The	Functions	of	Models How	to	do	Science	with	Models.	A	Philosophical	Primer By	Axel	Gelfert Axel	Gelfert's	recent	book	How	to	do	Science	with	Models.	A	Philosophical	Primer constitutes a short but important contribution to a growing literature devoted to explore	a	number	of	philosophical	issues	raised	by	the	ubiquity	of	models	within	the sciences	and	also	by	the	great	variety	of	existing	models	and	modeling	practices	as well	as their indispensability to the	scientific	enterprise.	As	Gelfert	remarks in the introduction, philosophical inquiry on models and modeling has been vigorously pursued	in	the	last	few	decades,	but	with	a	limited	scope.	Indeed,	for	Gelfert,	most scholars	working	on	models	have	either	focused	on	(1)	developing	a	comprehensive theory	of	models	that	can	reveal	their	nature	and	account	for	their	representational capacities	or	(2)	offering	in-depth	analyzes	of	particular	models	that	illuminate	the specific	mechanisms	through	which	each	individual	model	is	created	and	functions. To	circumvent	the	limitations	of	each	approach,	Gelfert	(p.	iv)	suggests	the	adoption of a key methodological assumption, which is that 'careful attention to scientific modeling as a practice	may itself be a source of insight about	what gives	modelbased	science	its	cohesion	and	makes	it	successful.' On	the	basis	of	this	assumption,	Gelfert	presents	a	thorough	and	compelling	case throughout	the	book	for	this	thesis:	rather	than	having	an	underlying	nature,	what unifies	models and	what explains their success in science is the fact that they	are typically	constructed	and	used	as	tools	to	perform	a	variety	of	different	functions.	In particular,	Gelfert	argues	that,	though	scientific	modeling	is	often	done	to	represent some	phenomenon, the construction and deployment of	models also serves other functions	beyond	scientific	representation.	In	order	to	argue	for	this	thesis,	Gelfert proceeds as follows. In Chapter 1, Gelfert presents and rehearses the traditional ontological	debate	about	the	nature	of	models.	One	of	the	virtues	of	this	chapter	is that Gelfert adroitly shows through a historical discussion of different positions (which include the analogy view of Mary Hesse, the semantic view that Patrick Suppes	and	Bas	van	Fraassen	embrace	and	various	versions	of	the	fictionalist	view defended by Nancy Cartwright,	Mauricio Suárez and Roman Frigg) that there are serious	doubts	concerning	whether	any	of	these	of	these	positions	can	account	for the huge diversity of existing models in a way that unifies them, thus providing support	for	an	pragmatic	position	relying	on	the	thesis	that	(p.	20)	'what	models	are is crucially determined by their being the result of a deliberate process of	model construction.' If	this is	the	case,	then	there	is	no	intrinsic	nature	that	models	have, but	what	they	are	turns	out	to	depend	on	the	particular	function(s)	they	have. This characterization of	models as functional entities (which Gelfert adopts in chapter	2)	is	then	applied	to	address	certain	questions	that	arise	with	respect	to	the use	of	models	in	scientific	representation.	As	Gelfert	shows,	philosophers	of	science have traditionally toiled to provide an account of how	models can represent and have	put forth	different	proposals. In	particular,	Gelfert presents and	discusses in detail the	DDI	account	developed	by	Gabriele	Contessa	and	the inferential	account articulated	by	Suárez	after	examining	briefly	the	issue	of	whether	there	is	anything distinctive about scientific representation that sets apart from other forms of representation (e.g., artistic). One of the great accomplishments of Gelfert in this chapter	consists	in	showing	how	viewing	models	as	functional	entities	allows	us	to provide	an	account	of	models	that	subsumes	the	best	ideas	of	Contessa	and	Suárez: models are able to represent in certain cases	because they can	perform functions such	as	denotation,	demonstration	and	interpretation	vis-à-vis	their	targets	(which are	the	three	core	elements	of	Contessa's	DDI	account)	or	because	they	can	be	used to	undertake	other	specific	functions,	such	as	drawing	inferences	from	their	targets (which is the core of Suárez's account). Finally, Gelfert shows at the end of the chapter	how	the	functional	view	of	models	can	help	us	make	sense	of	the	thesis	that, even if models are strictly speaking false, they can nevertheless make key contributions	to	scientific inquiry	not	only	through	their	representational	uses	but also	through	other	uses. The last three chapters contain, in	my view, Gelfert's	most important insights and contributions. In chapter 3, Gelfert offers a thorough analysis of several case studies	of	models	in	various	disciplines	to	try	to	identify	recurring	patterns	in	model building.	As	he	tries	to	chart	a	middle	path	between	the	abovementioned	options	(1) and	(2),	Gelfert	shows	through	a	detailed	study	of	several	examples	(in	particular, the	BCS	model,	the	Hubbard	model	and	the	Lotka-Volterra	model)	that	these	models are	always	developed	with	certain	specific	purposes in	mind:	prediction in	certain cases,	explanation	in	others,	testing	in	further	others.	Thus,	one	of	the	key	recurring patterns	that	Gelfert	identifies	in	his	analysis	is	that	model	construction	is	sensitive not to the	specific	disciplines (e.g.,	physics,	biology,	etc.)	where it is	practiced,	but rather	to	the	specific	functions	that	the	model	developers	intend	their	creations	to perform. The identification of this pattern enables	Gelfert to explain	why	Richard Levins'	contention	that	model	building involves trade-offs	between	many	different desiderata (e.g., generality, accuracy, complexity, etc.) is correct. Indeed, just as a good	wrench	is	built	for	a	specific	function	and	is	consequently	ill-suited	to	perform other functions (e.g., cutting	wood), so	a	model, if it is	developed	and	successfully used to perform a specific function (e.g., predicting changes in rainfall in some region), is	often ill-suited to	perform	other functions (e.g., representing the	whole target	system). The	last	two	chapters	offer	further	support	to	Gelfert's	central	thesis	by	showing that	different	models	have	different	functions.	In	chapter	4,	Gelfert	defends	the	view that	some	models	have	an	exploratory	function. In	this	respect, they	are	similar	to certain	experiments	which	aim	'not	just	at	bringing	about	a	well-defined	observable change	in	the	world,	but	also	serve	as	a	testing	ground	for	new,	yet	to	be	stabilized concepts'	(p.	76).	After introducing	this	claim	and	providing	some	general	support for	it	based	on	the	views	of	computer	scientists	such	as	John	Holland	and	physicists such	as	Nigel	Gogenfeld,	Gelfert	offers	a	taxonomy	of	different	ways	in	which	models functions as exploratory tools. This taxonomy includes the use of models (a) as starting	points,	(b)	as	key	parts	in	proof-of-principle	demonstrations,	(c)	as	ways	to develop potential explanations and (d) as tools to explore the suitability of the target.	Finally, in	chapter	5,	Gelfert	argues for	the	view	that	certain	models	do	not only	function	as	mediators	(a	thesis	previously	defended	by	Margaret	Morrison	and Mary	Morgan),	but	also	as	contributors	and	enablers	of	scientific	knowledge.	This	is the most interesting chapter of the book and contains the richest philosophical insights. In particular, Gelfert shows how	models that are built using 'formalismdriven' construction not only integrate various theoretical and experimental elements, but also often contribute	new	elements. For instance, in the case of the Hubbard model, Gelfert shows how the model can provide new contributions at various levels.	At	a	basic level,	Gelfert	argues that 'new	quantities	and	parameters may be generated by combining different elements of the model' (p. 110). At a deeper level, the	model	can	contribute	rigorous	results,	which	are	a	class	of 'exact mathematical relationships between certain mathematical variables, or certain structural components, of the mathematical model' (p. 111). In addition, Gelfert shows	how	models	can	function	as	enablers	of	scientific	knowledge	insofar	as	they 'enable	different	kinds	of	user-model-target	relations'	(p.	120).	Drawing	on	the	work of	Don	Ihde,	Gelfert	distinguishes	embodiment	relations	from	hermeneutic	relations and	uses	this	framework	to	show	how	models	function	as	enablers	of	knowledge	in different	ways.	More	specifically,	Gelfert	argues	that	certain	models	are	enablers	of scientific	knowledge	insofar	as	they	function	in	ways	similar	to	glasses	or	telescopes (which	are	treated	as	extensions	of	one's	body),	while	other	models	are	enablers	as they	function	as	in	ways	similar	to	written	texts	or	maps	which	provide	information about	the	world	only	through	a	certain	interpretation.	Furthermore,	Gelfert	argues by	considering	in	detail	two	examples	(namely,	the	Phillips	machine	and	interactive computer	graphics	used	in	contemporary	protein	modeling)	that,	in	certain	contexts and	for	certain	purposes,	model	users	emphasize	embodiment	relations	whereas,	in other contexts and for other purposes, they emphasize hermeneutic relations. In virtue of this, models may, for Gelfert, 'function as mediators between different user-model-target relations' (p. 124). In my view, this claim is the most original insight	of	the	book. The	only	minor	reservation	that	I	have	about	Gelfert's	book	is	that	the	taxonomy that	he	offers	in	chapter	4	is	incomplete.	In	particular,	Gelfert	forgets	to	mention	the use	of	certain	highly	abstract	models	(which	are	a	kind	of	thought	experiments)	for exploratory	purposes,	which	had	been	identified	and	discussed	by	Ernst	Mach.	But this	is	only	a	small	shortcoming	and,	other	than	this,	the	book	is	an	outstanding	and original	piece	of	scholarship.