this	atheist	will	naturally	also	believe that	it's	possible	that	God	does	not	exist. But	it	seems	inappropriate	to	attribute doubt	that	God	exists	to	her,	since	she's	certain	that	God	does	not	exist. Certainty that	~p	seems	to	entail	the	lack	of	doubt	that	p. Hence,	Doubt1	is	false. In	reply,	I	agree	that	it	is	inappropriate	to	attribute	doubt	to	her. But	it	also seems	inappropriate	to	attribute	to	her	the	belief	that	it's	possible	that	God	does	not exist. Why? In	discussion	of	a	similar	topic,	Keith	DeRose	(2009,	87)	has	pointed out	that	there	is	a	conversational	rule	that	we	should	assert	the	stronger,	that	"when you're	in	a	position	to	assert	either	of	two	things,	then,	other	things	being	equal,	if you	assert	either	of	them,	you	should	assert	the	stronger	of	them."	This	is	why	it seems	inappropriate	to	say,	of	a	strong	atheist	who	believes	there's	a	100% probability	that	God	does	not	exist,	that	she	believes	that	it's	possible	that	God	does not	exist. Similarly,	of	a	strong	atheist	who	is	certain	that	God	does	not	exist,	it	will also	seem	inappropriate	to	assert	that	she	has	doubt	that	God	exists. So,	it	might seem	inappropriate	to	attribute	doubt	not	because	there	is	no	doubt,	but	because	of the	violation	of	the	conversational	rule. Hence,	this	is	not	strong	evidence	that	there is	no	doubt. 29 Is	there	evidence	that	doubt	is	present?44	Yes. Notice	that	it	does	seem	right to	say	of	her:	"She	doesn't	just	doubt	that	God	exists;	she's	certain	that	God	does	not exist."	The	seeming	truth	of	the	sentence	is	evidence	that	she	can	have	both certainty	that	God	doesn't	exist	and	doubt	that	God	does	exist. This	reply	is	similar	to the	one	given	to	those	who	think	knowledge	does	not	require	belief	because	it seems	right	to	say,	"She	doesn't	believe	that	Fred	will	be	late;	she	knows	he	will	be late."	The	reply	is	that	that	sentence	is	really	just	shorthand	for,	"She	doesn't	merely believe	that	Fred	will	be	late;	she	knows	he	will	be	late,"	which	is	evidence	that	she both	believes	and	knows	in	that	case. Here	is	the	second	potential	counterexample. Suppose	someone	believes that	~p	but	has	not	formed	the	more	complex	belief	that	~p	is	possible. Doesn't	such a	person	have	doubt	that	p?45	Answering	this	question	requires	care. For	ordinary humans,	in	many	cases	that	one	believes	~p,	the	person	has	also	believed	that	it's possible	that	~p. To	construct	the	relevant	case,	we	must	make	it	unreflective	and simple. Suppose	Adam,	while	walking	by	a	window,	glances	outside	and	nonchalantly says,	"Oh,	the	sun	isn't	out,"	expressing	his	unreflective	belief	that	the	sun	is	not	out. He	also	has	not	formed	the	more-complex	belief	that	it's	possible	that	the	sun	isn't out. After	making	his	remark,	he	walks	on	to	think	about	other	things. Does	Adam 44	Following	DeRose	(2009,	112)	again,	perhaps	we	should	"check	the	negations"	of	the	relevant doubt	ascription. While	it	seems	inappropriate	to	attribute	doubt	to	the	strong	atheist,	it	seems worse	to	say	of	her,	"She	lacks	doubt	that	God	exists,"	"She	doesn't	doubt	that	God	exists,"	and especially,	"She	has	no	doubt	that	God	exists."	Is	this	good	evidence	that	there	is	doubt? No. These sentences	also	have	a	false	implicature;	they	imply	that	she	believes	that	God	does	exist,	which	is certainly	false! Therefore,	the	intuition	of	the	falsity	or	inappropriateness	of	those	negations	might not	be	because	doubt	is	present,	but	because	they	falsely	imply	that	belief	is	present. 45	Thanks	to	Brad	Rettler	for	this	objection. 30 have	doubt	that	the	sun	is	out? Suppose	you	are	checking	the	refrigerator	to	see what	food	you	have. You	observe	that	there	is	no	hummus,	form	the	spontaneous and	unreflective	belief	that	there's	no	hummus,	and	quickly	go	on	to	other	food options. At	no	point	do	you	also	believe	that	it's	possible	that	there	is	no	hummus. Do	you	have	doubt	that	there	is	hummus? Before	sharing	my	take	on	whether	there's	doubt,	I	want	to	emphasize	just how	easy	it	is	to	believe	it's	possible	that	~p. For	example,	if	you	had	been	checking for	hummus,	you	likely	would	have	had	the	belief	that	it's	possible	that	there's	no hummus;	that's	why	you	were	checking	for	it. If	Adam	had	thought	even	a	little about	the	weather	before	checking,	it	would	have	been	very	easy	to	form	the	belief that	the	sun	might	not	be	out. So,	in	both	cases,	we	must	clear	from	our	minds	that any	such	belief	is	present. With	the	clarifications	made,	it	at	least	does	not	clearly	seem	that	there	is doubt	present. So,	at	the	very	least,	I	do	not	take	this	to	be	a	clear	counterexample. Furthermore,	it	seems	that	there	is	no	doubt	present,	although	I	admit	that	this intuition	is	not	very	strong. Since	the	intuitions	about	the	case	are	unclear,	I	am moved	to	engage	in	reflective	equilibrium	and	let	my	theory	sway	what	I	think	about the	case. As	mentioned	before,	doubt	requires	something	more	reflective;	this	is	why simple-minded	animals	do	not	have	doubt. And	in	this	situation,	the	"something more	reflective"	is	the	more-complex	belief	that	it's	possible	that	the	sun	is	not	out	or that	it's	possible	that	there's	no	hummus. Such	beliefs	have	not	been	formed. I conclude,	on	the	basis	of	my	theory,	that	there	is	no	doubt	present	in	the	cases. 31 Just	to	be	clear,	I	am	not	flat-footedly	saying	that	there	is	no	doubt	just because	my	theory	says	so. I	am	saying	that	because	the	intuitions	about	the	cases are	unclear,	they	fail	as	clear	counterexamples;	it	is	thereby	rationally	permissible	to use	my	otherwise	well-supported	theory	–	Doubt1	–	to	determine	my	judgment about	the	unclear	cases. I	conclude	that	there	is	no	doubt	in	the	scenario,	and furthermore,	that	mere	belief	that	~p	is	insufficient	for	doubt	that	p;	belief	in	the possibility	that	~p	is	required.46 3.4	Fine-tuning Doubt1	predicts	the	right	intuitions	in	most	cases. However,	it	requires	some	finetuning. Consider	that	some	epistemologists	do	not	take	skepticism	seriously	in	the slightest	bit. They	might	say,	"Well,	it's	possible	that	I'm	beguiled	by	an	evil	demon, and	so	I	don't	have	hands,	but	I	don't	have	the	slightest	bit	of	doubt	that	I	have hands. I	just	can't	take	that	possibility	seriously."	There	seems	to	be	no inconsistency	in	this	speech. As	such,	I	think	that	it	provides	us	with	a counterexample	to	Doubt1.47 Here	is	another	example. Suppose	that	all	of	the	mathematicians	in	the	world have	come	to	agree	that	theorem	T,	which	you	haven't	seen	the	proof	for,	is	true. You	turn	to	your	spouse	and	say,	"There's	no	doubt	about	it. T	is	true." Your	spouse points	out	that	if	a	group	of	aliens	injected	a	virus	in	these	mathematicians	that made	them	form	only	false	beliefs	about	T,	then	T	is	false. Your	spouse	says,	"You 46	Thanks	to	Kenny	Boyce	and	Daniel	Howard-Snyder	for	helpful	conversation	about	the	previous objections	and	how	to	respond	to	them. 47	Thanks	to	Matt	Duncan	for	helpful	conversation. 32 believe	in	the	possibility	of	aliens	and	the	possibility	of	an	odd	virus,	right? And there's	a	possibility	that	they'd	do	this	to	the	mathematicians,	right? So,	it's	possible that	T	is	false. Doesn't	that	make	you	have	some	doubt	that	T	is	true?"	Incredulous, you	say,	"Well,	that's	possible,	but	no,	that	possibility's	so	ridiculous	that	it	doesn't make	me	have	even	a	bit	of	doubt	about	T."	It	seems	that	if	a	possibility	is	taken	to be	sufficiently	ridiculous,	then	you	could	believe	in	the	possibility	that	you	are wrong	without	having	a	corresponding	doubt. I	therefore	propose	the	following	revision: Doubt2:	S	has	some	doubt	that	p	if	and	only	if	S	believes	that	~p	is	possible, and	it's	not	the	case	that	S	believes	that	the	possibility	that	~p	is	insignificant. Doubt2	both	blocks	the	above	counterexample	and	also	has	all	of	the	earlier advantages	of	Doubt1. Originally,	I	formulated	Doubt2	so	that	the	analysans	more simply	said	that	S	believes	there's	a	significant	possibility	that	~p. However,	I believe	that	this	overintellectualizes	doubt.48	It	would	require	the	small	child	who has	doubt	that	mom	is	home	to	believe	that	there's	a	significant	possibility	that	mom is	not	home. I	believe	that	this	requires	too	much. The	current	version	of	Doubt2 only	requires	the	absence	of	belief	that	there	is	an	insignificant	possibility. But	what	is	it	to	believe	that	a	possibility	is	insignificant? We	can	answer	this question	by	considering	examples. The	possibility	that	one	has	been	beguiled	by	a demon,	and	the	possibility	that	aliens	have	injected	the	mathematicians,	were	both believed	to	be	insignificant	in	my	earlier	examples. Those	possibilities	were	not taken	seriously. However,	Fred	does	not	believe	that	the	possibility	that	Sally	will 48	I	am	thankful	to	a	referee	of	this	journal	for	the	objection	to	that	analysis	of	doubt,	which	in	turn led	to	the	current	formulation	of	Doubt2	here. 33 not	arrive	on	time	is	insignificant. To	be	clear,	one	can	believe	that	the	probability of	p	is	extremely	low	but	also	still	not	believe	that	the	possibility	of	p	is	insignificant. For	example,	we	do	not	think	that	the	possibility	that	our	lottery	tickets	will	win	is insignificant,	which	is	why	we	do	not	discard	them,	even	though	we	believe	that	the probability	of	winning	is	extremely	low. One	might	object	that	it	seems	that	our	determination	of	whether	someone believes	that	the	possibility	that	~p	is	insignificant	is	determined	by	whether	we think	the	person	has	some	doubt	that	p. If	this	is	true,	then	we	can	only	understand the	analysans	of	Doubt2	only	insofar	as	we	already	understand	what	doubt	is;	hence, it	is	circular. In	response,	suppose	Doubt2	did	contain	some	circularity. This	would not	be	a	good	reason	to	reject	it. Doubt2	could	be	an	analysis	according	to	Peter Strawson's	(1992,	21)	connective	model	of	analysis,	i.e.,	an	illuminating	set	of necessary	and	sufficient	conditions. Some	circular	biconditionals	are unilluminating,	like	S	knows	that	p	if	and	only	if	S	knows	that	p. However,	Doubt2 illuminates	the	concept	of	doubt	by	connecting	it	with	concepts	such	as	belief	and possibility. Accomplishing	this	much	is	philosophically	valuable.49 My	second	response	is	to	provide	an	account	of	significant	possibility. Fantl and	McGrath	(2009,	20–23)	hold	the	view	that	a	chance	that	~p	is	significant	if	it	is sufficiently	high	to	rule	out	knowing	that	p.50	Consider	now, Significance:	the	possibility	that	~p	is	significant	for	S	if	and	only	if	the possibility	or	probability	that	~p	for	S	precludes	S's	knowing	p. 49	For	more	defense	of	the	value	and	philosophical	respectability	of	this	sort	of	analysis,	see	chapter	2 of	Strawson	(1992),	especially	pp.	18-20. 50	They	are	building	on	the	work	of	Dougherty	and	Rysiew	(2009,	130),	who	also	endorse	this	claim, though	more	hesitantly. 34 Let	infallibilism	be	the	view	that	S	knows	that	p	only	if	it	is	impossible	for	S	that	~p. Fallibilists	deny	this	but	will	still	hold	that	there	are	cases	where	the	possibility	that ~p	rules	out	knowing	that	p.	(Alternatively,	they	will	think	that	there	is	some	degree of	probability	that	~p	that	is	high	enough	to	preclude	knowing	that	p.)51	So, following	Significance,	infallibilists	will	think	that	the	cases	in	which	there	is	some possibility	that	~p	(or	a	non-zero	probability	that	~p)	and	the	cases	in	which	there is	a	significant	possibility	that	~p,	are	coextensive. They	will	think	that	any possibility	or	non-zero	probability	that	~p	is	significant	and	can	destroy	knowledge. Fallibilists,	on	the	other	hand,	will	likely	think	that	the	mere	possibility	that	~p	and a	significant	possibility	that	~p	do	not	completely	overlap. They	will	likely	say	that it	is	possible	that	an	evil	demon	is	beguiling	them,	but	it's	not	a	significant possibility. With	the	majority	of	epistemologists,	I	will	assume	that	fallibilism	is true. However,	even	those	who	accept	infallibilism	should	still	know	the	general types	of	probability	or	possibility	that	fallibilists	think	is	compatible	with	knowledge (e.g.,	our	being	beguiled	by	a	demon). The	plausibility	of	Doubt2	and	Significance	can	be	seen	by	introspection. Suppose	you	see	a	weather	forecast	that	predicts	a	high	likelihood	of	rain	tomorrow. You	will	probably	still	have	some	doubt	that	it	will	rain. Furthermore,	in	accord with	Doubt2,	you	will	find	that	you	believe	that	it	might	not	rain. And	with	further reflection,	you	will	find	that	you	don't	believe	that	the	probability	that	it	will	not 51	For	reasons	to	define	fallibilism	and	infallibilism	in	something	like	this	way,	see	Fantl	and	McGrath (2009,	7–15). Fallibilists	will	differ	on	when	the	degree	of	probability	is	high	enough	to	preclude knowledge. Proponents	of	pragmatic	encroachment,	like	Fantl	and	McGrath	(2009,	25–26),	think that	the	threshold	is	determined	at	least	in	part	by	pragmatic	factors. 35 rain	is	insignificant;	in	accord	with	Significance,	you	won't	believe	that	that probability	is	low	enough	to	be	compatible	with	knowing	that	it	will	rain.52 The	reflection	can	go	in	the	opposite	direction. Suppose	you	lack	the	belief that	the	probability	that	it	will	not	rain	is	compatible	with	knowing	that	it	will	rain. Then,	in	accord	with	Significance,	you	will	not	believe	it	to	be	an	insignificant possibility. If	you	also	believe	that	it	might	not	rain,	then,	in	accord	with	Doubt2,	you will	find	that	you	have	some	doubt	that	it	will	rain. In	summary,	my	first	reply	to	the	question,	"What	is	it	to	believe	that	there	is an	insignificant	possibility	that	~p?"	is	to	give	examples. One	might	charge	that	our intuitions	about	those	cases	depend	on	our	intuitions	about	whether	doubt	is present;	this	makes	my	analysis	circular. I'd	reply,	"Yes,	it	is	circular;	but	we	still have	an	illuminating,	connective	analysis	of	doubt."	If	someone	continues	to	press me	for	a	definition	of	significance,	I	will	point	to	Significance. It	is	beyond	the	scope of	this	paper	to	explore	in	detail	the	success	of	Significance,	but	I	believe	that	it	is worth	exploring	for	further	research. Conclusion Given	the	many	ingenious,	counterexample-making	philosophers	in	our	profession,	I suspect	that	Doubt2	will	not	be	immune	to	strong	objections. Hence,	I	hold	to Doubt2	with	some	doubt;	I	believe	it	might	be	false. (I	also	don't	believe	that	the probability	that	it	is	false	is	compatible	with	my	knowing	Doubt2.) However,	in 52	To	repeat,	this	process	requires	reflection. Consider	my	earlier	example. It	might	be	that	S	knows that	p	if	and	only	if	S	has	ungettiered,	justified,	true	belief	that	p. It	does	not	follow	that	if	you	believe an	instance	of	the	analysandum,	you	will	automatically	believe	the	relevant	instance	of	the	analysans. That	would	take	reflection. 36 addition	to	my	goal	of	presenting	a	counterexample-free	account	of	doubt,	I	have also	aimed	to	1)	present	an	interesting,	new	puzzle;	2)	illuminate	our	understanding of	doubt;	and	3)	get	the	issue	of	what	doubt	is	on	the	table. Despite	the	prominence of	doubt	in	the	history	of	philosophy	–	back	to	Descartes	and	further	–	it	is surprising	that	so	little	time	has	been	spent	on	it	by	analytic	philosophers. I	believe that	Doubt2	is	a	step	in	the	right	direction,	and	I	welcome	further	counterexamples or	alternatives	to	it	to	further	our	understanding	of	doubt.53 Works	Cited Alston,	William	1996:	"Belief,	Acceptance,	and	Religious	Faith,"	in	Faith,	Freedom, and	Rationality,	ed.	Jeff	Jordan	and	Daniel	Howard-Snyder	(Lanham,	MD: Rowman	&	Littlefield,	1996) Audi,	Robert	1994:	'Dispositional	Beliefs	and	Dispositions	to	Belief'.	Nous,	28,	pp. 419-34. Carruthers,	Peter	2006:	The	Architecture	of	the	Mind.	Oxford:	Clarenden	Press. 53	I	am	thankful	for	helpful	feedback	from	the	audience	at	Dalhousie	University's	philosophy colloquium	(10/2013),	the	philosophy	faculty	of	Western	Washington	University	(12/2013),	the audience	at	the	Central	APA	(2/2014)	(especially	my	commentator,	Earl	Conee),	the	participants	of the	Notre	Dame	Belief	and	Credence	reading	group	(9/2016)	(including	Hugh	Burling,	Brian	Cutter, Liz	Jackson,	Ross	Jensen,	Ting	Cho	Lau,	and	James	Nguyen),	and	the	audience	at	a	Saint	Louis epistemology	brown	bag	session	(9/2016)	(especially	Jonathan	Nebel,	Jonathan	Reibseman,	and	Julia Staffel). Thanks	to	Jon	Kvanvig,	Daniel	Howard-Snyder,	and	Trent	Dougherty,	for	allowing	me	to participate	in	the	Summer	Seminar	on	the	Nature	of	Faith	(6/2014–7/2014). The	paper	benefitted from	discussions	with	the	following	participants	of	that	seminar:	Kenny	Boyce,	Daniel	McKaughan, Rik	Peels,	and	especially	Daniel	Howard-Snyder. Thanks	to	the	Center	for	Philosophy	of	Religion	at Rutgers	University	and	the	Center	for	Philosophy	of	Religion	at	University	of	Notre	Dame	for research	time	and	funding	for	this	project. Thanks	to	Peter	Markie,	Jon	Matheson,	Kevin	McCain, Matthew	McGrath,	and	Paul	Weirich	for	helpful	written	comments	on	§2. In	addition	to	those mentioned	in	the	footnotes	throughout	the	paper,	I	am	also	thankful	for	helpful	conversations	with Bob	Beddor,	Chris	Gadsden,	Richard	Fumerton,	Simon	Goldstein,	Peter	Markie,	Kevin	McCain, Matthew	McGrath,	Andrew	Melnyk,	J.L.	Schellenberg,	Hayoung	Shin,	John	Turri,	Peter	van	Elswyk, Jonathan	Vertanen,	Paul	Weirich,	and	Julie	Zykan. Lastly,	I	am	thankful	to	Ting	Cho	Lau	for	helpful editing	that	led	to	clarifications	and	improvements	in	the	paper. 37 Clarke,	Roger	2013:	'Belief	is	Credence	One	(in	Context)'.	Philosopher's	Imprint,	13, pp.	1–18. Cohen,	L.	Jonathan	1992:	An	Essay	on	Belief	and	Acceptance.	Oxford:	Clarendon Press. DeRose,	Keith	1991:	'Epistemic	Possibilities'.	The	Philosophical	Review,	100,	pp.	581605. DeRose,	Keith	1995:	'Solving	the	Skeptical	Problem'.	The	Philosophical	Review,	104, pp.	1–52. DeRose,	Keith	2009:	The	Case	for	Contextualism,	Oxford:	Oxford	University	Press. Dougherty,	Trent	and	Patrick	Rysiew	2009:	'Fallibilism	and	Concessive	Knowledge Attributions'.	Philosophy	and	Phenomenological	Research,	78,	pp.	123–132. Egan,	Andy	and	Brian	Weatherson	2011:	Epistemic	Modality.	Oxford:	Oxford University	Press. Erikkson,	Lina	and	Alan	Hajek	2007:	'What	Are	Degrees	of	Belief?'	Studia	Logica,	86, pp.	183-213. Fantl,	Jeremy,	and	Matthew	McGrath	2009:	Knowledge	in	an	Uncertain	World, Oxford:	Oxford	University	Press. Foley,	Richard	1993:	Working	Without	a	Net:	A	Study	of	Egocentric	Epistemology, New	York:	Oxford	University	Press. Gettier,	Edmund	1963:	'Is	Justified	True	Belief	Knowledge?'.	Analysis,	23,	pp.	121-23. Greco,	Daniel	2015:	'How	I	Learned	to	Stop	Worrying	and	Love	Probability	1'. Philosophical	Perspectives,	29,	pp.	179–201. 38 Hawthorne,	John;	Rothschild,	Daniel;	Spectre,	Levi	2016:	"Belief	is	Weak" Philosophical	Studies,	173,	pp.	1393–1404. Howard-Snyder,	Daniel	2013:	'Propositional	Faith:	What	it	is	and	what	it	is	not'. American	Philosophical	Quarterly,	50,	pp.	357–372. Huemer,	Michael	2007:	'Epistemic	Possibility,'	Synthese,	156,	pp.	119-42. Jeffrey,	Richard	1992:	Probability	and	the	Art	of	Judgment.	Cambridge:	Cambridge University	Press. Kratzer,	Angelika	1977:	"What	'Must'	and	'Can'	Must	and	Can	Mean".	Linguistics	and Philosophy,	1,	pp.	337–355. Lewis,	David	1981:	'A	Subjectivist's	Guide	to	Objective	Chance'.	In	Ifs.	Harper,	W,	R. Stalnaker,	and	G.	Pearce	(ed)	Dordrecht:	D.	Reidel. Peels,	Rik	(ms):	'Doubt'. Currently	unpublished. Plantinga,	Alvin	1993:	Warrant:	The	Current	Debate.	New	York:	Oxford	University Press. Schellenberg,	John	2005:	Prolegomena	to	a	Philosophy	of	Religion.	Ithaca:	Cornell University	Press. Schwitzgebel,	Eric	2002:	'A	Phenomenal	Dispositional	Account	of	Belief'.	Nous,	36, pp.	249–275. Sennet,	Adam	2016:	'Ambiguity'.	In	Stanford	Encyclopedia	of	Philosophy, http://plato.stanford.edu/entries/ambiguity/#DeteAmbi,	February	8,	2016 version. Smithies,	Declan	2012:	'The	Mental	Lives	of	Zombies'.	Philosophical	Perspectives,	26, pp.	343–372. 39 Stanley,	Jason	2005:	'Fallibilism	and	Concessive	Knowledge	Attributions,'	Analysis, 65,	pp.	126-31. Strawson,	Peter	1992:	Analysis	and	Metaphysics:	An	Introduction	to	Philosophy. Oxford:	Oxford	University	Press. Unger,	Peter	1975:	Ignorance:	A	Case	for	Skepticism.	Oxford:	Oxford	University	Press. Yalcin,	Seth	2007:	'Epistemic	Modals'.	Mind,	116,	pp.	983-1026. Yalcin,	Seth	2011:	'Nonfactualism	About	Epistemic	Modality'.	In	Epistemic	Modality. Andy	Egan	and	Brian	Weatherson	(ed)	Oxford:	Oxford	University	Press,	pp. 295–332.