volume	13,	no.	17 august	2013 Tarski and Primitivism About Truth Jamin Asay Lingnan University © 2013 Jamin	Asay This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. <www.philosophersimprint.org/013017/> 1. Introduction The	view that truth is	a	primitive, indefinable	notion	was	of	central importance	to	the	originators	of	analytic	philosophy.	Moore	and	Russell adopted the view	after abandoning their idealism (though they soon	turned	to	correspondence	accounts),	and	Frege	subscribed	to	it until	the	end	of	his	life.1	But	save	for	some	attention	given	to	the	view by	Davidson	(1990,	1996),	primitivism	about	truth	has	laid	low	for	the last	century.	During	that	time,	by	far	the	dominant	force	in	the	theory of	truth	has	been	Tarski,	and	much	subsequent	discussion	has	been focused	around	the	question	of	whether	Tarski's	work	better	motivates a	robust,	correspondence-style	theory	of	truth,2	or	a	more	deflationary approach.3	I	reject	this	dichotomy,	and	argue	in	this	paper	that	Tarski's work	on truth is	actually	most	consonant	with	a	primitivist	perspective	on	truth;	hence,	his	views	should	not	be	thought	to	lend	support to	either correspondence	or	deflationary theories.	Given that	Tarski shows	how	to	offer	a	definition	of	truth,	the	congeniality	between	his views	and	primitivism	may	not	be	immediately	obvious,	and	my	aim	is to	draw	the	appropriate	connections.	I	do	not	argue	that	Tarski	himself subscribed to a	primitivist conception	of truth, though I shall show how	the	view	is	open	to	him,	and	is	more	amenable	to	his	views	on truth	than	are	the	more	familiar	theories	of	truth. 1. See,	inter alia,	Moore	1899,	Russell	1904,	and	Frege	1956. 2. See,	e. g.,	Popper	1963:	223–228	and	1979,	Davidson	1969:	758,	Jennings	1987, Horwich	1990:	9,	Kirkham	1992:	170,	Niiniluoto	1999,	and	Fernández	Moreno 2001.	Woleński	argues	that	Tarski	employs	a	form	of	"weak	correspondence" (1993). Others demur from the correspondence interpretation: see, e. g., Haack	1976	and	1978,	Keuth	1978,	Putnam	1985:	72,	Davidson	1990,	1996:	268, and	1999:	110,	Künne	2003:	213,	and	Simmons	2009:	555–556. 3. See, e. g., Black 1948: 63, Horwich 1982, Soames 1984: 416 and 1999: 238, Stoutland 1999: 83, and	Patterson 2010: 25. Those	who argue against the deflationary	interpretation	include	Davidson	1990,	1996:	269,	and	1999:	110, Schantz 1998,	Ketland 1999,	Horwich 2005, and Simmons 2009: 556–558. See	Field 1994:	269–270 for	an intermediate	view.	Obviously,	much turns on	what	exactly	is	meant	by	'correspondence	theory'	and	'deflationism',	and so	some	subtlety	in	interpreting	these	attributions	is	called	for.	For	general discussion	about	how	to	interpret	Tarski's	view	vis-à-vis	correspondence	and deflationism,	see	Kirkham	1992:	170–173,	Künne	2003:	208–213,	and	Patterson	2012:	140–143. ImprintPhilosophers' jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 2 – vol.	13,	no.	17	(august	2013) what	it is	that	makes	truth	bearers	true;	discussion	of	the	concept	of truth,	by	contrast, focuses	on	what it is for	us	as	cognitive	agents to possess	a	notion	of	truth,	and	what	it	means	for	us	to	deploy	it	in	our thought	and	language. Primitivism is the view that truth is a fundamental concept. As such, it cannot	be	analyzed,	defined,	or reduced into	concepts that are	more fundamental.6	Accordingly, primitivism is opposed to the traditional	substantive	theories	of	truth,	such	as	the	correspondence, coherence,	and	pragmatic	theories,	which	hold	that	truth,	while	a	substantive	notion,	is	nevertheless	analyzable	into	those	further	notions. Primitivism	is	also	opposed	to	deflationism,	which	rejects	the	claim of	truth's	fundamentality.	Horwich,	for	example,	argues	that	truth	can be	defined,	albeit	implicitly,	by	the	T-sentences	(e. g.,	'The	proposition that	2	is	prime	is	true	if	and	only	if	2	is	prime'),	which	he	claims	are the	"fundamental	principles"	of	truth	(1990:	18).	Primitivists,	by	contrast,	deny	that	there	are	any	such	fundamental	principles	about	truth. If	there	were,	truth	itself	wouldn't	be	fundamental.	Far	from	being	a fundamental concept	of	preeminent	philosophical	worth, truth, say deflationists,	is	a	rather	innocuous	notion	of	mere	expressive	utility. Primitivism, like the other theories of truth, aims to offer an account of our most general concept of truth, whatever it is that is shared	by	all	who	can	be	said	to	possess	the	concept,	regardless	of which language	they	speak	or	how	complex their thoughts	may	be. Tarski	never	attempts	to	give	such	an	account,	and	at	times	makes	remarks	that	might	appear	to	disparage	any	such	endeavor.	He	observes, for	example,	that	no	one	has	adequately	explained	to	him	what	"the philosophical	problem	of	truth"	is,	and	that	he	does	not	understand what	it	is	to	offer	the	"essence"	of	a	concept	like	truth	(1944:	361).	The primitivist	acknowledges	that	truth	has	no	essence,	at least if	something's	essence	is	constituted	by	its	analysans.	Primitivism	takes	as	its target	our	most	basic	notion	of	truth,	against	which	the	adequacy	of 6. Some	primitivists admit that truth can	be	defined,	albeit in terms	of	other concepts	that	are	equally	fundamental	(thereby	forming	a	circle	of	interdefinable	fundamental	concepts).	See	Strawson	1992	for	a	view	of	this	sort. To	begin,	I	explain	what	primitivism	is,	and	how	it	offers	a	perspective	on	truth	that	competes	with	both	correspondence	and	deflationary	theories. I then	review	the	aspects	of	Tarski's	work	on	truth	that are	most	relevant	to	the	primitivist	theory	of	truth.	In	so	doing,	I	show how	Tarski	is	a	natural	ally	to	defenders	of	primitivism,	and	how	primitivism is	a favorable	view for	Tarski to	hold. I conclude	by	showing how	we	can	use	primitivism	to	help	frame	and	respond	to	some	familiar	charges,	due	to	Putnam	and	Etchemendy,	that	have	been	brought against	the	merits	of	Tarski's	project. 2. Primitivism About Truth The	primitivist	theory	of	truth	that	I	shall	be	addressing	offers	a	substantive	account	of	the	concept	of	truth.	The	theory	is	substantive	(i. e., non-deflationary) in that it	admits that truth is	a	philosophically important	notion, one that	has explanatory value that outstrips its linguistic and	expressive features.	By contrast, deflationary theories	of truth	typically	hold	that	all	there	is	to	the	theory	of	truth	is	an	account of truth's	utility in	disquotation, forming	generalizations,	expressing infinite conjunctions and disjunctions, etc. Hence, for deflationists, truth	has	no	explanatory	role	to	play	in	philosophy;	the	truth	predicate is	merely	of	expressive use	in	giving	accounts	of	other	notions	such	as assertion,	belief,	and	meaning.4 Furthermore,	the	primitivism	I	am	defending	involves	most	fundamentally the concept of truth, as	opposed to the	property of truth (or words	like	'true'	and	'truth').	Whether	or	not	the	property	of	truth	should be	understood	in	a	"metaphysically	robust"	way	is	a	separate	question, and	one	that	I	shall	set	aside	for	present	purposes.5	Discussion	of	the property	of	truth	is	a	fundamentally	metaphysical	enterprise	that	concerns	the	feature(s)	that	truth	bearers	possess	when	they're	true,	and 4. See,	e. g.,	chapter	3	of	Horwich	1990,	Field	1994,	and	Williams	1999. 5. In	my	forthcoming,	I	defend	a	metaphysically deflationist	account	of	the	property	of truth: I argue that truth is best understood	merely as an	abundant property,	and	not	a	sparse	property,	regardless	of	how	one	might	draw	that distinction.	See	Lewis	1983	for	an	account	of	sparse	and	abundant	properties. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 3 – vol.	13,	no.	17	(august	2013) correspondence	theorists	(though	not	pragmatists	or	coherentists).	In fact,	Tarski	thinks	his	work	outperforms	correspondence	theory:	"I	do not	have	any	doubts	that	our	formulation	does	conform	to	the	intuitive	content	of	that	of	Aristotle.	I	am	less	certain	regarding	the	latter [correspondence] formulations of the classical conception, for they are	very	vague	indeed"	(1944:	360). By	offering	a	precise	definition	of	truth,	Tarski	is	hoping	to	make the	notion	safe	from	those	who	have	voiced	skepticism	about	the	very idea	of	truth.	Semantic	concepts	like	truth,	Tarski	writes, have	been	treated	for	a	long	time	with	a	certain	amount of	suspicion.	From	a	historical	standpoint,	this	suspicion is	to	be	regarded	as	completely	justified.	For	although	the meaning	of	semantic	concepts	as	they	are	used	in	everyday	language	seems	to	be	rather	clear	and	understandable, still	all	attempts	to	characterize	this	meaning	in	a	general and	exact	way	miscarried.	(1944:	346;	cf.	1956b:	401) Bearing	in	mind	that	Tarski's	work	on	truth	was	developed	in	the	heyday	of logical	positivism,	his	concern	here	is	understandable.	His	intent	is	to	offer	a	precise	definition	of	truth	that	is	free	of	any	"alleged metaphysical	implications",	so	that	any	lingering	distrust	in	the	notion of	truth	may	"evaporate"	(1944:	364;	cf.	1956a:	252). Part	of	the	project	of	making	the	notion	of	truth	"safe"	for	philosophy	and	science	involves	developing	a	metaphysically	neutral	account of	the	concept;	the	other	crucial	part	is	showing	that	the	notion	is	not infected	with	paradox.	The	semantic	paradoxes	-	including,	most	notoriously,	the	liar	paradox	-	threaten	to	undermine	the	legitimacy	of the	notion	of	truth.	To	see	why,	consider	that	in	order	to	ensure	that the	semantic	conception	of	truth	conforms	to	the	classical	Aristotelian conception,	Tarski	offers	his	famous	adequacy	condition.	In	order	for a	given	language's	definition	of	truth	to	be	adequate	it	must,	for	every sentence	of	the	language,	imply	an	instance	of	the	schema: (T) X	is	true	if	and	only	if	p. Tarski's	definitions	are	tested.	Tarski	is	rightly	skeptical	that	that	basic notion	admits	of	any	precise	definition;	but	that	does	not	mean	that he	thinks	there	is	no	such	notion.	As	we	shall	see,	Tarski	thinks	that we do have an intuitive conception of truth (however vague or illdefined)	that	is	prior	to	how	it	is	employed	in	language.	That	conception	is	the	primitivist's	focus. For	our	purposes, the	dimensions	of	primitivism	most	relevant to Tarski's	work	on	truth	are	truth's	indefinability,	explanatory	value,	metaphysically	neutral	character,	and	relationship	to	the	T-sentences.	These aspects	of	the	primitivist's	conception	of	truth	are	shared	with	Tarski's basic	perspective	on	truth,	and	will	form	the	basis	of	our	discussion. 3. Tarski's Theory of Truth In	his seminal	work	on truth,	Tarski (1944, 1956a) advances and	defends	what	he	calls	the	"semantic	conception"	of	truth.	His	main	goal is	to	offer	a	satisfactory	definition	of	truth	for	a	language	that	(i)	avoids paradox,	(ii)	deflects	positivist	skepticism,	and	(iii)	remains	true	to	our "classical	conception"	of	truth. Consider	first	the	third	desideratum.	"The	desired	definition,"	Tarski	writes, "does	not aim to specify the	meaning	of a familiar	word used	to	denote	a	novel	notion;	on	the	contrary,	it	aims	to	catch	hold of the	actual	meaning	of	an	old	notion" (1944:	341).	The	old	notion is the intuitive view of truth that Tarski attributes to Aristotle, and which	he	thinks	contemporary	correspondence	theorists	are	attempting	to	uphold.	According	to	Aristotle,	"A	falsity	is	a	statement	of	that which	is	that	it	is	not,	or	of	that	which	is	not	that	it	is;	and	a	truth	is a	statement	of	that	which	is	that	it	is,	or	of	that	which	is	not	that	it	is not"	(1966:	70;	1011b25–28).	Tarski	saw	his	work	as	offering	"a	more precise	expression	of	our	intuitions"	to	the	effect	that	truth	somehow consists	in	a	kind	of	correspondence	with	reality	(1944:	343;	cf.	1956a: 153).	Hence,	it's	understandable	why	many	have	taken	Tarski's	work	to motivate	-	or	even	just	be	-	a	kind	of	correspondence	theory	of	truth. So	Tarski	clearly	thinks	that	his	work	aims	to	do	justice	to	our	classical conception	of truth, a	goal that	he takes	himself to share	with jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 4 – vol.	13,	no.	17	(august	2013) that	includes	names	for	all	the	sentences	of	the	object	language	and other	resources	necessary	for	defining	semantic	predicates	for	the	object language. If truth	is to	be	defined	for	some	language	O,	then	O cannot	include	the	truth	predicate	'true-in-O'.	The	predicate	is	instead a	part	of the	metalanguage	M.	Because	O	does	not contain its	own truth	predicate,	liar	sentences	cannot	be	formulated	within	O,	and	so paradox	is	avoided. Hence,	for	Tarski,	truth	is	definable	only	relative	to	certain	sorts	of languages.	Those	languages	cannot	be	"semantically	closed",	which is to say that they cannot include their own semantic machinery, such as names for their sentences and their own truth predicate. Truth	predicates	for	a	given	object	language	can	be	defined	only	from within	a	metalanguage	that	is	expressively	more	powerful	than	the object	language. Given	these	constraints,	we	can	now	offer	a	definition	of	'true-in-O' for	any	qualified	object	language	O.	The	definition	is	constructed	via the	notion	of	satisfaction.	Satisfaction,	ordinarily,	is	a	relation	between objects	and	the	sentential	functions	that	constitute	a	given	language. First	we	define	the	satisfaction	relation	by	listing	out	the	most	basic cases:	for	example,	Socrates	satisfies	the	sentential	function	'x	is	a	philosopher',	and	the	sequence	<Socrates,	Plato>	satisfies	the	sentential function 'x is a teacher	of	y'.	We then	define satisfaction recursively by	showing	how	the	satisfaction	conditions	for	compound	sentential functions	(and	those	involving	quantification)	are	to	be	given	in	terms of	the	satisfaction	conditions	for	the	basic	functions. For	Tarski,	the	definition	of	satisfaction	is	somewhat	more	involved, since	he	defines	it	as	a	relation	between	sentential	functions	and	infinite	sequences	of	objects.	To	see	how	the	definition	works,	we	first need	to	establish	a	correlation	between	variables	and	the	objects in the	infinite	sequences.	If	we	set	up	the	list	of	variables	in	the	standard way	(i. e.,	<a, b, c, d, ..., x, y, z, a1,	...>), then	x is correlated	with the twenty-fourth	object	in	the	sequence.	Now	we	can	say	that	a	sequence satisfies	'x	is	a	philosopher'	if	and	only	if	the	twenty-fourth	object	in the	sequence	is	such	that	it	is	a	philosopher.	A	sequence	satisfies	'x	is	a The	'X'	is	to	be	replaced	by	a	name	of	a	sentence	of	the	target	language whose	truth	predicate	is	being	defined,	and	'p'	by	a	translation	of	that sentence	in	the	language	doing	the	defining.7	A	definition	that	meets this	condition	offers	necessary	and	sufficient	conditions	for	the	truth of	every	sentence	of	the	language	in	question	in	a	way	that	fits	with Aristotle's dictum (1944: 344). The adequacy condition reveals that Tarski	thinks	we	do	have	a	pre-linguistic	conception	of	truth,	and	that any	purported	definition	of	truth	had	better	conform	to	it.8 Paradox	arises	when	we	apply	sentences	like	the	following	to	the truth	schema: (L) The	first	named	sentence	in	section	3	of	"Tarski	and	Primitivism	About	Truth"	is	not	true. If	we	plug	(L)	into	our	schema,	we	have: (TL) (L)	is	true	if	and	only	if	the	first	named	sentence	in	section 3	of	"Tarski	and	Primitivism	About	Truth"	is	not	true. Bearing	in	mind	the	identity	of	(L),	we	can	see	that	(TL)	is	equivalent	to: (TL*)	(L)	is	true	if	and	only	if	(L)	is	not	true. (TL*)	is	contradictory,	and	so	any	language	that	allows	the	formation of	(L)	and	meets	the	adequacy	condition	concerning	schema	(T)	will produce	a	contradiction	(assuming	classical	logic). Tarski's	positive	account	of truth is formulated	so	as to	be inoculated from	paradox.	Most crucially,	Tarski offers	definitions	of truth that	are	relative to a particular language	(1944:	342).	Rather	than	offering a	general	definition	of truth	that	applies	across	all languages,	Tarski defines	language-relative	truth	predicates,	such	as	'true-in-L1',	'true-inL2',	and	the	like.	Secondly,	truth	cannot	be	defined	within	the	language for	which it is being defined. Instead, truth	must be defined in the metalanguage.	The	metalanguage for	an	object language is a language 7. Whether	Tarski	intends	the	condition	as	a	necessary	or	sufficient	one	is	contentious;	see	Patterson	2006a	for	discussion. 8. Cf.	Heck	1997:	541–542. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 5 – vol.	13,	no.	17	(august	2013) between truth	and the	T-sentences, and the	metaphysically	neutral character	of	truth. 4.1. Indefinability Primitivism	begins	with the thesis that truth cannot	be	defined	or analyzed.	So	how	can	Tarski's	work,	which	shows	how	to	offer	precise definitions of truth,	motivate primitivism and its key commitment	to	the	indefinability	of	truth?	To	resolve	this	tension,	we	need only attend to the limitations inherent to Tarski's method. As we have	seen,	Tarski	shows	how	to	define	truth	for a particular language, and	only	for	languages of a particular type.	The	languages	in	question are	(i)	formal languages	which	are	(ii)	not	semantically closed	but	(iii) satisfy	the	condition	of	essential richness.	Absent	these	features,	truth is	indefinable. First, the language	needs to	be formal (1956a: 165).	This	criterion is	important	because	it	enables	us	to	offer	a	precise	definition	of	the notion	of	satisfaction,	which	relies	on	there	being	a	precise	account	of what	the	sentential	functions	of	the	language	are.	Tarski	writes:	"The problem of the definition of truth obtains a precise meaning and can be solved in a rigorous way only for those languages whose structure has been exactly specified.	For	other	languages	-	thus,	for	all	natural,	"spoken"	languages	-	the	meaning	of	the	problem	is	more	or	less	vague,	and	its	solution can	have	only	an	approximate	character"	(1944:	347).	"Our	everyday language,"	Tarski	goes	on	to	say,	"is	certainly	not	one	with	an	exactly specified	structure.	We	do	not	know	precisely	which	expressions	are sentences"	(1944:	349).	Tarski	thus	draws	a	crucial	distinction	between natural	and	formal	languages,	and	is	explicit	that	his	methods	apply only	to	the	latter. Next,	Tarski	requires	that	the	languages	for	which	truth	can	be	defined	not	be	"semantically	closed"	(1944:	348).	A	semantically	closed language is,	essentially,	a language	that includes its	own	semantics. Hence,	a	semantically	closed	language	includes	names	for	all	its	constitutive sentences; if the sentence 'Snow is white' belongs to the language, so too does the name of that sentence, ''Snow is	white''. teacher	of	y'	just	in	case	the	twenty-fourth	member	of	the	sequence	is a	teacher	of	the	twenty-fifth	member	of	the	sequence.	Now	consider sentences,	which	are	just	sentential	functions	with	no	free	variables. Any sequence whatsoever satisfies 'Socrates is a philosopher' and 'Socrates	is	a	teacher	of	Plato',	as	they	involve	no	variables	at	all.	For the	existentially	quantified	sentence	'There	is	some	x	such	that	x is	a philosopher',	a	sequence	S	satisfies	it	just	in	case	there	is	a	sequence S'	that	differs	from	S	at	most	with	respect	to	the	objects	in	their	twenty-fourth	positions,	and	whose	twenty-fourth	object	is	a	philosopher. So long	as there is some	philosopher in	existence, there	will	be	an S'	with	a	philosopher	in	the	twenty-fourth	position.	As	a	result, the existential	will	be	satisfied	by	every	infinite	sequence	should	there	be a	philosopher,	and	satisfied	by	no	infinite	sequence	should	there	not be	any	philosophers. This	procedure	defines	the	satisfaction	relation	for	a	given	language, which	can	now	be	used	to	define	truth	itself.	Sentences	are	true-in-O if	and	only	if	they	are	satisfiedO	by	each	and	every	infinite	sequence	of objects;	sentences	are	false-in-O	if	and	only	if	they	are	satisfiedO	by	no object	or	sequence	of	objects	(1944:	353;	1956a:	195).	Hence	we	have arrived	at	Tarski's	definition	of	truth:	true	sentences	are	those	that	are satisfied	by	every	infinite	sequence	of	objects. 4. Tarski and Primitivism We	have	now	seen	Tarski's semantic conception	of truth in	outline, and	the	method	he	provides	for	defining	truth	for	a	given	language. My contentions are that, of all the contemporary theories of truth, primitivism	is	the	most	compatible	with	the	semantic	conception,	and that	primitivists	can	take	advantage	of	Tarski's	work	for	their	own	purposes.	Traditionally,	Tarski's	work	has	been	thought	to	motivate	either correspondence	accounts	or	deflationary	accounts;	I	reject	both	suggestions.	To	see	why, let	us turn	now to four	crucial	aspects	of	Tarski's	work,	namely,	his	contention	that	truth	is	ultimately	indefinable, his admission that truth is explanatorily valuable, the relationship jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 6 – vol.	13,	no.	17	(august	2013) language, so to speak, then the semantic	paradoxes	will be at	play, and	the	definition	won't	succeed. 10 In	fact,	Tarski	offers	a	proof	for	why	truth	cannot	be	defined	within a	language	(or	from	a	metalanguage	of	the	same	or	lower	order).	Tarski's	formal	"indefinability"	proof	employs	some	of	the	same	diagonal reasoning that lies behind	Gödel's	work on incompleteness. I shall offer	only	a	brief informal sketch	of the	proof	here,	which	basically presents the proof as a form of Grelling's heterological paradox (a connection	Tarski	observes	at	his	1956a:	248,	footnote	2).11	For	some language	of	sufficient	expressive	power	L,	we	first	suppose	that	there is a predicate 'Tr' such that its extension contains all and	only true sentences	of L.	But	we can	now form	a	new	predicate, 'is not	Tr	of itself',	and	ask	whether	it	holds	of	itself	or	not.	If	'is	not	Tr	of	itself'	is not	Tr	of itself, then it	belongs in its	own	extension,	and	so is	Tr	of itself	after	all.	But	if	'is	not	Tr	of	itself'	is	Tr	of	itself,	then	it	is	not	Tr	of itself,	given	that	the	predicate	holds	only	of	predicates	that	are	not	Tr of themselves.	Either	way,	contradiction follows.	The	assumption	reduced	to	absurdity	is	that	there	is	such	a	predicate	'Tr'	that	contains	all and	only	true	sentences	of	L.	There	is	no	such	predicate,	and	so	truth is	not	definable	for	L. 10. In the	original	version	of "The	Concept	of	Truth in	Formalized	Languages", the languages that satisfy the condition of essential richness are the "languages	of	finite	order"	discussed in section	4, such	as the language	of the calculus	of	classes	(1956a:	209),	and	simple	first-order	languages.	Languages that	don't	satisfy	the	condition	are	the	languages	of	infinite	order	discussed in	section	5,	such	as	the	general	theory	of	classes.	For	these	languages,	the satisfaction relation cannot be defined	by the	method	previously outlined, and	so	no	Tarski-style	definition	of	truth	can	be	constructed	for	them	(1956a: 244).	However,	Tarski later revises	his view	on this	point in the	postscript to	"The	Concept	of	Truth	in	Formalized	Languages"	(1956a:	268–278).	There, Tarski	argues	that	truth	in	languages	of	infinite	order	can	be	defined,	so	long as	it	is	defined	from	a	language	of	a	higher	order,	which	is	now	possible	given Tarski's	embrace	of	the	transfinite.	Hence,	what	matters	for	Tarski	is	the	nature	of	the	relationship	between	the	object	language	and	metalanguage,	and not	whether	the	object	language	in	question	is	of	finite	or	infinite	order. 11. For	more	formal	presentations	of	Tarski's	proof,	see	Simmons	1990:	288–289, 1993, and 2009: 550–553, Patterson 2006a: 16–24 and 2012: 144–160, and chapter	2	of	Field	2008.	See	Martin	1968	for	more	on	Grelling's	paradox. Semantically	closed	languages	also	include	their	own	truth	predicate, whose	extension	includes	sentences	of	that	very	language.	As	a	result, semantically closed languages enable the formation of paradoxical liar	sentences,	which	disqualifies	them	from	Tarski's	method.	Natural languages	exhibit	semantic	closure	by	way	of their "universality": "A characteristic	feature	of	colloquial	language	(in	contrast	to	various	scientific	languages)	is	its	universality.	It	would	not	be	in	harmony	with the	spirit	of	this	language	if	in	some	other	language	a	word	occurred which	could	not	be	translated	into	it"	(1956a:	164).	Hence,	in	his	positive	account,	Tarski	must	rely	on	the	object language/metalanguage distinction,	for	the	truth	predicate	to	be	defined	cannot	belong	to	the language	to	which	it	applies. One	final	criterion	remains: the	metalanguage	defining	truth	for its	object	language	must	satisfy	the	condition	of	"essential	richness". What	is	required	is	that	the	metalanguage	doing	the	defining	be	essentially richer than the	object language.	Tarski	notes that it is	not easy	to	give	a	precise	characterization	of	essential	richness.9	What	he does	say is that "If	we restrict	ourselves to languages	based	on the logical	theory	of	types,	the	condition	for	the	meta-language	to	be	"essentially	richer"	than	the	object-language	is	that	it	contain	variables of	a	higher	logical	type	than	those	of	the	object-language"	(1944:	352). If	the	metalanguage	fails	to	be	richer	than	the	object	language,	then an	interpretation	of	the	metalanguage	can	be	offered	within	the	object language.	This, in turn,	will permit the	possibility	of constructing self-referential sentences that enable the semantic antinomies to	resurface.	Hence,	the	condition	of	essential	richness	is	in	place	in order	to	ensure	that	the	right	sort	of	relationship	exists	between	the object	language	and	the	metalanguage.	The	metalanguage	needs	to be	richer	than	the	object	language	so	that	it	can	offer	a	"broader"	or "higher"	perspective	from	which	to	contain	and	define	truth	in	the	object	language.	If	the	metalanguage	is	on	the	same	level	as	the	object 9. See	DeVidi	and	Solomon	1999	for	an	argument	that	no	tenable	account	of essential	richness	is	available	to	Tarski,	and	Ray	2005	for	a	defense	of	Tarski. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 7 – vol.	13,	no.	17	(august	2013) First,	Tarski	despairs	of the	attempt to	offer	a	definition	of truth in	natural	language.	If	any	truth	predicate	were	to	express	our	most general	notion	of truth	(for	which	primitivism	hopes	to	account), it would	be	the	truth	predicate	of	natural language.	But	Tarski is	committed	to	the	view	that	his	methods	cannot	offer	a	definition	of	that most	wide-ranging truth	predicate, for	natural languages fail	his requirements of formality and	of not being semantically closed	As it turns	out,	Tarski	thinks	the	matter	goes	beyond	indefinability:	given natural	language's	semantic	universality,	the	very	consistency	of	our use	of	truth	within	it	is	suspect.13	Tarski	writes:	"the	very	possibility	of a	consistent	use	of	the	expression	'true	sentence'	which	is	in	harmony with	the	laws	of logic	and	the	spirit	of	everyday	language	seems	to be	very	questionable,	and	consequently	the	same	doubt	attaches	to the	possibility	of	constructing	a	correct	definition	of	this	expression" (1956a:	165;	emphasis	removed).	Note	Tarski's	hedged	language	here. He does not claim to have "proved" that truth in natural language is	indefinable	or	inconsistent.14	Later	he	writes	that	"We	may	at	best only	risk	the	guess	that	a	language	whose	structure	has	been	exactly specified	and	which	resembles	our	everyday language	as	closely	as possible	would	be inconsistent" (1944: 349).	Absent a	definitive	account	of	the	nature,	structure,	and	limits	of	natural	language,	Tarski refuses to	make a definitive pronouncement on the definability of truth	in	natural	language	(1944:	347). 13. See	Ray	2003	and	Patterson	2006b	and	2012:	160–168	for	more	on	Tarski	and the	potential	inconsistency	of	natural	languages. 14. Davidson	repeatedly	claims	that	Tarski	has	"proved"	that	the	concept	of	truth is	indefinable	(1990:	285–286,	1996:	265,	269–270,	275–276),	but	it's	unclear what	proof	he	is	referring	to.	Tarski's	formal	indefinability	proof	(as	found	in section	5	of	Tarski	1956a)	applies	only	to	formal	languages	that	fail	to	satisfy the	condition	of	essential richness.	As for	Tarski's	pessimistic remarks	concerning the	definability	of truth for	natural languages (as found in section 1	of	Tarski	1956a), these	do	not	constitute	a	proof,	as the	hedged language of the	passages	quoted in this	paragraph reveals. Like	Davidson, I believe that	primitivists	can	find	plenty	of	value	in	Tarski's	work	on	definability,	but I	do	not	believe,	as	Davidson	appears	to,	that	Tarski	has	proven	the	truth	of primitivism	(or	that	Tarski	believes	himself	to	have	done	so).	See	also	GarcíaCarpintero	1999:	142–143. Where	the	condition	of	essential	richness	is	not	satisfied,	truth	cannot	be	defined	in	Tarskian	fashion.	Interestingly,	however,	Tarski	notes that	a	different	road	is	left	open	to	these	languages.	Though	truth	cannot	be	defined	within	them,	we	can	introduce	a	primitive	term	'true'	and then	give	an	account	of	it,	not	by	way	of	definition,	but	axiomatization: If	we	want to	develop the theory	of truth in	a	meta-language	which	does	not	satisfy	this	condition	[of	essential richness],	we	must	give	up	the	idea	of	defining	truth	with the exclusive	help of those terms	which	were indicated above [...].	We	have then to include the term "true," or some	other	semantic	term,	in	the	list	of	undefined	terms of	the	meta-language,	and	to	express	fundamental	properties	of	the	notion	of	truth	in	a	series	of	axioms.	There	is nothing	essentially	wrong	in	such	an	axiomatic	procedure, and	it	may	prove	useful	for	various	purposes.	(1944:	352) Tarski	goes	on	to	provide	some	of	the	details	as	to	how	such	an	axiomatization	would	proceed (1956a:	255–265).	Here	we	see	one	way in	which	Tarski	thinks	we	can	make	use	of	a	primitive	notion	of	truth. For	some	of	the	languages	for	which	truth	cannot	be	defined,	we	can nevertheless	make	"consistent	and	correct	use"	of	the	concept	of	truth by	way	of	taking	truth	as	a	primitive	notion,	and	giving	it	content	by introducing	the	relevant	sorts	of	axioms	(1956a:	266).12 Let	us	now return the	discussion to conceptual	primitivism.	The primitivism	about	truth	that	I	am	defending	is	not	about	truth	as	defined	for	any	particular	language.	Primitivism	concerns	our	concept	of truth,	which	in	turn	gives	content	to	the	various	truth	predicates	and operators	that	occur	in	our	natural	and	formal	languages.	So	we	must be cautious about drawing implications for primitivism too quickly from	Tarski's	work.	Nevertheless,	a few	points	of	connection	are important	to	note. 12. See	Halbach	2011	and	Horsten	2011	for	contemporary	treatments	of	the	axiomatic	approach	to	truth. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 8 – vol.	13,	no.	17	(august	2013) justice	to	our	classical,	intuitive	conception	of	truth,	they	by	no	means exhaust	that	conception. Tarski's	work	on	truth,	at	the	end	of	the	day,	offers	no	positive	solution	to	the	problem	of	defining	the	notion	of	truth	at	its	most	basic and	fundamental	level.	As	a	result,	Tarski	would	reject	the	traditional substantive	theories	of	truth	that	intend	to	do	precisely	that.	In	particular,	Tarski	would	reject	the	correspondence	theorist's	attempt	to	define	truth	in	terms	of	the	more	fundamental	notions	of	correspondence and	reality	(or	facts).	But	as	we	saw,	Tarski	thought	of	himself	as	partly engaged	in	the	same	project	as	correspondence	theorists,	in	the	sense that	both	are	interested	in	giving	an	account	of	truth	that	adheres	to the	traditional	classical	conception	of	truth.	(Hence,	as	we	have	seen, many	commentators	have	interpreted	Tarski	as	a	correspondence	theorist.)	What	we	may	appreciate	is	that	Tarski	thinks	that	the	best	way of	staying	true	to	the	classical	conception	is	not	by	analyzing	truth	by way	of	correspondence,	but	by	holding	one's	theory	of	truth	accountable	to	the	T-sentences formed	from	schema	(T).	As	a	result,	we	do not	see	Tarski	try	to	give	accounts	of	the	notion	of	correspondence and fact,	and	then	use	those	notions	to	define	truth.	Here	we	have	another point	of	intersection	between	Tarski	and	primitivism:	the	best	way	to account	for	the	"correspondence	intuition"	(i. e.,	whatever	basic	understanding	of	truth	it	is	that	Aristotle's	formulation	intends	to	capture) is	not	by	way	of	defining	truth	in	terms	of	correspondence,	but	by	way of	adherence to the	T-sentences.16	Tarski, like the	primitivist, rejects correspondence	theory	(understood	as	the	project	of	trying	to	define truth	in	terms	of	correspondence)	as	a	way	of	understanding	the	nature	of	truth	itself.	The	correspondence	theorist's	definition	is	not	necessary	for	capturing	what's	right	about	the	thought	that	truth	in	some sense	consists	in	a	kind	of	correspondence	with	the	world. 16. Below,	and	in	my	2011,	I	go	further	and	argue	that	attention	to	truthmaking, and	not	the	nature	of	truth	itself,	is	vital	to	understanding	what's	right	about the	"correspondence	intuition".	The	best	way	to	capture	the	correspondence intuition,	I	argue,	is	not	simply	by	upholding	the	T-sentences,	but	by	offering in	addition	a	theory	of	truthmaking. Despite	Tarski's	caution,	primitivists	may	take	some	solace in	his conclusions regarding natural language. Primitivists claim that our concept	of	truth	admits	of	no	analysis.	If	any	purported	definition	of	a truth	predicate	were	to	falsify	that	claim,	it	would	be	a	definition	of	the truth	predicate	of	natural language.15	At	the	very least,	Tarski	shows that	his	methods	for	definition	do	not	apply	to	the	natural	language 'true'.	So	the	lesson	primitivists	may	draw	from	Tarski	is	that	one	potential	source	of	falsification	to	their	view	is	of	no	threat.	Hence,	the primitivist	may	argue	as	follows:	if,	contra primitivism,	our	concept	of truth	is	definable,	then	the	natural	language	truth	predicate	should	admit	of	a	Tarski-like	definition.	However,	no	such	definition	is	available, and thus	our	concept	of truth is	not	definable.	Despite the fact that various	formal	languages	and	fragments	of	natural	language	admit	of	a definable	truth	predicate,	our	most	basic	and	general	concept	of	truth allows no such definition.	Of course,	whether there are other, nonTarskian	ways	of	defining	our	most	basic	concept	of	truth	is	an	open question,	and	Tarski	is	wise	not	to	pronounce	definitively	on	the	possibility	of	other	methods.	Still,	primitivists	may	share	Tarski's	suspicion that	the	prospects	for	definition	are	grim. The	primitivist	argues	that	our	general, inter-linguistic	notion	of	truth is	what	cannot	be	defined.	Tarski	appears	to	be	in	full	agreement	with this	particular	thesis.	His	entire	approach	to	the	theory	of	truth	can	be taken	as	an	argument	in	favor	of	it	(though	not,	as	we	have	seen,	some kind	of	conclusive	proof).	Truth	can	be	defined	only	with	respect	to certain	limited	kinds	of	languages.	As	for	our	most	basic	notion	of	truth, definition	is	not	to	be	had.	Hence,	even	though	Tarski's	definitions	do 15. I	happen	to	doubt	the	truth	of	the	antecedent	here,	since	I	believe	that	our concept	of	truth	is	prior	to	its	use	in	our	language,	and	is	not	fully	exhausted by	the	use	that	'is	true'	plays	in	our	language.	(For	example,	it's	not	clear	how a	Tarski-style	definition	of	truth	can	illuminate	what	it	means	to	say	that to assert is to present as true.	Cf.	Bar-On	and	Simmons	2007	and	Textor	2010.)	But	I suspect	that	Davidson	believes	something	along	these	lines,	since	he	appears to	take	Tarski's	negative	results	concerning	the	possibility	of	defining	a	fully general,	inter-linguistic	truth	predicate	to	establish	the	primitive	nature	of	our concept	of	truth. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 9 – vol.	13,	no.	17	(august	2013) terms	of	satisfaction	at	all,	but	rather	by	a	process	of	axiomatization. So	we	may	conclude	that,	formally	speaking,	truth	is	not	"univocal"	as it	appears	in	formal	languages	that	do	or	do	not	satisfy	the	condition of	essential	richness.	Sometimes	truth	is	defined	in	terms	of	satisfaction, sometimes it is introduced through axiomatization. But if	we believe	there	to	be	one	more	basic	notion	at	hand	behind	both	kinds of	languages,	then	we	must	reject	the	idea	that	truth	is	to	be	understood	in	terms	of	the	more	fundamental	notion	of	satisfaction.	That's not the	kind	of	analysis that	Tarski	offers.	Such	an	analysis is	what correspondence	theorists,	coherence	theorists,	and	pragmatists	offer. They	define	truth	in	terms	of	more	fundamental	notions.	But	Tarski	is not	engaged	in	such	a	process,	even	when	he	is	offering	definitions of	truth.	Consequently,	Tarski's	work	on	truth	leaves	it	entirely	open how	we	are to	understand the	basic	meaning	or intension	of truth. The	most	natural	position	for	Tarski	to	take	is	that	we	cannot	define this	more	general	notion	of	truth;	here	again	we	see	Tarski	and	primitivism	being	natural	allies. All	told,	where	Tarski	shows	truth	to	be	indefinable,	primitivists	can readily	agree.	The	kind	of	indefinability	of	truth	that	primitivists	advocate	is	precisely	the	kind	of	indefinability	that	Tarski's	work	allows	for and	motivates.	Where	Tarski advocates the definability of truth, it's clear that his definitions should	not be thought of as capturing the nature	of truth in	more fundamental terms.	That is to	say,	while	his definitions	represent	an	important	kind	of	formal	achievement,	they should	not be thought of as capturing the nature of truth in a	way similar	to	the	attempts	of	correspondence,	coherence,	and	pragmatic theorists.	Nor	is	there	any	reason	to	think	that	this	result	caused	Tarski any	despair.	As	we	shall	see	in	the	next	section,	Tarski	puts	his	definition	to	work	in	the	service	of	a	variety	of	mathematical	and	logical tasks	(among	others).	Tarski's	definitions	of	truth	are	best	appreciated in	light	of	these	more	formal	accomplishments. Finally,	it's	worth	noting	that	even	for	those	languages	where	a	Tarskian	definition	of truth is available, it's	unclear that	his	definitions capture	the	real	nature	-	or	intension,	we	might	say	-	of	truth.	If	they don't,	then	Tarski's	definitions	do	not	in	any	way	conflict	with	primitivists'	claims	regarding	the	indefinability	of	truth.	For	primitivists	argue that	no	definition	of	truth	can	reveal	the	nature	of	truth	in	more	fundamental	terms.	If	Tarski	isn't	even	intending	to	do	that	-	see	Patterson	2008a:	178	-	then	we	can	appreciate	how	Tarski's	project	is	in	full harmony	with	primitivists'.	Tarski	defines	true	sentences,	where	they are	definable,	as	those	that	are	satisfied	by	every	infinite	sequence	of objects.	As	Tarski	shows,	this	definition	is	"materially	adequate"	and "formally correct" (1944: 341, 1956a: 152).	That is to say, it entails all the	T-sentences	(and	therefore	captures	our	intuitive	notion	of	truth, and not something else), and suffers no internal problems such as circularity. Furthermore, the definition captures the right extension: it	includes	all	and	only	true	sentences	of	the	language.	However,	it's quite	implausible	to	think	that	Tarski's	definitions	have	hit	on	the	correct	intension	or	meaning	of	truth.17	One	way	to	press	the	point	is	as follows.	Granted, sentences	are true if and	only if they	are satisfied by	all	infinite	sequences	of	objects.	But	are	they	true	because	they	are satisfied	by	each	and	every	infinite	sequence	of	objects?	Is	the	right account	of	the	truth	of	'Snow	is	white'	that	every	infinite	sequence	satisfies	it,	or	does	the	right	account	have	something	to	do	in	particular with	snow	and	its	color?	If	the	former	answer	seems	insufficient	(as	it does	to	me),	then	there	is	reason	to	suppose	that	Tarski's	definitions were	never	intended	to	capture	the	nature	of	truth	and	its	intension	in more	fundamental	or	basic	terms.18 This conclusion becomes all the more apparent given Tarski's recognition	that	for	some	languages,	truth	is	not	to	be	cashed	out	in 17. For	one	thing,	Tarski's	discussion	of	indefinability	in	section	5	of	Tarski	1956a reveals	that	he	thinks	his	satisfaction-based	method	of	definition	is	in	a	certain sense arbitrary.	Appealing to satisfaction for languages	of finite	order works,	so	he	uses	it.	But	Tarski	is	open	to	the	idea	that	had	satisfaction	not worked,	some	other	notion	might	have. 18. Cf.	Patterson	2006b:	162–163. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 10 – vol.	13,	no.	17	(august	2013) on	the	basis	of	its	definition	-	the	concept	of	truth	is	sterile,	he	must	accept	the	further	conclusion	that	all	defined notions	are	sterile.	But	this	outcome	is	so	absurd	and	so unsound	historically	that	any	comment	on	it	is	unnecessary.	In	fact,	I	am	rather	inclined	to	agree	with	those	who maintain	that	the	moments	of	greatest	creative	advancement	in	science	frequently	coincide	with	the	introduction of	new	notions	by	means	of	definition.	(1944:	359) Hence,	Tarski	resists	any	suggestion	that	truth's	importance	is	in	any way	compromised	by	establishing	its	definability	or	subsequent	eliminability	from	the	language.	In	fact,	truth	won't	even	belong	to	those languages	for	which	truth	can	be	defined!	Nonetheless,	understanding	the	notion	of	truth	for	a	language	is	paramount	for	understanding that	language. For	Tarski,	the	importance	of	seeking	a	definition	of	truth	is	not	so as	to	eliminate	the	notion,	but	to	put	it	to	work.	What	can	truth	do	for us?	Tarski	is	adamant	that	his	work	on	truth	and	semantics	"can	find	applications	in	various	domains	of	intellectual	activity"	(1944:	364).	Tarski argues that	his	work can	produce important results,	not	only for	philosophy,	but	for	both	the	empirical	and	deductive	sciences.19	As	to	philosophy,	Tarski	notes	that	his	definition	can	be	taken	to	have	addressed "one	of	the	fundamental	problems	of	the	theory	of	knowledge"	(1956b: 407).	Tarski	also	thinks	that	his	approach	to	truth	plays	a	vital	role	in	"establishing	semantics	on	a	scientific	basis"	(ibid.),	and	thereby	produces various	empirical	and	logical	fruits.	His	research	has	obvious	direct	ramifications	for	the	study	of	linguistics,	and	"indirect"	implications	for	the natural	sciences,	by	way	of	the	use	of	truth	and	other	semantic	notions within the	methodology	of science	and	scientific theory	construction and acceptance (1944: 366–368). Furthermore, Tarski points out that his	definition	of	truth	leads	to	important	results	in	logic,	mathematics, and	metamathematics	(1944:	368–369).	His	definition	of truth	can	be 19. See	also	Soames	1999:	100–107. 4.2. Explanatory value The	previous	section	serves to illustrate	some	of the	grounds	Tarski has	for	rejecting	the	traditional	substantive	theories	of	truth	(grounds that	he	may	happily	share	with	primitivists).	Those	theories	purport to	analyze	in	full	our	concept	of	truth,	a	project	that	Tarski	rejects	and may	well	deem	impossible.	In	this	section	we	can	turn	to	why	Tarski can	also	side	with	primitivists	(and	now	against	deflationists)	in	favor of	truth's	explanatory	capabilities. The	first	point	to	notice	is	that	Tarski	explicitly	rejects	the	idea	that if	truth	were	to	be	definable	and	so	in	principle	eliminable	from	language	without	expressive	loss,	then	the	notion	of	truth	would	thereby be	"sterile": Consequently,	the	term	"true"	when	occurring	in	a	simple sentence	of	the	form	"X is true"	can	easily	be	eliminated, and the sentence itself,	which	belongs to the	meta-language,	can	be	replaced	by	an	equivalent	sentence	of	the object-language	[...].	Some	people	have	therefore	urged that	the	term	"true"	in	the	semantic	sense	can	always	be eliminated,	and	that	for	this	reason	the	semantic	conception	of	truth	is	altogether	sterile	and	useless.	And	since the	same	considerations	apply	to	other	semantic	notions, the	conclusion	has	been	drawn	that	semantics	as	a	whole is	a	purely	verbal	game	and	at	best	only	a	harmless	hobby.	(1944:	358) Not	all	deflationists	would	draw	the	conclusion	that	truth	is	a	sterile and	useless concept, but the standard	deflationist line is that careful	attention	to	truth's	logical	and	linguistic	role	does	reveal	truth	to carry little philosophical or explanatory	worth (e. g.,	Horwich 1990 and	Williams	1999).	But	Tarski	detects	a	fallacy	in	inferring	sterility from	definability: If,	however,	anyone	continues	to	urge	that	-	because	of the theoretical possibility of eliminating the	word "true" jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 11 – vol.	13,	no.	17	(august	2013) most	fundamental	principles	about	truth,	in	terms	of	which	we	grasp the	concept	(e. g.,	Horwich	1990).20	T-sentences	thus	play	the	role	that other	principles	(which	might	involve	correspondence,	coherence,	or utility)	play	in	other	theories.	Primitivists	reject	the	idea	that	there	are any	fundamental	principles	about	truth,	in	terms	of	which	the	concept can	be	defined,	reduced,	or	analyzed,	and	so	must	reject	this	deflationary	interpretation	of	the	T-sentences.	On	this	point,	Tarski	can	also	be found	to	side	with	primitivists. The T-sentences figure into Tarski's account of truth by way of serving	as	a	kind	of	"check"	on	the	material	adequacy	of	any	purported	definition	of	truth;	theories	meet	the	condition	when	they	entail all	of	the	T-sentences.	The	notion	of	material	adequacy	at	hand	is	not simply	extensional	adequacy	(Patterson	2012:	109–111).	Tarski's	interest	is	instead	in	defining	relativized	truth	predicates	that	conform	to our	intuitive	notion	of	truth.	Entailing	the	T-sentences	is	one	way	of guaranteeing that the	notion	defined	hasn't strayed away from	our most	basic	notion	of	truth.	As	Davidson	puts	the	point,	the	T-sentences	"alone	constitute	an	unmistakable	test	that	a	theory	has	captured	a concept	of	truth	we	are	interested	in"	(1973:	77). If the T-sentences are taken to be the fundamental facts about truth,	in	terms	of	which	truth	may	be	defined,	then	Tarski's	adequacy condition	is	empty.	If	the	deflationary	conception	of	truth	is	defined by the	T-sentences, then	of course the	deflationary	conception	will meet	the	adequacy	condition	by	entailing	them.	Hence,	the	deflationary	perspective	on the truth	schema	and its	T-sentences	makes	Tarski's	adequacy	condition	vacuous	and	trivial.	Since	Tarski	did	not	take the	condition	to	be	empty,	we	may	appreciate	at	once	how	Tarski	rejects	the	idea	that	the	T-sentences	provide	the	most	fundamental	facts about truth.21	Primitivists, like	Tarski,	maintain	that the	T-sentences 20.	See	also	the	deflationary	definitions	of truth	that involve	the	truth	schema, as	found	(but	not	always	endorsed)	in	Leeds	1978:	121,	Field	1986:	58,	Resnik 1990:	412,	and	David	1994:	107. 21. I hasten to add that this fact also shows that Tarski does not think of the T-sentences as being empirically empty logical truths, contra Putnam 1985, Etchemendy	1988,	and	Heck	1997.	If	they	were,	then	the	adequacy	condition used	to	prove	the	metalogical	versions	of	the	laws	of	non-contradiction and	of	excluded	middle	(1956a:	197;	cf.	1944:	354).	It	can	also	illuminate the	notions	of	provability,	definability,	consistency,	and	completeness (1944:	368–369).	In	summarizing	the	potential	positive	benefits	of	his approach	to	truth	for	the	deductive	sciences,	Tarski	writes	that	"the	establishment	of	scientific	semantics,	and	in	particular the	definition	of truth,	enables	us	to	match	the	negative	results	in	the	field	of	metamathematics	with	corresponding	positive	ones,	and	in	that	way	to	fill	to	some extent	the	gaps	which	have	been	revealed	in	the	deductive	method	and in	the	very	structure	of	deductive	science"	(1956b:	408). In	short,	Tarski	believes	that	the	notion	of	truth	can	play	an	important,	explanatory	role	in	other	areas	of	thought,	inside	and	outside	of philosophy.	Rather	than	thinking	of	his	project	as	having	deflationary results,	Tarski	believed	his	work to	be	quite constructive, and	only increase the import	of the	notion	of truth.	This	attitude toward the theory of truth is shared	by primitivism. For primitivists, truth is a foundational	notion;	its	importance	is	demonstrated	by	showing	how the	notion	can	be	put	to	work	in	other	kinds	of	intellectual	projects (including those that	Tarski addresses).	One	of the reasons to take some	notion	as	primitive is to	show	how	it	can	then	be	put to	various kinds of explanatory	work. Primitivists	may grant to deflationists that 'true'	plays	various	kinds	of logical	and	expressive	roles in ordinary	language,	and	that	in	many	cases	expressions	with	'true'	are equivalent	to	expressions	that	lack	it.	But	primitivists	and	Tarski	are in	agreement	that	such	facts	about	truth	do	not	exhaust	all	that	there is	to	be	said	about	it;	on	the	contrary,	truth	is	a	central,	key	notion	that is	highly	relevant	to	our	understanding	of	other	important	notions	in science,	mathematics,	and	philosophy. 4.3. T-sentences A	third	connection	between	primitivism	and	Tarski	(and	one	that	also serves to further distance him from deflationism) involves the relationship between the T-sentences and the concept of truth. A standard	deflationary	interpretation	of	the	T-sentences	is	that	they	are	the jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 12 – vol.	13,	no.	17	(august	2013) their	theory.	Consider	also	mathematical	and	analytic	truths:	to	what are they	supposed to	correspond?	My intention is	not to	show	that such	questions	cannot	be	answered;	rather,	it's	that	correspondence theories	immediately	face	a	distinctively	metaphysical	challenge	that Tarski and primitivists can avoid. Any fully fleshed out correspondence	theory	must	give	a	comprehensive	account	of	the	nature	of	the corresponding	objects,	and	in	so	doing	will	impose	a	particular	metaphysical	view	onto	the	nature	of	truth. Similarly,	coherence	theorists	and	pragmatic	theorists	can	be	understood	as incorporating	partisan	metaphysical	views	into	their	accounts of truth. If the truth	of 'Snow is	white' consists in a certain kind	of	coherence	between	our	beliefs,	then	this	highly	suggests	an (at	least	in	part)	idealist	metaphysics	that	connects	the	whiteness	of snow	with	features	of	what	other	beliefs	we	hold.	If	the	truth	of	my beliefs	is	in	part	a	function	of	what	other	beliefs	I	hold,	then	it's	not the case that the truth	of 'Snow is	white' is a	matter fully independent	of	me	and	my	particular	beliefs.	Likewise,	if	the	truth	of	'Snow	is white'	is	in	part	a	function	of	what	it's	useful	for	me	to	believe,	then the truth	of the	matter is	again	mind-dependent.	Hence,	coherence and pragmatic accounts of truth, just like correspondence theories, cannot	embrace	the	metaphysical	neutrality	inherent	to	primitivism and	Tarski's	semantic	conception	of	truth. To	say	that	Tarski's	theory	of	truth	is	neutral	is	to	allow	that	it	could be	paired	with	the	metaphysical	ideas	underlying	the	traditional	substantive	theories	of	truth,	if	one	were	so	inclined.	Hence,	Tarski's	work on	truth	does	not	show	that	the	metaphysical	concerns	of	interest	to the	traditional	theorists	of	truth	are	nonsense,	or	that	they	disappear once	we	adopt	the	semantic	conception.	It's	just	that	these	concerns are	better	explored	not	from	the	perspective	of	the	theory	of	truth,	but from	the	theory	of	truthmaking (or	some	other	metaphysical	approach). According	to	Tarski,	any	adequate	theory	of	truth	will	usher	forth	the equivalences	like express	important	facts	about	truth.	(And,	perhaps	more	to	the	point, important	facts	about	the	truth conditions	of	sentences.)	But	one's	theory	of	truth	needs	to	explain	the	T-sentences	(and	not	the	other	way around,	as	deflationists	maintain). 4.4. Metaphysical neutrality One	final	core	issue	on	which	Tarski	and	primitivists	are	in	complete agreement	is	the	metaphysically	neutral	nature	of	truth.	To	accept	Tarski's	approach	to	truth	is	not	to	take	on	any	metaphysical	stance,	such as	realism	or	anti-realism:	"we	may	accept	the	semantic	conception	of truth	without	giving	up	any	epistemological	attitude	we	may	have	had; we	may	remain	naive	realists,	critical	realists	or	idealists,	empiricists	or metaphysicians	-	whatever	we	were	before.	The	semantic	conception is completely neutral toward all these issues" (1944: 362). Likewise, taking truth to	be	a	primitive,	undefinable	concept	also requires	no particular	metaphysical	stance. By	way of contrast, it's instructive to understand the traditional substantive	theories	of	truth	as	building	metaphysical	stances	directly into	their	accounts	of	truth.22	For	correspondence	theories,	something is	true	just	in	case	it	stands	in	the	correspondence	relation	to	some fact.	As	a	result,	truths	are	from	the	outset	entangled	with	ontology.	If p	is	to	be	true,	there	must	be	some	entity	E	for	it	to	correspond	to.	For correspondence theory, there is	no truth	without some	accompanying	ontology.	This	commitment	might	seem	innocuous,	but	consider some problematic cases. Take the sentence 'There are no hobbits'. One	might	think	that	this	sentence	can	be	true	without	the	benefit	of anything	existing:	after	all,	it	appears	that	it's	true	because	nothing	of	a certain	sort	exists.	But	correspondence	theorists	must	grant	that	there is	some	entity	for	it	to	correspond	to,	lest	they	allow	some	truths	to be	true	in	spite	of	not	corresponding	to	anything,	thereby	giving	up would	again	be	vacuous.	See	also	Davidson	1990	and	Patterson	2008b for further	criticism	of	this	reading. 22.	Deflationary	theories	of	truth,	however,	share	the	metaphysical	neutrality	of the	semantic	conception	and	primitivism. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 13 – vol.	13,	no.	17	(august	2013) neutral	perspective	is	yet	another	point	of	common	ground	between Tarski	and	primitivism. 5. Dissolving Objections As	we	have	seen,	Tarski's	semantic	conception	of	truth	has	sometimes been thought to	motivate correspondence theories, and sometimes deflationary	theories.	My	alternative	suggestion	is	that	Tarski's	work	is best	paired	with	the	primitivist	perspective	on	truth.	Primitivists	stress the	indefinability	of	our	most	general	concept	of	truth,	its	explanatory value,	and its	metaphysical	neutrality.	All	of these features, together with primitivism's perspective on the T-sentences, are shared with Tarski's semantic approach to truth.	Hence, although	Tarski himself never	says	anything	that	commits	him	to	primitivism,	he	says	plenty of things that	distinguish	him from	both the traditional substantive theories and	deflationary theories. If	Tarski	were to accept any contemporary	account	of	our	general	concept	of	truth,	primitivism	would be	the	view	most	acceptable	to	him.24	Likewise,	primitivists	can	find support	for	their	views	inside	Tarski's	work.	Tarski	argues	that	his	own method	of	definition	cannot	be	applied	to	the	general	notion	of	truth that	most	interests	primitivists.	Thus,	Tarski	leaves	open	the	possibility that	primitivism	offers	the	best	understanding	of	our	concept	of	truth. what	I	have	called	the	"correspondence	intuition".	If	the	correspondence	intuition	has	any	metaphysical	pull	to	it	-	and	I	believe	that	it	does	-	then	it ought	not receive	any support from	a	metaphysically	neutral	view.	On	my view,	consistency	with	the	T-sentences	is	necessary	but	not	sufficient	for	capturing	the	correspondence	intuition.	For	this	reason,	I	argue	in	my	2011	that deflationists	cannot	capture	the	correspondence	intuition	by	their	conformity to	the	truth	schema	alone,	contra	Horwich	1990.	What's	needed,	in	addition, is	a	particular	view	about	what	makes	truths	true. 24. Patterson	observes	that	"Tarski	had	no	specific	concerns	at	all	about	the	content	of the	concept	of truth itself"	(2012:	139).	On	Patterson's	view,	Tarski's fundamental	interest	is	not	in	analyzing	our	intuitive	notion	of	truth,	but	in showing	how	to	consistently	and	adequately	introduce	a	truth	predicate	(that conforms	to	the	intuitive	notion)	into	certain	kinds	of	languages.	If	so,	then Tarski	would	have	been	officially	neutral	regarding	primitivism;	my	contention	is	that	the	view	is	open	and	amenable	to	him,	if	he	were	to	throw	his	hat into	this	particular	philosophical	ring. 'Socrates	is	a	philosopher'	is	true	if	and	only	if	Socrates	is a	philosopher. What	we	have	here	is	one	sentence	(from	the	language	doing	the	analyzing)	being	used	to	give	the	necessary	and	sufficient	conditions	for the truth of another (not necessarily distinct) mentioned sentence (from	the	language	being	analyzed).	But	to	say	that	'Socrates	is	a	philosopher'	is	true	if	and	only	if	Socrates	is	a	philosopher	is	to	say	nothing	whatsoever	about	what	it	is,	if	anything,	that	makes	'Socrates	is	a philosopher'	true.	What	we	can't	say	is	this:	Socrates	is	a	philosopher makes true 'Socrates is a philosopher'. That's ungrammatical nonsense.	And	we	must	be	extremely	cautious	in	saying	that	what	makes 'Socrates is	a	philosopher' true is that	Socrates is	a	philosopher.	For what	does 'that	Socrates is	a	philosopher'	refer	to?	It	can't	refer	to	a proposition,	because	propositions	don't	make	true	the	sentences	that express	them.	If	it	refers	to	something	like	a	"fact"	or	"obtaining	state	of affairs",	then	we	have	entities	that	can	serve	as	truthmakers;	but	notice that	this	view	is	now	burdened	with	some	serious	metaphysical	commitments,	and	to	say	that	all	sentences	are	made	true	by	such	entities takes	one	perilously	close	to	a	traditional	correspondence	theory. Ultimately,	the	question	of	what,	if	anything,	makes	'Socrates	is	a philosopher'	true	is	a	separate	metaphysical	question	left	unanswered by	everything	that	Tarski	says.	Perhaps	it's	made	true	by	a	fact,	or	state of	affairs	(Armstrong	1997),	or	by	a	trope	(Lowe	2007),	or	by	Socrates under	a	counterpart	relation	(Lewis	2003).	Perhaps	it	doesn't	have	a truthmaker	at	all	(Lewis	2001).	Perhaps	it's	made	true	by	the	relations that	obtain	between	my	beliefs,	or	by	the	utility	to	me	that	would	exist were	I	to	believe	what	the	sentence	says.	Regardless	of	which	metaphysical	view	is	correct,	we	can	all	agree	that	the	Tarskian	equivalence above	is	true.	Metaphysical	disputes	regarding	what	it	is	that	makes truth bearers true are best explored from within the metaphysical enterprise of truthmaking, and	not the theory	of truth itself. 23 This 23. It's	worth	noting	that	Tarski's	claim	to	metaphysical	neutrality	is	in	some	tension	with	his	claim to	be	doing justice to	our	classical conception	of truth, jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 14 – vol.	13,	no.	17	(august	2013) Tarski in	order to learn the	ultimate	nature	of truth, for	Tarski	may well agree	with	primitivists that no such theory can	be	provided.26 However,	this	doesn't	show	that	Tarski's	work	fails	as	a	"philosophical"	theory,	for	that	response	presupposes	that	the	only	philosophical theory	of	truth	worth	having	is	a	reductive,	non-primitivist	one.	We may	grant	to	Putnam	that	equivalences	like	''Snow	is	white'	is	true-inL	if	and	only	if	snow	is	white'	(even	if	read	in	Putnam's	problematic way,	as	necessary	logical	truths)	do	not	reveal	at	all	the	real	nature	of truth.	But	that	was	never	their	purpose.	Tarski	offers	his	definitions	of truth	in	order	to	provide	semanticists,	logicians,	mathematicians,	interpreters	of	science,	and	others	predicates	that	are	safe	from	paradox and	metaphysical	baggage,	and	yet remain true to	our	basic	understanding	of	the	notion	of	truth.	The	T-sentences,	again,	provide	a	kind of "check" that	his	definitions	conform	to that	basic	understanding; they	are	not	themselves	supposed	to	be	defining	our	basic	concept	of truth.	Putnam's	objection	misunderstands the role that	T-sentences play	in	the	theory	of	truth,	and	supposes	Tarski	to	be	up	to	something that	he	doesn't	think	can	be	done. Etchemendy (1988)	has	also	voiced	a	number	of influential criticisms of Tarski's	work.	He argues that Tarski's project of defining truth is actually at odds	with the project of understanding semantics, despite appearances to the contrary. Etchemendy argues that Tarski, in order to define a notion of truth that does not succumb to	paradox,	effectively	stipulates	a	definition	of	truth,	and	any	such stipulative definition cannot contain the empirical information essential	to	the	semantic	theory	of	a	language.	Tarski's	definitions	will usher	forth	equivalences	such	as	''Snow	is	white'	is	true	(in	the	Tarskian	sense)	if	and	only	if	snow	is	white',	guaranteeing	that	truth	(in the Tarskian sense) gets the right extension. But this equivalence doesn't	give	us	any	semantic	information	about	the	English	sentence 'Snow	is	white'.	To	do	that,	we	need	not	the	(supposedly)	logical	truth 26.	Putnam	briefly	suggests	that	the	primitivist	line	is	not	open	to	Tarski	(1985: 72),	but	he	does	not	say	why.	Perhaps	he	has	in	mind	the	sorts	of	considerations	Etchemendy	considers,	as	discussed	below. Tarski's	reticence	regarding	what	we	should	say	about	our	natural language	understanding	of	truth	has	led	several	philosophers	to	protest that	by	restricting	his	positive	views	to	formal	languages,	Tarski's	work fails	to	be	of	any	philosophical	interest.	Armed	with	our	primitivist	perspective	on	Tarski's	views,	we	can	confront these	objections	directly. For	example,	according	to	Max	Black,	"The	philosophical	relevance	of [Tarski's]	work	will	depend	upon	the	extent	to	which	something	similar [to	his	formal	language	definitions]	can	be	done	for	colloquial	English" (1948: 56). But this response begs the question against primitivism: Tarski's	work	on	the	limits	of	definability	encourages	the	thought	that truth	as	conceived	in	ordinary	thought	and	speech	is	not	definable,	and this	fact	is	of	profound	philosophical	relevance.	The	question	of	which of	our	concepts	are	foundational	and	fundamental	is	an	important	one; Black,	to	the	contrary,	assumes	that	showing	something	to	be	indefinable	and	primitive	cannot	be	philosophically	relevant. Other	philosophers	have	also	objected	to	Tarski's	theory	of	truth	on the	grounds	that	it	has	little	to	offer,	philosophically	speaking.	In	the most	infamous	case,	Putnam	declares	that	"As	a	philosophical	account of	truth,	Tarski's	theory	fails	as	badly	as	it	is	possible	for	an	account	to fail"	(1985:	64),	and	denies	that	what	Tarski	defines	"is	in	any	way	similar	in	meaning"	to	our	intuitive	use	of	truth	(1983:	37).	Putnam's	worry derives	from	his	view	of	Tarski's	truth	predicates,	which	(according	to Putnam)	apply to sentences regardless	of	what they	mean. In	effect, whether	or	not	a	sentence	possesses	Tarskian	"truth"	doesn't	depend on	what it	means,	and	so	Tarskian "truth"	can't	be real truth,	which does	depend	on	meaning. This	is	not	the	place	to	evaluate	Putnam's	objection	in	full;25	what we	may appreciate instead is how a Putnam-style	worry simply dissolves	when	we	view	Tarski's	work	through	the	primitivist	lens.	Tarski's ambitions	did	not	include	offering	anything	like	a	reductive	definition in	the	mold	of	the	traditional	theories	of	truth.	One	should	not	turn	to 25. For	further	discussion,	see	Davidson	1990,	Raatikainen	2003	and	2008,	and Patterson	2008a	and	2008b.	See	also the	closely related	discussions in	Soames	1984,	Etchemendy	1988,	and	Heck	1997. jamin	asay Tarski and Primitivism About Truth philosophers'	imprint – 15 – vol.	13,	no.	17	(august	2013) least,	about	the	truth	conditions	of	our	sentences),	and	not	vacuous logical	truths.	So	whereas	Etchemendy	sees	a	prior,	primitivist	conception	of	truth	as	somehow	conflicting	with	Tarski's	project,	the	correct interpretation	is	that	Tarski's	project	relies	on	there	being	such	a	prior conception.	As	I	have	argued,	primitivism	about	that	prior	conception is	the	view	that	is	most	consonant	with	Tarski's	project. What	remains	to	be	seen	is	whether	primitivists	can	convince	Tarski that our	use	of truth in	ordinary thought can	be consistent.	Tarski	worried	that	our	use	of	truth	in	natural	language	was	inconsistent, though	he	stopped	short	of	definitively	drawing that	conclusion.	So the	question	arises	how	the	primitivist	may	approach	the	semantical paradoxes	as	they	arise	in	natural	language.	That	topic	-	primitivism and	paradox	-	is	one	that	we	shall	have	to	take	up	elsewhere.27, 28 References Aristotle.	1966.	Metaphysics.	Trans.	Hippocrates	G.	Apostle.	Bloomington:	Indiana	University	Press. Armstrong,	D.	M. 1997.	A World of States of Affairs.	Cambridge:	Cambridge	University	Press. Asay,	Jamin.	2011.	Truthmaking, Truth, and Realism: New Work for a Theory of Truthmakers.	Doctoral	dissertation.	Chapel	Hill:	University	of North	Carolina. ---.	Forthcoming.	Against	truth.	Erkenntnis. Bar-On,	Dorit,	and	Keith	Simmons.	2007.	The	use	of	force	against	deflationism:	assertion	and	truth.	In	Truth and Speech Acts: Studies in 27. See	also	Patterson	2006b	for	thoughts	on	how	Tarski	may	approach	the	semantic	paradoxes	for	natural	language. 28.	My thanks go to the referees for Philosophers' Imprint for their thorough, helpful	comments.	I'd	also	like	to	thank	Keith	Simmons,	both	for	his	careful reading	of the	paper,	and	also for	his	patience in	helping	me	develop	my thoughts	on	Tarski.	Any	interpretive	errors,	of	course,	are	entirely	mine.	Material	from	this	paper	will	be	incorporated	into	my	monograph	The Primitivist Theory of Truth,	forthcoming	with	Cambridge	University	Press. above	involving	(Tarskian)	truth,	but	rather	the	equivalence	''Snow is	white'	is	true	(in	the	ordinary	sense)	if	and	only	if	snow	is	white'. Unlike	Tarski's	equivalence	(according	to	Etchemendy),	this	second equivalence	expresses	contingent,	empirical information	about the sentence 'Snow is	white'. Tarski's equivalence	might help define a notion	that	dodges	paradox,	but	it	won't	tell	us	anything	about	the semantics	of	natural	language. Now,	Etchemendy	goes	on	to	claim	that	one	can	move	from	Tarski's	"list-like"	definition	of	truth	for	a	language	to	a	semantic	theory for	that	language	by	employing	a	primitive	notion	of	truth	(1988:	59). On	this	approach,	we	take	the	additional	theoretical	step	of	holding that any particular truth predicate defined in Tarskian fashion expresses	our	ordinary	notion	of	truth,	and	thus	hold	that	anything	true (in the Tarskian sense) is true (in the ordinary sense). So it	might appear	that	one	can	use	(a	properly	supplemented	form	of)	Tarski's project	to	aid	in	semantics.	But	the	appearances	here	are	deceptive, says	Etchemendy,	and	"little	more	than	a	fortuitous	accident"	(1988: 52).	For	Etchemendy	argues	that	amending	Tarski	in	this	primitivist fashion	is	in	conflict	with	Tarski's	ambitions.	Tarski	wants	an	eliminative	notion	of	truth	-	and	so	one	that	can	be	properly	inoculated	from paradox	-	and	the	attempt	to	make	Tarski's	theory	philosophically	informative	ends	up	relying	on	an	uneliminated	primitive	conception of	truth. Even	setting	aside	my	aforementioned	doubts	that	Tarski	reads	the T-sentences	as	being	purely	stipulative	logical	truths,	I	do	not	believe that	we	need	to	follow	Etchemendy	in	seeing	the	primitivist	maneuver	as	being	antithetical to	Tarski's	ambitions.	As	we	have	seen,	Tarski's interest	was	never in	replacing	our	ordinary	conception	of truth with	the	kind	of	definitions	he	offers.	Rather,	Tarski's	definitions	work in conjunction	with our ordinary conception	of truth.	We know that Tarski's	definitions	are	successful	only	if	they	are	materially	adequate, in	which	case they	entail	all the	T-sentences.	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