volume	17,	no.	25 december	2017 The Eightfold Way: Why Analyticity, Apriority and Necessity are Independent Douglas Ian Campbell University of Canterbury © 2017 Douglas Ian Campbell This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. <www.philosophersimprint.org/017025/> 1. Introduction In	this	paper	I	defend	what	I	frankly	admit	may	appear	on	first	inspection	to	be	a	preposterous	position.	I	say	it	may	appear	"preposterous" advisedly,	because	every	philosopher	I	have	discussed	it	with	has	earnestly assured me it is preposterous - until, that is, the argument has been	explained,	whereupon	much	chin	rubbing	and	head	scratching ensues.	If	the	argument	has	a	weakness,	then	it	is,	I	think,	not	obvious where	it	is. The	position	concerns	the	three	great	modal	dichotomies: The metaphysical dichotomy. A true statement is necessary	iff it	is	impossible	for	it	to	be	false.	Otherwise	it	is	contingent.1 The epistemic dichotomy. A true statement is a priori	iff	it	can be	known independently	of experience.	Otherwise it is empirical (or a posteriori). The semantic dichotomy. A true statement is analytic	iff	it	is true	in	virtue	of	meaning	alone.	Otherwise	it	is	synthetic.2 1. By	a	'statement'	I	mean	a	sentence	produced	in	a	context.	Here	I	focus	only	on true	statements.	If	both	true	and	false	statements	are	considered,	then	we	get not	a	dichotomy	but	a	trichotomy	-	between	necessary truths, necessary falsehoods and contingencies.	The same	goes,	mutatis mutandis, for the	epistemic and	semantic	dichotomies. 2. It is presently something	of a received	view: (i) that the	necessary/contingent and a priori/empirical	dichotomies	apply	in	the	first	instance	to propositions; (ii) that these two	dichotomies also apply	derivatively to statements that	express	propositions,	with	a	statement	inheriting	the	metaphysical	and epistemic	statuses	of	the	proposition	it	expresses;	but	(iii)	that	the	analytic/ synthetic	dichotomy	instead	applies	only to statements, not to the propositions they	express.	I	won't	challenge	this	received	view	in	the	present	paper.	Accordingly, I	will	work always at the level of statements, not that of propositions. However, I will argue elsewhere that the received view is poorly motivated and that there are strong reasons for thinking that all three modal dichotomies apply in the	first instance to propositions. It is also sometimes suggested	that	the	analytic/synthetic	dichotomy	applies	to	sentences.	This	is implausible, since statements	have	determinate	meanings	while sentences (often)	don't	(Hospers,	1967,	163).	For	example,	an	utterance	of	the	sentence 'Banks are	monetary institutions'	might be either an analytically true statement	or	a	synthetic	falsehood,	depending	on	whether	the	context	is	indicative douglas	ian	campbell The Eightfold Way philosophers'	imprint – 2 – vol.	17,	no.	25	(december	2017) A	modal	category	"has	members"	if	statements	belonging	in	that	category	exist. It is "empty" if there	are	no	statements	of that type.	For example,	NAA	has	members	iff	there	is	at	least	one	statement	that	is necessary,	a priori	and	analytic.	On	the	plausible	assumption	that	(1)	is such	a	statement,	NAA	does	indeed	have	members: (1) All	bachelors	are	unmarried. The	position	I	will	defend	is	this: Octopropositionalism: All eight modal categories have members.	None	is	empty. Octopropositionalism	appears	preposterous	because	it	flies	in	the	face of	received	opinion	going	right	back	to	Hume.	Hume	famously	held that there are just two types of statements, relations of ideas and matters of fact.	The	former	are	(in	my	terminology)	NAA	statements,	being necessary,	a priori	and	analytic.	An	example	is	(1).	The	latter	are	CES statements, being contingent, empirical and synthetic. An example is	(2): (2)	The	sun	will	rise	tomorrow. The	doctrine	that	only	these	two	types	of	statements	exist is	Hume's fork.	Octopropositionalism	lies	at	one	extremity	of	a	spectrum	that	has Hume's	fork	at	the	other	extremity.3	For	Hume,	the	three	modal	dichotomies are co-extensive and collapse into a single dichotomy	-	that between relations of ideas and	matters of fact. For the octopropositionalist,	in	contrast,	the	three	modal	dichotomies	are	maximally	noncoextensive.	They	come	apart	every which way. 3. The	Quinean	position	that	all	three	modal	dichotomies	are	ill-posed	lies	at the	extremity	of	a	different	spectrum.	For	recent	rebuttals	of	Quine,	and	of related	arguments	by	Harman (1973, 1996), see (Juhl	&	Loomis,	2010), (G. Russell,	2008)	and	(Chalmers,	2012). These	three	dichotomies	can	be	combined	to	produce	the	tri-dichotomy	of	Figure	1: Figure 1. The	modal	tri-dichotomy. Figure	1	depicts	eight	modal	categories: NAA:	Necessary,	A priori and Analytic NAS:	Necessary,	A priori and Synthetic NEA:	Necessary,	Empirical	and	Analytic NES:	Necessary,	Empirical	and	Synthetic CAA:	Contingent, A priori and Analytic CAS:	Contingent, A priori and Synthetic CEA:	Contingent, Empirical	and	Analytic CES:	Contingent, Empirical	and	Synthetic of	Main	Street	or	a	river's	edge.	The	sentence	itself is thus	neither	analytic nor	synthetic. douglas	ian	campbell The Eightfold Way philosophers'	imprint – 3 – vol.	17,	no.	25	(december	2017) Kaplan	(1977,	509,	540)	has	also	argued	that	(7)	is	a priori,	contingent and	analytic,	making	it	a	CAA	statement: (7)	I	am	here	now. Pulling	these	ideas	together,	we	obtain	the	following	candidate	members	of	the	different	modal	categories: NAA:	Hume's	(1) NAS:	Kant's	(4) NEA:	-----------}	Kripke's	(5)	goes	in	one NES: -----------}	of	these	two	places CAA:	Kaplan's	(7),	-----------}	Kripke's	(6)	goes	in	one CAS:	Descartes'	(3), --------}	of	these	two	places CEA: CES:	Hume's	(2) This	list	comes	nowhere	close	to	vindicating	octopropositionalism.	In the	first	place,	neither	Descartes,	Kant,	Kripke	nor	Kaplan	provides	us with	a	putative	example	of	a	CEA	statement.	Second,	if	Kripke	is	right, then	(5)	is	a	member	either	of	NEA	or	of	NES,	but	it	can't	be	a	member of	both	-	which	leaves	one	of	these	two	sectors	vacant.	Third,	it	is	not obvious	the	ideas	of	Descartes,	Kant,	Kripke	and	Kaplan	can	or	should all	be	accepted	conjointly	-	potentially leaving	one	or	more	of	NAS, CAA	or	CAS	empty. In	short,	although	these	philosophers	have	produced	reasons for thinking statements are	more	modally diverse than	Hume's fork allows,	none	of	them	has	challenged	a	weaker	Humean	doctrine	to	the effect that some modal categories are empty. The octopropositionalist must	refute	even	this	weaker	doctrine,	which,	in	view	of	how	well	it has	stood	the	test	of	time	down	the	centuries,	would	appear	a	very	tall order	indeed. Setting aside the apparent unlikelihood of octopropositionalism's	being shown to be true, why, if it were true, would its truth matter? Its truth	would	be important for the	same	reasons that	Kripke's In arguing for his ‟fork",	Hume	(the	arch	empiricist)	was	partly	motivated	by	a	wish	to	deny	that	Descartes	(the	arch	rationalist)	was	correct	in	claiming	that	(3)	is	a priori: (3)	A	thinking	thing	exists. If	Descartes	were right	about	(3)	being	a priori,	then,	since	(3)	is	contingent	and	synthetic,	it	would	be	a	CAS	statement.4	This	Hume	took	to be	impossible.5 Kant argued, contra	Hume, that statements of a third type exist: namely,	NAS statements that are necessary and a priori on the one hand	but	synthetic	on	the	other.	(4)	is	an	example. (4)	Causation	exists. In	more	recent	times,	Kripke	(1980)	produced	examples	both	of	statements	that	are	necessary	but	empirical	-	e.	g.,	(5)	-	and	of	statements that	are	contingent	but	a priori	-	e.	g.,	(6).	The	former	are	members	of either	NEA	or	NES,	depending	on	whether	they	are	classified	as	analytic	or	synthetic.	The	latter	are	members	of	either	CAA	or	CAS. (5)	Water	is	H2O. (6) The Standard Meter Bar is one meter long, if anything	is.6 4. See	(Hintikka,	1962;	1963),	(Kitcher,	1983,	30)	and	(Burge	1988)	for	rational reconstructions	of	the	cogito	argument	that	shed	light	on	how	(3)	might	acquire	a	CAS	status. 5. For	Hume, (3) is instead	known	empirically,	via introspection,	making it a CES	statement. 6. I	add	an	'if	anything	is'	clause	to	cover	reference-failure	that	Kripke	doesn't include,	although	see	(Kripke,	1980,	110).	Evans' (1982,	31) 'Julius invented the	zip'	example	would	serve	just	as	well	as	(6),	as	would	similar	examples due	to	Swinburne	(1975,	234,	243). douglas	ian	campbell The Eightfold Way philosophers'	imprint – 4 – vol.	17,	no.	25	(december	2017) for constructing	members	of the remaining	categories. §3 considers the	proper framing	of the	analytic/synthetic	distinction.	§4	presents the	case	for	thinking	NAS	statements	exist.	§5	and	§6	do	likewise	for NEA	and	CAA	statements.	§7	wraps	things	up. 2. Conjunction and disjunction My argument for octopropositionalism hinges on the following ‟trumping	rules",	which	to	the	best	of	my	knowledge	have	heretofore gone	unnoticed	in	the	literature	on	the	three	modal	dichotomies:8 The conjunctive rules T1. In	a	conjunction	of two	truths,	p and q,	contingency trumps	necessity,	in	the	sense	that	if	either	p or q	is	contingent,	then	'p∧q'	is	contingent	too. T2.	In	a	conjunction	of	two	truths,	p and q,	empiricalness trumps apriority, in the sense that if either p or q is empirical,	then	'p∧q'	is	empirical	too. T3. In	a conjunction	of two truths,	p and q, syntheticity trumps	analyticity,	in	the	sense	that	if	either	p or q is synthetic,	then	'p∧q'	is	synthetic	too. The disjunctive rules T4.	In	a	disjunction,	necessity	trumps	contingency,	in	the sense that if either p or q	is	necessary,	then	'p∨q'	is	necessary	too. T5.	In	a	disjunction,	apriority	trumps	empiricalness,	in	the sense that if either p or q is a priori,	then	'p∨q'	is	a priori	too. 8. For	example,	they	are	not	discussed	by	(Swinburne,	1975),	(G.	Russell,	2008) or	(Juhl	&	Loomis,	2010). discoveries	about	statements	like	(5)	and	(6)	have	been	important.	In demonstrating	that	empirical	necessities	and	a priori	contingencies	are possible,	Kripke	showed	the	danger	in	the	common	practice	of	treating apriority as a reliable guide to	necessity and	vice versa. If octopropositionalism	were	correct,	then	the	same	lesson	would	apply	with absolute	generality:	no modal attribute of a statement would be a reliable guide to any other.	This	wouldn't	entirely	debar	us	from	appealing to	heuristics	such	as	'if	a	statement	is	synthetic,	then	it	is	empirical'	or 'if	a	statement	is	necessary,	then	it	is	analytic'.	But	it	would	mean	that such	heuristics	would	need	always to	be treated	with	caution	and	a careful	eye	to	known	classes	of	counterexamples. The	truth	of	octopropositionalism	would	also	have	major	implications with regards to the proper understanding of entailment. Three species	of	entailment	can	be	distinguished,	as	follows:7 φ	metaphysically	entails	ψ	iff	φ⊃ψ	is	necessary. φ	epistemically	entails	ψ	iff	φ⊃ψ	is	a	priori. φ	semantically	entails	ψ	iff	φ⊃ψ	is	analytic. Because	octopropositionalism implies that none	of the three	modal dichotomies	is	a	reliable	guide	to	any	other,	it	also	implies	that	none	of these	three	species	of	entailment	is	a	reliable	guide	to	any	other.	For	instance,	if	φ⊃ψ	were	empirical	but	analytic,	then	φ	would	semantically entail	ψ	without	epistemically	entailing	it.	Or	if	φ⊃ψ	were	necessary but	synthetic,	then	φ	would	metaphysically	entail	ψ	without	semantically	entailing	it.	And	so	on,	for	every	pairing	of	the	different	species of	entailment.	Octopropositionalism	therefore	has	the	upshot	that	the three	entailment	relations	are	completely	separable	and	distinct. Overview.	§2	explains	the	strategy	I	use	to	argue	for	octopropositionalism	-	a	strategy	which	involves	showing	that	NAS,	NEA	and CAA statements	exist,	and	then	using	these	statements	as	"raw	ingredients" 7. I	owe	this	point	in	part	to	(Pollock,	1974,	300). douglas	ian	campbell The Eightfold Way philosophers'	imprint – 5 – vol.	17,	no.	25	(december	2017) Table	2	does	the	same	for	disjunctions	(with	the	operative	trumping rules	being	T4,	T5	and	T6): Table 2. How	the	modal	categories	of	p and q determine the modal	category	of	p∨q. Tables	1	and	2	have	been	constructed	by	simply	applying	the	relevant trumping	rules	to	each	pair	of	‟parent"	statements,	in	order	to	deduce the	modal	status	of	the	"child"	statement. Most entries in these tables are (relatively) uninteresting for one or both	of	these	reasons: (a)	The	"child"	statement	obtained	by	conjoining	or	disjoining p with q	belongs	to	the	same	modal	category	as either p or q.	For	instance,	conjoining	an	NAS	statement with	an	NES	statement	merely	yields	another	NES	statement,	getting	us	nowhere. (b)	The	"child"	statement	is	a	Humean	NAA	or	CES	statement, of which bountiful uncontroversial examples already	exist. Entries	in	Table	1	which	are	not	"uninteresting"	for	either	of	these	reasons	are	indicated	in	bold.	There	are	only	three	of	them,	and	they	say the	following: T6. In a disjunction, analyticity trumps syntheticity, in the sense that if either p or q is analytic, then 'p∨q' is analytic	too.9 For	example,	let	p	be	any	contingent	truth.	Since	p	is	contingent,	it	is possible for p to	be	false.	Thus,	it is	possible	for	p∧q to be false, irrespective	of	whether	q	is	necessary	or	contingent	(p∧q being false if p is).	And	so,	p's	status	as	a	contingent	truth	is	inherited	by	p∧q.	In	short, contingency trumps necessity within conjunctions, which is what T1	says. T2–T6	are	easily	confirmed	using	similar	examples. Table	1	shows,	for	any	pair	of	truths,	p and q,	how	the	modal	category that p∧q	belongs	to	is	determined	by	which	categories	p and q belong	to.	The	operative	trumping	rules	are	T1,	T2	and	T3. Table 1.	How	the	modal	categories	of	p and q determine the modal	category	of	p∧q. 9. The conjunctive rules contain	a clause, 'of two truths', that the	disjunctive rules	lack.	The	clause	is	included	in	order	to	exclude	certain	problematic	cases	(e.	g.,	as	when	q=¬p)	from	the	scope	of	the	conjunctive	rules. douglas	ian	campbell The Eightfold Way philosophers'	imprint – 6 – vol.	17,	no.	25	(december	2017) Recipe 1. Start with "raw ingredients" consisting of: (i) any NAS statement;	(ii)	any	NEA	statement;	and	(iii)	any	CAA	statement.	Then construct	a	‟full	house"	as	follows: NAA:	NAS∨NEA	(by	Rule	10) NAS:	-raw	ingredientNEA:	-raw	ingredientNES:	NAS∧NEA	(by	Rule	1) CAA:	-raw	ingredientCAS:	NAS∧CAA	(by	Rule	2) CEA:	NEA∧CAA	(by	Rule	3) CES:	NAS∧NEA∧CAA	(by	Rule	4) Recipe 2. Start	with	"raw	ingredients"	consisting	of:	(i)	any	NES	statement;	(ii)	any	CAS	statement;	and	(iii)	any	CEA	statement.	Then	construct	a	"full	house"	as	follows: NAA:	NES∨CAS∨CEA	(by	Rule	9) NAS:	NES∨CAS	(by	Rule	6) NEA:	NES∨CEA	(by	Rule	7) NES:	-raw	ingredientCAA:	CAS∨CEA	(by	Rule	8) CAS:	-raw	ingredientRule	1:	NAS∧NEA=NES Rule	2:	NAS∧CAA=CAS Rule	3:	NEA∧CAA=CEA Table	1	also	implies	the	following	pair	of	rules	for	creating	CES	statements	(both	of	which	turn	out	to	be	marginally	useful): Rule	4:	NAS∧NEA∧CAA=CES Rule	5:	NES∧CAS=CES There	are	likewise	three	"interesting"	entries in	Table	2, indicated	in bold,	which	say: Rule	6:	NES∨CAS=NAS Rule	7:	NES∨CEA=NEA Rule	8:	CAS∨CEA=CAA Table	2	also	gives	us	these	two	rules	for	creating	NAA	statements: Rule	9:	NES∨CAS∨CEA=NAA Rule	10:	NAS∨NEA=NAA Putting	all these rules together,	we	obtain two "recipes"	by	which	a "full	house"	of	all eight types	of statements	can	be	constructed from only	three	"raw	ingredients". douglas	ian	campbell The Eightfold Way philosophers'	imprint – 7 – vol.	17,	no.	25	(december	2017) necessary to	show	that	condition	C2	obtains,	which	would	(in	part) require	demonstrating	the	existence	of	some	CEA	statement.	As	noted in	§1,	however,	plausible	examples	of	CEA	statements	are	decidedly thin	on	the	ground.	For	this	reason,	Recipe	2	is	unlikely	to	be	viable. Recipe	1 (which	uses	Rule	3 to	construct	CEA	statements from	NEA and	CAA	ingredients)	will	therefore	be	the	focus	from	now	on. On the	assumption that (4), (5) and (7) are	NAS,	NEA	and	CAA statements,	respectively,	Recipe	1	enables	all	eight	modal	categories	to be	filled	as	follows:11 NAA:	Causation	exists,	or	water	is	H2O. NAS:	Causation	exists. NEA:	Water	is	H2O. NES:	Causation	exists,	and	water	is	H2O. CAA:	I	am	here	now. CAS:	Causation	exists,	and	I	am	here	now. CEA:	Water	is	H2O,	and	I	am	here	now. CES: Causation exists, and water is H2O, and I am here	now. For	the	reader	who	is	happy	to	accept	that	(4),	(5)	and	(7)	are	indeed NAS,	NEA	and	CAA	statements,	that	completes	my	argument	for	octopropositionalism.	But for	readers	sceptical that	(4), (5)	and	(7)	are correctly	so-pigeonholed	(probably,	most	readers),	I	need	to	say	more by	way	of	showing	that	each	of	Recipe	1's	raw	ingredients	is	obtainable. 11. Here	I	use	(7),	rather	than	(6),	as	a	CAA	statement.	The	choice	is	arbitrary. CEA:	-raw	ingredientCES:	NES∧CAS	(by	Rule	5)10 Let	conditions	C1	and	C2	be	defined	as	follows: C1:	NAS,	NEA	and	CAA	statements	exist. C2:	NES,	CAS	and	CEA	statements	exist. If	C1	obtains,	then	all	eight	modal	categories	can	be	filled	using	Recipe 1,	so	octopropositionalism	is	true.	Likewise,	if	C2	obtains,	then	all	eight categories	can	be	filled	using	Recipe	2,	so	octopropositionalism	is	true. Hence	octopropositionalism	can	be	defended	either by showing that C1	obtains	or	by	showing	that	C2	obtains.	Whoever	denies	octopropositionalism must deny both	that	C1	obtains	and	that	C2	obtains. Notice the dramatic shift in burdens of proof that has just been achieved. It might have been thought that an octopropositionalist must	argue	independently	for	the	existence	of	each	of	the	eight	different	types	of	statement.	This	would	provide	her	opponent	with	eight independent	lines	of	possible	resistance.	But	it	has	just	been	shown that in practice the octopropositionalist only needs to demonstrate that three categories of statements exist, for she can then	use these three	to	construct	the	other	five.	Moreover	she	even	has	a	choice	as	to which	three	raw	ingredients	to	start	with:	NAS,	NEA	and	CAA,	if	she uses	Recipe	1,	or	NES,	CAS	and	CEA,	if	she	uses	Recipe	2. That's the	good	news for the	octopropositionalist.	The	bad	news is that	one	of these two	ways	of	proceeding can	be	almost immediately	discounted.	In	order	to	be	able	to	use	Recipe	2,	it	would	first	be 10. In practice it is obviously not necessary to construct	NAA and	CES statements	using	the	methods	contained	in	Recipes	1	and	2,	since	uncontroversial examples	of	such	statements	are	easily	found,	such	as	(1)	and	(2).	The	rules used	to	construct	these	statements	-	namely,	Rules	4,	5,	9	and	10	-	are	therefore	of	much	less	interest	and	importance	than	the	remaining	rules	-	Rules	1, 2,	3,	6,	7	and	8. douglas	ian	campbell The Eightfold Way philosophers'	imprint – 8 – vol.	17,	no.	25	(december	2017) analyticity,	making	Analyticity	Entails	Necessity	true	(and	octopropositionalism	false)	by	brute	definitional	fiat.13 Importantly, Kant did not	argue	for	Analyticity	Entails	Apriority	or Analyticity	Entails	Necessity	by	proposing	a	trivializing	definition	of analyticity. In	defining	analyticity,	he focused	specifically	on	affirmative	predicate-subject	statements	of	the	form	R(s).	In	his	words,	‟Analytic	judgments	say	nothing	in	the	predicate	except	what	was	actually thought	already in the	concept	of the	subject, though	not	so	clearly nor	with	the	same	consciousness"	(2004,	16).	That	is,	R(s)	is	analytic for	Kant	iff	R	is	contained	in	the	concept	of	s.	This	characterization	of analyticity	doesn't	make	it	true	by definition	that	analytic	statements	are necessary	and/or	a priori.	And	so,	at	least	for	Kant,	Analyticity	Entails Apriority	and	Analyticity	Entails	Necessity	do	not	themselves qualify as analytic judgements. (One can't discover that an analytic statement must	be	necessary	or	that	it	must	be	a priori	just	by	unpacking	Kant's definition	of	'analytic'.) Why then	does	Kant think	Analyticity	Entails	Apriority and	Analyticity	Entails	Necessity	are	true,	if	not	because	they	are	analytically true?	In	arguing	for	Analyticity	Entails	Apriority,	he	writes,	‟[I]t would be	absurd	to	ground	an	analytic	judgment	on	experience,	since	I	do not need to go	beyond	my concept at all in order to formulate the judgment,	and	therefore	need	no	testimony	from	experience	for	that" (1998,	B11).	Here	he	is	making	the	following	tacit	assumption: K1. The meaning (and thus the full truth-conditional import) of a concept, or of a thought, is accessible to a priori reflection. If R(s)	is	analytic,	then	K1	implies	that	a priori reflection	will	be	able	to detect	that	this	is	so	(i.	e.,	a priori	reflection	will	be	able	to	detect	that the	predicate,	R,	is	contained	in	the	idea	of	the	subject,	s),	from	which it follows that a priori	reflection	will	be	able	to	determine	that	R(s) is 13. See	(Casullo,	1992)	for	a	critique	of	other	trivializing	definitions	of	analyticity, as	given	by	Quinton	(1963)	and	Swinburne	(1975). To	do	this	I	will	begin	by	arguing	for	a	certain	position	regarding	the proper	framing	of	the	analytic/synthetic	distinction. 3. On the analytic/synthetic distinction The	analytic/synthetic	distinction	was	coined	by	Kant,	who	took	the following	pair	of	doctrines	to	be	true: Analyticity Entails Apriority: All analytic statements are a priori. Analyticity Entails Necessity: All analytic statements are	necessary. If	either	of	these	doctrines	is	indeed	true,	then	octopropositionalism is	false	(for	Analyticity	Entails	Apriority	implies	that	neither	NEA	nor CEA	statements	exist,	while	Analyticity	Entails	Necessity	implies	that neither	CAA	nor	CEA	statements	exist).	One	way	of	arguing	for	Analyticity	Entails	Apriority	or for	Analyticity	Entails	Necessity, and	of thereby arguing against	octopropositionalism,	would	be	by	adopting what	I	will	call	a	trivializing definition	of	analyticity.	By	this	I	mean	a	definition	which	builds	the	notion	of	apriority	and/or	of	necessity directly into the notion of analyticity, thereby, in	effect,	making it	analytic that octopropositionalism is false.	For	example,	Kripke	provides	a trivializing	definition	when	he	writes:12 [L]et's make it a matter of stipulation that an analytic statement is, in some sense, true by virtue of its meanings and true in all possible words by virtue of its meaning.	(Kripke, 1980,	39,	my	italics.) This	is	a	trivializing	definition	because	it	builds	the	notion	of	necessity (i.	e.,	of	being	true in	all	possible	worlds)	directly into the	notion	of 12. Kripke	later	acknowledges	that	analyticity	might	instead	be	defined	in	a	way that enables certain contingent statements, like (6), to count as ‟analytic" (1980,	122n). douglas	ian	campbell The Eightfold Way philosophers'	imprint – 9 – vol.	17,	no.	25	(december	2017) AnSyn1:	A	statement	is	"analytic"	iff	it	is	true	in	virtue	of meaning	alone.	Otherwise	it	is	"synthetic". AnSyn1	is	imprecise.	Three	ambiguities	that	need	resolving	are	these: 1.	AnSyn1	mentions	a	statement's	being	‟true"	in	virtue	of	meaning alone.	But	is	the	truth-value	in	question	the	statement's	truth-value	in the actual world	(the	world	we	inhabit	and	experience)	or	its	truth-value at all possible worlds?14	Depending	on	the	answer,	AnSyn1	unpacks into	either	AnSyn2	or	AnSyn3: AnSyn2:	A	statement	is	"analytic" iff	it is	actually	true	in virtue	of	meaning	alone.	Otherwise	it	is	"synthetic". AnSyn3:	A	statement	is	"analytic"	iff	it	is	necessarily	true (i.	e., true in all possible worlds) in virtue of meaning alone.	Otherwise	it	is	"synthetic". Notice	that	AnSyn3	is	a	trivializing	definition,	for	it	defines	analyticity as a subspecies of necessity. If Kant had intended the analytic/synthetic distinction to	be	understood along the lines	of	AnSyn3, then he	wouldn't	have	needed	to	rely	on	K1	and	K2	in	order	to	argue	for Analyticity	Entails	Necessity.	This	being	so,	we	must	endorse	AnSyn2, not AnSyn3, if we are to honor Kant's usage of the terms 'analytic' and	'synthetic'. 2.	Kripke's	and	Putnam's	examples	are	sometimes	taken	as	showing that	there	are	two	kinds	of	meaning	associated	with	a	statement,	these being:	(i)	a	narrow meaning	that	is	fully	accessible	to	a priori	reflection but	which sometimes falls short of determining a statement's truthvalue at a possible world; and (ii) a wide meaning that is sometimes inaccessible	to	a priori	reflection,	but	which	is	fully	capable,	all	by	itself, of	determining	a	statement's truth-value	at	a	possible	world	(Brown, 2016).	AnSyn2	(like	AnSyn1,	from	which	it	is	descended)	mentions	the ‟meaning"	associated	with	a	statement,	but	without	specifying	which 14. G.	Russell	(2008,	41,	52–57)	notes	the	same	ambiguity. true.	K1	therefore	implies	that	any	analytic judgement	will	be	knowable a priori,	just	as	Analyticity	Entails	Apriority	says. Kant's argument for	Analyticity	Entails	Necessity is	more complicated.	It	depends	on	K1	together	with	K2: K2.	Apriority	entails	necessity. Together	K1	and	K2	support	Analyticity	Entails	Necessity:	for	since	K1 implies	that	analytic	statements	must	be	a priori	while	K2	implies	that	a priori	statements	must	be	necessary,	they	jointly	imply	that	all	analytic statements	must	be	necessary,	just	as	Analyticity	Entails	Necessity	says. (Why	does	Kant	think	K2	is	true?	The	answer	doesn't	really	matter	for my purposes, but Kant's thought	was that judgements about necessity	could	not	be	empirical	and	must	therefore	be	triggered	by	judgements	about	apriority.	For	example,	he	writes:	"Experience	teaches	us, to	be	sure, that	something	is	constituted	thus	and	so,	but	not that it could	not	be	otherwise.	[Thus]	if	a	statement	is	thought	along	with	its necessity,	it	is	an	a priori judgment"	[1998,	B3].) K1 and	K2 are substantive, non-trivial, synthetic doctrines about the relation	between	meaning, rationality and	possibility.	This is revealed	by	the	fact	that	received	opinion	nowadays	is	that	they	are	false. Both	were	accepted	as	self-evidently	correct	by	philosophers	for	two centuries	after	the	Critique of Pure Reason's	publication,	until	-	to	universal astonishment	-	Putnam (1973) demolished K1 with his Twin Earth	thought	experiment	and	Kripke	(1980)	demolished	K2	with	his arguments in Naming and Necessity.	More	will	be	said	about	Putnam's and	Kripke's results	below.	For	now, the important	point is just that Kant,	innocent	as	he	was	of	Putnam's	and	Kripke's	ideas,	took	both	K1 and	K2	to	be	true,	and	it is	for	this	reason	-	and	not	because	of	any trivializing	definitional	stipulation	on	his	part	-	that	he	endorsed	both Analyticity	Entails	Apriority	and	Analyticity	Entails	Necessity. With this	point in	mind, let's turn to the	question	as to	how the analyticity/syntheticity	distinction	should	be	framed.	It	is	traditionally framed	as	follows: douglas	ian	campbell The Eightfold Way philosophers'	imprint – 10 – vol.	17,	no.	25	(december	2017) All	analytical judgments rest	entirely	on the law	of	contradiction.... For since the predicate of an affirmative analytical	judgment	is	already	thought	beforehand	in	the concept	of	the	subject,	it	cannot	be	denied	of	that	subject without	contradiction.	(2004,	17) And	so	it	appears	that	Kant	would	have	us	precisify	AnSyn5	as	follows: AnSyn6:	A	statement	is	"analytic"	iff	its	being	actually	true is	deducible,	via	LNC,	from	its	wide	meaning	alone.	Otherwise	it	is	"synthetic". However,	Kant is	being	a little	careless	here.	Suppose	p is	contradictory. LNC allows us to infer, on this basis, that p is false. But LNC doesn't	allow	us	to	get	from	the	falsity	of	p	to	the	conclusion	that	¬p is (analytically)	true.	This	step	instead	requires	the	use	of	another	fundamental law of thought - namely, the Law of the Excluded Middle (LEM), the	principle	that	every	statement	is	either	true	or	false.	LEM	is just as	important	as	LNC	within	the	deduction	of	¬p.	Making	this	explicit brings	us	to	AnSyn7: AnSyn7:	A	statement	is	"analytic"	iff	its	being	actually	true is	deducible,	via	LNC	and	LEM, from its	wide	meaning alone.	Otherwise	it	is	"synthetic". In	Kant's time	both	LNC	and	LEM	were	uncontroversial.	Nowadays, however, LEM is denied by constructivists and LNC by paraconsistentists, and	so	AnSyn7 rests	on	assumptions	about	deductive logic that	are	vigorously	contested.	Fortunately,	we	can	frame	the	analytic/ synthetic distinction in a way which avoids these controversial assumptions	about	the	foundational	principles	of	logic	by	simply	remaining silent	as	to	which	principles	a	sound	deductive	logic	will	use	-	as follows: AnSyn8:	A	statement	is	"analytic"	iff	its	being	actually	true kind	of	meaning	is	relevant	-	narrow	or	wide.	It	can	therefore	be	precisified	to	yield	either	AnSyn4	or	AnSyn5: AnSyn4: A statement is "analytic" iff it is actually true in virtue of its narrow meaning alone. Otherwise it is "synthetic". AnSyn5:	A	statement	is	"analytic"	iff	it	is	actually	true	in	virtue of its wide	meaning	alone.	Otherwise	it	is	"synthetic". According	to	AnSyn4,	the	kind	of	"meaning"	relevant	to	analyticity	is narrow	meaning,	which	just is the	kind	of	meaning	accessible	to	a priori reflection.	This	turns	analyticity	into	a	subspecies	of	apriority	as	a matter	of	definitional	stipulation,	making	Analyticity	Entails	Apriority trivial.	Thus,	AnSyn4	is	(like	AnSyn3)	a	trivializing	definition.	If,	when Kant	framed	the	analytic/synthetic	distinction,	he	had	had	something like	AnSyn4 in	mind, then	he	would	not	have	needed to rely	on	K1 to	argue for	Analyticity	Entails	Apriority. Indeed, it is	perfectly	clear that he can't have	had	AnSyn4	in	mind,	since	the	idea	that	statements have	a	"narrow	meaning"	in	addition	to	their	wide	meaning	occurred to	philosophers	only	after	Kripke's	and	Putnam's	discoveries	(and	remains	controversial	even	now).	It	would	be	anachronistic	to	attribute to	Kant	anything	similar	to	AnSyn4.	And	so,	if	we	are	to	respect	Kant's usage	of	the	terms	'analytic'	and	'synthetic',	we	should	choose	AnSyn5 in	preference	to	AnSyn4.15 3.	AnSyn5	(like	AnSyn1	and	AnSyn2,	from	which	it	is	descended) speaks of a statement being true in virtue of meaning alone.	How	precisely	are	the	italicized	parts	of	this	statement	to	be	understood?	For Kant,	the	answer	is	that	a	statement	is	an	analytic	truth	if	it	can	be	logically	deduced	by	what	he	calls	the	‟Law	of	Contradiction"	-	this	being the	principle,	now	more	commonly	known	as	the	Law of Non-Contradiction	(LNC),	that all contradictions are false.	For	instance,	he	writes: 15. If the notion of ‟narrow	content" is	ultimately incoherent (Stalnaker, 1989, 1990,	2008;	Wilson,	1995),	then	this	provides	another,	even	quicker	reason	to opt	for	AnSyn5. douglas	ian	campbell The Eightfold Way philosophers'	imprint – 11 – vol.	17,	no.	25	(december	2017) which	fundamental	laws	of	thought	are	sound,	it	yields	the	result	that (8)	is	analytic. The	problem	is	simply	that	this	classification	appears	incorrect.	The essential point here has been made many times down the ages - by Aristotle (Metaphysics,	IV,	4),	Leibniz	(1973,	93),	Carroll	(1895),	Frege (1964,	15)	and	Russell	(1912,	72),	among	others:	viz.,	logic	can't	lift	itself by	its	own	bootstraps;	it	can't	validate	its	own	foundational	principles except	on	pain	of	vicious	circularity.17	All	logical	analysis	presupposes certain	foundational	laws	of	thought,	such	as	LNC,	LEM	and	modus ponens,	and	these	are	therefore	not	themselves	susceptible	of	being	logically	proved.	Statements, like	(8),	that	assert	the	soundness	of	these laws	of	thought	are	hence	"pre-analytic".	Their	truth	must	be	assumed before	we	can	even	begin	to	make	sense	of	there	being	such	things	as ‟analytic	truths"	in	the	first	place.	Since	they	are	pre-analytic,	they	are not	analytic,	which	makes	them	synthetic. If	further	evidence	is	wanted	for	thinking	(8)	should	be	classified as	synthetic, it	can	be	obtained	by	noticing that (8)	seems	to	fit the bill	perfectly	for	being	a	Kantian	a priori	synthetic	truth.	Is	(8)	knowable a priori?	It	would	certainly	seem	so,	for	deductive	logic	is	a	source of a priori	knowledge	if	anything	is,	and	deductive	logic	assumes	the truth	of	(8).	(If	(8)	were	false,	then	deductive	logic	-	whether	classical, constructive	or	paraconsistent	-	could	not	be	trusted	to	yield	true	conclusions	from	true	premises.)	This	being	so,	(8)'s	status	as	an	a priori truth	must	be	at	least	as	secure	as	the	a priori	status	of	any	deductively proved	result	-	which	is to	say,	as	secure	as	could	ever	be.	But	how can	(8)	be	a priori,	given	it	cannot	be	logically	proved	without	begging the question? Kant held that a priori synthetic truths are	known	via a special kind of deduction	-	a transcendental deduction - that draws on	rational insights	into	the	limits	of	possible	experience	and	imagination.	According	to	Kant,	φ will be a priori	and	yet	synthetic if	φ is not	provable	by	logic	(i.	e.,	it	is	not	analytic)	but	if	the	rational	mind can	recognize	of	itself	that	it	is	incapable	of	coherently	perceiving	or 17. For	a	more	recent	discussion,	see	(Boghossian, 1997, 339, 345–350). is	deducible,	via sound logical	principles, from its	wide meaning	alone.	Otherwise	it	is	"synthetic". AnSyn8	has	the	virtue	of	letting	two	questions	be	separated.	The	first question	is	how	analyticity	should	be	defined.	AnSyn8	follows	Kant's lead	by	defining analyticity in terms	of	what can	be	deduced	using sound	principles	of logic.	The	second	question	concerns	what	these "sound	principles	of	logic"	are.	AnSyn8	refers	to	such	principles	without specifying	their	identity.	There	is	therefore	room	for	classical	logicians, constructivists and paraconsistentists to agree in accepting	AnSyn8 even	while	diverging	radically	in	their	answers	to	the	second	question. A	problem	remains.	Consider	(8): (8) At least one of the following logical principles is sound:	LEM,	LNC	or	modus ponens. (8)	makes an exceedingly modest claim about the foundations of logic	-	a claim	so	modest it	will	be	accepted	not	only	by classical logicians,	but	also	by	constructivists	and	paraconsistentists.	Constructivists	repudiate	LEM	and	paraconsistentists	repudiate	LNC,	but	it	would be	a	very rare logician indeed	who	would	repudiate	not just	one	of these	fundamental	laws	of	thought,	but	all	of	them,	for	a	"logic"	that endorsed	neither	LEM	nor	LNC	nor	modus	ponens	would	be	so	weak as	to	be	inferentially	useless.16	Because	all	reputable	logics	assume	at least	one	of	these	principles,	the	truth	of	(8)	is	trivially	provable	in	all such	logics,	by	simply	invoking	the	laws	themselves	-	the	very	laws whose truth is in question. Such a proof is obviously	worthless for persuasive	purposes,	since	it	presupposes	what	is	being	proved,	but AnSyn8 doesn't prohibit viciously circular deductions. For this reason,	when	AnSyn8	is	combined	with	any	remotely	tenable	view	about 16. In	the	unlikely	event	of	a	coherent	and	useful	new	logic	being	proposed	that disclaimed	LNC	and LEM	and modus ponens, my overall point would still stand, since	I	could	simply	further	weaken	(8)	by	adding	to	the	disjunction	a	principle	that	the	new	logic	relies	on. douglas	ian	campbell The Eightfold Way philosophers'	imprint – 12 – vol.	17,	no.	25	(december	2017) laws that "it seems	to	me	an	attempt to jump	out	of	one's	own	skin against	which	I	can	do	no	more	than	urgently	warn	them"	(1964,	15). In	order	to	capture	the	idea	that	(8)	is	synthetic	rather	than	analytic, we need	merely	modify AnSyn8 by including a prohibition against question-begging logical deductions.	The	result	is	AnSyn9: AnSyn9:	A	statement	is	"analytic"	iff	its	being	actually	true is	deducible,	via	non-question-begging	use	of	sound	logical	principles,	from	its	wide	meaning	alone.	Otherwise	it is	"synthetic". AnSyn9	has	the	following	important	virtues: 1.	It	is	fully	consistent	with	the	traditional	formulation	of the	analytic/synthetic	distinction	-	namely,	AnSyn1	-	because	it	is	merely	a	disambiguated	version	of	AnSyn1. 2. For reasons just explained, it disambiguates AnSyn1 in a way that appears to honor Kant's linguistic intentions. Since Kant both coined the analytic/synthetic distinction and made groundbreaking use of it in his own	hugely influential	philosophical system,	one	could break	usage	with	Kant and	use the terms 'analytic' and 'synthetic' at cross-purposes to him only at the price of introducing unwonted muddle and confusion into philosophical	language. I	will	now	attempt	to	show	that	each	of	Recipe	1's	raw	ingredients exists.	My	arguments	will	assume	that	AnSyn9	is	an	adequate	formulation	of	the	analytic/synthetic	distinction. 4. Why NAS statements exist Kant	reputedly	showed	long	ago	that	NAS	statements	(which	are	necessary, a priori and	synthetic)	exist.	He	provided	many	examples,	including	(4).	Matters	might	just	be	left	there.	But	some	of	Kant's	examples conceiving	any	state	of	affairs that	would falsify	or	contradict	φ. (8) fulfills	this	condition.	We	find	that	the	rational	mind	can	only	coherently imagine,	experience	and	conceive the	world	as	conforming to such laws	of thought	as	LNC,	LEM	and	modus ponens.	From	this	we draw	the	conclusion	that	the	world	we	cognize	and	experience	must itself	be	such	a	world	-	i.	e.,	a	world	where	(8)	is	true.	In	other	words, the	rational	mind	finds	itself imprisoned	in	certain	ways	of	thinking, imagining and experiencing, with logic being, so to speak, the science	that	studies	the	bars	of	its	prison.	Any	world	that	a	rational	mind coherently	imagines	or	experiences	must,	for	this	reason,	be	a	world where	the	ways	of	thinking	that	logic	describes	hold	good,	which	is	to say,	a	world	where	(8)	is	true.	This	is	a	transcendental	deduction:	the rational	mind	shows	(8)	to	be	an	a priori	truth	by	reflecting	on	its	own inability	to	imagine	or	conceive	a	counterexample	to	(8). This	idea	-	that	the	laws	of	thought	are	known	via	a	transcendental deduction	-	was	not	explicitly	defended	by	Kant,	but	was	defended by	Schopenhauer: It	is	by	means	of	a	kind	of	reflection	which	I	am	inclined to	call	Reason's	self-examination,	that	we	know	that	[the laws	of	thought,	including	the	LNC	and	LEM]	express	the conditions	of	all	thinking,	and	therefore	have	these	conditions	for	their	reason.	For,	by	the	fruitlessness	of	its	endeavors to think in opposition to these laws, our Reason acknowledges them	to	be the	conditions	of	all	possible thinking:	we then	find	out, that it is just as impossible to think in opposition to them, as it is to move the members of our body in a contrary direction to their joints. (1974,	128) Frege	also	gestures	at	the	transcendental	nature	of	(8)	when,	after	noting	that	the	laws	of	thought	cannot	be	proved	by	logic	without	circularity, he writes of people who would question the soundness of these douglas	ian	campbell The Eightfold Way philosophers'	imprint – 13 – vol.	17,	no.	25	(december	2017) described	by	deductive	logic,	and	so,	in	part,	by	(8).	As	Wittgenstein put it, ‟The	truth	is,	we	could	not	even	say of an 'unlogical' world how it	would	look"	(1922,	§3.031).	In	virtue	of	the	mind	having	these	imaginative	limits,	(8)	must	be	true,	not	just	in	the	world	we	experience,	but also	in	every	world	a	rational	mind	can	coherently	conceive	or	imagine - making it not just actually true but also necessarily	true. Finally,	is	(8)	analytic	or	synthetic?	We	saw	above	that	AnSyn9	implies	it is	synthetic.	We	also	saw	that	there	are	various	powerful	reasons	to	think	this	is	the	correct	classification.	Viz.,	(8)'s	truth	must	be assumed	before	we	can	make	sense	of	there	being	any	such	things	as analytic	truths	in	the	first	place,	from	which	it	follows	that	(8)	is	preanalytic	(and	thus	synthetic).	Moreover,	our	knowledge	that	(8)	is	true appears	to	have	a	transcendental	source,	just	as	would	be	expected	if it were Kantian a priori	synthetic	knowledge. In	short,	(8)	appears	to	be	necessary,	a priori	and	synthetic	-	making	it	a	NAS	statement. 5. Why NEA statements exist For	an	example	of	an	NEA	statement,	we	need	look	no	further	than	(5): (5)	Water	is	H2O. That	(5)	is	empirical	is	obvious:	'water'	is	a	name	for	the	transparent liquid	that	fills	the	lakes,	rivers	and	oceans	on	Earth.	This	substance might	conceivably	have	turned	out	to	be	something	other	than	H2O when	subjected	to	empirical,	scientific	analysis. That	(5)	is	necessary	was	shown	by	Kripke.	'Water'	is	a	rigid	designator:	it	refers,	in	every	possible	world,	to	whatever	substance	it	refers to	actually. 'H2O'	is	likewise	a	rigid	designator:	it	refers	in	every	possible	world	to	samples	of	a	certain	type	of	molecule,	composed	of	one oxygen	atom	and	two	hydrogen	atoms.	Given	both	'water'	and	'H2O' are rigid designators, and given that, as an empirical	matter of fact, they actually	refer	to	the	same	substance,	it	follows	that	they	co-refer in	every	possible	world	-	i.	e.,	necessarily. have	stood	the	test	of	time	poorly	(e.	g.,	his	claim	that	determinism	is a priori	and	necessary),	and	none	of	his	examples	is	uncontroversial. In	my	view,	(4)	is	a	plausible	example	of	a	NAS	statement.	On	the one hand, (4)'s denial (namely, 'Causation doesn't exist') is pretty clearly	non-contradictory,	making	(4)	synthetic.	But	on	the	other	hand, it	also	seems	that	we	cannot	cognize	or	imagine	a	world	except	as	having	a	causal	structure,	making	(4)	necessary	and	a priori.18 However,	although	(4)	arguably	makes	a	useful	"Exhibit	B"	for	the octopropositionalist,	a	compelling	"Exhibit	A"	is	still	wanted.	The	"Exhibit	A"	I	have	in	mind	is	already	familiar	-	namely,	(8): (8) At least one of the following logical principles is sound:	LEM,	LNC	or	modus ponens. Is	(8)	a priori?	The	answer	is	affirmative,	for	reasons	explained	above. To	recap:	(8)'s	status	as	an	a priori	truth	must	be	at	least	as	secure	as	the a priori	status	of	any	deductively	proved	result	(i.	e.,	as	secure	as	could be),	since	deductive	logic	(whether	classical	or	non-classical)	assumes the	truth	of	(8). Is	(8)	necessary?	(8)	could	fail	to	be	necessary	only	if	it	were	possible for	(8)	to	be	false,	but	deductive	logic	is	our	guide	when	we	judge	what is	possible	and	impossible,	and	(8)	makes	an	extraordinarily	modest claim	about	the	foundations	of	deductive	logic	itself.	In	attempting	to imagine	a	world	where	(8)	is	false,	we	would	be	attempting	to	imagine a world where deductive logic doesn't work, and the idea of there being such	a	(logically)	possible	world	is	an	oxymoron.	We	cannot	imagine such	a	world,	because	our	imaginative	capabilities	have	limits	-	limits 18. Why	necessary?	Because, in	Hume's	words, "It is an established	maxim in metaphysics,	That	whatever	the	mind	clearly	conceives,	includes	the	idea	of possible	existence,	or	in	other	words,	that	nothing	we	imagine	is	absolutely impossible.	We can form the idea	of a golden	mountain, and from thence conclude	that	such	a	mountain	may	actually	exist.	We	can	form	no	idea	of a	mountain	without	a	valley,	and	therefore	regard	it	as impossible"	(Hume, 2000,	§1.2.2).	In	short,	causation's	existence	is	necessary	because	conceivability	and	inconceivability	are	our	guide	to	possibility	and	impossibility	(Chalmers,	2002)	and	because	we	can't	conceive	of	its	non-existence. douglas	ian	campbell The Eightfold Way philosophers'	imprint – 14 – vol.	17,	no.	25	(december	2017) implies	that	'Water	is	H2O'	is	analytic,	the	wide	meaning	of	'water'	being	enough	to	determine	all	by	itself	that	'Water	is	H2O'	is	actually	true (and, indeed, not only actually true, but necessarily	true).19 Chief	among	the	reasons	why	octopropositionalism	appears	prima facie implausible is because	most philosophers remember Kant's famous	argument	against	the	existence	of	analytic	empirical	statements: viz.,	if	a	statement	is	true	in	virtue	of	meaning	alone,	then	a priori reflection	will	be	able	to	detect	that	this	is	the	case,	so	that	analyticity entails	apriority.	This	argument	withers	in	the	face	of	Putnam's	demonstration that ‟meanings ain't in the head" (Rey, 2016, §4.2). It assumes	that	the	meanings	of	one's	words,	and	their	truth-conditional import, are	accessible to	a priori rational reflection (K1, above).	The main	lesson	from	Twin	Earth	is	that	this	assumption	is	wrong.	Oscar and	Toscar	mean	different	things	when	they	say	"water",	but	they	are psychologically	identical	and	so	the	facts	about	what	their	own	words mean	are	cognitively	inaccessible	to	them.	(If	Oscar	could	access	the full	truth-conditional	content	of	his	words	via	rational	reflection,	then (5)	would,	since	it	is	a	necessary	truth,	also	be	an	a priori	truth,	which it	obviously	isn't.) 6. Why CAA statements exist As	mentioned in	§1,	prospective	examples	of	CAA	statements	-	i.	e., statements that are contingent, a priori and analytic	-	include both Kripke's	(6)	and	Kaplan's	(7): (6) The Standard Meter Bar is one meter long, if anything	is. (7)	I	am	here	now. 19. More generally, any statement of the form R(D)=R(E) will be of type NEA, where:	(i)	D and E	are	a	pair	of	non-rigid	definite	descriptions	(like	'the	morning	star'	and	'the	evening	star')	that,	as	an	empirically	discoverable	matter	of fact,	designate	the	same	thing	in	the	actual	world;	(ii)	R(x) rigidly designates whatever is actually designated	by the	definite	description,	x; and (iii) x=y returns at world w	iff	x and y designate the same thing in w. Finally, is (5)	analytic	or	synthetic?	AnSyn9 implies that it is	analytic,	for	reasons	I	will	explain	by	reference	to	Putnam's	‟Twin	Earth" thought experiment. It involves two people	-	Oscar, who inhabits Earth,	and	Toscar,	who	inhabits	another	planet,	Twin	Earth.	Both	use 'water'	to	rigidly	designate	the	substance	that	is	actually	the	dominant transparent	liquid	on	their	own	home	planet.	In	Oscar's	case	this	liquid	is	H2O.	In	Toscar's	case	it	is	a	different	chemical	compound,	'XYZ', which is, however, superficially indistinguishable from H2O. Oscar and Toscar are	molecule-for-molecule doppelgängers of each other, and	hence indistinguishable	with regards to their internal	psychologies.	But	Putnam	points	out	that	their	psychological	similarity	doesn't stop them meaning radically different things when they say, ‟Water is	H2O."	Given	that 'water' is	a	rigid	designator,	the	statement	Oscar makes	when	he	utters	this	sentence	is	a	necessary	truth,	extensionally and	truth-conditionally	equivalent	to	'H2O	is	H2O'.	The	statement	Toscar	makes	is	instead	a	necessary	falsehood,	equivalent	to	'XYZ	is	H2O'. Putnam infers,	on this	basis, that semantic	externalism is true	-	i.	e., that "'meanings'	just	ain't	in	the	head!"	(1973,	704,	his	italics).	That	is, the	proposition	an	utterance	expresses	potentially	depends	not	only on	the	internal	psychology	of	the	person	who	makes	the	utterance,	but also	on	relevant facts	about the	surrounding	environment	-	such	as whether	the	local	watery	stuff	is	H2O,	or	XYZ. As mentioned above, philosophers sometimes distinguish wide meaning from narrow.	Wide	meaning	is	the	kind	of	meaning	that	‟ain't in	the	head",	while	narrow	meaning	is	a	kind	of	meaning	that	is	in	the head.	On	this	way	of	telling	the	story,	when	Oscar	and	Toscar	each	say, "Water	is	H2O",	their	words	have	different wide meanings while sharing the same	narrow	meaning.	We	may	put	the	point	by	saying	that	Oscar and	Toscar	make	different	statements	-	statements	truth-conditionally	equivalent	to	'Water	is	H2O'	and	'Twater	is	H2O'	respectively	-	but that	these	two	statements	are	perfectly	alike	with	respect	to	their	cognitively	accessible	‟narrow	content". Recall	that	according	to	AnSyn9	a	statement	is	analytic	if	its	being actually	true	is	deducible	from	its	wide meaning.	This	being	so,	AnSyn9 douglas	ian	campbell The Eightfold Way philosophers'	imprint – 15 – vol.	17,	no.	25	(december	2017) actually (if not necessarily) true by virtue of meaning (both its narrow meaning	and	its	wide	meaning)	alone.21 The	octopropositionalist	needs	only	one	example	of	a	CAA	statement,	but	in	(6)	and	(7)	she	has	two.22 7. Concluding remarks My	arguments	of	§2	showed	octopropositionalism	must	be	true	if	NAS, CAA	and	NEA	statements	exist,	and	my	arguments	of	§4–6	showed that	each	of	these	three	types	of	propositions	does	indeed	exist.	My conclusion:	octopropositionalism	is	true. In	order	to	reject	octopropositionalism,	one	must	either:	(i)	deny the	soundness	of the	trumping	rules	described	in	§2;	or	(ii)	deny	of both	(4)	and	(8) that they	are	NAS	statements;	or	(iii)	deny	that	(5) is an	NEA	statement;	or (iv)	deny	of	both (6) and (7) that they	are CAA	statements.	Option (i) appears	hopeless.	Options (ii), (iii) and (iv)	would	almost	certainly	involve	denying	that	AnSyn9	adequately characterizes	the	analytic/synthetic	distinction.	But	on	what	grounds might	AnSyn9	be	challenged?	Not	on	the	grounds	that	it	is	inconsistent	with	the	traditional	formulation	of	the	analytic/synthetic	distinction	-	namely,	AnSyn1	-	because	AnSyn9	is	obtained	from	AnSyn1	by disambiguation.	Nor	on	the	grounds	that	in	disambiguating	AnSyn1	I have failed	to	respect	historical	usage,	because in	deriving	AnySyn9 from	AnSyn1	I	have	used	Kant	as	my	guide,	and	Kant	is	the	canonical historical	source. In	arguing	for	octopropositionalism	I	have	relied	on	the	idea	that 21. Kripke	(1980,	122n)	himself	acknowledges	that	a priori	contingencies	like	(6) might	be	counted	as	analytic. 22. More generally, any statement of the form F(D)∨(R(D)=D) will be of type CAA,	where:	(i)	D	is	some	non-rigid	definite	description	that	picks	out	its	referent	by	describing	an	accidental	property	of	the	referent	(like	'the	inventor of	bifocals');	(ii)	F(D)	returns	TRUE	at	world	w	iff	D fails to designate anything in w; (iii) R(D) rigidly designates whatever is actually designated by D; and (iv) x=y	returns	TRUE	at	world	w iff	x and y designate the same thing in w. Similar	examples	of	CAA	statements	can	be	manufactured	on	the	model	of 'It	is	raining	if	it	is	actually	raining'	(as	pointed	out	to	me	by	an	anonymous reviewer). There	are	very	strong	grounds	for	thinking	both	(6)	and	(7)	are	CAA statements.	The	case	for	holding	(7)	to	be	a	CAA	statement	-	as	articulated	by	Kaplan	(1977)	and	G.	Russell	(2008)	-	is	straightforward.	(7) is	contingent	because	although	it	is	actually true that I am here now, counterfactually	I	might	not	have	been:	I	could	have	been	somewhere else	now, instead. (7) is	a priori	because	mere	rational reflection	suffices to	establish that 'I	am	here	now' is (actually) true,	and	no	possible	experience	could	disconfirm	this	claim.20	Finally,	(7)	is	analytic because the	meanings (both	wide and	narrow) of the terms 'I', 'am', 'here' and 'now' suffice by themselves to determine that (7) is actually (albeit not necessarily)	true.	(The	definition	of	'here'	is	such	that	in my	mouth	it	rigidly	designates	the	spatial	location	where	I	actually am now,	so	that in	the	actual	world, if	not in	other	possible	worlds,	the expressions	'here'	and	'where	I	am	now'	must	co-refer.) Next,	(6).	Let's	make	it	a	matter	of	definitional	stipulation	that	'one meter'	is	a	rigid	designator	that	denotes	the	actual	length	of	the	Standard	Meter	Bar.	With	this	stipulation	in	place,	it	is	clear	that	(6)	is	contingent.	There	are,	for	example,	possible	worlds	wherein	the	Standard Meter	Bar	is,	say,	twice as long as	it	is	in	the	actual	world,	which	is	to say, two meters	long.	(6)	will	be	false	in	such	counterfactual	worlds	despite	being	true	in	the	actual	world.	That	(6)	is	a priori	is	also	obvious. Mere	consideration	of	the	foregoing	definition	of	'one	meter'	suffices to establish that if the Standard	Meter Bar exists, then it is	actually (if	perhaps	not	counterfactually)	one	meter	long,	and	thus	that	(6)	is actually	(if	not	always	counterfactually)	true.	(One	needn't	empirically measure	the	length	of	the	actual	Bar	to	determine	its	length	in	meters, the	Bar's	length	being	itself	the	ultimate	arbiter	and	reference	point	for all	such	measurements.)	Finally,	AnSyn9 implies that	(6) is	analytic: for	given	that	we	can	deduce	that	(6)	is	actually	true	by	merely	contemplating	the	above	definition	of	'one	meter',	it	is	obvious	that	(6)	is 20.	This	assumes	that	Descartes	was	right	and	that	one	can	know	a priori that the 'I' exists. If	Descartes	was	wrong	-	i.	e., if	one	can	know	only	via	empirical introspection	that	the	'I'	exists	-	then	(7)'s	status	as	a	CAA	statement	can	be preserved	by	adding	a	reference-failure	clause,	as	follows:	'Either	I	don't	exist, or	I	am	here	now'. douglas	ian	campbell The Eightfold Way philosophers'	imprint – 16 – vol.	17,	no.	25	(december	2017) have	shown	that	Recipe	1	can	be	used	to	construct	logically compound statements belonging in the NAA, NES, CAS, CEA and CES	categories. Which	of	these	categories	can	also	be	filled	with	atomic statements (not manufactured using the trumping rules)?23 Third, octopropositionalism	implies	that	metaphysical,	epistemic	and	semantic	entailment	are not	reliable	guides	to	each	other	(as	explained	in	§1).	For	any	two	of these	three	kinds	of	entailment,	what	are	the	precise	conditions	under which	one	can	come	apart	from	the	other?	Fourth,	the	dichotomy	between truths that are knowable a priori and knowable empirically	can	be turned	into	a	trichotomy	by	also	recognizing	truths	that	are	unknowable (a	plausible	example	being	Goldbach's	conjecture).24 This gives rise to twelve	modal	categories, rather than	the	eight.	Do	all twelve have members?25 Fifth, G. Russell (2008, 56) and Juhl and Loomis (2010,	219)	have	recently	proposed	rival	ways	of	construing	the	analytic/synthetic	distinction.	What	are	the	relative	virtues	and	dis-virtues	of their	proposals	as	compared	with	AnSyn9? These	questions	are	topics	for	future	work.26 References Boghossian,	P.	A.	(1997).	Analyticity.	In	B.	Hale	&	C.	Wright	(Eds.),	A Companion to the Philosophy of Language	(331–368).	Blackwell. Brown, C. (2016). Narrow	Mental Content. In E.	N. Zalta (Ed.),	The Stanford Encyclopedia of Philosophy (Summer	2016).	Metaphysics	Research	Lab,	Stanford	University.	Retrieved	from	https://plato.stanford.edu/archives/sum2016/entries/content-narrow/. Burge,	T.	(1988).	Individualism	and	Self-Knowledge.	Journal of Philosophy,	85(11),	649–663. 23. The	most	difficult	categories	to	fill	with	atomic	statements	appear	to	be	NES and CEA. 24. See	(Swinburne,	1975,	184,	188). 25. Simple	extensions	to	arguments	in	this	paper	yield	an	affirmative	answer. 26.	Many	thanks to the	anonymous	reviewers for their	numerous	constructive suggestions.	Thanks	too	to	Carolyn	Mason,	Tarn	Somervell	Fletcher	and	Michael-John	Turp. Kripke	and	Putnam's	discoveries	show	-	contrary	to	what	Kant	imagined possible	-	that analytic statements can be empirical (i.	e., that Analyticity	Entails	Apriority	is	false)	and	contingent	(i.	e.,	that	Analyticity	Entails	Necessity	is	false).	An	opponent	of	octopropositionalism might	be	tempted	to	insist	that	Analyticity	Entails	Apriority	and	Analyticity	Entails	Necessity	are	not	up	for	negotiation,	and	to	deal	with purported Kripkean and Putnamian counterexamples to Analyticity Entails	Apriority	and	Analyticity	Entails	Necessity (e.	g., (5)	and	(6)) by adopting a trivializing	construal	of	the	analytic/synthetic	distinction, like	AnSyn3	and/or	AnSyn4.	To	borrow	a	line	from	Bertrand	Russell (1919, 72), this is an approach	with ‟many advantages; they are the same	as	the	advantages	of	theft	over	honest	toil".	If	one	redefines	analyticity	to	make	it	a	matter	of	brute	definitional	stipulation	that	no	"analytic"	statement	can	be	contingent	or	empirical,	then,	of	course,	one gets the result that Analyticity Entails Apriority and Analyticity Entails	Necessity	are	true	and	that	octopropositionalism	(so	conceived) is	false.	By	the	same	token,	ornithologists	might	have	saved	the	theory that	all	swans	are	white	when	they	met	their	first	black	swan	by	redefining	'swan'	to	mean	what	was	formerly	meant	by	'white	swan'.	Surely, we should register Kripke's and Putnam's groundbreaking discoveries about	possibility and	meaning	by saying that	Analyticity	Entails Apriority	and	Analyticity	Entails	Necessity	have	turned	out	to	be	false, not	by	moving	the	goalposts	and	redefining	'analyticity'	to	make	Analyticity	Entails	Apriority	and	Analyticity	Entails	Necessity	come	out	as trivially	true.	If	we	are	to	avoid	mutilating	the	meanings	of	the	terms 'analytic'	and	'synthetic'	and	introducing	unwonted	equivocations	into the	language,	then	we	must	respect	Kant's	usage.	And	as	discussed	in §3,	it	appears	clear	that	for	Kant	it	was not	a	matter	of	brute	definitional stipulation that all analytic statements	must	be	a priori, or that they must	be	necessary. My	arguments	in	this	paper	raise	several	questions.	First,	epistemic two-dimensional semantics	provides	a	unified	explanation	of	necessity	and	apriority	(	Chalmers,	2004).	Can	it	be	merged	with	AnSyn9 to	yield	a	unified	explanation	of	all three	modal	distinctions?	Second,	I douglas	ian	campbell The Eightfold Way philosophers'	imprint – 17 – vol.	17,	no.	25	(december	2017) Leibniz, G. (1973). The	Nature of Truth. In	G.	H.	R. Parkinson (Ed.), Leibniz: Philosophical Writings.	Everyman's	Library. Pollock,	J.	(1974).	Knowledge and Justification.	Princeton	University	Press. Putnam, H. (1973). Meaning and Reference. Journal of Philosophy, 70(19),	699–711. Quinton,	A.	(1963).	The	"A Priori"	and	the	Analytic.	Proceedings of the Aristotelian Society,	64(n/a),	31–54. Rey,	G.	(2016).	The	Analytic/Synthetic	Distinction.	In	E.	N.	Zalta	(Ed.), The Stanford Encyclopedia of Philosophy	(Winter	2016).	Metaphysics Research Lab, Stanford University. Retrieved from https://plato. stanford.edu/archives/win2016/entries/analytic-synthetic/. Russell,	B.	(1912).	The Problems of Philosophy.	Oxford	University	Press. Russell,	B.	(1919).	Introduction to Mathematical Philosophy.	Routledge. Russell,	G.	(2008).	Truth in Virtue of Meaning: A Defense of Analytic-Synthetic Distinction.	Oxford	University	Press. Schopenhauer,	A.	(1974).	On the Fourfold Root of the Principle of Sufficient Reason.	Open	Court. Stalnaker,	R.	(1989).	On	What's	in	the	Head.	Philosophical Perspectives, 3(n/a),	287–319. Stalnaker,	R.	(1990).	Narrow	Content.	In	C.	A.	Anderson	&	J.	Owens (Eds.),	Propositional Attitudes: The Role of Content in Logic, Language, and Mind.	. Stalnaker,	R.	(2008).	Our Knowledge of the Internal World.	Oxford	University	Press. Swinburne, R.	G. (1975). Analyticity, Necessity and Apriority. Mind, 84(334),	225–243. Wilson,	R.	A.	(1995).	Cartesian Psychology and Physical Minds: Individualism and the Sciences of the Mind.	Cambridge	University	Press. Wittgenstein, L. (1922). Tractatus Logico-Philosophicus. Dover Publications. Carroll, L. (1895). What the Tortoise Said to Achilles. Mind, 4(14), 278–280. Casullo,	A.	(1992).	Analyticity	and	the	A Priori.	Canadian Journal of Philosophy,	22(sup1),	113–150. Chalmers,	D.	(2012).	Constructing the World.	Oxford	University	Press. Chalmers,	D.	J.	(2002).	Does	Conceivability	Entail	Possibility?	In	T.	S. Gendler	&	J.	Hawthorne	(Eds.),	Conceivability and Possibility (145– 200).	Oxford	University	Press. Chalmers,	D.	J. (2004).	Epistemic	Two-Dimensional	Semantics. Philosophical Studies,	118(1–2),	153–226. Evans,	G.	(1982).	The Varieties of Reference.	Oxford	University	Press. Frege,	G.	(1964).	The Basic Laws of Arithmetic.	University	of	California Press. Harman,	G.	(1973).	Thought.	Princeton	University	Press. Harman,	G.	(1996).	Analyticity	Regained?	Noûs,	30(3),	392–400. Hintikka,	J.	(1962).	Cogito,	Ergo	Sum:	Inference	or	Performance?	Philosophical Review,	71(1),	3–32. Hintikka, J. (1963). Cogito, Ergo Sum as an Inference and a Performance.	Philosophical Review,	72(4),	487–496. Hospers, J. (1967).	An Introduction to Philosophical Analysis (2nd ed.). Routledge	and	Kegan	Paul. Hume,	D.	(2000).	A Treatise of Human Nature.	Oxford	University	Press. Juhl,	C.,	&	Loomis,	E.	(2010).	Analyticity.	Routledge. Kant,	I.	(1998).	Critique of Pure Reason	(Trans.	and	Ed.	by	Paul	Guyer	& Allen	W.	Wood).	Cambridge	University	Press. Kant,	I.	(2004).	Prolegomena to Any Future Metaphysics That Will Be Able to Come Forward as Science: With Selections from the	Critique	of	Pure Reason	(Ed.	by	Gary	Hatfield,	2nd	Edition).	Cambridge	University Press. Kaplan,	D.	(1977).	Demonstratives.	In	J.	Almog,	J.	Perry,	&	H.	Wettstein (Eds.),	Themes from Kaplan	(481–563).	Oxford	University	Press,	1989. Kitcher, P. (1983).	The Nature of Mathematical Knowledge.	Oxford	University	Press. Kripke,	S.	A.	(1980).	Naming and Necessity.	Harvard	University	Press.