Are	Perspectival	Shapes	Seen	or	Imagined? An	Experimental	Approach* John	Schwenkler	(Florida	State	University)	and	Assaf	Weksler	(University	of	Haifa) This	paper	proposes	a	novel	experimental	approach that	would	help to	determine whether	perspectival	shapes,	such	as	the	elliptical	profile	of	a	tilted	plate	or	coin,	are part of perceptual experience. If they are part of perceptual experience, then it should be possible to identify these shapes simply by attending appropriately to them. Otherwise, in order to identify perspectival shapes they must first be constructed in the visual imagination. We propose that these accounts of perspectival identification can be tested by measuring the interference between visual and verbal working memory load, respectively, and the identification of perspectival	shapes	in	the	appearance	of	a	3D	object. 1.	Introduction Philosophers	and	psychologists	often	characterize	the	visual	experience	of	3D shape	as	involving	a	duality	of	aspects.	One	of	these	aspects	corresponds	to	the objective	shape	of	visible	objects	as	they	exist	in	the	environment	at	a	distance	from the	viewer:	for	example,	the	rectangular	shape	of	the	surface	of	a	desk,	or	the circular	shape	of	a	coin.	The	other	aspect	concerns	what	we	will	call	the	perspectival shape	of	an	object,	i.e.	to	the	viewer-relative,	2D	shape	that	would	outline	or	occlude an	object	from	a	given	point	of	view1	For	example,	the	surface	of	a	desk	will	have	a perspectivally	rectangular	shape	if	it	is	seen	from	straight-on,	but	its	perspectival shape	will	be	that	of	an	irregular	quadrilateral	or	trapezium	when	it	seen	from	a different	angle;	and	the	perspectival	shape	of	a	coin	will	be	circular	when	viewed from	straight-on	but	elliptical	from	a	more	sideways	angle.2 Let	us	give	the	name	perspectivalism	to	the	thesis	that	visual	experience	has these	two	aspects.	Many	contemporary	analytic	philosophers	endorse perspectivalism:	for	example,	Brogaard	(2010),	Cohen	(2010),	Fish	(2009),	Harman (1990),	Hellie	(2006),	Hill	(2009),	Lycan	(1996),	Noë	(2004),	Schellenberg	(2008), Smith	(2002),	and	Tye	(2002).	So	do	many	experimental	psychologists,	including Gibson	(1950),	Mack	(1978),	Palmer	(1999),	and	Rock	(1983).	By	contrast,	a *	Both	authors	contributed	equally	to	this	work. 1	We	use	"perspectival	shape"	instead	of	"apparent	shape"	since	there	is	a	clear	sense	in	which the	object	shape	is	also	apparent:	e.g.	the	white	face	of	the	cube	in	Figure	1	clearly	looks	square,	and the	billiards	rack	looks	like	an	equilateral	triangle,	etc. 2	The	properties	of	distance	and	slant	(in	3D)	are	viewer-relative	but	do	not	count	as perspectival	properties	for	our	purposes.	That	is	because	we	consider	them	instead	to	be	part	of	our experience	of	the	3D	world	around	us.	For	example,	the	rim	of	a	cup,	when	viewed	obliquely, looks circular,	slanted	in	depth,	and	located	some	distance	away.	What	we	call	"perspectival	properties"	are (roughly)	those	that	a	painter	would	draw	on	a	2D	canvas,	i.e.,	those	that	3D	objects	project	onto	a flat	medium,	perpendicular	to	the	line	of	sight.	These	do	not	include	3D	slant	and	distance. 1 comparatively	smaller	number	of	philosophers	and	psychologists	have	rejected	(or at	least	doubted)	this	thesis	and	endorsed	(or	at	least	expressed	sympathy	towards) anti-perspectivalism	instead	(Briscoe	2008;	Gibson	1986;	Hopp	2013;	Schroer	2008, 2017;	Schwitzgebel	2011;	Siewert	2006).	According	to	anti-perspectivalists,	we	do not	literally	see	perspectival	shapes,	nor	does	the	ability	to	recognize,	draw,	or describe	the	2D	shape	that	would	occlude	an	object	in	one's	line	of	sight	depend	on	a visual	experience	of	any	such	shape. The	debate	between	perspectivalism	and	anti-perspectivalism	is	a	complex phenomenological	debate	that	has	proven	recalcitrant	to	the	methods	of	philosophy. Can	philosophical	disputes	of	this	sort-and	this	dispute	in	particular-be "translated"	into	a	scientific	dispute?	Tradition	has	it	that	the	answer	is	negative. After	all,	the	dispute	belongs	to	the	realm	of	phenomenological,	conceptual,	and metaphysical	analysis.	Ask	a	scientist	about	it,	and	she	will	probably	reply	with comments	about	cognitive	mechanisms	and	performance	in	some	task,	which	in turn	will	likely	strike	the	philosopher	as	orthogonal	to	her	concerns. Our	paper	models	a	two-stage	strategy	by	which	a	philosopher	can	overcome this	apparent	impasse.	First,	she	may	show	that	the	competing	philosophical	views implicate	different	mechanisms	(or	kinds	of	processes)	in	the	accomplishment	of	a certain	task.	Once	this	is	done,	the	dispute	will	"belong"	to	science	in	some	minimal sense.	The	philosopher	can	now	present	her	puzzle	to	the	scientist	in	a	way	that makes	sense	to	her,	as	a	dispute	within	cognitive	psychology.	Second,	she	may	then propose	experiments	that	would	help	to	reveal	which	of	these	mechanisms	are operative	in	performing	the	task	in	question.3	To	anticipate,	in	this	paper	we	suggest that	the	task	is	to	identify	perspectival	shapes,	the	possible	mechanisms	for identifying	it	are	selective	attention	(according	to	perspectivalism)	and	constructive imagination	(according	to	anti-perspectivalism),	and	the	experiments	for	testing which	mechanism	is	operative	use	dual-task	paradigms,	pairing	perspectival identification	with	a	working	memory	task. One	might	question	the	need	for	second	stage	in	the	strategy	just	outlined.	Isn't the	first	stage	enough	for	successful	"translation"	of	a	philosophical	problem	into	a scientific	one? We	think	not.	The	craft	of	experimental	psychology	is	precisely	to take	a	complex	theoretical	issue	and	squeeze	it	into	the	constraints	of	the	lab-constraints	which	often	are,	to	philosophical	eyes,	simply	unbelievable.	The experiments	often	involves	measuring,	in	milliseconds	(!),	the	response	time	of	key presses,	to	very	simple	displays,	themselves	presented	for	a	few	hundred milliseconds	or	less.	Furthermore,	the	task	must	be	designed	in	such	a	way	that	the participants	will	be	motivated	to	use	a	specific	strategy	to	solve	it	–	the	strategy	that the	experimenter	wants	to	probe.	If	there	are	shortcuts,	the	participants	will	take them,	making	the	results	useless.	Also,	all	experiments	must	contrast	a	target	group with	a	control	group,	which	is	identical	to	the	target	group	except	for	the	specific variable	the	experimenters	need	to	measure.	Finally,	experiments	often	work	in	one direction	only.	That	is,	experimenters	manipulate	a	variable	and	look	for	an	effect.	If it	is	found,	then	the	experiment	is	successful.	If	it	is	not	found,	then	it	is	not	clear 3	For	earlier	examples	of	this	strategy,	applied	to	debates	about	the	content	of	perspectival experience	and	the	thesis	of	attentional	transparency,	see	Weksler	(2016)	and	(2017),	respectively. 2 that	anything	could	be	inferred,	since	any	number	of	things	can	be	invoked	to explain	this. In	short,	it	could	be	that	one	succeeds	in	translating	the	philosophical	dispute into	psychological	categories,	but	not	in	a	way	that	situates	the	dispute	within	the constraints	of	experimental	practice.	In	that	case,	science	will	not	be	able	to contribute	to	the	debate,	and	we	must	continue	conducting	it	from	the	armchair.	For this	reason,	this	paper	will	develop	our	experiment	sketches	in	some	detail	in	order to	make	a	more	convincing	case	that	they	could	actually	be	run	in	a	way	that	might yield	significant	results. Note	that	despite	using	the	word	"translation,"	we	do	not	mean	to	suggest	that philosophical	distinctions,	e.g.,	between	imagination	and	attention,	are	simply identical	the	categories	of	cognitive	psychology.	For	all	we	are	saying,	the connection	between	imagination	and	working	memory	load,	and	the	connection between	attention	and	working	memory	load,	are	both	contingent.	Perhaps	in	other possible	worlds	imagination	and	attention	do	not	interact	with	working	memory	at all.	What	matters	is	that	in	the	actual	world	they	do.	Without	a	doubt,	it	would	be interesting	to	try	to	analyze	imagination	and	attention,	in	the	philosophical	sense,	by reference	to	working	memory,	but	this	project	is	not	our	aim	here. Section	2	of	our	paper	focuses	on	the	first	stage	of	the	strategy	described	above, namely	mapping	the	philosophical	dispute	onto	scientific	categories.	Section	4	will focus	on	the	second	stage,	namely	experimental	design.	In	between,	in	Section	3,	we explain	why	we	do	not	think	that	the	dispute	between	perspectivalism	and	antiperspectivalism	can	be	settled	simply	by	appeal	to	introspection. 2.	First	Stage:	Philosophical-Scientific	Mapping Consider	the	shapes	shown	in	Figure	1.	You	will	likely	be	able	to	recognize	easily enough	that	the	white	face	of	the	cube	shown	on	the	left	is	objectively	a	square,	and the	shape	of	the	billiards	rack	on	the	right	is	objectively	an	equilateral	triangle, though	with	curved	corners.	But	likely	you	can	also	recognize,	with	comparable ease,	that	the	perspectival	appearance	of	each	of	those	shapes	is	irregular:	for example,	you	can	see	that	if	you	had	to	draw	the	cube	as	it	looks	to	you,	or	match	its appearance	with	a	corresponding	line	drawing,	the	corners	of	the	top	face	at	the	top left	and	bottom	right	of	the	image	should	be	more	acute	than	those	at	the	top	right and	bottom	left;	and	that	if	you	had	to	draw	the	billiards	rack,	or	match	its appearance	with	a	line	drawing,	the	line	at	the	bottom	would	be	longer	than	the other	two,	and	the	top	angle	wider	than	the	ones	at	the	bottom.4	If	you	can	make these	judgments,	you	are	capable	of	what	we	will	call	perspectival	identification	of 4	Notice	that	we	are	not	committed	to	saying	that	your	perspectival	identification	judgment	is accurate.	Indeed,	Thouless	(1931a,	1931b)	has	famously	shown	that	perspectival	identification reports	are	distorted	in	the	direction	of	the	objective	shapes.	For	example,	while	people	can	judge that	the	left	perspectival	angle	of	the	billiard	rack	in	Figure	1	is	smaller	than	60	degrees,	they probably	overestimate	its	size	(it	is	actually	45	degrees).	For	our	purposes,	it	is	enough	that	people can	identify	the	perspectival	shape	of	an	object	at	least	roughly. 3 the	shapes	in	a	visual	scene.	And	this	is	is	the	task	which	we	propose	will	connect the	philosophical	dispute	over	perspectivalism	to	the	categories	of	experimental psychology. Figure	1:	Two	images.	RH	image	credit:	The	authors.	LH	image	credit:	Wikimedia Commons. Now	let	us	ask:	What	underlies	our	capacity	for	perspectival	identification?	It might	seem	that	the	only	possible	explanation	for	it	is	that	perspectival	shapes	are, at	least	when	we	direct	our	attention	appropriately,	part	of	the	content	of	visual perception.5	This	would	render	incredible	the	anti-perspectivalist	position	of	J.J. Gibson	in	The	Ecological	Approach	to	Visual	Perception: No	one	ever	saw	the	world	as	a	flat	patchwork	of	colors-no	infant,	no cataract	patient,	and	not	even	Bishop	Berkeley	or	Baron	von	Helmholtz,	who believed	firmly	that	cues	for	depth	were	learned.	The	notion	of	a	patchwork of	colors	comes	from	the	art	of	painting,	not	from	any	unbiased	description	of visual	experience.	(Gibson	1986,	p.	286) Similarly,	Eric	Schwitzgebel,	in	his	Perplexities	of	Consciousness,	writes: What	exactly	is	my	sensory	experience	as	I	stare	at	a	penny	[obliquely]?	My first	and	recurring	inclination	is	to	say	that	the	penny	looks	just	plain circular,	in	a	three-dimensional	space--not	elliptical	at	all,	in	any	sense	or	by any	effort	I	can	muster.	(Schwitzgebel	2011,	p.	19) Gibson's	position,	and	the	position	that	Schwitzgebel	is	inclined	to	endorse,	is radical.	It	is	different	from	the	position	that	Gibson	had	advanced	in	The	Perception of	the	Visual	World,	according	to	which	it	is	possible	to	perceive	a	visible	scene	"as	if 5	Thus	Cohen	(2010)	says	(in	our	terminology)	that	the	fact	of	our	capacity	for	perspectival identification	"gives	us	reason"	to	believe	that	visual	perception	represents	perspectival	properties. However,	he	does	not	claim	that	this	is	the	only	way	to	explain	perspectival	identification. 4 it	consisted	of	areas	or	patches	of	colored	surface,	divided	up	by	contours",	as	long as	one	adopts	the	appropriate	perceptual	attitude: To	do	so,	you	must	fixate	your	eyes	on	some	prominent	point	and	then	pay attention	not	to	that	point,	as	is	natural,	but	to	the	whole	range	of	what	you can	see,	keeping	your	eyes	still	fixed.	The	attitude	you	should	take	is	that	of the	perspective	draftsman.	...	If	you	persist,	the	scene	comes	to	approximate the	appearance	of	a	picture.	You	may	observe	that	it	has	characteristics somewhat	different	from	the	former	scene.	This	is	what	will	here	be	called the	visual	field.	It	is	less	familiar	than	the	visual	world	and	it	cannot	be observed	except	with	some	kind	of	special	effort	...	lt	is	strictly	an introspective	or	analytic	phenomenon.	One	gets	it	only	by	trying	to	see	the visual	world	in	perspective	and	to	see	its	colors	as	a	painter	does.	(Gibson 1950,	pp.	26-27) The	Gibson	of	1950	puts	forward	what	we	will	call	an	attentional	account	of perspectival	identification,	according	to	which	perspectival	properties	can	be identified	by	adopting	a	distinctive	attentional	focus.	The	attentional	account	holds that,	at	least	when	this	focus	is	adopted,	perspectival	shapes	and	colors	are	seen--it is	an	aspect	of	visual	experience	that	we	identify	from	within	this	introspective	or "painterly"	attitude.	On	a	view	like	this,	identifying	perspectival	properties amounts	to	a	Stroop-like	task.	In	a	Stroop	task	one	must	classify	stimuli	correctly despite	the	influence	of	incongruent	and	dominant	perceptual	representations.	For example,	in	the	numerical	Stroop	task	(Figure	2),	comparing	physical	size	is difficult	because	the	numerical	value	interferes.	To	succeed	in	the	task,	subjects must	filter	out	the	numerical	value	using	selective	attention.	And	Gibson's	1950 description	of	perspectival	identification	suggests	something	similar:	it's	a	matter of	selectively	attending	to	the	perspectival	characteristics	of	the	visual	field,	and overcoming	the	natural	habit	of	attending	instead	to	the	objective	shapes,	colors, etc.	that	are	our	usual	objects	of	concern.	If	this	account	is	correct,	then perspectival	identification	requires	selectively	attending	to	certain	visible	features while	suppressing	attention	to	others.6 6	To	clarify:	We	are	not	putting	this	account	forward	in	the	spirit	of	interpreting	Gibson's	actual views.	These	were	quite	complicated,	and	settling	what	they	were	falls	outside	the	scope	of	this paper. 5 Figure	2:	The	numerical	Stroop	task	(Henik	and	Tzelgov	1982).	Participants	are faster	to	recognize	the	digits	or	classify	their	sizes	correctly	in	congruent	trials	(the larger	number	is	physically	larger)	than	incongruent	ones.	Image	credit:	Wikimedia Commons. By	contrast,	anti-perspectivalists	like	Schwitzgebel	and	the	later	Gibson	must reject	the	attentional	account,	since	on	their	view	the	"patchwork	of	colors"	that	one would	paint	in	order	to	depict	a	visible	scene,	or	describe	in	identifying	its perspectival	appearance,	is	not	something	we	can	see	at	all	(with	or	without	a special	exercise	of	visual	attention).	How	else	might	they	account	for	our	capacity for	perspectival	identification?	We	are	not	aware	of	any	place	where	Gibson	or Schwitzgebel	address	this	question	directly,	but	a	possible	answer	to	offer	on	their behalf	is	that	the	"visual	field"	of	perspectival	shapes	and	colors	is	something imagined,	rather	than	seen.	Consequently,	perspectival	identification	depends	on	a top-down	process	in	which	a	two-dimensional	patchwork	corresponding	to	a	visible 3D	scene	is	constructed	in	the	eye	of	the	mind.7	Such	a	constructive	account	of perspectival	identification	has	been	proposed	by	Robert	Briscoe,	who	describes perspectival	identification	as	a	perceptual-cum-imaginative	process	of	"makeperceive": In	general,	one	engages	in	make-perceive	when	one	projects	or 'superimposes'	a	mental	image	on	a	certain	region	of	the	visually	perceived world.	Thus,	as	Rick	Grush	observes,	one	might	use	a	mental	image	to	decide where	in	egocentric	space	a	vase	should	be	placed	in	order	best	to	obscure	a picture	on	the	desk	(2004,	p.	390).	Similarly,	when	deciding	how	to	arrange	the furniture	in	a	new	home,	one	might	begin	by	visualizing	how	things	would	look were	one	to	place	an	armchair	in	a	certain	empty	corner,	or	were	one	to	hang	a painting	on	a	certain	unadorned	wall.	It	seems	clear	that	one	does	not	in	any literal	sense	see	the	visualized	armchair	in	the	empty	corner	or	the	visualized painting	on	the	wall.	Perhaps	the	best	and	most	familiar	example	of	makeperceive	is	the	experience	of	noticing	a	constellation	in	the	night-time	sky. Noticing	a	constellation	is	a	hybrid	visual-imaginative	experience:	it	involves both	seeing	the	stars	in	the	constellation	and	imagining	the	lines	that	connect them	at	the	same	time.	(Briscoe	2008,	p.	479) In	the	present	case,	"make-perceiving"	an	object's	perspectival	shape	could	involve, as	Briscoe	puts	it,	pretending	to	trace	an	outline	"on	an	imaginary	pane	of	glass"	(p. 480),	or	imagining	the	shape	of	a	planar	figure	which,	if	stood	upright	and	placed 7	Noë	(2004)	holds	both	that	sensory	experiences	are	'perspectival',	and	also	that	such 'perspectival	sensing'	plays	a	role,	i.e.	has	a	function,	in	everyday	perceiving.	As	Noë	notes,	this	is	in keeping	with	long	tradition	in	philosophy	and	in	psychology.	Our	definition	of	the	attentional	and constructive	accounts	is	supposed	to	be	neutral	on	this	issue.	Seeing	or	visualizing	perspectival shapes	may	or	may	not	play	a	role	in	everyday	perceiving.	If	the	reader	doubts	that	imagined perspectival	shapes	could	play	a	role	in	everyday	perception,	we	invite	her	to	consider	the phenomenon	of	amodal	perception.	Arguably,	it	involves	mental	imagery	(Nanay	2010)	and, nevertheless,	it	plays	a	role	in	everyday	perception.	For	example,	an	amodally	completed	object	can be	the	focus	of	object-based	attention	(Lee	and	Vecera	2005). 6 appropriately,	would	perfectly	occlude	a	certain	portion	of	the	perceived	scene. Each	of	these	would	be	a	way	to	construct	within	the	visual	imagination	a	2D	shape corresponding	to	the	appearance	of	an	object	from	a	certain	angle.	While	this construction	draws	on	materials	that	are	provided	in	visual	experience,	there	is	an important	respect	in	which	it	goes	beyond	them.	And	it	seems	possible	in	principle to	account	in	this	way	for	the	ability	to	draw,	recognize,	or	describe	the	perspectival shapes	of	objects	in	a	visible	scene,	even	on	the	assumption	that	those	shapes	are not	elements	of	visual	experience	itself.8 We	propose,	then,	that	this	contrast	between	attentional	and	constructive accounts	of	perspectival	identification	amounts	to	a	translation	of	the perspectivalism/anti-perspectivalism	dispute	into	the	categories	of	cognitive psychology,	as	attention	and	mental	imagery	are	topics	routinely	studies	by cognitive	psychologists.	This	completes	the	first	stage	of	the	strategy	described above. 3.	The	Limits	of	Introspection Sometimes	it	seems	easy	to	tell	whether	a	given	perceptual	judgment	rests	on top-down	visual	construction	rather	than	attention	to	a	feature	that	is	present	in visual	experience.	For	example,	consider	the	tasks	illustrated	in	Figure	3.	It	seems clear	that	each	of	(a),	(b),	and	(c)	requires	an	exercise	of	visual	imagination	that goes	beyond	what	is	presented	immediately	in	visual	experience.	In	(a)	this	process seems	to	involve	tracing	a	path	through	a	maze	in	imagination,9	in	(b)	it	involves repeatedly	multiplying	a	percept	in	the	imagination	until	a	certain	length	is	reached, and	in	(c)	it	involves	imaginatively	rotating	one	percept	in	order	to	compare	it	with a	different	one.	Things	are	not	so	clear	when	we	consider	the	Kanizsa	illusion	in	(d), where	the	illusory	triangle	seems	as	if	it	is	"seen"	to	be	present	simply	in	the	original experience,	even	though	some	of	its	contours	are	no	part	of	the	visible	scene	itself. In	each	of	(a),	(b),	and	(c)	the	task	involves	a	constructive	process:	it	involves something	more	than	just	categorizing	what	is	already	seen.	It	is	harder	to	say whether	or	not	the	same	is	true	of	(d)	as	well. 8	For	another	constructivist	account	of	perspectival	identification,	see	Schroer	(2017). Unfortunately	this	paper	came	to	our	attention	too	late	for	us	to	consider	it	in	our	essay. 9	Or,	perhaps,	"filling	in"	the	maze	from	the	origin	point	until	an	exit	is	reached. 7 Figure	3:	Examples	illustrating	the	distinction	between	visual	perception	and visually-based	"make-perceive".	In	(a)	the	task	is	to	say	which,	if	any,	of	A,	B,	and C	can	be	reached	via	the	entrance	to	the	maze.	In	(b)	the	task	is	to	say	how	many times	longer	the	bottom	segment	is	than	the	top	one.	Figure	(c)	is	a	classic	mental rotation	task:	Are	the	two	shapes	equivalent?	And	(d)	is	the	Kanizsa	Triangle-a 'borderline'	case	that	is	harder	to	characterize	confidently	just	through introspection.	Image	credit	for	(a)	and	(b):	The	authors.	Image	credit	for	(c)	and (d):	Wikimedia	Commons. Suppose	for	the	sake	of	argument	that	we	are	justified	in	thinking,	on	the	basis	of introspection,	that	the	first	three	tasks	in	Figure	3	rely	on	constructive	visualization, but	that	we	are	not	so	justified	in	being	confident	either	way	about	the	Kanisza illusion.10	How	about	the	question	of	whether	or	not	perspectival	identification requires	a	process	of	constructive	visualization?	Some	philosophers	seem	to	think that	this	is	a	question	that	introspection	can	decide	on	its	own.	For	example,	here	is Alva	Noë's	response	to	"philosophers	[who]	will	not	scruple	to	acknowledge commonplaces	such	as	this"-where	this	is	the	claim	that	e.g.	a	circular	plate	seen from	an	oblique	angle	looks	elliptical: It	is	just	not	true	that	the	plate	looks	elliptical,	[anti-perspectivalist philosophers]	will	say.	But	how	can	we	take	this	seriously?	Certainly	it	is	the case	that	we	wouldn't	likely	judge	the	plate	to	be	elliptical,	on	the	basis	of how	it	looks.	Nor	is	it	likely	that	we	would	say	that	it	looks	elliptical.	But surely	it	does	look	elliptical	from	here!	(Noë	2004,	78) What	could	ground	Noë's	confidence	that	the	thesis	he	defends	is	"certainly"	or "surely"	correct?	It	seems	most	charitable	to	take	this	statement	as	a 10	To	be	clear:	nothing	in	our	argument	will	rest	on	this	assumption.	Indeed,	the	experimental methods	we	explore	below	could	give	a	way	of	testing	it. 8 phenomenological	description	of	the	character	of	his	visual	experience,	based	on	the reflexive	awareness	of	experience	that	can	be	secured	through	introspection.	This	is the	same	kind	of	awareness	that	justifies	saying	that,	e.g.,	the	correct	path	in	Figure 3a	is	not	part	of	our	visual	experience	of	the	maze,	but	does	not	justify	a	similar verdict	about	the	white	triangle	in	Figure	3d.	Except	in	the	face	of	special	evidence to	the	contrary,	we	tend	to	trust	one	another's	introspective	reports	about	what	our experience	is	like,	and	about	how	we	go	about	solving	various	perceptual	tasks.	Is there	any	such	reason	to	doubt	what	Noë	says	in	the	quotation	above?11 Some	of	the	possible	reasons	for	skepticism	have	already	been	discussed	in important	work	by	Eric	Schwitzgebel	(2011).	For	example,	if	it	really	were	certainly or	surely	the	case	that	the	surface	of	a	coin	seen	from	an	oblique	angle	looks elliptical,	then	we	would	expect	there	to	be	widespread	agreement	about	this-that is,	agreement	not	on	which	perspectival	shape	would	correspond	to	the	coin's	surface, but	on	whether	that	shape	is	a	feature	of	visual	experience	itself,	prior	to	any constructive	exercise	of	the	visual	imagination.	Yet	as	we	have	seen,	there	is	no widespread	agreement	about	this	matter,	even	among	philosophers	and psychologists	who	have	given	it	a	lot	of	consideration.	As	Schwitzgebel	(2011) points	out,	this	disagreement	is	prima	facie	evidence	for	the	unreliability	of introspection	in	this	case. As	further	evidence	of	the	difficulty	of	settling	this	question	just	by	an	appeal	to introspection,	consider	again	the	images	shown	in	Figure	1,	and	try	to	answer	the following	questions	about	them: (1)	Are	the	perspectival	angles	at	the	top	right	and	bottom	left	of	the	cube	equal, or	is	the	top	one	slightly	wider? (2)	Is	the	perspectival	angle	at	the	top	of	the	billiards	rack	acute,	obtuse,	or	90 degrees? As	you	answer	these	questions,	do	you	find	it	certain	or	obvious	that	all	you	have	to do	is	attend	selectively	to	an	aspect	of	your	visual	experience,	and	not	construct	a further	shape	in	the	imagination?	When	we	shared	an	image	like	that	of	the	billiards rack	in	an	informal	poll	on	Facebook	and	asked	for	descriptions	of	its	perspectival angles,	respondents	offered	a	diverse	range	of	explanations	of	how	they	approached this	task,	some	of	which	sounded	primarily	attention-driven	while	others	suggested processes	of	constructive	visualization	or	"make-perceive".	Here	is	a	representative sample	of	those	replies: ● ...	I	imagine	various	angles	and	try	to	reconcile	them	with	my	perception	of	the image.	Knowing	that	the	object	would	be	an	equilateral	triangle	in	actuality 11	To	clarify,	this	question	concerns	not	"first-order"	certainty	that	the	perspectival	shape	of	the plate	in	the	world	is	elliptical	(though	perhaps	we	should	not	have	such	certainty,	because perspectival	identification	is	somewhat	inaccurate,	as	discussed	in	fn.	4	above).	The	question concerns	Noë's	"second-order"	certainty	that	the	perspectival	shape	is	seen	(even	if	inaccurately) rather	than	imagined. 9 impedes	my	ability	to	imagine	other	angles	and	restrict	them	to	the	2d	image (indeed	I	have	to	ignore	portions	of	the	image	to	do	so). ● I	had	to	mentally	rotate	it	to	the	perpendicular,	otherwise	the	acute	angle	of	the 3D	shape	tends	to	override	the	perspectival	appearance.	I	also	have	to	really attend	to	just	that	corner,	otherwise	it's	difficult	not	to	see	it	as	just	an equilateral	triangle. ● Perspectively	[the	angle]	appears	to	me	to	be	obtuse.	I	come	to	this	conclusion by	rotating	the	image	so	that	the	side	that	appears	longest	is	vertical.	The	other side	is	tilted	above	horizontal	so	the	apparent	angle	is	greater	than	90. ● Initial	vision	suggested	[that	the	angle	was]	acute,	but	I	now	see	it	as	obtuse	after sort	of	comparing	its	sides	to	the	rectangular	outline	in	which	FB	places	the image. ● I've	spent	part	of	the	morning	working	in	Light	Room	recropping	photos	so	that they're	straight	up	and	down.	The	program	uses	a	grid	overlay,	and	you	tilt	the image	using	some	vertical	part	of	the	image.	And	I	felt	like	I	was	just	doing	the same	thing.	But	I	think	the	edges	of	the	frame	are	what	I	used. ● It	appears	to	be	an	equilateral	triangle	on	casual	viewing	and	one	has	to	step back	and	view	it	in	a	very	detached	way	to	see	it	as	obtuse. For	the	reasons	explained	above,	we	believe	that	each	of	these	descriptions	should be	treated	with	considerable	skepticism.	But	so,	by	the	same	token,	should	Noë's introspective	judgment	about	the	presence	of	an	elliptical	shape	in	his	visual experience	when	he	looks	from	an	oblique	angle	at	a	plate.	Mere	introspection	is	not sufficient	to	distinguish	between the	perceptual,	cognitive,	and	imaginative processes	that	we	may	bring	to	bear	in	the	task	of	perspectival	identification. 4.	Second	Stage:	Possible	Experimental	Approaches We	are	considering	the	dispute	between	an	attentional	account	of	perspectival identification,	on	which	perspectival	shapes	can	be	identified	by	attending appropriately	to	an	aspect	of	visual	experience,	with	the	constructive	account,	on which	perspectival	shapes	are	not	seen	but	rather	visualized,	in	the	same	way	as one	can	construct	in	the	imagination	the	solution	of	a	maze	or	the	appearance	of	a 2D	or	3D	shape	that	has	been	rotated	in	space.	We	argued	in	section	3	that introspection	alone	cannot	decide	which	of	these	accounts	is	correct.	The	present section	will	describe	a	possible	experimental	approach	to	the	question,	which	turns on	the	possibility	of	operationalizing	the	roles	of	visualization	and	selective attention	in	perspectival	identification. Simplifying	things	quite	a	lot,	the	experiments	we	describe	will	test	the	following predictions.	First,	since	on	the	constructive	account	perspectival	identification requires	top-down	construction	of	a	mental	image	that	is	"superimposed"	onto	one's perception	of	the	visual	world,	the	constructive	account	predicts	that	there	will be	interference	between	perspectival	identification	and	other	tasks	that	draw on	the	same	cognitive	resources	as	constructive	visualization.	And	second, since	on	the	attentional	account	perspectival	identification	requires	selective 10 attention	to	perspectival	shapes,	the	attentional	account	predicts	that	tasks	that interfere	with	selective	visual	attention	will	also	interfere	with	perspectival identification.	Each	account	can	be	falsified	by	testing	these	predictions. Sections	4.2	through	4.4	describe	a	series	of	experiments	that	could	do	this.	First, in	section	4.1	we	consider	a	related	proposal	by	Sean	Kelly,	explaining	why	it	is inadequate	to	our	purposes.12 4.	1	Kelly's	proposal Sean	Dorrance	Kelly	proposes	a	way	of	experimentally	probing	the	presence	of perspectival	shapes	in	visual	experience	in	his	contribution	to	a	2008	symposium	on Noë's	Action	in	Perception.	Referring	to	the	passage	from	Noë's	book	that	we	quoted in	section	3,	Kelly	writes	that	if	Noë's	claim	about	the	experience	of	perspectival shapes	is	correct,	"there	ought	to	be	some	evidence	of	this	experience"	that	an appropriate	experiment	could	detect	(Kelly	2008,	p.	687).	Specifically,	Kelly proposes	to	investigate	whether	there	is	a	priming	effect	of	perspectival	shapes	on subsequent	judgments	of	2D	stimuli	that	correspond	to	them.	He	writes: The	experiment	I	imagine	will	make	use	of	the	primed	matching	paradigm, and	it	will	go	like	this:	first	present	the	priming	stimulus,	a	circular	object like	a	plate	presented	at	an	angle	...	Then	present	as	targets,	among	other controls,	a	pair	of	ellipses	and	a	pair	of	circles.	If	Noë	is	right,	then	judgments about	the	similarity	of	the	ellipses	should	be	facilitated	equally	if	not	more than	judgments	about	the	similarity	of	the	circles.	I	predict,	however,	that judgments	about	the	similarity	of	the	circles	will	be	primed,	but	judgments about	the	similarity	of	the	ellipses	will	not.	(ibid.,	pp.	688-689) Kelly	also	reports	that	the	preliminary	results	of	an	experiment	along	these	lines supported	his	position	over	Noë's:	"using	a	picture	of	a	penny	at	an	angle	as	the prime	we	get	a	10%	facilitation	effect	for	similarity	judgments	regarding	circles,	and no	effect	whatsoever-neither	facilitation	nor	interference-for	similarity judgments	about	ellipses"	(ibid.,	p.	689).	This,	he	says,	puts	the	burden	of	proof	on Noë	to	explain	why,	if	perspectival	shapes	are	part	of	ordinary	visual	experience, they	do	not	give	rise	to	a	priming	effect. While	we	share	Kelly's	desire	to	look	for	experimental	evidence	that	bears	on this	dispute,	the	logic	of	his	proposed	experiment	can	be	challenged	in	both directions.	First,	as	Kelly	admits	(2008,	p.	687)	a	finding	that	perspectival	shapes 12	Before	moving	on,	let	us	briefly	explain	why	work	on	distortions	in	perspectival	identification from	the	first	half	of	the	twentieth	century	(starting	with	Thouless	1931a	and	1931b)	seems	to	us	to be	neutral	with	respect	to	the	attentional/constructive	dispute.	This	body	of	work	has	apparently shown	that	perspectival	identification	is	distorted	by	cues	for	depth	or	shape	constancy.	That	could be	because	subjects	are	make-perceiving	the	visual	field	on	the	basis	of	a	visual	experience	that represents	three-dimensional,	"objective"	features	exclusively.	Or	it	could	be	because	the computational	processes	that	generate	the	perspectival	dimension	of	experiences	are	influenced	in some	way	by	3D	information	(a	view	like	this	is	endorsed	by	Hill	2009).	So	the	body	of	work	in question	is	apparently	consistent	with	both	the	attentional	and	the	constructive	views. 11 have	a	priming	effect	on	subsequent	judgments	could	be	explained	within	an	antiperspectivalist	framework	by	the	hypothesis	that	non-conscious	or	subliminal representations	of	perspectival	shape,	e.g.	representations	in	"early	vision"	that correspond	to	retinal	input	rather	than	distal	properties	of	the	environment, influence	subsequent	perceptual	judgments	(for	an	example	of	subliminal	visual priming	see	Bar	and	Biederman	1998).	Given	this	possibility,	if	Kelly's	proposed experiment	were	to	be	run	again	with	a	larger	number	of	participants	and	find evidence	of	a	priming	effect	by	perspectival	shapes,	this	would	not	count	as evidence	in	support	of	perspectivalism.13 Second,	Kelly's	preliminary	finding	that	there	is	no	such	priming	effect	could	in principle	be	explained	by	the	hypothesis	that	the	relevant	priming	effects	are modulated	by	the	task-relevance	of	the	priming	stimuli.	And	there	is	some	evidence for	this	possibility:	for	example,	using	a	masked	priming	paradigm	in	which	a priming	stimulus	was	shown	very	briefly	followed	by	a	target	stimulus	that	had	to be	identified,	Enns	and	Oriet	(2007)	found	that	identification	of	the	target	was facilitated	only	when	the	prime	resembled	it	in	respects	that	were	explicitly	relevant to	the	classification	task.	Similarly,	Pohl	et	al.	(2010)	found	that	subconscious primes	facilitated	identification	of	a	target	stimulus	only	when	the	prime	resembled the	target	in	a	task-relevant	dimension.14	Finally,	reviewing	a	large	corpus	of	data from	social	psychology,	Eitam	and	Higgins	(2010)	develop	the	ROAR	(Relevance	of	a Representation)	framework,	on	which,	in	general,	priming	depends	on	relevance. Given	these	findings	we	should	question	whether	Kelly's	preliminary	finding	that perspectival	shapes	do	not	prime	subsequent	judgments	supports	the	conclusion that	these	shapes	are	absent	from	ordinary	experience--as	instead	this	lack	of	an effect	could	be	due	to	the	task-irrelevance	of	perspectival	shapes.	In	Kelly's	study,	as we	understand	it,	participants	were	presented	with	tilted	objects	(as	primes). Subsequently,	they	had	to	compare	ellipses,	circles,	and	other	shapes	to	each	other. At	no	stage	in	the	experiment	were	participants	instructed	to	focus	on	perspectival shapes,	and	nothing	in	the	task	required	them	to	do	so.	All	this	gives	reason	to suspect	that	the	visual	system	had	deemed	perspectival	properties	irrelevant	in	the context	of	Kelly's	study,	and	this	task-irrelevance	could	explain	why	they	did	not give	rise	to	any	priming	effect. Finally,	notice	that	the	dispute	between	Kelly	and	Noë	concerns	a	different question	than	the	one	we	are	focused	on	here.	Kelly	is	a	perspectivalist	in	the	sense we	have	defined:	he	holds	that	"it	is	possible	to	experience	[the]	apparent	ellipticalness"	of	e.g.	a	tilted	plate	(2008,	p.	685),	and	he	seems	to	regard	this	experience	as 13	Note	that	while	falling	short	of	establishing	perspectivalism,	finding	the	priming	effect	in question	would	establish	something	interesting,	namely	that	visual	representations	of	perspectival shapes	activate	shape	concepts.	Once	activated,	such	concepts	can	facilitate	and	bias	judgments related	to	them.	On	such	a	view,	representations	of	perspectival	shapes	do	more	than	just	feed	into modules	that	calculate	objective	shapes;	they	can	influence	our	cognitive	lives	in	a	more	global	way. 14	Note	that	there	is	a	much	larger	body	of	literature	about	the	effects	of	task-relevance	on	the phenomenon	of	"priming	of	pop-out,"	in	which	a	prime	leads	to	faster	location	of	a	unique	target resembling	it,	in	a	visual	search	task	(for	a	review	see	for	example	the	introduction	in	Michal,	Lleras, and	Beck	2014). 12 perceptual	rather	than	imaginative.	What	Kelly	denies	is	only	that	it	is	possible	to experience	both	objective	and	perspectival	shapes	at	once.	Thus	he	writes: Look	at	a	plate	presented	at	an	angle	and	pay	attention	to	its	shape.	When you	are	seeing	it	to	be	circular	try	also	to	see	its	elliptical	aspect.	It	seems	to me	clear	that	focusing	on	the	real	shape	pushes	the	apparent	one	out	of experience,	and	focusing	on	the	apparent	shape	likewise	makes	the	real	one go	away	...	The	problem	seems	to	me	similar	to	the	problem	of	trying	to	see the	duck	and	the	rabbit	simultaneously	in	the	duck-rabbit	image.	I	can	switch back	and	forth	between	them,	but	I	can't-or	at	least	I	can't	without	extreme effort-experience	both	of	them	at	the	same	time.	(ibid.,	p.	685) According	to	Kelly,	perspectival	shapes	can	be	seen	when	we	adopt	the	right perceptual	attitude,	and	once	this	result	has	been	achieved	the	new	perceptual attitude	excludes	from	experience	the	"real"	or	objective	aspects	of	things	that	had been	present	in	experience	beforehand.	By	contrast,	what	Noë	says	is	that perspectival	and	objective	features	are	present	in	experience	no	matter	what perceptual	attitude	we	take.	Kelly's	proposed	experiment	is	supposed	to	help	decide between	these	views:	he	is	offering	a	way	to	discover	if	perspectival	shapes	are present	in	visual	experience	even	when	we	are	not	focused	on	them	(which	is exactly	why	he	did	not	instruct	participants	to	do	this).	However,	the	question	we have	posed	is	more	fundamental	than	this:	for	if	the	constructive	account	is	correct then	what	Kelly	calls	"focusing	on	the	apparent	shape"	is	really	a	way	of	constructing such	a	shape.	In	that	case	both	his	view	and	Noë's	would	be	incorrect. 4.2	Testing	the	role	of	visual	working	memory	in	perspectival	identification Our	challenge	is	to	find	a	way	of	deciding	between	a	constructive	account	of perspectival	identification,	according	to	which	an	exercise	of	visual	imagination	or "make-perceive"	is	involved	in	identifying	the	perspectival	shapes	corresponding	to regions	in	a	3D	display,	and	an	attentional	account,	according	to	which	perspectival identification	involves	attending	selectively	to	perspectival	shapes	and	directing attention	away	from	objective	ones.	In	the	present	section,	we	will	explain	how	the constructivist	proposal	can	be	tested	by	employing	a	dual-task	paradigm	in	which	a perspectival	identification	task	is	paired	with	a	task	that	is	known	to	place	high demands	on	visual	working	memory.	We	will	argue	that	if	perspectival identification	involves	a	constructive	visualization,	then	it	should	place	demands	on visual	working	memory	as	well,	and	thus	the	tasks	should	interfere	with	one another.	Finding	that	there	is	no	such	interference	between	the	tasks	would undermine	the	constructivist	account. 13 Figure	4:	Hyun	and	Luck's	experimental	paradigm.	The	change-detection	task required	comparing	the	first	display	(leftmost	box)	to	the	last	(rightmost	box).	Each display	contains	four	colored	squares.	The	imagery	task	required	indicating whether	the	letter	shape	(central	box)	was	canonical	or	mirror-reversed.	In	the dual-task	condition,	both	had	to	be	performed	simultaneously.	Credit:	Hyun	and Luck	(2007). As	an	illustration	of	how	the	dual-task	paradigm	works	(and	also	a	main	reason to	think	that	visualization	draws	on	visual	working	memory),	consider	a	study	by Hyun	and	Luck	(2007).	They	gave	participants	the	task	of	determining	whether	a given	2D	shape	was	a	canonical	or	mirror-reversed	letter	-a	task	that	is	supposed to	require	imaginatively	rotating	the	figure	in	order	to	determine	its correspondence	or	non-correspondence	with	the	relevant	letter	shape.	In	the	key manipulation,	participants	had	to	perform	this	task	concurrently	with	a	changedetection	task	that	drew	on	visual	working	memory,	as	pictured	in	Figure	4:	they were	shown	a	visual	stimulus	that	they	had	to	remember,	followed	by	a	letter	shape that	was	to	be	identified	as	canonical	or	mirror-reversed,	followed	by	a	further stimulus	that	was	to	be	compared	with	the	first	one. Hyun	and	Luck's	study	found	interference	in	both	directions,	as	shown	in	Figure 5:	performance	in	the	mental	rotation	task	was	impaired	by	the	concurrent	changedetection	task,	and	the	mental	rotation	task	interfered	with	the	change	detection task	as	well.	Moreover,	the	interference	was	rotation-dependent,	as	it	increased	as	a function	of	degree	of	rotation:	in	the	zero-degree	condition,	i.e.	when	the	letter	was presented	in	its	canonical	orientation,	the	concurrent	memory	task	did	not	interfere at	all	with	classifying	the	letter	shape	(Figure	5a)	and	the	letter	task	interfered	with visual	memory	only	a	small	amount	(Figure	5b)	in	comparison	with	the	other	two conditions.	Additionally,	the	interference	between	both	tasks	was	greater	in	the ±144-degree	condition,	when	the	letter	was	most	significantly	rotated,	than	the	±72degree	one.	As	Hyun	and	Luck	write,	this	interference	confirms	the	prediction	that in	the	mental	rotation	task,	"[s]ome	sort	of	buffer	[is]	necessary	to	hold	an intermediate	representation	of	the	object	while	it	is	being	rotated"	(2007,	p.	154). This	buffer	is	also	drawn	on	in	the	visual	change-detection	task	but	not	in	the	zerodegree	condition	of	the	mental	rotation	task,	where	the	original	sensory representation	is	sufficient	to	make	the	judgment. 14 Figure	5:	Dual-task	interference	in	Hyun	and	Luck	(2007).	In	(a),	open	circles represent	performance	in	the	mental	rotation	task	on	its	own,	and	filled	colored boxes	represent	performance	in	the	mental	rotation	task	while	also	performing	the memory	task.	In	(b),	open	diamonds	represent	performance	in	the	memory	task	on its	own,	and	colored	boxes	represent	performance	in	the	memory	task	while	also performing	the	mental	rotation	task.	Credit:	Hyun	and	Luck	(2007). Following	Hyun	and	Luck,	we	take	these	findings	to	support	the	hypothesis	that visual	working	memory	acts	as	a	"buffer"	underlying	the	capacity	for	visual imagination	and	visual	memory.	And	since	the	constructive	account	of	how perspectival	shapes	are	recognized	credits	visual	imagination	with	a	crucial	role	in this	process,	that	account	yields	the	prediction	that	the	identification	of perspectival	shapes	will	interfere	with	concurrent	tasks	that	place	demands on	visual	working	memory	and	vice	versa.	This	prediction	can	be	tested	by pairing	a	task	requiring	the	identification	of	perspectival	shapes	with	a	visual change-detection	task	like	the	one	used	by	Hyun	and	Luck.	The	display	will comprise	three	stimuli,	as	shown	in	Figure	6A:	a	group	of	colors,	followed	by	a	photo or	realistic	rendering	of	a	3D	shape15	with	two	2D	outline	shapes	below	it,	followed by	a	single	color	stimulus.	In	the	memory	task	participants	will	have	to	indicate whether	the	color	shown	at	the	end	was	included	in	the	original	configuration,	and in	the	perspectival	identification	task	participants	will	have	to	indicate	which	of	the two	2D	shapes	match	the	perspectival	shape	of	a	region	of	the	3D	image.16	The difficulty	of	the	perspectival	identification	task	will	depend	on	the	congruence	or incongruence	between	the	real	and	perspectival	shapes	in	the	photograph:	in	a	case where	they	coincide	because	the	relevant	region	is	displayed	from	straight-on, seeing	the	objective	shape	will	be	enough	to	identify	the	perspectival	shape,	and	so constructive	visualization	should	not	be	required	(because	subjects	know	in advance	that	when	a	shape	is	viewed	from	straight	on,	its	perspectival	shape	is identical	to	its	objective	shape).	However,	if	the	viewing	angle	is	oblique,	so	that	the real	and	perspectival	shapes	are	divergent,	then	there	should	be	reliance	on 15	Section	4.3	will	address	some	difficulties	with	using	2D	images	for	this	purpose. 16	The	task	and	stimuli	illustrated	assumes	that	retaining	color	information	pertinently	engages the	resources	underlying	retention	of	imagined	outline	shape.	We	follow	Hyun	and	Luck	(2007)	here. In	their	task	(see	Figure	6),	participants	retain	color	information,	which	interferes	with	retention	of the	imagined	(rotated)	letter. 15 visualization.	As	we	explain	just	below,	our	claim	is	that	the	constructive	account predicts	that	there	will	be	a	difficulty-dependent	interference	between	the	visual memory	task	and	the	perspectival	identification	task.	That	is,	the	interference	will increase	with	the	degree	of	non-correspondence	between	the	perspectival	shape and	the	corresponding	objective	one.	Finding	no	such	pattern	of	interference	will count	as	evidence	against	the	constructive	account. Figure	6.	A	sketch	of	the	experiments	we	propose.	Participants	need	to	memorize colors	(visual	memory,	A)	or	letters (verbal	memory,	B).	Next,	they	need	to	indicate which	of	the	two	2D	shapes	match	the	perspectival	shape	of	the	white	face	of	the	3D shape.	Finally,	they	need	to	indicate	whether	the	color	(letter)	probe	appearing	in the	last	display	matches	one	of	the	colors	(letters)	from	the	first	display.	In congruent	trials,	the	3D	shape	will	be	presented	from	straight	on. A	point	of	clarification	may	be	necessary.	The	prediction	of	"difficultydependent"	levels	of	interference	is	needed	in	order	to	show	that	interference between	the	tasks	is	not	due	just	to	a	general	dual-task	cost,	i.e.	the	simple	difficulty of	doing	two	different	things	at	once.	If	the	two	tasks	draw	on	a	common	resource, i.e.	the	"buffer"	that	both	holds	a	remembered	stimulus	and	allows	for	the	visual construction	of	a	perspectival	shape,	then	the	interference between	perspectival	identification	and	visual	memory	should	increase	as	the former	task	is	made	more	taxing.	If	the	level	of	interference	were	found	to	be independent	of	differences	in	the	non-correspondence	between	objective	and perspectival	shapes,	this	would	be	inconsistent	with	the	constructive	account. Let	us	sum	up	our	proposal	so	far.	Since,	on	the	constructive	account, perspectival	identification	involves	an	exercise	of	constructive	visualization,	the account	predicts	that	there	will	be	interference	between	perspectival	identification and	another	concurrent	task	that	taxes	visual	working	memory,	and	that	the	degree of	interference	will	increase	with	the	difficulty	of	the	task.	We	have	sketched	a	way to	test	this	prediction.	In	section	4.4	we	will	show	how	a	similar	series	of 16 experiments	could	be	used	to	test	a	prediction	of	the	attentional	account	as	well. First,	let	us	consider	an	important	methodological	concern. 4.3	Perspectival	shapes	in	two	and	three	dimensions In	the	experiment	described	in	section	4.2,	we	proposed	to	use	photographs	or other	realistic	images	of	3D	objects	as	the	stimuli	for	perspectival	identification tasks.	However,	since	images	themselves	are	planar	figures,	it	may	seem	that perspectival	properties	of	the	3D	objects	that	an	image	depicts	can	be	seen	simply by	directing	one's	attention	to	the	properties	of	the	2D	display.	One	might	worry that	if	this	is	correct,	then	any	findings	about	how	perspectival	identification	is achieved	within	an	experimental	paradigm	that	utilizes	photographs	or	other	2D images	might	fail	to	generalize	to	other	conditions.	In	particular,	a	finding	that	visual memory	load	does	not	interfere	with	perspectival	identification	would	show	only that	the	constructive	account	is	incorrect	concerning	our	perception	of	pictures	of 3D	objects,	whereas	it	might	be	correct	when	3D	objects	are	seen	"in	the	flesh".17 (a) (b) Figure	7:	A	photograph	of	a	book	(a)	and	an	anamorphic	transformation	of	it	(b).	In (b),	the	3D	shape	of	the	book	appears	distorted	when	viewed	directly,	but	if	you look	at	the	page	from	an	oblique	angle	with	the	bottom	of	the	image	closer	to	you, the	shape	will	appear	veridical.	For	a	full-size	version,	visit	tinyurl.com/yc35dwmo. Image	credit:	The	authors. One	way	to	address	this	problem	is	to	enrich	the	stimulus	image	with	3D	cues, and	remove	2D	pictorial	cues,	thereby	making	the	experience	more	similar	to	a genuine	experience	of	a	3D	object	(for	relevant	discussion,	see	Vishwanath	2014). For	example,	because	participants	could	gain	information	about	the	2D	shape	of	the stimulus	by	moving	their	head,	experimenters	should	stabilize	the	head	of participants.	Similarly,	experimenters	should	mask	the	computer	edges,	and/or	use a	dark	room	so	that	the	2D	context	of	the	stimuli	will	not	be	apparent.	These	two suggestion	aim	to	remove	2D	cues.	It	is	also	possible	to	add	3D	cues	by	using stereoscopic	goggles	(for	a	recent	study	using	this	technology	see	Hibbard	et	al. 17	Alva	Noë	makes	a	related	point	in	his	(2008),	at	pp.	694-695. 17 2017).	These	measures	will	probably	not	lead	to	a	perfect	3D	experience	(for example,	focus	cues	will	be	inconsistent	with	the	experienced	3D	object,	see	Watt	et al.	2005).	They	are	still	helpful,	however,	because	they	allow	experimenters	to manipulate	the	difficulty	of	the	perspectival	identification	task.	For	example, perspectival	identification	with	stereoscoping	goggles	should	be	more	difficult	than without	them.	Using	this	manipulation,	experimenters	could	test	the	prediction	that there	is	a	difficulty-dependent	interference	between	perspectival	identification	and change	detection. We	note	as	well	that	as	an	alternative	to	the	strategy	of	manipulating	2D	and	3D cues,	the	problem	of	using	a	flat	display	can	also	be	addressed	by	using	inverse perspective,	or	anamorphosis,	to	create	images	of	3D	objects	that	are	meant	to	be viewed	from	an	angle.	An	example	of	this	is	shown	in	Figure	7.	Viewed	from	directly ahead,	the	image	in	(a)	will	appear	veridical	and	the	one	in	(b)	distorted.	However,	if you	take	the	page	on	which	this	figure	appears,	sit	down	at	a	desk	or	table,	and	place the	paper	a	short	distance	in	front	of	you,	then	viewed	from	this	angle	the	3D	shape of	the	book	in	the	distorted	image	(b)	will	now	appear	veridical.	However,	from	this angle	the	perspectival	shape	of	the	book's	cover	(see	Figure	8a)	is	not	the	same	as	its shape	on	the	page	(Figure	8b)	-which	makes	it	impossible	to	identify	the perspectival	shape	just	by	attending	to	the	properties	of	the	image. (a) (b) Figure	8:	Perspectival	shapes	of	the	cover	of	the	book	in	Figure	7,	as	seen	from	two perspectives.	In	(a)	the	shape	traces	the	original	photograph	in	7a,	and	will correspond	to	the	perspectival	shape	of	the	cover	when	the	figure	is	viewed	from the	appropriately	oblique	angle.	In	(b)	the	shape	traces	the	distorted	image	in	7b. Credit:	The	authors. Our	second	proposal,	then,	is	to	construct	the	stimuli	for	our	perspectival identification	tasks	using	reverse	perspective,	and	display	them	on	a	screen	that	is slanted	away	from	the	participant's	line	of	sight.	In	this	condition,	participants	will experience	objective	shapes,	and	will	also	be	able	to	identify	perspectival	shapes corresponding	to	the	appearance	of	the	display	as	seen	from	their	point	of	view,	but the	latter	will	not	match	the	actual	2D	shapes	that	are	shown	on	the	display. 4.4	Disentangling	the	roles	of	working	memory	in	perception	and	imagination 18 In	section	4.2	we	described	a	study	to	test	the	hypothesis	that	perspectival identification	is	an	exercise	in	constructive	visualization.	If	this	constructive	account is	correct,	then	there	should	be	interference	between	visual	memory	and perspectival	identification	in	a	dual-task	condition.	The	dual-task	experiment	we described	in	section	4.2	was	a	way	to	test	this	prediction.	In	the	present	section	we will	describe	how	the	same	kind	of	experiment	could	be	used	to	test	one	of	the predictions	of	the	attentional	account,	namely	that	verbal	memory	tasks	will interfere	with	perspectival	identification	more	than	visual memory	tasks. Before	describing	the	experiments	that	could	be	used	to	test	this	prediction,	we	will explain	the	prediction	in	more	detail,	and	also	explain	why	we	think	it	is	yielded	by the	attentional	account. According	to	the	attentional	account,	perspectival	identification	involves	first selecting	perspectival	shapes	as	objects	of	visual	attention,	then	classifying	the properties	of	the	shapes	one	attends	to.	The	study	by	Hyun	and	Luck	(2007) discussed	in	section	4.2	gives	reason	to	think	that	the	classification	of	a	visual stimulus	will	not	interfere	significantly	with	visual	working	memory:	recall	that	in their	study	there	was	no	effect	of	visual	working	memory	load	on	the	classification of	letter	shapes	in	the	zero-degree	(unrotated)	condition.18	However,	since	control of	selective	attention	requires	remembering	which	stimuli	are	task-relevant	and which	are	not,	one	might	expect	there	to	be	be	interference	between	working memory	tasks	and	tasks	that	require	selective	attention.	And	there	is	indeed evidence	for	this	hypothesis	in	the	experimental	literature.	For	example,	de	Fockert et	al.	(2001)	had	participants	perform	a	working	memory	task	(remembering	a series	of	digits)	concurrently	with	a	visual	task	that	required	selective	attention (classifying	a	written	name	while	ignoring	a	distractor	face),	and	found	that	the behavioral	effects	of	distractor	interference	were	significantly	greater	in	the	highload	condition	of	the	working	memory	task.19	These	findings	suggest	a	role	for working	memory	in	the	control	of	visual	selective	attention. However,	there	is	also	compelling	evidence	that	the	modality	of	a	working memory	task	makes	a	difference	to	its	interference	with	selective	attention	-and these	differences	enable	us	to	draw	out	a	testable	prediction	of	the	attentional account.	In	Baddeley	and	Hitch's	influential	(1974)	account	of	working	memory, visual	and	verbal	working	memory	draw	on	distinct	and	dissociable	cognitive resources	specialized	to	carry	a	specific	sort	of	information.	That	is,	while	visual working	memory	allows	for	the	storage	of	the	visual	features	of	a	stimulus,	such	as the	colored	box	patterns	used	by	Hyun	and	Luck	(2007;	Figure	4	above)	or	the	dot patterns	in	Figure	9,	verbal	working	memory	allows	for	storage	of	verbal	or phonological	features,	such	as	words,	letters,	or	digits.	The	distinctness	of	these 18	There	was	a	small	interference	in	the	opposite	direction,	but	Hyun	and	Luck	attributed	it	to	a general	dual-task	cost	(see	discussion	at	the	end	of	section	4.2). 19	The	task	in	question	involves	names	and	distractor	faces,	which	are	special.	But	there	are other	studies	from	Lavie's	lab	that	use	ordinary	stimuli	(e.g.,	letters)	and	equally	support	the conclusion	that	WM	load	interferes	with	selective	attention	(see	Lavie	2005	for	a	review). 19 forms	of	working	memory	is	shown	by	the	different	ways	that	visual	and	verbal working	memory,	respectively,	are	drawn	on	in	a	given	task.	For	example,	Robbins et	al.	(1996)	found	that	a	concurrent	visuo-spatial	task	has	more	of	a	disruptive effect	than	a	concurrent	verbal	task	on	chess	players'	ability	to	remember	the configuration	of	pieces	on	a	chessboard	and	solve	tactical	chess	positions	(i.e., identify	the	correct	move	to	make	at	a	given	point	in	a	game).	In	Baddeley	and Hitch's	framework,	what	accounts	for	this	difference	is	that	visual	memory	relies	on a	"visuo-spatial	sketchpad"	that	represents	characteristics	such	as	form,	color,	and movement	in	an	internal	mental	image,	while	verbal	memory	is	carried	through	an "articulatory	loop"	in	which	stimuli	are	rehearsed	subvocally	in	order	to	guard against	decay.	Within	this	framework	the	explanation	of	the	finding	by	Robbins	et	al. (1996)	is	thus	that	the	visuospatial	sketchpad,	rather	than	the	articulatory	loop, plays	a	primary	role	in	cognition	in	chess. As	another	illustration	of	the	distinction	between	the	functions	of	visual	and verbal	working	memory,	consider	a	study	by	Sims	and	Hegarty	(1997).	Their interest	was	in	whether	spatial	visualization	is	involved	in	the	mental	animation	of the	workings	of	a	mechanical	system.	If	mental	animation	involves	spatial visualization	then	it	should	draw	on	the	visuo-spatial	sketchpad,	and	so	there should	be	more	interference	between	a	primary	mental	animation	task	and	a secondary	task	that	draws	on	visuo-spatial	memory	than	between	the	mental animation	task	and	a	secondary	task	that	requires	verbal	memory	instead.	Sims	and Hegarty's	two	"secondary"	tasks	are	shown	in	Figure	9:	the	first	one,	memorizing	a pattern	of	dots,	draws	on	the	resources	of	the	visuo-spatial	sketchpad,	while	the second,	memorizing	a	series	of	letters,	draws	on	the	articulatory	loop	instead.20	In line	with	the	hypothesis	that	mental	animation	involves	spatial	visualization,	Sims and	Hegarty	found	greater	interference	between	mental	animation	and	memory	of	a dot	pattern	than	between	mental	animation	and	verbal	memory,	while	the	opposite pattern	was	observed	when	they	replaced	the	mental	animation	task	with	a	task that	required	verbal	reasoning:	in	this	latter	case	there	was	more	interference between	the	two	verbal	tasks	than	between	the	verbal	task	and	the	visuo-spatial one. 20	A	clarification	may	be	necessary	here.	In	Baddeley	and	Hitch's	framework,	what	determines whether	a	given	stimulus	is	stored	in	verbal	or	visual	working	memory	is	not	the	modality	in	which the	stimulus	is	displayed,	but	rather	the	aspect	of	its	content	that	is	retained	for	later	processing.	For example,	in	the	study	by	Sims	and	Hegarty	(1997)	the	letter	strings	that	had	to	be	remembered	in	the verbal	secondary	tasks	were	presented	as	part	of	the	visual	display,	as	in	Figure	9B.	Nevertheless, since	participants	were	instructed	to	remember	the	letters	themselves	rather	than	the	form	or	color of	the	stimulus,	they	read	the	letters	silently	and	thus	"converted"	the	information	into	a phonological	form	that	was	then	carried	by	the	articulatory	loop. 20 Figure	9:	Visual	(A)	vs.	verbal	(B)	memory	tasks.	Both	tasks	use	visual	stimuli,	but task	(B)	is	assumed	to	activate	verbal	WM	(the	articulatory/phonological	loop), while	(A)	draws	on	visual	WM	(the	visuo-spatial	sketchpad).	Image	credit:	Sims	and Hegarty	(1997). In	light	of	the	above,	return	now	to	the	study	by	de	Fockert	et	al.	(2001)	that	we used	to	motivate	the	hypothesis	that	increased	working	memory	load	disrupts	the capacity	for	selective	visual	attention.	It	is	important	to	notice	that	in	this	study	the memory	task	that	disrupted	the	control	of	selective	visual	attention	drew	on	verbal rather	than	visual	working	memory:	the	task	in	question	was	to	remember	a	series of	digits,	which	though	displayed	visually	were	then	stored	in	verbal	memory	by repetition	in	the	articulatory	loop.	(On	this	point,	see	our	clarification	in	fn.	20.)	And other	studies	suggest	precisely	the	opposite	effect	of	visual	memory	load	on	the capture	of	attention	by	task-irrelevant	visual	distractors:	for	example,	Konstantinou et	al.	(2014)	found	that	performance	in	a	visual	classification	task	that	required suppressing	attention	to	an	irrelevant	distractor	was	impaired	by	a	concurrent verbal	memory	task	(remembering	a	series	of	symbols),	but	facilitated	by	a concurrent	task	that	drew	instead	on	visual	memory	(remembering	a	colored pattern).	What	seems	to	explain	this	difference	is	that	while	the	concurrent	verbal memory	task	interferes	with	the	top-down	control	of	attention,	the	concurrent visual	memory	task	consumes	the	attentional	resources	that	are	needed	for processing	visual	stimuli,	as	a	consequence	of	which	task-irrelevant	stimuli	are automatically	not	attended,	and	thus	there	is	no	need	to	actively	suppress	attention to	them.21 21	In	making	this	suggestion,	Konstantinou	et	al.	(2014)	rely	on	a	central	thesis	from	Lavie's perceptual	load	theory	(see	Lavie	2005),	namely	that	attentional	resources	are	allocated	to	taskrelevant	stimuli,	and	only	if	there	are	leftover	resources,	they	are	allocated	to	task-irrelevant	stimuli. 21 The	bottom	is	line	is	that	while	there	is	a	good	deal	of	evidence	that	verbal working	memory	load	interferes	with	cognitive	control	of	distractor	processing, there	is	no	evidence	suggesting	that	visual	working	memory	load	has	a	similar effect.	On	the	contrary,	studies	testing	the	matter	have	found	either	facilitation	of selective	attention,	as	in	the	study	by	Konstantinou	et	al.,	or	found	no	effect	on selective	attention	at	all	(Yi,	et	al.	2004).22	Moreover,	the	facilitation	effect	of	visual memory	on	selective	attention	has	nothing	to	do	with	cognitive	control	of	distractor processing,	but	is	instead	a	byproduct	of	the	visual	maintenance	function	of	visual working	memory,	as	explained	in	the	previous	paragraph.	Apart	from	interference due	to	general	dual-task	cost,	it	appears	that	visual	working	memory	load	does	not interfere	with	selective	attention,	or	if	it	does,	the	effect	is	not	manifested	in	extant dual-task	experiments	designed	to	test	it.	By	contrast,	verbal	working	memory	load interferes	significantly	with	selective	attention	(over	and	above	a	general	dual-task cost),	by	drawing	on	the	memory	resources	required	to	control	attention	in	a	topdown	manner	(i.e.,	resources	responsible	for	remembering	which	stimuli	are	taskrelevant). This	difference	between	the	effects	of	verbal	and	visual	memory	load	on selective	visual	attention	offers	a	way	to	test	the	attentional	account.	On	this account,	perspectival	identification	is	essentially	a	selective	attention	task,	and	so	if the	account	is	correct	then	we	should	expect	to	find	that	a	concurrent	verbal working	memory	task	interferes	more	with	perspectival	identification	than	a concurrent	visual	working	memory	task	(if	indeed	the	latter	interferes	at	all).	That is,	the	attentional	account	predicts	that	verbal	working	memory	load	will interfere	with	perspectival	identification	more	than	visual	memory	load. Finding	otherwise	would	be	evidence	against	the	attentional	account. (a) (b) Figure	10:	Possible	stimuli	for	our	modified	Stroop	task.	In	(a)	the	size	of	each	image is	congruent	with	the	size	of	the	animal	that	it	is	an	image	of.	In	(b)	the	size	of	the In	the	dual	task	situation	in	question,	there	are	two	tasks	that	require	resources	of	visual	attention, and	consequently	there	are	no	leftover	attentional	resources	that	could	be	allocated	to	taskirrelevant	stimuli. 22	A	study	by	Park	et	al.	(2007)	is	an	exception.	The	study	found	that	visual	memory	load	can impair	selective	attention,	but	it	can	do	so	only	when	the	remembered	item	(face)	matches	the	target category	(face)	and	not	the	distractor	category	(house)	in	the	selective	attention	task.	We	can	safely avoid	this	complication,	as	long	as	we	make	sure	that	in	our	proposed	experiments,	it	is	not	the	case that	the	visual	item	to	be	remembered	matches	the	category	of	the	target,	but	not	of	the	distractor,	in the	selective	attention	task.. 22 image	is	incongruent	with	the	size	of	the	animal.	Given	the	instruction	to	identify either	the	larger	or	smaller	animal	or	the	larger	or	smaller	image,	a	measure	of distractor	suppression	will	be	the	extent	to	which	congruent	performance	is superior	to	incongruent	performance.	Image	credits:	Wikimedia	Commons. This	prediction	of	the	attentional	account	could	be	tested	in	the	following	pair	of experiments.	First,	the	control	experiment	will	compare	the	effects	of	verbal	and visual	memory,	respectively,	on	a	visual	task	that	requires	selective	attention	to	a particular	aspect	of	the	display.	This	could	be	done	using	the	Stroop	task	shown	in Figure	10,	where	participants	need	to	attend	either	to	the	size	of	the	image	or	to	the size	of	the	animal	that	it	depicts:	here	the	expected	result	would	be	that	the influence	of	the	task-irrelevant	stimulus	dimension	will	be	increased	significantly	by a	concurrent	verbal	memory	task	(which	interferes	with	selective	attention), whereas	a	concurrent	visual	memory	task	will	not	have	this	effect.	Second,	the crucial	experiment	will	pair	verbal	and	visual	memory	tasks,	respectively,	with	a perspectival	identification	task,	as	shown	in	Figure	6.	If	the	attentional	account	is correct	then	the	pattern	of	interference	should	resemble	the	one	found	in	the control	experiment.	If	a	different	pattern	is	observed,	this	would	count	against	the attentional	account. The	reason	why	the	control	experiment	is	so	important	is	that	there	is conflicting	data	about	whether	spatial	separation	between	target	and	distractor stimuli	make	a	difference	to	the	way	that	selective	attention	interacts	with	working memory	load.	For	example,	Gao,	Chen,	and	Russell	(2007)	found	that	verbal	WM load	did	not	influence	the	magnitude	of	distractor	interference	in	a	standard	Stroop task	that	required	reading	a	stimulus	word	while	ignoring	its	color.	This	suggests that	the	influence	of	verbal	working	memory	load	on	distractor	processing	requires spatial	separation	between	target	and	distractors.	However,	as	mentioned	before,	de Fockert	et	al.	(2001)	found	that	verbal	working	memory	load	increases	distractor interference	in	a	Stroop-like	task	in	which	names	are	superimposed	on	faces.	This suggests	that	the	influence	of	verbal	working	memory	load	on	distractor	processing does	not	require	spatial	separation	between	target	and	distractor.	Since	perspectival and	objective	properties	are	not	spatially	separated	(in	the	sense	that	when attention	is	directed	to	the	location	of	one	of	them,	it	is	apparently	also	directed	to the	location	of	the	other),	we	are	not	entitled	to	assume	from	the	outset	that	verbal memory	load	will	interfere	with	perspectival	identification	even	if	the	latter requires	selective	attention.	The	control	experiment	is	needed	in	order	to	show	that the	attentional	account	yields	this	prediction. 5.	Conclusion This	paper	can	be	seen	as	a	proof	of	concept.	Is	it	possible	to	use	experimental methods	to	help	make	progress	in	a	complex	phenomenological	debate	that	has proven	recalcitrant	to	the	methods	of	philosophy?	Our	answer	is:	Yes,	though	this approach	will	have	the	same	limitations	and	uncertainties	that	attend	to	any	other experimental	endeavor.	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