John	R.	Smythies'	Theories	of Mind,	Matter,	and	N-Dimensional	Space Conspectus	of	part	of	his	Analysis	of	Perception	(1956) -	Peter	Sjöstedt-H	- MMXVIII John Raymond Smythies (b. 1922) is a neuroscientist and philosopher of	mind, cousin to Richard	Dawkins	and	Graham	Greene.	The	following	is	a	summary	of	his	ideas	on	phenomenal space – the space of one's imagination, dreams, psychedelic experiences,1 somatic sensations,	visions,	hynagogia,	etc.	–	and	its	relation	to	physical	space. – '(visual	and	somatic)	sense-data	really	are	spatial	entities.'	(p.	13) o [This is in contradistinction to the common Cartesian belief that the fundamental difference between	matter and	mind is that	matter is spatial (extended)	and	mind	is	non-spatial	(unextended).] § 'Descartes	made	the	mistake	of	confusing	a	part	of	the	mind	(the	Ego and	its	thoughts)	with	the	whole	mind.'	(p.	58) • [William	James	made	a	similar	point	earlier	(1904).] o Smythies	uses	'sense-data'	synonymously	with	'sensation',	which	he	also	(p. 10)	defines	as	that	which	changes	in	an	'experiential	event'	(e). – Smythies writes that visual sensations [such as imagining two triangles simultaneously]	are	spatial	considering	the	fact	that	they	have	spatial	properties	and relations	–	thus	(non-exhaustively): o Sensations/sense-data 'may be inside or outside other sense-data in a topological	sense	...	.	In	general	sense-data	may	satisfy	many	of	the	axioms	and theorems	of	topology.'	(p.	10) § 'Topology': 'A term meaning 'science of place' ... . The branch of mathematics	concerned	with	those	properties	of	figures	and	surfaces which	are independent	of	size	and	shape	and	are	unchanged	by	any deformation	that	is	continuous,	neither	creating	new	points	nor	fusing existing	ones;	hence,	with	those	of	abstract	spaces	that	are	invariant under	homoeomorphic	transformations.' (Oxford	English	Dictionary) o 'Two	sense-data	may	share, in	part,	a	common	boundary-i.e.	they	may	be contiguous	...	[or]	non-contiguous.'	(pp.	10–11) o 'Some	sense-data	...	may	be	held	to	be	"punctuate"	and	not	extended.	Even	if so,	and	it	is	a	debatable	point	[!],	such	sense-data	can	be	located	...	and	bear spatial	relations	to	other	sense-data...'	(p.	11) 1	At	the	start	of	Aldous	Huxley's	seminal	book	on	psychedelics,	The	Doors	of	Perception	(1954),	he	writes	that	'at	least	one professional	philosopher	has	taken	mescalin	for	the	light	it	may	throw	on	such	ancient,	unsolved	riddles	as	the	place	of	mind in	nature	and	the	relationship	between	brain	and	consciousness'.	The	footnote	here	refers	to	John	R.	Smythies,	and	mentions his	paper	of	1953,	'The	Mescaline	Phenomena'. 2 o Individual	sense-data	are	parts	of	the	total	visual	field,	and	their	location	can be	'divided	into	sections-i.e.	two	hemispheres-right	and	left,	or	upper	and lower;	or	four	quadrants;	or	into	a	central	region	and	a	peripheral	region;	etc.' (p.	12) o 'Sense-data	also	have	shapes	and	(relative)	sizes	and	may	even	be	subjected to	a	form	of	measurement	...	[and]	an	area''	(p.	13) – Smythies	next	asks	(with	thought	to	mind	and	matter),	'How,	in	general,	can	a	class	of events	a	be	related	to	a	class	of	events	b?	There	are	five	possible	answers.'	(p.	14) i. Identity	of	a	and	b (a=b) ii. a	as	a	proper	subset	of	b (b	(a) ) iii. b	as	a	proper	subset	of	a (a	(b) ) iv. a	and	b	intersect (a	()	b) v. a	and	b	as	mutually	exclusive (a) (b) – How	then	may	the	class	of	events	e	[experiential	events]	be	related	to	the	class	of events	p	[physical	events]? o [That	is	the	question!	The	mind-body	problem/hard	problem	of	consciousness] – 1.	&	2.	Smythies	writes	that	we	'can	say	at	once	that	e	and	p	cannot	be	identical,	nor can	p	be	a	proper	subset	of	e'	(p.	15).	[I.e.	not	i	or	ii] o i.e.	not	naïve	realism [nor	idealism]. o Not	naïve	realism	because	the	temporal	index	of	a	physical	event	such	as	star light-to-eye	is	non-identical	to	the	temporal	index	of	its	perception. § [Smythies promotes a representationalist theory of perception, but that	is,	in	my	view,	ultimately	irrelevant	to	his	views	on	spatiality.] § [He does not explain why 2. (idealism) cannot be the case, though dismisses	it	in	passing	on	p.	30.] – 3.	Smythies	next	considers	the	relation	of	p	and	e	under	relation	iii	(e	as	proper	subset of	p).	He	writes	that	this 'is the	theory	of	psycho-neural identity	theory	which	has been	largely	abandoned	by	neorologists'	(p.	16). o [This statement itself is of interest because it is commonly held that the psycho-neural	identity	theory	was	first	advanced	in	1956	(by	U.	T.	Place),	but that	is	the	year	of	this	very	book	of	Smythies	who	already	rejects	it.] o [Psycho-neural	identity	theory	(PN-IdT)	is	the	idea	that	a	sensation	simply	(and strictly) is its 'correlated'	brain	process. That the two terms	have the same referent,	as	do	the	'morning	star'	and	'evening	star'	(i.e.	Venus).] o [It	may be	wondered	why Smythies considers PN-IdT as relation 3 (subset) rather than relation 1 (identity), considering its name and purport. But Smythies is fundamentally correct in this classification	because	PN-IdT	does not	take	mind	and	matter	to	be	identical	but	rather	it	eliminates	mind	to	leave matter	as	fundamental	(i.e.	e	as	subset	of	p),	thereby	really	forfeiting	its	right to	call	itself	an	'identity'	theory.	(See	my	PhD	thesis,	chapter	4	for	details.)] 3 o Smythies	then	uses	the	reality	of	the	phenomenal	space	he	described	above against	PN-IdT: § 'Two	groups	of	events	arranged	in	a	spatial	order	may	not	be	said	to	be identical unless they are geometrically congruent. ... [E]vents in the cerebral cortex ... concerned in a particular perception are geometrically	non-congruent	with	the	sense-data	that	these	events	are alleged, under this [identity] theory, to be. ... [This] can be used to refute	with	equal	finality	the	theory	of	psycho-neural	identity.'	(p.	16) – 4.	e	and	p	cannot	intersect	because	at	the	intersection	e	and	p	would	be	identical	(i.e. have	the	same	referent),	which,	as	we	saw	above	cannot	be	correct. – 5.	Smythies	does	not	use	the	term	dualism,	and	as	we	shall	see	this	is	fair.	He	begins by	stating: o A	physical	(p)	spatial	location	can	be	determined	by	'a	system	of	co-ordinate axes	OX,	OY,	OZ	set	at	right	angles	to	each	other'	and	with	time	(OT)	(p.	23).	As we	saw	with	phenomenal	spatiality,	(e)	can	also	have	axes	for	location:	'sensedata	can	certainly	be	located	by	using	a	set	of	co-ordinates'	(pp.	23–4) o Smythies then	writes that the 'location	of sense-data is	only	quantitatively different	and	not	qualitatively	different	from	the	location	of	physical	objects, which	we	saw	was	also	true	in	the	case	of	measurements	of	sense-data	and physical	objects'	(p.	24). § That	is,	though	the	phenomenal	spatial	location	using	a	set	of	axes	may not be accurately determinable, this is neither the case in physical space.	Location	here	is	a	matter	of	degree	not	of	kind. – Now,	a	fundamental	question	is	asked: o 'what	are	the	spatial	relations	between	these	two	sets	of	spatial	axes	at	any time	instant?'	(p.	25) o There	are	only	two	possible	answers	he	writes: § Theory	I:	'There	may	be	no	spatial	relations	between	the	two	sets	of axes.'	(p.	25) § Theory II: 'The	two	sets	may	be	conjoined	to	determine	a	single	sixdimensional	manifold.'	(p.	25) o i.e.	Is	phenomenal	space	separate	from	physical	space	[a	position	taken	by, e.g.,	H.	H.	Price,	A.	N.	Whitehead	and	Bertrand	Russell],	or	is	it	conjoined	in	a single	higher	dimensional	space? – If	we	delve	deeper,	we	can	fathom	a	further	division	of	possibilities: o I:	that	each	individual	has	their	own	separate	phenomenal	space,	in	which	case we	must	(for	phenomenal	space)	'use	(m	+	1)	sets	of	co-ordinate	axes	in	the case	of	m	human	individuals	(with	three	spatial	[and	one	temporal	axis]	in	each set)'	(p.	25). 4 § [It is not explained why the variable 'human' is mentioned (as presumably	other	organisms	can	have	phenomenal	space).] § Thus	if	there	were	100	people	in	the	universe,	then	there	would	be	100 three-dimension	axes for	the	phenomenal	spaces,	plus	one	common physical	3D	space	(and	one	temporal	dimension	common	to	all). • In a footnote here (p. 25) Smythies acknowledges the disputability of assuming that only one temporal dimension could	be	common	to	all	phenomenal	spaces	–	it	is	'beyond	the scope	of this	book'. In	other	words, it could	be the	case that separate phenomenal spaces have temporal dimensions incongruent	with	other	phenomenal	and	physical	spaces.	[This is something considered in, e.g., A. N. Whitehead's essay 'Uniformity	and	Contingency',	in	relation	to	dream	time	and	the theories	of	Relativity.] o In	this	case	(I),	'All	these	worlds	['world	≡	spatial	system'	(p.25)]	would	be	quite separate	and	their	contents	would	be	held	to	bear	no	spatial	relations	to	each other but only temporal relations, causal relations and relations of class membership'	(p.	25). – II:	Alternatively,	it	may	be	the	case	that	the	phenomenal	worlds	are	not	separate	but that	'the	contents	of	each	world	[including	the	physical]	...	are	spatially	related'	(p.	25) –	(i.e.	as	well	as	related	temporally,	causally,	and	taxonomically). o In	this	case,	rather	than	(m	+	1)	sets	of	axes,	there	would	be	'a	single	(3m	+	3) dimensional	manifold'	(p.	25).	(Or	a	[4m	+	4]	spatiotemporal	manifold,	if	we include	time	as	a	dimension.) § i.e.	(3-dimensions	x	number	of	individuals)	+	(3	dimensions	of	physical space)	as	one	single	spatial	manifold. § [Note that it is assumed here the phenomenal space is threedimensional. That it may be two-dimensional is an issue Smythies addresses	(and	rejects)	in	later	papers.] – 'In	either	case	[I	or	II]	we	are	dealing	with	a	far-reaching	development	in	cosmology	... there	is	not	one	Space-Time	(as	is	thought	at	present)	but	...	there	are	many	SpaceTimes.'	(p.	27) – In	summary	of	this	section	Smythies	writes: o 'In	[I]	the	physical	universe	becomes	but	one	of	many	spatial	universes	in	which events	ordered	in	a	spatio-temporal	system	occur.	In	[II]	the	physical	universe becomes	merely	a	section	of	the	total	spatio-temporal	Universe	of	events.	... Thus	to	give	a	proper	account	of	experiential	events	and	their	relation	to	brain events,	we	may	have	to	exchange	the	four-dimensional	geometry	in	current use	in	cosmology	for	an	n-dimensional	geometry.'	(p.	27) § 'n	=	(3m	+	3)'	(p.	28) o Summarized	further: 5 – The	two	formal	cosmological	theories	are: o THEORY I: 'Sense-data ...	are	spatial	entities	distinct from	physical	objects and	bear	temporal	and	causal	relations	but	no	spatial	relations	to	physical objects.'	(p.	27)	–	i.e.	the	exclusive	theory. o THEORY	II: 'Sense	data	...	are	spatial	entities	distinct	from	physical	objects and	bear	both	temporal	and	causal	relations	and	higher-dimensional	spatial relations	to	physical	objects.'	(p.	28)	–	i.e.	the	inclusive	theory. – Smythies	now	defines	a	mind: o 'A mind is a complex composite of sense-data organised into sense-fields, together	with	images,	thoughts,	affects	and	perhaps	a	Pure	Ego.'	(p.	28) § He then adds that the 'mind thus defined is a part of the total organism-an	extra	part	which	we	have	previously	failed	to	recognise because	of	its	particular	geographical	location	and	because	some	of	its constituent parts (sense-data) have been confused with physical objects'	(p.	28). • That	is	to	say	that	because	an	organism	fundamentally	includes its mind, an organism is a higher-dimensional entity in its totality, such that a four-dimensional description of the organism	cannot	be	sufficient. • 'There are also higher-dimensional geometries available to describe the (4m	+	4)-dimensional spatio-temporal system	of Theory	II.'	(p.	29) • In	Appendix	I,	Smythies	states	that:	'There	is	no	a	priori	reason why	we	should	not	develop	the	ability	to	appreciate	directly an	n-dimensional	spatial	system.'	(p.	124)	(n>3) o [Smythies mentions the mescaline experience in this book	(p.	47	–	but	only	in	respect	to	H.	H.	Price's	version of Theory I). But I refer interested readers again to Smythies' 1953	paper (which inspired	Aldous	Huxley's The Doors of Perception [1954]), 'The Mescaline Phenomena'.] – Smythies argues that both these theories are compatible with psycho-neural interaction and psycho-neural parallelism, which, he writes, are not essentially different	on	a	Humean	analysis	of	causation. o Note	that	'psycho-neural	interaction'	(p.	29)	is	generally	considered	to	be	the causal	operandi	of	dualism	(that	mind	and	body	are	distinct).	But	recall	that Smythies (in Theory II) is advancing a single n-dimensional	manifold, i.e. a monism.	In	fact,	the	very	reality	of	phenomenal	space	is	contrary	to	the	axioms of	Cartesian	dualism	(which	denies	extension	to	mental	states).	Against	such	a dualism,	Smythies	aims	the	following	remarks: 6 § '[The]	spatiality	of	sense-data	is	given	no	less	than	their	colour. § If	the	mind	is	thought	to	be	non-spatial	how	can	spatial	sense-data	and images	belong	to	such	a	mind? § How	can	that	which	is	spatial	belong	to	that	which	is	non-spatial? § How	can	an	entity	be	both	wholly	non-spatial	and	spatial	and § How	can	a	non-spatial	whole	be	composed	of	spatial	parts?'	(p.	30) • It is thus interesting to note that Smythies rejects both the psycho-neural identity theory (a theory of materialism, or material	monism)	as	well	as	rejecting	the	traditional	theory	of dualism.	[So	'the	physical	is	an	abstraction'] • Thus	it	is	a	'pseudo-dilemma'	to	ask,	"How	can	the	unextended and	non-spatial	mind	and	the	extended	brain	interact?"	(p.	30) [Smythies	now	goes	through	potential	objections	to	this	theory,	and	develops	his	'television theory	of	perception'	–	which	in	this	conspectus	I	shall	omit.] – Smythies refers to E. A. Abbott's classic novel Flatland (1926) – where the twodimensional polygon people cannot sufficiently perceive nor imagine a threedimensional	world	– when	Smythies	writes 'there is	no	a	priori reason	why there should	not	be	higher-dimensional	spatial	relations	between	sense-data	...	on	the	one hand	and	physical	objects	on	the	other.'	(p.	48) o Smythies points to Bertrand Russell on this possibility, specifically his texts Mysticism and Logic (1918) and	Human Knowledge (1948), but claims that Russell	tends	towards	Theory	I. – Developing	Theories	I	and	II,	Smythies	writes	(p.54): o A	is	a	point	in	a	phenomenal	space;	B	is	a	point	in	physical	space. o If	Theory	II	is	true,	then: § 'A	cannot	be	the	same	point	as	B.' § 'There	will	be	no	line	in	the	physical	world	parallel	to	AB.' § 'The angle ABC [where C is another synchronous point in physical space]	will	always	be	a	right	angle.'	(see	below) o If	Theory	I	is	true,	then: § 'There	can	be	no	line	joining	A	to	B.' § 'There	can	be	no	such	angle	as	ABC'. – Smythies illustrates metaphorically the 'psychophysical geometry' of Theory II ndimensionality	(in	the	Appendix	II,	p.	127)	by	means	of	a	4D	tesseract:	the	inner	cube represents	physical	space	and	six	contiguous	flat-top	pyramids	(which	are	additional 3D cubes illustrated perspectively) represent contiguous three-dimensional phenomenal	spaces	(where	m	=	6). 7 o [Note	that	this	is	a	3D	representation	of	a	4D	object,	which	as	such	cannot	be imagined	directly	(at	least	for	most	of	us	without	chemical	assistance).] o [But	the	location	of	a	point	in	4D	space	is	easily	represented	algebraically.	For the	3	axes	(x,	y,	z)	of	3D-space	we	can	locate	a	point-h	by	3	respective	values	– e.g.	(x2,	y3,	z4).	For	4D-space	we	simply	add	another	axis	w:	point-h:(x2,	y3,	z4, w5).	And	so	on	for	D>4.	This	representational	method	is	known	as	the	Cartesian coordinate	system.] o [That 'angle ABC will always be a right angle' (p. 54) in Theory II is not elaborated upon by Smythies, but that axes x, y, x are orthogonal to one another	serves	at	least	inductively	as	reason	for	w	to	be	orthogonal	thereto yet	again,	notwithstanding	the	fact	that	such	a	possibility	is	intelligible	for	us conceptually	rather	than	prosaically	imaginably.] – Smythies	now	considers	the	theories	in	relation	to	the	causal	processes	between	the mind	and	the	brain	–	represented	by	psi:	ψ o [In	the	philosophical	tradition,	we	can	generalize	to	say	that	there	are	three main	options	for	such	causation: § non-existent	(if	mind=matter	[strict	identity]	then	no	causal	path;	or	in parallelism); § interaction	1	–	matter-to-mind	(emergentism,	epiphenomenalism); § interaction 2 – mind-to-matter (mental causation [inc. free will], in most	emergentism,	dualism,	idealism	[as	projection],	etc.)] o Theory I: non-spatial causal processes 'crossing the unimaginable void between the public physical spatial system and each private experiential spatial	system'	(p.	55). § [such	causal	processes	would include those	hypothesized to	exist	by the transordinal nomologies/psychophysical bridge laws of the emergentists	[e.g.	J.	S.	Mill,	C.D.	Broad].	That	such	laws	are	not	laws	of physics is one reason for the rejection of emergentism as an unscientific	theory	(e.g.	by	J.	J.	C.	Smart	[1959]).] o Smythies now splits Theory II into two further types so to address this	ψ question: 8 o Theory	II	A: § The	'psychical	spatial	system'	is	a	term	Smythies	coins	to	refer	to	the possibility that the	phenomenal spatial field	at	any	specious	present transcends	that	which	is	actually	sensed. • 'Each private sensed spatial system may thus be set in or embedded in a larger unsensed system of the same dimensionality	(i.e.	the	same	set	of	three	spatial	axes...)'	(p.	56) • There	could	exist	in	this	theory	'unsensed	psychical	entites'	(p. 56). • [This	is	a	rather	radical	proposal.	If	we	applied	it	to	phenomenal dream	space, it	would	mean that the	dream	world	extended beyond that	which one actually experienced in one's dream: the	dream	would	be	larger	than	your	experience	of	it.] • Further	still,	Smythies	speculates	that	a	'psychical	mechanism' that forms	one's	actual sensations	could lie	un-sensed in this phenomenal	space,	thus	also	insensible	in	physical	spatiality. • In	the	2D	Flatland	(from	Abbott),	the	inhabitants	could	perceive a	x-y	boundary,	but	they	would	be	unaware	that	there	was	also a	(x-y)-z	connection	('interface').	Likewise,	there	could	be	an	(xy-z)-w	interface	for	us: o 'Similarly	our	physical	universe	may	be	separated	from each	of	our	private	universes	by	a	dimensional	interface, and	our	own	private	universes	may	be	separated	from those	of	other	people	by	other	dimensional	interfaces.' (p.	57) o Smythies speculates that there could be transdimensional processes [i.e. only appearing systematic	from	a	transdimensional	perspective]. § [Just as 3D processes would appear unsystematic, irregular, and largely obscured when	interfacing	a	2D	Flatland.] o 'Normally the only transdimensional processes are conducted	by	ψy	[connections	of	sensory	areas	of	brain to the sense fields of experience] and ψx [process whereby will is transmitted to motor cortex], which correlate	the	phenomena	occurring	in	all	these	worlds.' (p.	57) o 'There is	no	problem	about	how	such	processes	could react	with	the	brain	as	every	point	in	the	brain	can	be contiguous	with	the	unsensed	psychical	mechanism.'	(p. 57) § [i.e. via the (for us) unsensed dimensional interface between physical and unsensed phenomenal	spatiality.] 9 o Theory	II	B: § 'Sense-data	...	might	still	bear	higher	dimensional	spatial relations	to physical	objects,	yet	there	would	be	not	any	such	unsensed	psychical spatial	system	as	postulated	in	Theory	II	A.'	(pp.	57–8) • 'ψ	would	then	be	a	non-spatial	causal	process	as	described	in Theory	I.'	(p.	58) • But	in	contradistinction	to	Theory	I,	the	Universe	would	still	be a single (3m + 3) dimensional one rather than multifarious separate	3D	universes. • Theory II B would have to stipulate 'a non-spatial part connecting	two	spatial	parts:	the	brain	and	the	sensory	fields' (p.	58) o i.e. a causality that involves an aspatial bridge, as it were. o This	is	not	impossible,	Smythies	says,	and	the	competing hypotheses	could	be	gauged	in	terms	of	plausibility	via empirical	means	based	on	the	different	predictions	that the	theories	could	proffer	–	Smythies	speculates. – Smythies concludes by listing how these theories are advantageous to Cartesian dualism. o Such	dualism	cannot	give	an intelligible	account	of	the interaction	between sense-data	and	the	brain. o Theories I & II both view an organism as a	unitary mind-body entity, that cannot	be	parsed.	In	dualism	the	mind	(soul)	can	live	on	after	the	(3D)	body dies. o 'The Cartesian dualism is a dualism of substance whereas the theories presented	here	are	dualisms	of	spatial location.	They	are	however	monistic theories	in	the	logical	field	of	causal	relation	and	organisation.'	(p.	59) o 'It should	be	possible to investigate causal relations	between	a	brain	and	a mind	by	constructing	an	"n"-dimensional	physics	based	on	an	"n"-dimensional geometry'	(p.	59). – Though Smythies rejects dualism it should be recalled that he also rejects the psychoneural	identity	theory.	He	also	rejects,	by	implication	of	the	spatial	argument he	sets	forth	above,	emergentist	theories: o 'Nor	do	we	have	to	postulate	that	cerebral	events	"underlie"	mental	events, or	form	a	mysterious	"substratum"	for	them'	(p.60) § This is because the three-dimensional space of the brain is not the totality	of	the	space	of	reality,	and	is	not	a	more	fundamental	ontology: • 'it	may be that an accurate and comprehensive neurological account of perception cannot be given solely in terms of physical objects including brains and the language system	of physics,	but it	may	have	to include	<sense-datum>	among its basic	terms'	(p.	60) 10 Thus	Smythies	offers	hypotheses	of	the	mind-matter	relation	based	on	an	analysis	of	space. They	are	certainly	speculative,	but	certainly	speculations	that	can	be	analysed	further	(e.g.	in relation	to	possible	multiple	temporal	axes).	It	is	of	note	that	this	book	of	Smythies	begins (Prologue,	p.	xiii)	with	a	long	quotation	–	a	suggestion	from	mathematician	and	metaphysician A.	N.	Whitehead: 'How	do	we	know	that	only	one	geometry	is	relevant	to	the	happenings	of	nature?	... Perhaps in the dim future mankind, if it then exists, will look back to the queer, contracted three-dimensional universe from	which the nobler, wider existence has emerged.' (Modes	of	Thought) –	–	–