Are	all	primitives	created	equal? JTM	Miller Forthcoming	in	The	Southern	Journal	of	Philosophy Pre-proof	version Abstract: Primitives	are	both	important	and	unavoidable,	and	which	set	of	primitives	we	endorse will greatly shape our theories and how those theories provide solutions to the problems that we take to be important. After introducing the notion of a primitive posit,	I	discuss	the	different	kinds	of	primitives	that	we	might	posit.	Following	Cowling (2013), I distinguish between ontological and ideological primitives, and, following Benovsky	(2013)	between functional	and	content	views	of	primitives. I then	propose that these two distinctions cut across each other leading to four types of primitive posits. I then argue that theoretical virtues should be taken to be meta-theoretical ideological	primitives.	I	close	with	some	reflections	on	the	global	nature	of	comparing sets	of	primitives. 1.	Primitives	and	Theories A	term	is	primitive	within	a	theory	when,	relative	to	that	theory,	the	term	cannot	be	defined	in	a non-circular	way.	Given	that	circularity	of	definition	provides	no	further	insight	into	the	meaning of	the	term	that	we	are	attempting	to	define,	a	primitive	must	be	accepted	as	non-definable,	or un-analysable.	All theories	require	primitives,	and	primitives	are	explanatorily	basic.	No	theory that hopes to be explanatory can forever introduce new terms in order to define other terms. Without primitives, a theory would contain an infinite regress of terms. The choice of primitive(s)	is	up	to	the	creator	of	the	theory.	Anyone	is	free	to	declare	any	part	of	their	theory	as primitive.	Some	disagreements	between	theories	can	be	analysed	as	disagreements	about	what to take as primitive. This is especially the case if we think that the commitments of a theory should be derivable from the primitives of that theory, or that the primitives	will provide the ultimate	explanation	of	various	aspects	of	the	theory. For	example,	and	as	has	been	discussed	extensively in	Benovsky	(2013,	2016), take	the	debate about attribute agreement in	metaphysics. The central question is 'how is it possible that two objects	share	the	same	property?'	The	debate	is	highly	complex,	but	let	us	focus	on	three	possible solutions. First, there are those that posit a bare particular that instantiates a repeatable, multiply located	universal.	Under	this	view, two	objects	a	and	b share	the	same	property	F if	a and b both instantiate the numerically identical universal F-ness (see Armstrong 1978,	Mertz 2001). Second, the tropes-bundle view. This view holds that there is no bare particular or substrata, and that instead all that an object is is a bundle of compresent non-repeatable and non-multiply	locatable	property	tropes.	Two	objects	a	and	b	share	a	property	if	they	both	have	as part (or as constituent of, or have as a member) numerically distinct F-tropes that are qualitatively	identical	(see	Williams	1953,	Paul	2017).	Third,	we	could	take	objects	as	a	primitive, 2 non-analysed	entity.	This	'resemblance	nominalism'	view	holds	that	a	and	b	both	share	the	same property	if	they	are	both	members	of	the	same	resemblance	class	(see	Rodriguez-Pereyra	2002). Each of these views has been defended in the literature recently, and each seems to be a currently	live	option	to	explain	attribute	agreement. These	briefly	sketched	solutions	to	the	metaphysical	puzzle	all	posit	important	primitive	notions. The first says that there is	a	primitive identity	relation	between	one instance	of	a	universal,	Fness,	and	another	instance	of	F-ness;	the	second	holds	that	a	primitive	exact	resemblance	holds between	two	property tropes;	and	the	third	says	that there is	a	primitive	resemblance	relation between objects	a and	b. In each case, (at least) a primitive relation is appealed to, and, as it happens,	in	theories	two	and	three	a	resemblance	relation. The primitives in all three theories play a central role in providing an answer to the original question	of	when	is	it	the	case	that	two	objects	share	the	same	property.	This	kind	of	primitive	is what Benovsky calls a 'problem-solver' (2013: 344). Without these primitives, each of the theories	would	not	be	able	to	solve	the	original	problem.	That	the	primitives	play	this	important explanatory	role is	not	a	problem	for	the	theories.	Positing	a	primitive	that	does	no	theoretical work would seem needlessly profligate, as it is commonly accepted that primitives should be explanatory. Given that they sit at the most explanatorily basic level, if a primitive has no explanatory	role,	then	it	would	appear	to	be	redundant. However, there is a lingering problem: are the primitives that we pick to play the role of problem-solvers ad hoc? An intuitive way to understand if a posit is ad hoc is if the posit is introduced	to	save	a	theory	from	a	particular	problem	and	there	is	no	additional	reason	to	posit it	except	to	solve	that	problem.1	The	issue	is	that	primitives	will	often,	at	least	to	those	who	wish to object to the theory in question, look like they are ad hoc. To the person who accepts universals and so uses a numerical identity relation between universals to explain attribute resemblance,	the	trope	theorist's	posit	of	a	resemblance	relation	looks	ad	hoc.	And	vice	versa.	We are	taught	that	we	should	avoid	ad	hoc	posits,	but	whether	we	think	that	a	primitive	is	ad-hoc	or not	seems	to	depend	on	the	viewpoint	from	which	you	are	viewing	the	posit	in	question.	Those inclined	towards	a	theory	will	likely	not	find	a	posit	to	be	ad	hoc;	to	those	opposed	to	the	theory, the	opposite	could	well	be	the	case. What	we	need is	a	way	to	compare	primitive	choices to	see	which is to	be	preferred.	Typically this	is	done	through	a	consideration	of	a	range	of	theoretical	virtues,	the	relative	importance	of which	is	not	universally	agreed	upon.	This	means	that	what	counts	as	a	good	or	more	favourable primitive is decided by a range of further concerns and commitments,	many of	which are not always	fully	explicated,	or	are,	I	will	argue,	themselves	further	primitive	commitments. In	the	rest	of	this	paper,	I	will	take	up	this	question	of	how	we	pick	between	primitives.	Are	all 1 This	is	not	offered	as	a	precise	definition	of	what	makes	a	posit	ad	hoc.	Nothing	in	this	paper	rests	on	a specific	notion	of	what	it	is	for	something	to	be	ad	hoc,	only	that	there	is	a	distinction	between	ad	hoc and	non-ad	hoc	posits. 3 primitives	created	equal?	Are	there	some	that	are	inherently	better	than	others?	I	will	begin	by sketching	some	distinctions	that	are	important	in	understanding	the	different	kinds	of	primitives that a theory	might appeal to, before commenting on how	we	might begin to choose between primitives.	My	examples	will	come	from	metaphysics,	but	primitive	choice	is	an	important	issue in	all	theories	and	as	such	what	I	say	here	will	carry	over	into	other	areas. 2.	Ideology	vs.	Ontology The difference between ideology and ontology is a much-discussed distinction dating back at least	to	Quine: Given	a	theory,	one	philosophically	interesting	aspect	of	it	into	which	we	can inquire is its ontology: what entities are the variables of quantification to range	over	if	the	theory	is	to	hold	true?	Another	no	less	important	aspect	into which	we	can	inquire	is	its	ideology	(this	seems	the	inevitable	word,	despite unwanted	connotations):	what ideas	can	be	expressed in it? ... It is	clearer, I think, to	recognize in	ontology	and ideology	two	distinct	domains	of inquiry (Quine,	1951:	14). Ontology	is	what	exists;	ideology	concerns	the	concepts	that	appear	within	the	theory.	Primitive ontological	commitments	are those	entities	within	our theory	that	are	non-reducible to further entities;2	primitive ideological commitments	are those concepts	within	a theory that cannot	be defined	in	terms	of	other	concepts.3 It is	often	held	that the	non-primitives	aspects	of	a theory	will 'come	for free',	what	Armstrong described as an 'ontological free lunch' (1997: 12).	His focus	was specifically on those entities that	supervene	on,	or	are	entailed	by the	primitive	entities.	But the	notion	can	be	expanded to cover	ideology	too.	An 'ideological	free	lunch'	then	refers	to	those	concepts	that	we	get	for	free once	we	have	accepted	the	primitive	ideological	concepts.	The	'free'	concepts	are	definable	from the	primitive	ideology. The	decision	to	favour	(primitive)	ontological	or	ideological	posits	within	the	theory	is	a	choice that	can	have	a	wide	influence	on	the	character	of	that	theory.	Take	as	an	example	debates	about modality.	An	actualist	wants	to limit	their	ontology	to just	those	entities	that	exist in	the	actual world, denying the existence of mere possibilia. There are many ways to do this, but one 2 One	alternative	way	to	understand	this	would	be	to	say	that	the	primitive	ontological	commitments	are those	entities	we	take	to	be	fundamental.	Under	this	conception,	the	fundamental	entities	are	the	most basic elements of reality, from	which other elements of reality are derived, or ultimately ground the non-fundamental. Nothing I say here rests on this notion of fundamentality. See Bliss (2017) for a discussion	of	various	roles	that	the	notion	of	'fundamental'	can	play	in	our	theorising. 3 To see the difference in action, in the example about attribute agreement, in theory one, the bare particulars	and the	universals	would	be	ontologically	primitive, and the instantiation	relation	and the identity relation between universals a primitive ideological commitment. In theory two, the tropes would	be	the	sole	ontological	primitive,	and	the	instantiation	relation,	the	compresence	relation,	and	the resemblance relation	would be ideologically primitive. In theory three, the objects	would be the sole ontological primitive, and the resemblance relation between those objects would be ideologically primitive. 4 prominent	route	is	to	refuse	to	analyse	the	modal	operators.	The	modal	operators	are	accepted as	primitive	bits	of	ideology	within	the	theory,	thereby	allowing	us	to	limit	the	number	of	entities that	we	are	committed	to	in	our	ontology.	This	kind	of	actualist	favours	ontological	parsimony	at the	cost	of	a	more	complicated	ideology	(see	Fine	1977). In contrast, Lewis' modal realism (1986) favours ideological parsimony over the ontological variant.	Lewis	wants	to	reduce	modal	claims,	rejecting	the	idea	that	modal	claims	are	irreducibly intensional.	Instead,	modal	claims	are	extensional	claims	about	worlds,	and	the	entities	in	those possible	worlds.	These	are real, concrete	entities	and	Lewis is fully	ontologically committed to them. This delivers ideological simplicity for Lewis as he no longer is required to accept unanalysable	modal	operators.	It	is	for	similar	reasons	that	Lewis	accepted	the	existence	of	sets	in order	to	gain	the	benefits	of	set	theory: It	offers	an	improvement	in	what	Quine	calls	ideology,	paid	for	in	the	coin	of ontology. It's an offer you can't refuse. The price is right; the benefits in theoretical	unity	and	economy	are	well	worth the	entities... the	benefits	are worth	their	ontological	cost	(Lewis,	1986:	3–4). The moral here is that ontological and ideological parsimony will often be a trade off. An ontological	posit	might	reduce	ideological	cost	and	vice	versa,	but	it	is	far	from	clear,	prima	facie, which we should prefer. Why should we think that ontological parsimony is better than ideological	parsimony?	Given	that,	as	noted	above,	we	all	must	posit	some	primitives	within	our theories,	which	of these	kinds	of	primitives should	we	prefer? Should	we in	our theories	posit ontological	or	ideological	primitives?	From	debates	about	modality,	we	can	see	that	this	choice	is not	a	clear	one.4 A	further	consideration	that	appears	when	we	want	to	decide	on	whether	to	posit	ontological	or ideological	primitives	has	been	discussed	by	Cowling	(2013).	This	relates	to	two	distinct	ways	in which a theory might be ontologically parsimonious and two ways in which it might be ideologically	parsimonious: NO-Parsimony: Quantitative ontological parsimony, which concerns the number	of	ontological	commitments. KO-Parsimony: Qualitative ontological parsimony, which concerns the number	of	kinds	of	ontological	commitments. NI-Parsimony: Quantitative ideological parsimony, which concerns the number	of	ideological	commitments. KI-Parsimony: Quantitative ideological parsimony, which concerns the 4 See Shapiro (1993) for a	more detailed discussion of the ontology-ideology trade-off, and the use of Occam's	razor	in	the	case	of	modality	(though	Shapiro	does	not	discuss,	as	I	do	here,	the	question	of	the primitiveness	of	the	theoretical	virtues	themselves).	The	moral	of	Shapiro's	discussion	is	much	the	same as mine – a reduction of ontology for ideology, or vice versa must be philosophically justified, and Occam's	razor	cannot	be	'wielded	blindly'	(1993:	473). 5 number of kinds of ideological commitments. (see Cowling 2013: 3897; 2017). Thus, the choice between favouring a parsimonious ontology or ideology is	more complicated than	it	first	seemed	to	be.	Take	Lewis'	acceptance	of	the	existence	of	sets.	Lewis	could	claim	that whilst he is rejecting NO-Parsimony as he accepts the existence of sets, he is respecting KOParsimony as the entities that he is accepting are all of the same kind. As Lewis states: 'I subscribe	to	the	general	view	that	qualitative	parsimony	is	good	in	a	philosophical	or	empirical hypothesis;	but	I	recognize	no	presumption	whatever	in	favour	of	quantitative	parsimony'	(1973: 87). Cowling is less clear about how	we	might draw the kind vs. number distinction in the case of ideological	parsimony.	The	reason	for	this	is	that	we	have	less	of	a	grip	on	how	it	could	be	that some	bits	of	ideology	are	of	the	same	kind.	Perhaps	ideological	kindhood	is	too	mysterious	to	be useful.	However,	as	Cowling	notes: KO-Parsimony does not come	with a comprehensive analysis of ontological kindhood,	but	has	not	been	dismissed	on	these	grounds.	And,	while	one	might propose that ontological kinds are simply natural kinds like tiger and electron, such a proposal precludes a suitably general application of ontological parsimony to contexts where theoretical virtues are crucial but natural	kinds	are	not	relevant	(e.g.,	murder	mysteries	and	set	theory).	There is, then, no settled account of ontological kindhood.	But, since this	does	not license	us to	reject (KO-Parsimony),	we	have	no	compelling	reason to	reject or	dismiss	(KI-Parsimony)	(Cowling,	2013:	3898). Whilst	I	agree	with	Cowling	on	this	point,	we	can	at	least	point	to	an	example	of	a	debate	where we	seem	to	understand	the	idea	of	an	ideological	kind	to	show	that	we	do	have	a	working	grasp of the idea. The example comes from recent defences of 'big-G Grounding' (hereafter just 'grounding'). Proponents of grounding argue that grounding is one relation that can replace instances of a variety	of	metaphysical	relations	that	we	previously	have	thought	to	be	distinct.	Grounding	is	a unitary	notion,	and	one	that	can	replace	various	more	variegated	relations	that	metaphysicians have	otherwise	been	interested	in	(see	Audi	2012;	Rosen	2010;	Schaffer	2009).	Grounding	is	also widely taken to be a primitive (see Fine 2012;	Rodriguez-Pereyra 2005;	Rosen 2010; Schaffer 2009;	Witmer	et	al.	2005).	Importantly	for	my	purposes	here,	grounding	is	additionally	taken	to be	an	internal	relation.5	This	means	that	it	is	not	a	further	ontological	posit,	but	rather	holds	just 5 That	grounding	is	internal	is	a	common	assumption	within	the	literature;	see	Raven	(2015),	and	Rosen (2010). Indeed, that grounding is internal is part of	why Bernstein (2016) and Schaffer (2016) both argue	that	grounding	and	causation	must	be	distinguished,	as	causation	is	not	internal.	Bennett	(2011: 33)	goes	further	to	argue	that	grounding	is	'superinternal',	though	note	that	Bennett	is	explicit	that	the claim	that	grounding	is	superinternal	should	not	lead	us	to	think	that	it	is	not	internal,	as	she	holds	that every	superinternal	relation	is	also	internal. 6 in virtue of the existence of the relata it relates, and the intrinsic nature of those relata. Grounding	is,	I	will	assume,	a	bit	of	ideology,	not	ontology. Schaffer	provides	the	relations	between	the	following	entities	as	'clear	examples	of	grounding': (i)	the	entity	and	its	singleton, (ii)	the	Swiss	cheese	and	its	holes, (iii)	natural	features	and	moral	features, (iv)	sparse	properties	and	abundant	properties (v)	truthmakers	and	truths	(Schaffer,	2009:	375) For its proponents, grounding simplifies and unifies an otherwise overly complex family of relations	that	are	all	variants	of	ontological	dependence,	and	this	parsimony	is	certainly	a	major part	of	why	grounding	is	popular.6 However, not everyone is convinced. One prominent line of dissent has been to argue that grounding	is	not	a	unitary	relation.	The	argument	here	is	not	to	deny	that	there	are	metaphysical relations	between	entities	of	the	kinds	listed	above,	but	just	that	the	relations	are	not	the	same. Koslicki (2015) argues that two claimed examples of grounding relations – the determinabledeterminate	relation	and	the	Aristotelian	genus-species	relation	–	are	importantly	different	and cannot	actually	be	instances	of	the	same	relation.	Wilson	(2014)	independently,	but	to	a	similar conclusion,	argues that	a	number	of the	relations	which	are taken to	be instance	of	grounding, such as token identity, realization, the classical extensional part-whole relation, the set membership	relation,	the	proper	subset	relation,	and	the	determinable-determinate	relation	are too	distinct	to	be	unified	under	one	course-grained	metaphysical	relation. The	grounding	proponents are therefore arguing that grounding is a	univocal ideological kind. Many	of	the	more	fine-grained	relations	that	metaphysicians	had	previously	been	focused	on	are replaced	with	instances	that	kind.	However,	the	dispute	is	not	about	the	number	of	instances	of the	relations	that	there	are.	Rather	it	is	about	whether	all	the	instances	are	in	fact	instances	of	a single univocal kind. The objections held that instead	we need a number of different kinds of ontological	dependence	relations	(at	least	some	of	which,	presumably,	would	be	primitive).	The disagreement is over the numbers of	kinds, not about the number of instances. The two sides might	agree	on	how	many	instances	of	grounding	or	ontological	dependence	relations	hold	in	the world;	they	disagree	about	whether	we	need	to	posit	one	or	more	ideological	kinds. The	example	of	grounding	illustrates	that	we	have	some	grip	on	the	idea	of	an	ideological	kind. We	can	also	point	at	a	potential	instance	of	kindhood	in	ideology	that	will	significantly	influence 6 The applications for grounding have so far included (amongst others) metaphysical foundationalism (Schaffer 2010a), truthmaking (Cameron forthcoming; Liggins 2012; Schaffer 2010b), intrinsicality (Witmer	2014,	Rosen	2010),	perceptual	knowledge	(Chudnoff	2011),	temporal	ontology	(Baron	2014), and the nature of mental content (Trogdon 2015). Whilst of course these papers overlap, they are independent	discussions	of	grounding,	relative	to	the	specific	aims	listed	here. 7 the very plausibility of the theory in question. This time consider ontological pluralism. The ontological	pluralist	believes	that	there	are	multiple	different	ways	in	which	things	can	exist	(or, if	preferred,	multiple	ways	of	being).	Aristotle,	Aquinas,	Descartes,	Russell,	Moore,	and	Heidegger have	all	at	different	times	been	seen	as,	or	perhaps	accused	of	being,	ontological	pluralists	(see Turner	2010;	see	McDaniel	2009,	2017	for	a	recent	defence).	My	focus	will	be	to	comment	on	one particular	argument	against	ontological	pluralism,	namely	that	it	is	an	unparsimonious	theory,	as it	requires	the	positing	of	multiple	quantifiers. Quantifiers	are	a	classic	example	of	bits	of ideology.	Quantifiers	do	not 'exist' in the	way	that	a table	does.	Quantifiers	rather	are	bits	of	our	theorising	that	help	us	understand	the	commitments and	consequences	of	those	theories.	Thus,	the	claim	against	the	ontological	pluralist	is	that	they posit	an	unneeded	multiplication	of	ideology.	Occam's	razor	is	invoked,	and	ontological	pluralism is	rejected.	The	ontological	pluralist	might	respond	by	rejecting	the	underlying	Quinean	criterion of ontological commitment, but let us assume that they wish to maintain the criterion. Our ontological	pluralist	therefore	will	likely	say	something	like	this: ontology is	about	what	existential	quantifiers	range	over. I simply	deny that there is	only	one	of them.	Rather, there	are	many	-	maybe	one, '∃1',	which ranges over abstracta, for instance, and another, '∃2' which ranges over concreta.	If	you	want	to	talk	about	abstracta,	you	have	to	use	'∃1';	if	you	want to	talk	about	concreta,	you	have	to	use	'∃2'	(Turner,	2010:	7-8). Of course, saying this is what allows room for the parsimony argument. Why posit multiple quantifiers	when,	at	least	so	the	ontological	monist	will	say,	we	can	make	do	with	just	one?	I	will leave aside here Turner's discussion on the parsimony argument (what he calls the 'economy argument';	2010:	28-34).	His	responses	may	be	sufficient	for	ontological	pluralists.	I	wish	to	offer at	least	the	seeds	of	a	further	response	that	could	be	developed. The new response holds that	whilst the ontological pluralist	might be rejecting	NI-Parsimony, they	accept	and	embrace	KI-Parsimony,	which	says	that	the	number	of	primitives	in	a	theory	is not	important.	What	is	important	is	the	number	of	kinds	of	primitives.	It	certainly	does	seem	to be possible for the ontological pluralist to argue that they are positing only one kind of ideological	primitive	–	primitive	existential	quantifiers	–	just	like	the	ontological	monist. Working out the full details of this response is beyond the scope of this paper. Perhaps the monist	will	respond	that	the	distinct	quantifiers	are	in	fact	different	kinds	after	all.	My	contention is only that given that this option would at least prima facie be available to the ontological pluralist,	then	we	can	see	that	ideological	kindhood,	and	the	difference	between	the	four	forms	of parsimony	listed	above	is	important	when	it	comes	to	creating	and	defending	a	theory.	It	is	not enough for the ontological monist to complain that ontological pluralism is unparsimonious simpliciter.	They	must	also	argue	that	we	should	be	motivated	by	NI-Parsimony.	How	we	might do	that	without	begging	the	question	against	the	ontological	pluralist	is	less	clear. 8 3.	Functional	Role	vs.	Content A	further	distinction	that	is	relevant	to	comparing	primitives	comes	from	Benovsky	(2008,	2013, 2016). This concerns the role and nature of the primitive within our theories. The first understands primitives through the function that the primitive is introduced to play. Such primitives are introduced with little (or even no) comment as to the specific nature of the primitive	itself.	Their	nature	remains	something	like	a	Lockean	'we-know-not-what',	and	they	are introduced	instead	just	as	a	'we-do-know-what-they-do'	(Benovsky	2013:	345).	The	nature	of	the primitive remains a	mystery, but	we get a grip on the primitive through the functional role it plays. A good example of this is instantiation. Relatively little is said about the nature of instantiation.	Armstrong,	when	introducing	instantiation	only	remarks	that	it	is	a	tie	that	holds	a universal	and	a	bare	particular	together	(1997).	What	the	primitive	does	is	more	important	than what	it	is. Alternatively, a content view of primitives says that there is	more to a primitive than just its functional	role.	As	Benovsky	notes:	'under	this	view,	if	two	primitives	perform	the	same	function, they	may still not	be the same thing, and thus they	may	not	be	metaphysically equivalent, but only theoretically equivalent (that is, equivalent for all theoretical purposes). The slogan goes: even	if	they	do	the	same	thing,	they	are	not	the	same	thing'	(2013:	346). Perhaps one way to grasp this distinction is through an analogy to the debate between the categoricalist and dispositionalist about properties. The dispositionalist will say that there is nothing	more to	a	property than	what it	disposes	an	object to	do –	nothing	beyond the causal powers	that	it	bestows	upon	the	property.	The	'disposition	is	thought	to	be	a	persisting	state	or condition	that	makes	possible	the	manifestation'	(Mumford	2010).	A	property	in	the	actual	world is	the	same	property	in	some	possible	world	iff	it	bestows	the	same	causal	profile	on	the	object	in that	possible	world that instantiates it as it	does in the	actual	world.	The categoricalist rejects this.	For	example,	Armstrong	(1989,	1997)	says	that	there	is	a 'quiddity'	to	a	property	–	a	thisness	for	properties.	This	means	that	the	same	property	could	have	a	different	causal	profile	(or bestow	alternative	causal	powers	to	an	object)	in	different	possible	worlds.	Properties	are	more than	just	their	causal	profile.7 Analogously, if a	primitive is	understood	purely functionally, then there is	no	sense in	which	a different	primitive	could	play the	same functional role. If	a	primitive	plays the	same functional role	in	a	different	theory,	then	they	are	the	same	primitive.	In	contrast,	under	the	content	view, numerically	different	primitives	could	play	the	same	functional	role. Benovsky's distinction is a valid one, but overlooked is how the ideology/ontology distinction plays into this.	Benovsky largely	skates	over the ideology/ontology	distinction,	or reduces that distinction	to	one	of	the	primitives	having	a	different	functional	profile.	For	example,	he	states: 7 Not all categoricalists	will accept quiddities, however these	more complex details do not bear on the analogy	being	used	here.	For	an	overview	of	this	debate,	see	Choi	and	Fara	2012. 9 Think	of	the	claim	that	one	theory's	problem-solver	is	a	relation	and	the	other theory's problem-solver is a substratum, and so they are entities with a different	nature.	What	does	such	a	claim	amount	to?	Perhaps	what	one	wants to say here is that there are some differences between the two problemsolvers like, for instance, the fact that a substratum is 'ontologically independent'	(that	is,	it	can	exist	without	exemplifying	any	properties)	while the relation	of compresence cannot just 'be there' and relate	nothing.	But if that were the difference between the two problem-solvers, interestingly, it would	be	a functional	difference: it	would	be	something the	substratum	can do ('standing alone', tying	no	properties together) that compresence cannot do. So, in such a case, the Functional View applies: there is a difference between	the	two	problem-solvers,	and	it	is	a	functional	one	(Benovsky,	2013: 349-50). Benovsky takes the difference between the primitives to be one of function as part of his argument that we should prefer the functional view over the content view. However, a more natural	understanding	of this is through the ideology/ontology	distinction. Let	us consider the first	two	options	from	the	above	discussion	of	attribute	agreement	to	explore	this	fully. The substrata-universal theory posits two primitive ontological entities – universal properties and substratum – and two ideological primitives – an instantiation relation and an identity relation	between	instances	of	the	same	universal.	We	might	be	inclined	to	initially	think	of	these relations	as	further	ontological	entities	but	that	would	be	wrong.	These	relations	are	taken	to	be formal.	They	are	formal	in	the	same	way	that	ontological	categories	are	formal	and	thus	are	not further	elements	of	reality	beyond	the	existence	of	the	entities	that	fall	under	those	categories.8 The	same	goes for	the	relations	of instantiation	and identity.	They	are ideological	primitives	as they	cannot	be	defined	or	analysed further	within that theory;	but they	come	at	no	ontological cost	(they	are	an	'ontological	free	lunch'),	as	they	are	internal	relations.9 Alternatively,	the	bundle-trope	theorist	posits	just	one	primitive	ontological	entity	–	tropes	–	and 8 Ontological	categories	are	part	of	the	ideology	of	our	theory.	They	do	not	exist	as	further	entities	over and	above	of	the	entities	that	fall into	those	categories.	The	members	of	the	categories	are	ontological commitments;	the	categories	are	ideological.	See	Lowe	(2006)	for	a	view	like	this,	and	Miller	(2016)	for defence	of	that	view. 9 Internal relations are contrasted with 'external' relations, which are additional entities – additional ontological posits. In contrast, internal relations are part of the ideology of a theory as statements involving	the	relations	will	express	truths	('Object	O	instantiates	property	p'	expresses	a	truth	about	O), but the truthmakers for the	statement	will	be	non-relational. If, say, causal relations	are	external (see references	in	footnote	5,	though	see	Lowe	(2016),	Simons	(2016),	Heil	(2016)	for	arguments	against	the externality	of	causation)	then	statements	about	causal	relations	also	express	truths,	but	the	truthmakers for	those	statements	will involve	the	positing	of	a	relational	property.	This	would	mean	that	causation will	be	a	genuine relational	property	within	our	ontology,	not just	our ideology.	None	of this, though, rules	out	some	internal	relations	that	are	part	of	our	ideology	being	primitive	as	in	the	case	of	identity and instantiation.	They	are internal for the	reasons	stated,	and	primitive	as they	cannot	be	defined	or analysed	further	within	that	theory.	External	relations	may	also	be	primitive	ontological	commitments. For example, if we believe that causal relations cannot be reduced to non-causal properties then causation	would	appear	to	be	a	primitive	ontological	commitment	of	that	theory.	For	examples	of	this, see	Tooley	(1987)	and	Carroll	(1994). 10 three ideological primitives – an instantiation relation, a compresence relation, and an (exact) resemblance relation. These relations are ideological in the same	way as under the substratauniversal	theory.	They	are	no	'addition'	to	our	ontology.	They	are	formal	concepts	that	we	use	in order	to	describe	the	nature	of	reality. Once again leaving aside debates about which of these views is correct (and various more complex	versions	of	these	views),	we	can	see	the	difference	in	what	'problem-solving'	primitive has	been invoked.	As	Benovsky	states: 'one theory's	problem-solver is	a relation	and the	other theory's problem-solver is a substratum' (2013: 349). This means that one is an ontological primitive	whilst	the	other	is	an	ideological	primitive.	To	clarify,	my	claim	is	not	to	deny	that	there is	potentially	a	difference	here	in	function	or	in	content.	That	may	be	the	case.	My	claim	is	only that	there	is	at	least	also	a	difference	in	choosing	an	ontological	or	an	ideological	primitive	in	this case.	The	difference	between	the	primitives	is	at	least	partly	explained	by	the	difference	that	one is	ontological	and	the	other	ideological. With this in	mind, I propose that these two distinctions cut across each other leading to four options	for	a	primitive.	A	primitive	that	we	posit	could	be: 1)	A	purely	functional	ideological	posit 2)	A	purely	functional	ontological	posit 3)	A	non-purely	functional	ideological	posit	(the	content	view) 4)	A	non-purely	functional	ontological	posit	(the	content	view). This	four-way	distinction	illustrates	quite	how	different	primitives	can	be.	However,	I	will	outline one	further	kind	of	primitive	before	commenting	on	how	we	go	about	primitive	choice. 4.	Theoretical	Virtues	as	Primitives We have seen that a primitive can come in four types, as created by the intersection of the ideology/ontology	and	the	functional/content	distinctions.	We	have	also	seen	how	when	we	try to	compare	primitives,	we	must	be	aware	of	quantative	and	qualitative	parsimony.	This	means that	at	least	with	respect	to	parsimony,	we	can	favour	(or	reject)	kind	or	number	parsimony	for each	of these	primitive	types.	Given	this,	and	the	potential	effect that	parsimony	could	have	on our	primitive choice,	we	might	ask	what	parsimony	really is.	My	claim	will	be that	parsimony, and	other	theoretical	virtues,	are	primitives	too,	albeit	ones	that	do	not	fit	neatly	into	any	of	the above	categories. We have already seen that parsimony comes in many different forms. However, those distinctions	provide	neither	a	definition	nor justification	of	parsimony.	Why	should	we	believe that	parsimony is	a	virtue in	our theories? I am	not the first to	question	what	our	warrant for 11 accepting	parsimony	(or	the	related	notion	of	simplicity)	is.10 There are two initial reasons why we might support parsimony. First, we could argue that parsimony	is	epistemologically	justified.	A	parsimonious	theory	proves	a	greater	understanding of	the	target	phenomenon	compared	to	an	alternative	equally	explanatory	but	less	parsimonious theory.	Second,	we	might think that	nature itself is	parsimonious.	Following	Newton,	we	could think	that: We	are	to	admit	no	more	causes	of	natural	things	than	such	as	are	both	true and	sufficient	to	explain	their	appearances.	To	this	purpose	the	philosophers say	that	Nature	does	nothing	in	vain,	and	more	is	in	vain	when	less	will	serve; for	Nature	is	pleased	with	simplicity,	and	affects	not	the	pomp	of	superfluous causes	(Newton,	1846:	Book	3;	p.	384). We	might	reject	either	or	both	of	these	claims,	but	that	we	can	reject	parsimony	tells	us	nothing about	whether	it	is	a	primitive	or	not.	So,	why	should	we	think	of	parsimony	as	a	primitive?	To see	this,	consider	the	discussion	of	theoretical	virtues	in	Nolan	(2015).	Nolan	considers	how	we might justify theoretical virtues. One method is to support one theoretical virtue through a further	virtue (or	virtues). For	example,	parsimony	might	be	a	valuable theoretical virtue	as it leads	to	simplicity,	which	is	itself	a	theoretical	virtue.	The	problem	is	that	we	now	need	to	justify simplicity. Nolan concludes his assessment of this method of justifying theoretical virtues by saying	that: such justifications of theoretical virtues tend to bring the problem of justifying the other virtues into sharp focus; but to some extent this sort of bump-shifting is unavoidable unless there is a way to justify a method without	using	any	method.	And	there	isn't.	(Nolan,	2015:	225) Our initial characterisation of a primitive was that a term is primitive within a theory when, relative	to	that	theory,	that	term	is	not	defined	except	in	a	circular	way.	The	'bump-shifting'	that Nolan mentions suggests that theoretical virtues are primitive-like. On this first method, we cannot justify parsimony	without appealing to other theoretical virtues,	which in turn,	will be justified	through	other	theoretical	virtues,	including	parsimony.	The	justification	is	circular,	and so	we	are	ultimately	forced	to	accept	them	as	primitives	within	our	theory. The	second	method	of	justification	for	theoretical	virtues	that	Nolan	discusses	is	to: look at past successes in inquiry and diagnose what was good about the method that yielded those successes. If simplicity was crucial to Einstein's breakthroughs about relativity, or to the Copernican/Galilean/Newtonian revolution in cosmology, for example, then that may provide us with good reason to think that simplicity, of the relevant sort, is a theoretical virtue 10 See	inter	alia	Baker	(2003,	2016),	Brenner	(2017),	Derkse	(1992),	Forster	and	Sober	(1994),	and	Sober (1981,	2015)	for	various	discussions	of	parsimony	and	simplicity,	both	applied	to	particular	cases	and	in general. 12 (Nolan,	2015:	225). The	view is that the theoretical	virtue	as it is	applied	shows	us that it is	valuable.	However,	as Nolan	points	out,	how	do	we	evaluate	'success'?	We	cannot	simply	assign	favour	to	those	theories that	already	display those theoretical	virtues that	we	are interested in. If 'success' is shown	by theories having explanatory power whilst being parsimonious, then we have not justified parsimony in looking at the success of those theories. We cannot justify the adoption of a theoretical virtue	on the	grounds that it brought success if those successes are at least in	part taken	to	be	successes	in	virtue	of	them	exemplifying	that	virtue. As	Nolan	comments, this	problem	whilst	not	negligible, is	also	not insurmountable.	Sometimes, we	do	discover	what	characteristics	our	inquiry	should	have	by	seeing	what	has	worked	before. However, this again illustrates the primitive-like nature of theoretical virtues.	Much like other examples	of	primitives,	we	cannot	endorse	a	theoretical	virtue	except	by	showing	how	that	virtue helps	us	to	explain	what	we	are	trying	to	explain.	This	is	the	same	as	the	positing	of	ontological primitives and then showing that through positing that primitive we can explain the phenomenon	we	want	to	explain.11	It	seems	reasonable	therefore	to	think	that	theoretical	virtues play	a	primitive-like	role	within	our	theories. Parsimony, and	other theoretical virtues	potentially, therefore seem to	be	primitive-like.	What about the ontological/ideological distinction? Theoretical virtues are clearly not ontological. Even	if	reality	is	best	thought	of	as	parsimonious,	this	is	not	because	reality	contains	some	entity that is 'parsimony'. It is clear that	we	should	not reify	parsimony,	nor	posit it as	a	property	of entities.	If	parsimony	is	a	property	at	all,	then	it	is	a	property	of	theories,	not	things. Perhaps	we	should	therefore	think	of	theoretical	virtues	as	further	bits	of	ideology.	If	this	is	the case,	then	theoretical	virtues	might	be	a	particular	example	of	some	kind	of	primitive	discussed earlier.	However, if	we take theoretical virtues to be	parts of our ideology, and, as argued,	we take	them	to	be	primitive	because	they	resist	further	analysis,	then	we	must	recognise	that	these theoretical virtue ideological primitives play a very different role than other ideological primitives. This is because the normal role for theoretical virtues is to allow us to compare competing theories. This means that theoretical virtues, unlike other posited ideological primitives,	are 'inter-theoretic'	– they	are	not	part	of	any	single theory,	but	are,	at	best,	part	of some	more	(perhaps	maximal)	general	methodological	theory.12 There is, however, a further issue for those who take theoretical virtues to be instances of ideology. Ideology is sometimes taken to be 'external' or 'in the world'. I have in mind here people	like	Sider	(2011)	who	argues	that	the	existential	quantifier	carves	reality	at	its	joints.	This therefore	is	a	piece	of	ideology	that	is	non-formal	in	some	sense.	It	is	'in'	the	world	even	if	it	does not	exist;	it	is	ontic,	yet	it	is	a	bit	of	ideology. 11 Sider	similarly	suggests	that	the	choice	of	primitive	can	be	justified	if	that	choice	leads	to	an	explanatory and	predictively	successful	theory	(see	Sider	2011:	14-16,	51,	114). 12 I	am	grateful	to	an	anonymous	reviewer	on	this	point. 13 If	we	accept	that	ideology	can	be	like	this,	then	we	should	resist	the	idea	that	theoretical	virtues are	ideology.	Theoretical	virtues	are	unavoidably	formal.	They	are	epistemological	limits	on	our theories	and	should	never	be	taken	to	be	ontic	even	if	we	believe	that	reality	conforms	to	them	– or perhaps more accurately that a theory that abides by such theoretical virtues accurately describes	the	world	or	the	phenomenon	in	question.	Even	if	we	believe	that	reality	contains	very few	posits	that	does	not	mean	that	reality	is	parsimonious.	The	reason	for	this	is	that	parsimony (and other theoretical virtues) are comparative. We can only make sense of a theory being parsimonious	in	relation	to	a	less	parsimonious	theory.	If	we	accept,	as	most	do,	that	there	is	only one	reality	(irrespective	of	how	many	ways	to	describe	reality	there	are),	then	reality	cannot	be compared to some further reality to see	which is	more parsimonious. There is no alternative reality	to	compare	reality	to	in	order	to	see	how	parsimonious	it	is.13 These issues point against simply taking theoretical virtues as being part of our ideology, and instead,	I	argue,	suggest	rather	that	theoretical	virtues	are	some	alternative	type	of	primitive	that does	not	fit	into	the	four-way	distinction	outlined	above.	Thus,	my	proposal	is	to	take	theoretical virtues to be meta-theoretical ideological primitives. This would distinguish them from the ideological primitives within first-order theories, but would maintain the importance of theoretical	virtues	in	our	theory-choice,	and	their	theory-shaping	role,	without	being	part	of	the theories that they	shape.	Theoretical	virtues	as	meta-theoretical ideological	primitives	explains how	theoretical	virtues	are	able	to	perform	their	role	as	criteria	by	which	we	can	compare	firstorder theories, without forcing us to admit of any primitive that is neither ontological or ideological. However, either way – whether we resist the above points and take them to be first-order ideological posits, or	meta-theoretical ideological posits – that theoretical virtues are	primitive bits	of	ideology	needs	to	be	explicitly	recognised.	The	choice	of	which	theoretical	virtue(s)	guide us	can	(at	least)	be	as	important	as	positing	a	primitive	resemblance	relation,	or	a	primitive	kind of	entity.	Theoretical	virtues	play	just	as	strong	a	structuring	role	within	our	theories	and	dictate constraints on that theory in the same	way as	more explicitly acknowledged primitive posits. However, theoretical virtues are not often discussed as important primitive ideological commitments in the	way that, say, the exact resemblance relation is debated as an ideological primitive in the bundle-trope theory of attribute agreement. Theories are expected to defend their positing of standard ideological or ontological primitives, but are rarely asked to defend their	appeal	to	a	particular	theoretical	virtue,	despite,	as	we	have	noted	with	parsimony,	the	lack of	clarity	about	those	theoretical	virtues. 5.	Primitive	Choice I have outlined a number of different kinds of primitives. What then are the prospects for comparing	primitives?	Are	all	primitives	created	equal?	First,	the	above	distinctions	have	shown that	there	are	a	number	of	different	kinds	of	primitives,	but	that	there	appears	to	be	no	definite 13 This	is	even	the	case	for	Lewis'	modal	realism	as	reality	for	Lewis	is	the	total	of	all	possible	worlds. 14 hierarchy	of 'better'	or 'worse'	primitive	posits.	Despite	all this, it is	not the	case that	anything goes.	We	still	need	to	be	able	to	adjudicate	between	different	sets	of	primitives.	I	cannot	offer	any fully	detailed	methodology	here,	but	I	offer	some	(hopefully	illuminating)	thoughts. Thankfully,	we	need	not	compare	sets	of	primitives in isolation.	We	can	compare	primitives	by looking at the consequences that a set of primitives entails. Take a theory, T. T posits a set of (ontological and/or ideological) primitives P. From P we should be able to derive the commitments	of	T.	From	P,	we	should	be	able	to	understand	how	T	would	provide	solutions	to the kinds of problems that we take to be important for theories in the domain to provide solutions	to.	The	value	of	the	primitives	can,	and	should,	be	assessed	with	respect	to	the	widest scope	of	the	theory	in	question.	The	set	of	primitives	P	can	in	this	way	be	compared	to	the	set	of primitives	P*	within	theory	T*	by	seeing	how	well	T	and	T*	provide	the	wanted	solutions	to	the relevant	questions	and	puzzles. This	suggests	that	the	best	way	to	compare	primitives	is	to	look	at	those	primitives	relative	to	the whole theory within which they are posited, thus requiring a global understanding and appreciation	in	our	theory	construction.	Put	another	way,	this indicates	an	explicit	need	for	socalled	'system-building'.	Once	we	have	rejected	those	theories	built	upon	sets	of	primitives	that are	either	at	first	glance,	or	through	more	detailed	analysis, inconsistent,	then	we	would	be	left with	a clearer range	of consistent	whole-theory	options.	Further conceptual	or	empirical	work may	strike	out	what	previously	seemed	to	be	a	possible	theory.	It	may	be	that	we	will	ultimately be	able	to	through	further	analysis	realise	that	only	one	option	remains	open	to	us,	though	this	is not	obviously	the	case.	How	we	decide	between	those	remaining	options is	a	difficult	question, and	may	change	from	domain	to	domain,	but	we	can	only	compare	sets	of	primitives	fully	if	we know the comparison class against which to compare them, and that requires a global perspective	on	a	theory	and	its	benefits.14 To	see	this	in	action,	and	going	back	to	a	previous	example,	grounding	theorists	seek	to	eliminate many of the relations that other metaphysicians have posited in favour of a single 'Big-G Grounding' relation. This, I've argued, can be interpreted as an attempt to focus on a specific primitive relation and consider whether this single primitive relation can explain what was previous	explained	through	a	set	of	primitive	(or	a	set	of	primitive	and	non-primitive)	relations. The	methodology of grounding theorists seems to have often (even if not by design) been to explain	on	a	case-by-case	basis	how	grounding	can	explain	various	phenomena.15	One	example	of grounding would not, by itself, be persuasive with respect to the claim that the various metaphysical	relations	can	be	replaced	with	a	single	unitary	notion	of	grounding. I	wish	to	remain	neutral	here	as	to	whether	this	metaphysical	account	is	correct.	My	point	is	that the	theory,	and	grounding	as	a	primitive	posit,	only	becomes	persuasive	if	we	consider	the	view 14 For a version of this view	within the domain of	metaphysics see Lowe (1998: chapter 1; 2011), and Miller	(forthcoming). 15 See references in footnote 6. Whilst these applications overlap, they are independent discussions of grounding,	relative	to	the	specific	aims	listed. 15 in a global way. The defence of grounding has been local with each new example taken up individually, but grounding as an overarching claim is only persuasive if multiple previously posited (primitive) relations can be subsumed under it. The way to compare the grounding account to its competitors is to compare the primitive(s) invoked relative to the wider metaphysics	that	they	are	within. Second,	we	must	be	open	about	both	what	our	primitives	are,	and	what	kinds	of	primitives	they are. Whilst there may not be anything inherently better or worse between, say, positing ontological rather than ideological primitives, that	we have posited ontological primitives	will mean	that	that	theory	is	importantly	different	from	one	that	favours	ideological	primitives.	It	is through	explicit	discussion	of	the	primitives	we	are	positing	within	our	theory	that	we	are	able	to then	compare	them.	Only	then	can	we	begin	to	see	which	theories	favour	ideology	over	ontology, or	kind	parsimony	over	number	parsimony,	or	are	ultimately	driven	by	a	commitment	to	certain theoretical	virtues.	Whether	or	not	we	find	the	theories	persuasive	will	at	least	partially	depend on	these	issues. 6.	Conclusion The aims of this paper have been both diagnostic and prescriptive. I have characterised	what primitives	are,	and	made	some	key	distinctions	between	types	of	primitives.	I	have	also	argued that there	are some	primitives	–	most centrally theoretical virtues	– that are	primitives in	our theories,	but	do	not	often	get	explicitly	treated	as	such. I	am	not	arguing	that	we	should	avoid	appealing	to	primitives,	or	to	primitive	theoretical	virtues. Quite	the	opposite	–	I	have	claimed	that	we	cannot	hope	to	avoid	primitives,	but	that	we	should be	open	and	honest	about	what	primitives	we	are	invoking.	Primitives	shape	a	theory	from	the ground	up.	Which	ones	we	adopt	is	a	crucial	part	of	a	theory.	We	should	not	be	worried	by	this. An	appeal	to	a	primitive	is	not	a	sign	that	the	theory	has	failed.	Rather,	identifying	the	primitives of	a	theory	allows	us	to	better	understand	how	the	elements	of	that	theory	tie	together.	Seeing how	positing	certain	types	of	primitives	will	affect	the	resultant	theory	is	one	of	the	best	ways	to explore	what	theoretical	or	conceptual	space	is	open	to	us.	Primitives	cannot,	and	should	not,	be eliminated	from	our	theories,	but	we	should	learn	to	recognise	the	different	kinds	of	primitives and	embrace	them	more	openly. References Armstrong,	D.	M.,	1978,	Nominalism	and	Realism.	Cambridge:	Cambridge	University	Press. Armstrong,	D.	M.,	1989,	A	Combinatorial	Theory	of	Possibility.	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