translation	copyright	©	2017	by	David	Forman "Apokatastasis	panton"	(1715)1 by	G.	W.	Leibniz,	translated	by	David	Forman (2017/7/31) Ἀποκατάστασις	πάντων2 One	can	determine	the	number	of	all	possible	books	of	a	given	size	composed	of meaningful	and	meaningless	words. I	call	a	book	of	a	"given	size"	that	which	consists	of	a	given	number	of	letters.	For example,	a	folio	consisting	of	10,000	pages,	with	100	lines	a	page	and	100	letters	a	line, would	be	a	book	of	100,000,000	letters.	Now	the	number	of	all	the	books	of	this	length, or	which	can	be	formed	from	100	million	letters	of	the	alphabet,	is	finite.	And	this number	can	be	obtained	from	the	calculus	of	combinations,	which	would	be	N.	It	is	also clear	that	all	possible	shorter	books	are	contained	in	these	longer	ones. Suppose,	moreover,	that	a	public	annual	history	of	the	earth	can	be	sufficiently	related	in a	book	of	this	length,	which	would	contain	100	million	letters:	it	is	also	clear	that	the number	of	possible	public	histories	of	the	earth	differing	among	themselves	is	limited; for	any	different	history	would	produce	a	new	book. Hence	it	follows	that	if	we	imagine	that	humanity	lasts	long	enough	in	the	state	it	is	in now,	past	public	histories	must	return.	For	if	we	assume	a	number	of	years	equal	to	the number	N,	I	say	that	during	these	N	years,	in	any	year	it	is	always	the	case	that	either new	histories	come	to	pass	that	differ	from	any	preceding	ones	from	these	years included	in	N,	or	else	the	history	of	some	prior	year	among	them	repeats.	If	the	second happens,	then	we	have	what	was	sought.	Otherwise,	that	is,	if	the	annual	history	is always	new,	it	follows	that	all	possible	public	histories	are	exhausted	in	this	number	of years	and	that	in	the	following	years	the	past	ones	would	return.	Q.E.D.	And	so	it	is necessary	that	our	Leopold	and	Louis	and	William	and	George	would	return	with	all	their deeds	within	this	time	span.3 1	LBr.	705	Bl.	72.	The	Latin	text	is	transcribed	in	M.	Fichant	(ed.),	De	l'	Horizon	de	la	Doctrine	Humaine (1693);	Ἀποκατάστασις	πάντων	(La	Restitution	universelle)	(1715),	(Paris:	J.	Vrin,	1991),	pp.60–66.	Fichant provides	a	French	translation,	which	I	have	consulted	in	preparing	the	present	translation. 2	This	title,	meaning	"restitution	of	all,"	derives	from	Acts	3:21.	See	Theodicy	§17	and	§156,	where	Leibniz uses	the	Greek	expression	to	refer	to	J.	W.	Petersen's	Μυστήριον	ἀποκατάστασεως	πάντων,	das	ist,	das Geheimniss	der	Wiederbringung	aller	Dinge	(1700).	Leibniz	published	an	(anonymous)	review	of	this	work	in the	April	1701	issue	of	the	Monatlicher	Auszug.	For	a	discussion	of	Leibniz's	interest	Petersen's	work,	see M.	Antognazza	and	H.	Hotson,	Alsted	and	Leibniz:	on	God,	the	Magistrate,	and	the	Millennium	(Wiesbaden: Harrassowitz,	1999),	pp.	170–198. 3	Leibniz	is	presumably	referring	here	to	recent	and	current	reigning	monarchs:	Holy	Roman	Emperor Leopold	I	(reigned	1658–1705),	King	William	III	of	England	(reigned	1689–1702),	King	Louis	XIV	of	France (reigned	1643–1715),	and	King	George	I	of	Great	Britain	(reigned	1714–1727). 62 60 2 translation	copyright	©	2017	by	David	Forman But	it	is	clear	that	this	is	the	same	if	we	descend	to	private	history,	the	only	difference being	that	the	work	will	be	conceived	with	a	longer	book	and	more	years;	for	a	book	of	a size	sufficient	to	relate	all	the	smallest	details	of	what	humans	have	done	on	all	the	earth within	a	year	is	certainly	possible.	Imagine	that	there	are	a	thousand	million	humans	on earth	(a	number	from	which	humanity	is	most	distantly	removed),	and	that	a	book	the size	we	granted	to	the	public	annual	histories,	thus	of	100	million	letters,	is	assigned	to each	human	to	relate	a	single	year	of	his	life	down	to	the	smallest	details.	For	even	if 10,000	hours4	are	granted	to	a	year,	a	sheet	of	10,000	letters,5	that	is,	a	page	of	100	lines each	with	100	letters,	would	still	surpass	what	is	needed	to	describe	each	hour	of	a human. Thus,	for	a	work	containing	the	annual	history	of	the	whole	of	humanity	down	to	the smallest	details,	it	would	be	sufficient	to	have	a	number	of	letters	that	would	reach	a hundred	thousand	million	millionions,6	if	'millionion'	were	to	mean	a	million	millions. Now	the	number	of	possible	works	of	this	size	differing	among	themselves	in	some measure	is	finite,	and	indeed	can	be	obtained	from	the	number	of	combinations.	Let	this number	be	called	Q.7 Hence	it	follows:	if	humanity	endured	long	enough	in	its	current	state,	a	time	would arrive	when	the	same	life	of	individuals	would	return,	bit	by	bit,	through	the	very	same circumstances.	I	myself,	for	example,	would	be	living	in	a	city	called	Hannover	located	on the	Leine	river,	occupied	with	the	history	of	Brunswick,	and	writing	letters	to	the	same friends	with	the	same	meaning.	For	the	same	demonstration	can	be	applied	to	the number	Q8	that	we	established	above	applied	to	the	number	N,	seeing	that	nothing would	be	different	except	for	the	size. But	these	[returns	will	happen]	not	just	once,	but	many	more	times,9	and	indeed	a greater	number	of	times	than	can	be	assigned,	should	humanity	endure	long	enough. And	the	ancients	seem	to	have	had	such	[returns]	in	mind,	which	were	called	'the revolutions	of	the	great	platonic	year,'10	although	the	reasons	for	their	opinion	have	not been	transmitted	to	posterity,	but	which	is	clear	from	what	they	say. 4	Reading	'10000	horae'	in	place	of	'1000	horae.' 5	Reading	'plagula	superforet	10000	literarum'	in	place	of	'plagula	superforent	10000	literarae.'	(Fichant instead	suggests	striking	'plagula'	and	making	'literae'	the	subject	of	the	clause.) 6	Leibniz	writes	'centies	mille	milliones	Millionionum'	(1023),	forgetting	to	strike	the	'milliones'	as	he	shifts to	his	neologism	for	orders	of	large	numbers.	The	corrected	text	would	read	either	'centies	mille	milliones millionum'	or	rather,	with	Leibniz's	neologism,	'centies	mille	millioniones,'	that	is,	'a	hundred	thousand millionion'	(1017). 7	Leibniz	first	wrote	'P.' 8	Following	Fichant's	correction	of	'Q'	for	'P.' 9	Reading	'saepius'	for	'saepies.' 10	Plato's	Timaeus	presents	the	idea	of	a	"complete"	or	"perfect"	year	that	is	achieved	when	all	eight celestial	revolutions	or	periods	return	to	their	starting	points	(39c–d). 64 3 translation	copyright	©	2017	by	David	Forman Finally,	even	if	humanity	did	not	always	endure,	assuming11	that	there	always	exist	minds that	know	and	seek	the	truth,	it	follows	that	minds	will	someday	reach	the	point	where	it would	be	necessary	to	repeat	truths	that	are	independent	of	the	authority	of	the	senses, that	is,	demonstrable	theorems	that	have	been	discovered	and	that	do	not	exceed	a given	size	(for	example,	a	page	if	they	are	written);	and	[this	follows]	all	the	more	for concise	statements	that	can	be	written	in	[a	few]	words.	Moreover,	new	theorems	to	be discovered	would	have	to	grow	in	size	to	infinity.	But	if	that	were	to	happen,	it	would	be necessary	that	minds	also	could	become	capable	of	grasping	such	long	theorems. But	sensible	truths,	that	is,	those	based	not	on	reason,	but	rather	on	experience,	are	able to	vary	to	infinity	even	if	they	do	not	become	lengthier,	since	the	senses	consist	in confused	perception,	which	can	be	varied	in	infinite	ways	while	preserving	conciseness; for	there	can	be	infinite	kinds	of	liveliness,	senses,	and	sensible	objects;	which	is	quite otherwise	than	with	theorems,	that	is,	with	truths	that	can	be	known	through	adequate or	perfect	demonstration. 11	Following	Fichant,	who	strikes	out	the	'quia'	at	the	beginning	of	this	clause.