Microsoft Word - Deflationary Representation, Inference, and Practice.docx


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Deflationary Representation, Inference, and Practice  

 

(Forthcoming in Studies in History and Philosophy of Science) 

 

Mauricio Suárez 

Complutense University of Madrid and University of London 

Email: Mauricio.suarez@sas.ac.uk; msuarez@filos.ucm.es 

 

 

Abstract: This paper defends the deflationary character of two recent views regarding 

scientific representation, namely RIG Hughes’ DDI model and the inferential 

conception. It is first argued that these views’ deflationism is akin to the homonymous 

position in discussions regarding the nature of truth. There, we are invited to consider 

the platitudes that the predicate “true” obeys at the level of practice, disregarding any 

deeper, or more substantive, account of its nature. More generally, for any concept X, a 

deflationary approach is then defined in opposition to a substantive approach, where a 

substantive approach to X is an analysis of X in terms of some property P, or relation R, 

accounting for and explaining the standard use of X. It then becomes possible to 

characterize a deflationary view of scientific representation in three distinct senses, 

namely: a “no-theory” view, a “minimalist” view, and a “use-based” view – in line with 

three standard deflationary responses in the philosophical literature on truth. It is then 

argued that both the DDI model and the inferential conception may be suitably 

understood in any of these three different senses. The application of these deflationary 

‘hermeneutics’ moreover yields significant improvements on the DDI model, which 

bring it closer to the inferential conception. It is finally argued that what these 

approaches have in common – the key to any deflationary account of scientific 

representation – is the denial that scientific representation may be ultimately reduced to 

any substantive explanatory property of sources, or targets, or their relations. 

 

 

Keywords: Deflationary Representation; models and idealization; deflationary accounts; 

theories of truth; inference.



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1. Scientific Representation: The State of Play 

 

  

 ‘Science represents through its models - and this representational aim is 

characteristic, or defining, of its model-building activity’. As stated – in this minimal 

and restricted sense – this is as uncontroversial a claim as one may encounter in 

contemporary philosophy of science. But what is it that science represents, and how 

does it do it? These are much harder questions, and there is intense debate nowadays 

amongst philosophers regarding how best to address them. i 

 

 The various attempts to answer these questions can be distinguished in a number 

of different ways. In this paper I focus on one particular distinction between what I call 

‘substantive’ and ‘deflationary’ accounts of representation. The former type claims that 

representation is some substantive or objective property or relation; the latter, by 

contrast, ‘deflates’ the notion of representation by claiming that there is no substantive 

property or relation at stake. These terms will be defined more fully below. Substantive 

accounts have traditionally been, implicitly if not explicitly, the norm in much of the 

discussion of scientific representation. Bas van Fraassen and Ronald Giere have often 

been thought to defend substantive analyses of representation (as isomorphism and 

similarity, respectively), although their views turn out to be in fact more subtle than has 

been supposed – and, in particular, their most recent and considered views are 

decisively deflationary (Giere, 2004; Van Fraassen, 2008). More recently, champions of 

substantive accounts include Pincock (2012), who defends structural isomorphism, and 

Weisberg (2013), who defends similarity; yet other attempts at substantive accounts 

include Bartels (2006), who defends homomorphism, French (2003) and his disciples, 

who defend partial isomorphism, and Contessa (2007), who defends a substantive 

version of the inferential conception. In all these cases the ostensive aim is to analyze 

away representation in virtue of some other relation or property, or set of relations and 

properties, that provide its reductive base.  

 

 In other words, these accounts are both substantive and reductive. It is worth 

noting that it is not the case that, for any concept X, a substantive account of it should 

be reductive. It is important in particular to distinguish ‘primitivist’ accounts from what 



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I will in the paper consider strictly ‘deflationary’ accounts: they are by no means the 

same. True, a ‘primitivist’ account about a concept X starts from the recognition that X 

may not be reduced or analysed away. But this is because, for a primitivist, X is 

substantive yet unanalysable. On such a view X is an explanatory primitive property or 

relation that bears no reduction to any other concept or set of concepts Y. For 

illustration it is instructive to consider the case of laws, causation, or time. A primitivist 

about these concepts claims them to be explanatory primitives. For instance, David 

Armstrong is widely held to defend primitivism about laws; and Tim Maudlin is a 

primitivist about (the passage of) time. Wesley Salmon may have been a primitivist 

about causal processes, etc. By contrast, a Humean considers all these concepts to have 

a problematic status calling for analysis in terms of other concepts that he or she 

considers to be unproblematic. The unproblematic concepts from the Humean point of 

view are empirically accessible – thus laws are to be reduced to regularities; causation is 

to be reduced to probability, typically understood as frequency; and time is to be 

reduced to open conjunctive forks, or oriented correlations. None of these views is 

deflationary in the sense that I will develop in this paper.  

 

 Another striking example of the distinction that I am appealing to here can be 

found in debates surrounding the nature of knowledge. Many philosophers have 

attempted to analyse ‘knowledge’ away in terms of notions they regard to be self-

explanatory, or at least less obscure, such as justification, truth, and belief. Yet others 

have resisted any such analysis, claiming instead that knowledge is an explanatory 

primitive that requires no analysis (notably Williamson 2000). Along the same lines, a 

primitivist about representation claims that representation is an explanatory primitive 

which bears no further reduction. It should thus be clear that this view is a non-

reductive kind of substantive account – certainly not an analysis –, and should be 

distinguished from both the deflationary and the reductive kind of substantive accounts 

that will be discussed here. ii 

 

 Deflationary views or accounts of scientific representation are inaugurated by 

Hughes (1997), include explicitly Suárez (2004) and Van Fraassen (2008) and – on the 

version of deflationism defended here – implicitly Giere (2004) and Elgin (2009). On 

such views, representation is not a substantive property or relation. Some of these 

deflationary views take it to be no property or relation at all; others take it to be a 



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property or relation, but not a substantive one – in some precise sense to be specified. 

Deflationary accounts are not typically reductionist – indeed it would be strange to first 

claim that representation is not a substantive property, or no property at all, and then go 

on to attempt to analyse it away anyway. (But note that the difficulty here is not logical 

or conceptual, but a pragmatic difficulty concerning the possible use of a reductive 

deflationism – for if X already fails to be, or to correspond to, a substantive property or 

relation then what cognitive gain could there be in reducing it to further deflationary 

properties or relations?) All the deflationary accounts of representation reviewed here 

(including ‘used-based’ accounts) are non-reductive in the weaker sense that they either 

do not provide an analysis in terms of necessary and sufficient conditions, or if they do 

provide such conditions, they claim them to have no explanatory purchase. Hence, the 

deflationary accounts reviewed here give up on the aim to provide an explanatory 

reduction of representation in terms of properties or relations between sources and 

targets, and this is what distinguishes them from reductive substantive accounts.     

 

 A critical issue for the purposes of this paper concerns the relationship between 

representation and model-building practice. In a substantive account this relation is 

contingent: if modellers’ practice is appropriate and effective it will latch on the 

relevant features of representation, but there is no logical or conceptual necessity for 

this to be so – the practice may in principle be fundamentally misguided. It is first the 

case that at the individual level, modellers can be better or worse at grasping the select 

set of features of a source that holds the representational relation R to the target. While 

collectively, there is nothing to guarantee that the practice is in any way geared towards 

a successful appraisal of the features and relations in question. In other words scientific 

practice may be more or less proficient in getting at genuine representational relations. 

At best, we can take scientific practice to provide some defeasible evidence for or 

against particular substantive accounts, and this only if we accept that our account of 

representation should aim to be descriptive, or explanatory, of the actual practice.iii In 

other words, if representation is a substantive relation, or property, then the practice of 

model-building provides at best an empirical benchmark to judge how appropriate the 

different accounts of this substantive relation are. But the practice and the account may 

in principle – i.e. logically or conceptually – differ markedly. 

 



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 By contrast, I argue in this paper, one thing that all deflationary accounts have in 

common is that the agreement between representation and model-building practice is, if 

not a priori, at least conceptually much tighter– for it turns out that on these accounts 

representation cannot be contradicted by the norms that inform that practice, or be 

explicitly at variance with them. On some deflationary accounts this is because there is 

nothing that the concept of representation per se says about representational or model 

building practice; on other deflationary accounts, representation is itself constituted in 

the practice. Either way representational practice is not an ‘empirical benchmark’ 

against which to judge our theories of representation. Of course, individual modellers – 

even whole communities or groups of scientists – may, whether intentionally or not, 

misrepresent, in the sense that they may mistakenly ascribe the wrong sources, or the 

wrong features of such sources to the wrong targets, or mistaken features thereof. 

However, whenever they do, there must be some failure on their part to follow the 

constitutive norms of the practice that explains their mistake. iv For it is impossible, on a 

deflationary account, for the concept of representation in any area of science to be at 

variance with the norms that govern representational practice in that area. Rather, 

representation in that area, if it is anything at all, is nothing but that practice. v 

 

 Now, beginning with Hughes (1997) and culminating in Van Fraassen (2008), 

the deflationary tradition has shown increasing concern with reductive substantive 

accounts (i.e. attempts at explanatory definitions) of representation. Consequently, I 

argue, the role of practice has shifted from a potential arbiter in disputes between 

accounts of representation towards a constitutive element of representation itself. In a 

deflationary approach, as I argue in this paper, practice does not merely adjudicate 

competing accounts of the concept. Rather to the extent that there is any concept at all, 

practice fully informs the concept. As a consequence, the functions and roles of 

representation may not be defined a priori independently of representational practice – 

but can be fully articulated only against the background of practice. And although this 

bare and general deflationary thesis seems to be becoming popular, its mere statement 

still leaves open important details, and is open to several interpretations.  

 

 

2. What is Deflationism? Three Views. 

 



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 My main claim in this paper is that both Hughes’ DDI model and my own 

inferential conception are deflationary accounts of scientific representation in some 

relevant respects. In order to make the claim precise I need to first characterize what 

those relevant respects are. My strategy is to employ an analogy with the debates 

regarding the nature of truth within metaphysics and the philosophy of language. By 

means of reference to those debates, I shall attempt to distinguish three different senses 

of “deflationism”, or more generally three distinct deflationary approaches to any 

concept: The ‘no-theory’, ‘abstract minimalism’ and ‘use-based’ approaches. The 

implications for scientific representation and, in particular, for the sort of philosophical 

work that is appropriately relevant to them, seem different in all three cases. However, 

in sections three and four, I go on to apply these three deflationary approaches to the 

DDI model and the inferential conception, and I will then claim that there is something 

that these three approaches have in common after all. They all emphasize the essential 

link to practice mentioned above that makes a substantial definitional approach helpless 

or impossible. An inquiry into the nature of scientific representation, on any of these 

views, is essentially an inquiry into a form of practice. vi Thus I shall end by urging 

philosophers of science to focus on the ways in which any deflationary approach may 

contribute to this common goal. vii  

 

 It will help us to understand deflationism if we first provide a sketch of its 

opponent – substantialism.  A substantive analysis of some concept X is a set of 

necessary and sufficient conditions that defines the concept and moreover explains its 

use. The defining conditions of the concept are thus also conditions for its use, which 

stipulate under what conditions the concept applies. Let us, for instance, consider the 

truth concept. A substantive analysis establishes some conditions that define the nature 

of the ‘truth’ predicate. Whatever property truth is then taken to be, it is possible to 

explain any correct or legitimate application of the predicate by reference to these 

conditions. The conditions may stipulate a particular type of relation that must obtain 

between on the one hand propositions, or sentences, and facts on the other hand. Or it 

may stipulate some property that propositions, or sentences, need to have in order to 

legitimately be said to be true, or truth-apt. viii 

 

 In accordance with this terminology, three substantive theories of truth may be 

said to have essentially emerged in the literature so far, which we may refer to as the 



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correspondence, coherence and pragmatist theories or accounts of the nature of truth. 

They all begin by accepting the equivalence or disquotational schema, which we may 

state as follows: ix 

 

 The Disquotational Schema (DS): ‘P’ is true if and only if P.  x 

 

 Each of the theories reviewed then establishes a set of defining conditions for 

the predicate “true” that are supposedly necessary and sufficient for legitimate 

applications of the predicate in whatever context. These conditions certainly include the 

(DS) but will add something else substantial in addition – whether a relation or a 

property of sentences. Yet, what each theory adds differs dramatically. Thus, the 

correspondence theory adds the idea that truth is correspondence to the facts – and 

understands this as a substantive or metaphysical relation between sentences and facts 

(the relata of the correspondence relation). The coherence theory adds the idea that truth 

is coherence with the rest of (an agent’s) beliefs, and again understands coherence as a 

logical relation amongst sentences. For the so-called ‘pragmatist’ theory, truth is 

supposed to consist in the property of cognitive utility in accordance to the maxim often 

ascribed to James: “to be true is to be useful to believe”. xi 

 

 The distinguishing mark of a substantive theory of truth (and by extension, of 

any concept) is therefore the laying down of conditions that define the concept and that 

moreover explain its use. Deflationary accounts, by contrast, give up on at least one of 

these distinct aims – if not both the definitional and the explanatory aim. Thus these 

accounts have in common the rejection of a defining set of application conditions that 

explain the use of the concept. In particular, with respect to truth, these accounts take it 

that there is no substantive nature to truth (i.e. no explanatory nature with respect to the 

use of the corresponding predicate) to be captured by philosophical analysis. Naturally, 

there are two ways to deny that such an explanatory analysis is possible. In the first 

instance by denying that an analysis is possible full stop; in the second instance, by 

accepting that an analysis is possible while denying that it is the kind of analysis that 

will shed explanatory light on our use of the concept. Thus many deflationists accept 

that truth is nominally a property, but deny that it is a substantive one – i.e. one that can 

be employed for explanatory purposes. 

 



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 I want to argue that we may helpfully distinguish in the literature on truth three 

different deflationary approaches. xii I shall refer to them as the ‘no-theory’, ‘abstract 

minimalism’, and ‘use-based’ approaches. I identify the first type of approach roughly 

with the so-called ‘redundancy’ theory of truth, in particular as espoused by Frank 

Ramsey. The second type of approach is best characterized by Crispin Wright’s 

‘minimalism’ about truth. The third and final type is roughly suggested by Paul 

Horwich’s variety of deflationism. All of these views have some explicit or implicit 

debt to Wittgenstein’s middle and late period thought, and indeed the core of what they 

share in common - when considered as generalized deflationary accounts of any concept 

- is perhaps some late Wittgenstenian attitude to conceptual analysis. Nevertheless, they 

do differ in the way they apply the central insight – and they correspondingly differ in 

some central claims they make regarding truth. I shall review them in turn with an eye 

on the central Wittgensteinian insight they share in common. 

 

 One of the first explicitly deflationary accounts of truth appears in Frank P. 

Ramsey’s works, in particular in “Facts and Propositions” (1927). The relevant 

passages have been discussed extensively, and Ramsey is often credited on their 

account with the inauguration of so called redundancy theories of truth. The basic 

thought is that the (DS) exhausts what we may informatively say regarding the truth 

predicate. Accordingly, to assert of some proposition ‘P’ that it is true is to assert 

nothing over and above whatever ‘P’ itself asserts. Hence the redundancy theory of 

truth extracts from the (DS) the idea that ‘true’ denotes no substantial property. The 

predicate ‘true’ is instead redundant, in the sense that to predicate of any proposition 

that it is ‘true’ adds nothing to the content of that proposition. There is no substantial 

property that all true propositions share. The ascription of the predicate ‘true’ to a 

proposition is rather taken to possess only a kind of honorific value: it merely expresses 

the strength of someone’s endorsement of a particular proposition. xiii Truth is, if it is a 

property at all, a redundant property. xiv 

 

 For our purposes here we may focus on the part of the redundancy theory that 

most closely approaches the view that the terms ‘truth’ and ‘falsity’ do not admit a 

theoretical elucidation or analysis, but that, since they may be eliminated in principle – 

if not in practice – by disquotation, they do not in fact require such an analysis. I will 

take this implicitly to mean that there are no non-trivial necessary and sufficient 



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conditions for these concepts. xv The generalization of this ‘no-theory theory’ for any 

given putative concept X is the thought that X neither possesses nor requires necessary 

and sufficient conditions because it is not in fact a ‘genuine’, explanatory, or substantive 

concept. The most that we can aim for is a more or less accurate account of the norms 

that appear to govern the use of the corresponding term; but this account does not (and 

cannot) provide an explanation of that use – it merely summarizes it.  

 

 Let us now move on to the second type of deflationary account of truth that I 

shall discuss, namely the view defended by Crispin Wright in his book Truth and 

Objectivity (1992). Wright refers to his view as ‘minimalism’ and he acknowledges that 

this can create confusion with other extant deflationary views that also go under that 

name (Wright, 1992, p. X). For this reason, among others, I will sometimes refer to 

Wright’s view more specifically as ‘abstract minimalism’. Wright believes that truth is a 

genuine property ruled by an abstract norm, and that this norm is provably distinct from 

the norm of warranted assertability. The view is nonetheless broadly ‘deflationary’ 

because the account of truth thus provided does not explain any of the actual uses of the 

‘truth’ predicate. What is more, there is no reason to suppose that such an explanatory 

account is forthcoming for the truth concept – for according to Wright there is a gap 

between the abstract property of truth and any concrete norm of use in any particular 

domain where it may be used. In order to explain a particular use we need to resort to 

further norms and properties that operate in the domain of the discourse where the 

predicate is employed – and there is no reason to believe that such norms will be unique 

or universal across domains. 

 

 The disquotational schema (DS) on this view just provides one of the platitudes 

of the truth predicate that can at best partially characterize the concept abstractly, but 

fails to explain any of the concrete uses of the concept in practice. There are, according 

to Wright, other platitudes of truth such as those “concerning negation and 

correspondence; and which we may wish to see augmented by considerations about 

stability and absoluteness”. xvi Besides, the (DS) itself is a consequence, for Wright, of 

the more fundamental thesis that to assert is to present as true. But to state all these 

platitudes does not add anything substantially explanatory to the concept. So while truth 

is legitimately a property, which is abstractly characterized by the platitudes, it is a 

property that cannot explain anything, in particular it fails to explain the norms that 



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govern its very use in practice. For that sort of explanation, Wright contends, we need to 

appeal to additional factors, which will be distinct for each different context of use, or 

domain of discourse. There is no general account of the use of truth across domains, and 

no comprehensive universal pattern to the application of the concept throughout. Hence 

‘abstract minimalism’ ably combines a general description of the platitudes that 

characterize the abstract concept with a pluralistic understanding of its diverse means of 

application. As we will see this combination has a straightforward analogy in the case of 

scientific representation. 

 

 Let me finally consider what I will refer to as the ‘use-based’ account and 

which, although sometimes known as “minimalism”, is very different from the kind of 

“abstract minimalism” that I just reviewed. On this account, which we may most closely 

associate to the work of Paul Horwich, truth is nominally a property, although not a 

substantive or explanatory one, which is essentially defined by the platitudes of its use 

of the predicate in practice. So the DS on this account fully defines truth – there is 

nothing else at all to say in addition. Truth is entirely captured by the schema and thus 

revealed to be a useful vehicle for semantic ascent (from the object language where P 

obtains to the meta-language where “’P’ is true” obtains) and generalization (in 

sentences such as “whatever Peter says is always true” or “she will never lie”). There 

are on this account no purposes beyond these pragmatic ones that the predicate “true” 

plays in our language, and there are no further properties beyond these formal ones that 

it may possibly refer to. 

 

 Amongst all the deflationary views reviewed, Horwich’s is arguably closer to a 

pure ‘use-theory” of truth; it certainly comes closer to the slogan that “the meaning of 

the truth predicate is given by its use”. The key differences with the other two accounts 

concern this close definitional connection with use. Thus the ‘no-theory theory’ flatly 

rejects that truth may be analysed – either by connecting it to use, or any other means. 

This is a crucial difference because according to the ‘no-theory theory’ truth is simply 

not a property and has no analysis, while the ‘use-based’ view accepts that it is a 

property and moreover one susceptible of philosophical analysis, but locates this 

property entirely in some features of the proper use of the corresponding predicate in a 

linguistic practice. In other words, the use-based minimal approach is reductive in a way 

the no-theory theory patently is not. Both views are deflationary in that they deny that 



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philosophical accounts of ‘truth’ can explain our ordinary uses of ‘truth’ – but they do 

so for different reasons. The ‘no-theory’ view denies that any analysis is possible, while 

use-based minimalism only denies that any explanatory analysis is possible. 

 

 Abstract minimalism too accepts that truth is a property but denies that it is an 

explanatory one. But there is again one major difference with the use-based view. The 

reason why the property of ‘truth’ is not explanatory of the use of the ‘true’ predicate is 

different in both cases. According to use-based minimalism ‘truth’ cannot explain its 

use precisely because it is defined in terms of this use. And nothing that is X can 

explain X itself – in a genuine explanation the explanans and explanandum must be 

distinct. By contrast, abstract minimalism contends that the property of truth is not 

explanatory of its use because the use does not follow from the property in the way the 

explanandum follows from the explanans in a genuine explanation. The property is 

abstract, and does not suffice, on its own, to explain any actual concrete use of the 

predicates. Rather, as was already saw, according to abstract minimalism the platitudes 

of truth – which include the DS – define the concept in the abstract, and do not 

determine or define the use of the corresponding predicate in practice. Any legitimate 

uses of the predicate must of course be in agreement with these ‘abstract’ platitudes; 

however, these platitudes do not suffice to prescribe or fix any of these uses – other 

norms must be invoked in order to explain the different application conditions of the 

corresponding predicate in different domains.xvii 

 

 I have now provided an outline of the main elements of three distinct 

deflationary approaches to truth: the ‘no-theory’, ‘abstract minimalism’, and ‘use based’ 

approaches. I claim that these three distinct deflationary strategies may be generalised 

and applied to other suitable concepts. xviii In particular, I aim to show that each of these 

‘hermeneutical’ strategies provides a legitimate strategy to deflate scientific 

representation. Each of them, in their own characteristic fashion, determines a possible 

deflationary account of representation. These accounts are distinct – along the lines just 

rehearsed above in relation to truth – but they share in common their refusal to provide 

a substantive reductive account of the practice of scientific representation. xix 

 

 

3. Deflationary Representation: Two Accounts 



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 In this section I review the elements of two accounts of scientific representation 

that have been claimed to be deflationary, namely RIG Hughes’ (1997) DDI model and 

my own inferential conception (2004). I shall defend their deflationary character in due 

course, but first some neutral terminology is needed. We shall say that, in model-

building science, a model source A typically represents a target B. This terminology 

implies no constraints on what types of objects A and B may be: These may be concrete 

or abstract, physical or mathematical, real or imaginary. Neither is it precluding the 

standard view according to which any scientific model must have a target in the real 

world and represent it via relations that hold between the properties of both source and 

target. Indeed, as discussed below, the standard view is constitutive of representation on 

most substantive accounts, which take representation to be a relation – and hence take 

both relata to be real. Yet, the terminology also leaves room for other views that do not 

require sources or targets (or both) to be real, and hence do not require representation to 

be a relation.  

 

 Thus, the types of objects that are sources can vary greatly – from concrete 

physical objects and diagrams to abstract mathematical structures or laws. Besides, 

different sources may represent one and only one target. Thus the solar system may be 

represented both by a concrete array of small balls strung together by means of wires, or 

by Kepler’s three mathematical laws. Targets may also vary: Some models represent 

concrete physical systems and their dynamical evolution, such as the solar system; other 

models represent more general phenomena, or effects, such as the Ising model for phase 

transitions; yet other models represent abstract properties, such as the second law of 

thermodynamics, which, in asserting that entropy increases in a closed system, also 

represents entropy. 

   

 Why are all these instances of ‘scientific representation’ - what do they have in 

common? In line with the distinctions introduced in the first section, we may classify 

responses to this question into two types: substantive and deflationary. Substantive 

approaches aim to provide answers to the question in terms of the properties of sources 

and targets – or, rather, their relation – that constitutes representation. In this paper I 

shall be concerned mainly with the other set of approaches, which we may refer to as 

‘deflationary’ – according to which there is in fact no substantive property or relation 



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that constitutes representation. On these deflationary views what is in common between 

the different cases of representation is rather related to the function that sources play 

with respect to targets, i.e. the uses that they are put to by agents towards their specific 

goals in their particular contexts of inquiry.  

 

 According to Hughes’ Denotation-Demonstration-Interpretation (DDI) account, 

scientific modelling is a three-part relation cum activity (more on the distinction 

between relations and activities later). According to this account a source A represents a 

target B when the following three conditions are met: i) The source stands for the target 

in the sense that it denotes it; ii) Some demonstration is carried out by an agent on the 

model; and iii) The results of this demonstration are then interpreted, so as to apply 

them to the target.  

 

 As an illustration, Hughes (1997) deploys the model that Galileo introduces in 

the Third Day of his Discourses Concerning Two New Sciences. Galileo there describes 

a kinematical problem in exclusively geometrical terms. He goes on to solve the 

problem in geometry, only then to apply the solution to the original kinematical 

problem. Thus he deduces that the space s traversed by a body in uniform motion with 

constant velocity in a given interval t is equal to that traversed by a uniformly 

accelerated body initially at rest, provided that the final speed of the accelerating body 

is twice that of the body in uniform constant motion. 

 

 The DDI model can be applied in a straightforward manner to the example, as 

follows. First, the kinematical situation must be described by means of a geometrical 

diagram that therefore denotes it (Figure 1). Thus Galileo denotes the time t that the 

body takes to traverse the space s by means of the segment AB of a line, and the speed 

of the body at any instant of the interval t by another segment of a line perpendicular to 

the first line. Thus AC denotes the speed of the body at A and BD the speed of the body 

at B. Second, a demonstration must be carried out on the diagram. Galileo demonstrates 

that the area of a rectangular shape ABCD is identical to the area of a triangle ABD’ 

where D’ is twice the value of D. Finally, we need to interpret this result back in the 

terms of the original kinematical problem. By interpreting the overall area covered as 

the space traversed by the body in its motion over the t interval, Galileo infers that the 

time t that a body in uniform motion takes to traverse s is identical to the time taken by 



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a body uniformly accelerated. Whatever the merits of the model, the combination of 

denotation, demonstration, and interpretation constitutes an act of representation, 

according to the DDI account. 

 

 The account is ostensibly deflationary in not providing necessary and sufficient 

conditions for representation; and in the claim that representation is a set of ‘speech 

acts’ (Hughes, 1997, p. 329). However, the overt appeal to denotation turns a 

substantive relation into a necessary condition on representation, thus compromising the 

strength of its deflationism. I discuss this in greater detail in section 4, where I 

endeavour to show that it is possible nonetheless to extend the DDI account in such a 

way as to render it genuinely deflationary.  

 

 At this point I wish to consider an alternative deflationary account of 

representation, the inferential conception, which I have defended in Suárez (2004). On 

this account, representation is characterised as a two-part activity involving the exercise 

of the inferential capacities of the model source (with respect to the target), and the 

setting of what I call representational force of the source towards the target. Both 

components are elements of practice and ensue in relations only in those contexts in 

which the practice’s outputs include the establishment of a particular match or 

comparison between source and target. But even in those cases, the inferential 

conception reveals that representation is properly speaking constituted by the practice 

and not the relation. xx “Capacity” and “force” are proper nouns and may thus be taken 

to implicitly refer to a property. However, when appropriately placed in their context, 

they are best understood to appropriately refer to properties of particular activities 

within a normative practice. Neither predicate picks up a property or relation in the 

objects themselves that play the role of representational targets or sources. (See 

Knuuttila (2009) for a similar claim). 

 

 Let me try to make the claim in full – for both “inferential capacity” and 

“representational force” – by means of a particular example, which I have already 

employed to a similar effect in the past, namely the Forth Rail Bridge. The case for the 

Forth Rail Bridge as a representational target has been thoroughly made by the 

distinguished British art historian Michael Baxandall in his classic book Patterns of 

Intention (1985). What is peculiar about architecture or engineering cases, such as this 



15	
  
	
  

one, is that the representational sources (the different diagrams and plans for the 

execution and construction of the bridge) precede the actual representational target. 

They are not merely representations of the bridge, but templates for, and instructions 

towards, its construction. It is thus worth reviewing the history of the bridge in some 

detail, since it sheds light on a number of the bridge’s roles as a representational target. 
xxi 

 

 The background to the development of the Forth Rail Bridge is the intense 

competition between rail companies in Northern England and Scotland in the last 

decades of the 19th century. It was government policy to encourage competition, and a 

number of regional firms fiercely invested from 1850’s onwards in developing tracks 

along the east and west coasts of Britain. The main direction of both passenger and 

cargo traffic was south- north of the border and back and - beyond that - between the 

populated conurbations of Edinburgh, Dundee and Aberdeen. Two companies in 

particular competed for traffic northwards from Edinburgh towards Dundee and beyond. 

The Caledonian Railway operated the western tracks, while the North British Railway 

Company owned and run the eastern routes. The western route from Edinburgh to 

Dundee involved a long detour around the main estuaries of the Firth and the Tay, but it 

was at least a continuous train journey. By contrast, the North British Railway 

Company could only bring passengers by track as far as the estuaries, where ferry boats 

would cross the passengers to awaiting trains at the other end. It was a long, 

complicated, and exhausting 3-hour journey to cover the merely 46 straight-line miles 

from Edinburgh to Dundee – and the North British Railway Company and its associated 

companies south and north of the border were quickly losing business to their 

competitors in the western routes.  

 

 The North British Railway Company effectively bridged the Tay in the period 

between 1871 and 1878. But bridging the Forth was a considerably more challenging 

task, given the depth of the berth, the stronger side winds, and the Admiralty’s 

stipulations for navigation under the bridge (to allow navy vessels to reach the 

dockyards at Queensberry). Thus in 1873, the North British Railway Company joined 

forces with another three associated companies with interest in running trains on the 

eastern coast (Great Northern, North Eastern, and Midland) to found the Forth Bridge 

Company, with the sole remit to bridge the Forth for train traffic. The Company 



16	
  
	
  

commissioned the design and construction to Sir Thomas Bouch – who had just been 

knighted for his work as lead engineer of the just completed iron wrought structure over 

the Tay. Works on the middle pier of the Forth Bridge at Inchgarvie Island had already 

started when disaster struck on the older bridge over the Tay on 28 December 1879. The 

Tay Bridge collapsed bringing down a train with 79 passengers with it – an event that, 

according to Petroski (1995, p. 70) “immediately affected the character of bridge design 

and construction endeavors throughout the world”.  

 

 The history is relevant to both the representational force and inferential 

capacities of all subsequent designs plans and graphs for the Forth Bridge, since it 

reveals the intent of later attempts to bridge the Forth (Figure 2). In particular the 

subsequent engineers, John Fowles and Benjamin Baker, worked under an absolute 

requirement to make sure the design would guarantee bridge stability under the 

strongest side winds imaginable – the board Trade stipulated an equivalence of at least 

56 pounds to the square foot (Baxandall, 1985, p. 19). This led Benjamin Baker – the 

younger partner and chief engineer in charge of the design – to discard both a girder 

bridge of the sort that had been employed at the Tay, and also a suspension bridge – the 

sort that had been originally planned by Bouch for the Forth. Baker instead chose a 

cantilever design – which was a rather novel approach for bridges as large as the one 

planned. xxii  

 

 The main principle in cantilever bridge design is tension-compression. In a 

cantilever bridge the lower arm of each lever is compressed while the upper arm is 

correspondingly in tension. In the central pier by contrast the lower girder is 

compressed while the upper one is in tension. This led Baker to choose different kinds 

of design for the different arms of the levers – those in tension would be built as lattices, 

while those in compression were tubular. These designs were made possible by the very 

recent availability of industrial steel. As ever the driving thought in this design 

concerned resistance to wind strength – Baker judiciously calculated that wind strength 

on the upper arms in tension would be maximal, while the lower arms had to be robust 

to resist greater compression shears. Lattices minimise resistance to wind pressure, 

while tubes maximise resistance to compression shears.  

 



17	
  
	
  

 The point of reviewing all these details concerning the bridge design is hopefully 

now clear. Baker and Fowler’s design was driven by a fundamental requirement – 

namely to overcome considerable side shear and torsion. All kinds of critical aspects of 

the design are conducive to the same goal to guarantee that the bridge would withstand 

the strongest side winds. The representational force of the graphs is not just towards ‘a 

bridge across the Forth’, but a very particular bridge capable of sustaining such 

strengths – and one moreover under no circumstances subject to the structural defects 

that led to the Tay bridge debacle. The inferential capacity of the graphic designs is thus 

geared towards showing clearly how – on the basis of the principles applied – a bridge 

built as designed would indeed withstand such shears and stresses. Baker and his 

colleagues thus fixed both the representational force and the inferential capacities of 

their designs, and it is only under a careful understanding of the normative practice of 

civil engineering at the time and other features of the historical context – of the sort 

provided by Baxandall (1985) – that the extent and sense of both features may be 

appreciated.  

 

 This shows that the twofold requirements of representational force and 

inferential capacities capture some of the essential surface features of representation in 

science. The force of a representation (such as the graph reproduced in figure 2) is 

essentially linked to a practice of interpreting features of the graph as standing for 

features of a (possible, but not actual at that time) bridge. The rubric on the graph makes 

the referent explicit, but more than that is required to appreciate the full force of the 

model – including an understanding of the principles of cantilever bridge building, and 

the recognizable shape of the diverse parts (such as tubes, girders, piers, and lattices). 

These principles are also required for an understanding of the design’s inferential 

capacities, but here more must be added, including principles of torsion, compression, 

tension and stress, all of them required for a precise calculation of the strength of the 

side winds that a bridge built in accordance to the specifications would be able to 

withstand.  

 

 Thus there is a close connection, according to the inferential conception, 

between representation and modelling practice. This intimate link between 

representation and the norms of application and inference within model-building 

science is also at the heart of the claim that the inferential conception is a deflationary 



18	
  
	
  

view. As I argue in section 4, even though the inferential conception may be understood 

in slightly different terms, each different construal issues – through the vital connection 

to practice just mentioned – a deflationary account of scientific representation in 

general. 

 

 

4. Deflationary Views and Representational Practice. 

 

 Let us quickly take stock of what has been achieved so far. In section 2 I 

reviewed, in connection to truth, three different strategies for ‘deflating’ – or rather 

more simply, displaying the deflationary nature of – any concept: ‘no-theory’, ‘abstract 

minimalism’, ‘use-based’ strategies. In the last section I reviewed in outline the 

elements of two accounts of scientific representation that have been claimed to be 

‘deflationary’: Hughes’ DDI account and the inferential conception. In this section I 

apply these three strategies to the two deflationary accounts of representation. I argue 

that each strategy is in principle applicable, and reveals some of the reasons why 

scientific representation is indeed a deflationary notion on these accounts. 

 

 I will also argue that the DDI account and the inferential account prima facie 

differ in the degree to which they lend themselves to the deflationary strategies; in fact 

the DDI account as originally presented by Hughes turns out to be deflationary in only 

one possible sense, namely the ‘no-theory’ sense. There is, however, a possible 

development of the DDI account that brings it closer to practice in such a way as to 

fulfil the conditions of at least the use-based approach. xxiiiThe development of this 

refined account already shows the deflationary strategies have some heuristic power of 

their own – in the sense that applying them to a particular philosophical approach to any 

concept may lead to improvements on the approach. 

  

 The DDI account is a deflationary approach to representation because, as 

presented by Hughes, it refrains from postulating necessary conditions in terms of 

robust relations between sources and targets. As Hughes (1997, p. 329) writes “Let me 

forestall possible misunderstandings. I am not arguing that denotation, demonstration, 

and interpretation constitute a set of speech acts individually necessary and jointly 

sufficient for an act of theoretical representation to take place”. Hughes is implicitly 



19	
  
	
  

denying that scientific representation is a substantive explanatory property – or that it 

possesses necessary and sufficient conditions. Nevertheless, there are a few features of 

the DDI account that may lead us to question the strength of its commitment to 

deflationism, and at any rate suggest that the DDI account does not rank very high on 

any ‘deflationary’ scale.  These features all follow from the surprising appeal to 

denotation – surprising since denotation is commonly understood as a substantive 

relation between the denoting sign and the denoted object. xxiv 

 

 Indeed the most striking feature in Hughes’ account is its hybrid nature. 

Denotation is a relation between source and target; while demonstration and 

interpretation are best understood as activities on the part of an interpreter / user. There 

is, of course, an activity of denoting – but this is commonly understood to either 

establish a relation, or ride upon an already established one. In other words, we may not 

use A to denote B without ipso facto establishing a relation of denotation between A 

and B or otherwise employing an already established one. This relation substantially 

informs the notion of representation at play, as revealed by the fact that we speak of the 

geometrical diagram as in itself denoting the kinematical problem, independently of any 

activity carried out by Galileo. 

 

 By contrast, a demonstration is a piece of reasoning carried out by someone 

entirely within the ‘space of reasons’ or framework provided by the model source – 

there is no obvious way to interpret this as a relation of any sort between source and 

target, since at this stage of the modelling process, the target is not taken into 

consideration at all. So, on the DDI account, in order for the geometrical model to 

represent (for us) the kinematical situation, we must carry out Galileo’s demonstration 

ourselves. Here, by contrast with the denotation part, it is the activity itself that is 

constitutive of representation, and there is no relation that may stand in its place. 

 

 Finally, ‘interpretation’, at least as the concept appears in model theory, may be 

understood as a relation. xxv In model theory an interpretation is a function mapping the 

elements of the language into a domain of independent entities endowed with their own 

properties. Hence, take a set of sentences in some particular language; the 

‘interpretative mapping’ is what, on this account, provides them with a ‘semantics’ 

under which they may be said to be true or false. However, this is not the kind of 



20	
  
	
  

‘interpretation’ that figures in the DDI account, since to the extent that the model source 

contains sentences at all, they already come fully interpreted in terms of the model 

itself. The third step in the DDI account rather corresponds to something that we may 

refer to as the ‘application’ of the model source to the target in order to derive results of 

interest regarding the target itself. And although any application of the model is 

constrained by the relation of denotation established in the first step, it also comes with 

a large degree of freedom in two respects at least, as follows.  

 

 Firstly, the denotation relation stipulates what is the appropriate target for the 

representational source at hand, but it does not stipulate which parts of the target object 

correspond to what parts of the source object. There is plenty of leeway here. For 

instance, in Hughes’ Galileo example, the mere statement that the geometrical diagram 

denote the kinematical situation, does not settle which parts of the diagram stand for 

which parts of the kinematics. Secondly, the denotation relation does not stipulate how 

the source is to be partitioned in the first place, i.e. how it is to be structured into its 

constituent parts in order to be so related to the target. The application of the source to 

the target, however, does require a partition of the source into relevant parts and 

properties (a “structure”), and the relating of such “structure” to a similar “structure” of 

parts and properties in the target. Thus in Galileo’s modelling example, the geometrical 

diagram must clearly distinguish vertical and horizontal lines at every point, and the 

area therein comprised. Similarly the kinematical problem must clearly identify time 

intervals, speed of motion at every instant, and constant or accelerated motion across the 

interval. These distinctions are all products of the activities whereby the users of models 

apply representational sources to their targets – and they are in no way fixed by the 

mere statement that the source denotes the target. 

 

 So, although ‘interpretation’ is constrained by the relation of denotation, it goes 

further, in ways that were not made entirely explicit by Hughes. It requires at least two 

types of activity on the part of the modellers. First of all, it requires the ascribing of 

some structure to the source and target objects, by judiciously partitioning them into an 

appropriate set of parts and their properties. Then it also calls for a mapping of the 

elements of the source structure onto some corresponding parts and properties of the 

target, again under some suitable partition. xxvi Both steps (‘ascribing’ – or more strictly 

‘partitioning’ –, and ‘mapping’) are activities within the modelling practice without 



21	
  
	
  

which interpretation is rendered impossible.  However, only mapping issues in a sort of 

relation akin to denotation between (elements of) the source and (elements of) the 

target. 

 

 Hughes’ account is therefore a hybrid of a relation (denotation, mapping), and a 

number of activities (demonstrating, ascribing, partitioning). It is deflationary only in 

one sense (no-theory theory), and we may wonder if some extension of the account may 

be fully deflationary in all the relevant senses. Now, the activities are typically regulated 

within a modelling practice that imposes particular norms of correctness. The relations 

by contrast seem to some extent independent of that practice. At the very least, they are 

conceptually distinct, if not pragmatically, since they can be in principle distinguished 

without appeal to the practice itself. We could perhaps say that they are end products of 

the practice, but it would not be right to include them as part of the practice itself. A 

deflationary strategy would recommend replacing both denotation and mapping with 

functional activities or features of the representational practice as well. 

 

 I believe that there are credible functional replacements for both denotation and 

mapping, which I shall refer to as denotative and inferential function, respectively. The 

resulting account may thus be named the Denotative Function-Demonstration–

Inferential Function (or DFDIF) account. It is an extension or version of the DDI 

account that is more faithful to modelling practice in so far as it relates all its various 

components directly to a number of salient features of the practice of model building.   

 

 The first replacement involves substituting “denotative function” (DF) in place 

of denotation. The best way to motivate this replacement is by reference to the recent 

literature concerning the role and nature of fictional representation in scientific practice. 

This literature emphasises the importance and centrality of scientific models that 

represent fictional or imaginary entities, processes, or phenomena. There is no need to 

rehearse here any of the many case studies developed; xxvii it is enough to note that the 

upshot is that any adequate account of scientific representation must accommodate 

representations with fictional or imaginary targets. To give just one illustrious example, 

Maxwell’s famous 1861 vortex model of the ether is a representation whatever 

ontological status its various components, including both vortexes and idle wheels – and 

for that matter the ether itself –, is taken to possess. xxviii  



22	
  
	
  

 

 The requirement of denotation would rule out such representations, but as Elgin 

(2009, pp. 77-78) has emphasised, this requirement can be weakened: “A picture that 

depicts a unicorn, a map that maps Atlantis, and a graph that charts the increase in 

phlogiston over time are all representations, although they do not represent anything. To 

be a representation, a symbol need not itself denote, but it needs to be the sort of symbol 

that denotes”.   The paragraph above expresses a residual commitment to the idea that a 

representation only represents something to the extent that it denotes it, xxix but it 

nonetheless rightly emphasises that for a source to function ‘as a representation’ it does 

not need to actually denote its target. The only condition that must obtain is what we 

may refer to as the ‘denotative function’ of the source, and this function can be carried 

out without eventuating in actual denotation. In other words, one crucial difference 

between denotation and denotative function is that the former is a success term (for it is 

impossible for it to be true that ‘x denotes y’ unless y is real) but the latter is not (since 

‘x has denotative function and its purported denotation is y” may be true even though y 

is not real but imaginary or fictional). And while the former (denotation) requires the 

latter (denotative function) the converse is not true – not even in the long term or in a 

hypothetical future.  

 

 A comparison with portrait painting is enlightening at this point. A portrait 

always has denotative function but does not always denote. Velázquez’s portrait of Pope 

Innocent VI both denotes and has denotative function; but it would seem to be a mistake 

to say of any of the series of canvasses that it inspired Francis Bacon to produce that it 

also denotes in spite of the obvious facts that they too are portraits. Or, consider the case 

of Leonardo’s Mona Lisa, which notoriously raises historical questions concerning 

whom exactly it denotes, and how. This question is logically and historically 

independent of the uncontroversial fact that the portrait has denotative function – 

precisely because it is a portrait. Similarly, Maxwell’s models of the ether may not 

denote anything. We nowadays take them to have no referent, and even though 

Maxwell, like any other 19th century physicist – at least at the time that he introduced 

the vortex model of the ether – was certainly committed to a carrier of electromagnetic 

waves, his attitude to both vortexes and particularly idle wheels was more nuanced. He 

thought of both as useful analogies but not as literal descriptions of the mechanisms 

underlying electromagnetic phenomena. The models seem clearly to function 



23	
  
	
  

representationally nevertheless – there seems to be no substantial difference between the 

methodology we employ for both demonstration and application in such ‘fictional’ 

models and that methodology described by Hughes in the – purportedly – non-fictional 

models employed by Galileo. Any representational work that denotation can perform 

within the DDI account, denotative function seems to perform just as well. Since 

denotative function allows us to account for a much larger family of bona fide scientific 

representations it seems reasonable to substitute denotative function in an appropriately 

extended version of the DDI account. 

 

 A similar move may be made for the ‘mapping’ part of interpretation. The 

crucial function of the ‘mapping’ relation is to transfer over the results of the 

demonstrations carried out on the source onto the target. Thus in Hughes’ example of 

Galileo’s model, the overall area of the triangle is interpreted as the space traversed by 

the body in its motion over the t interval. This is a sort of mapping that thus connects an 

element in the source system (area in the geometrical figure) with an element in the 

target system (space traversed by the body in motion in the kinematical system). The 

point of this mapping in practice is to allow Galileo to carry through some inferences 

with respect to the target, namely to allow him to infer that the time t that a body in 

uniform motion takes to traverse s is identical to the time taken by a body uniformly 

accelerated (from a lesser to greater speed). Hence the functional role of the ‘mapping’ 

relation is to constrain the set of inferences about the target that we may perform on the 

basis of a consideration of the source about the target – i.e. what is technically known as 

the set of legitimate surrogative inferences. 

 

 The deflationary thought is then that this constraint can be stipulated 

independently of any actual relation between the source and the target. In other words, 

“taking area to stand for space traversed” sets up a rule of inference that provides us 

with an equivalent statement to “accepting the conjunction of all the surrogative 

inferences licenced by the rules”, amongst which prominently is the claim that equal 

areas correspond to equal times travelled. There is a sense of mapping or 

correspondence that is preserved here, since certain claims about the source get 

transferred over to claims about the target, but note that this mapping is achieved 

without any need to invoke an independently existing actual ‘relation’ between the 

source and target. What the mapping rather relates, on this view, is a set of claims about 



24	
  
	
  

the source with a set of claims about the target.  And a mapping between claims of some 

sort and claims of some other sort need not require the establishment of any relation 

between the objects of those claims. In particular, such a mapping does not require that 

B, or A for that matter, be real entities. 

 

 This deflationary thought then sees the ‘mapping’ between source and target as 

merely an inference generation rule that determines the legitimate move from claims 

about the source to claims about the target. Talk about ‘mapping’ then is only genuinely 

responsive to talk about such inferential rules, and a ‘mapping’ is acceptable (or not) if 

the rule that it enacts is correspondingly acceptable (or not). It is in particular not 

possible to assess the propriety of the mapping independently, as it were – by merely 

looking into the source and target properties and assessing their similarity or 

resemblance. For the critical aspect of the ‘mapping’ does not lie in any relation 

between their properties but rather in the generation rule for inferences that it enacts. Of 

course, it is possible that the inference generating rules laid down also coincide with a 

genuine mapping between aspects of a real source and a real target. But this mapping is 

of a piece with the set of generating rules and not independent or prior to it. In particular 

it need not coincide with any recognizable antecedent similarity or resemblance. Thus in 

Hughes’s example of Galileo’s model, we would be at a loss to find any similarities or 

resemblances between the area of the geometrical figure and space traversed in a certain 

interval in the kinematical system – until the correspondence between area and space is 

set, and the set of legitimate surrogative inferences is naturally revealed.  

 

 These replacement moves accommodate fictional representation within the spirit 

of Hughes’ original account. But the moves have the additional virtue to turn the 

account deflationary in the third relevant sense. For as was noted what stands in the way 

of a ‘use-based’ deflationary reading of Hughes’ original DDI account is the appeal to 

mapping and denotation. More generally, the ‘use-based’ account of any concept 

eschews any reference to any substantive relation between that concept and anything 

else other than the use of the concept, or the norms that inform such use. There is no 

explicit or covert appeal to a relation between the concept and the world – beyond the 

aspects of the world that constitute or inform use. In particular, ‘truth’ is not to be 

understood as a relation between sentences and facts, states of affairs or any other 

aspect or parcel of reality. Similarly ‘representation’ is not to be understood as a relation 



25	
  
	
  

between representational models, on the one hand, and facts, states, effects, phenomena, 

etc, on the other hand. It must be essentially related to features of the use of 

representations instead.  

 

 This is where the other crucial difference between denotation and mapping, on 

the one hand, and denotative and inferential function, on the other, has bite. While the 

former are relations between symbols in a language system and their putative referents, 

the latter are merely features of use. Consequently, the DFDIF account is use-based also 

in the relevant sense of connecting all the essential features of representation to features 

of use within representational practice.  

 

 Let me now turn to the inferential conception. I want to argue that this is 

straightforwardly deflationary in any of the deflationary senses described here – ‘no-

theory’, ‘abstract minimal’ and ‘use-based’. And although these provide no 

‘deflationary strategies’ to develop the inferential conception further, the application of 

each of the three strategies so far discussed does bring into relief different features of 

the inferential conception. Let us consider them in turn. 

 

 From the point of view of ‘no-theory’ deflationism, the inferential conception is 

deflationary in the straightforward sense that it refuses to lay down necessary and 

sufficient conditions on any instances of representation. Representational force and 

inferential capacity are taken to be only general features (and therefore at best necessary 

conditions) on representation, but they are neither jointly nor individually sufficient for 

representation. Normally some other conditions – such as isomorphism or similarity – 

would need to obtain in each concrete case of representation. The underlying thought is 

of course the deflationary one that ‘representation’ is not a genuine, explanatory, or 

substantive concept – and that it therefore does not call for philosophical analysis. 

However, just as philosophers in the deflationary tradition have found a number of 

illuminating things one can say about the workings of the truth predicate in agreement 

with the DS schema, so may we find a number of useful things to say about the 

workings of representation in agreement with the two ‘platitudes’ that appear in the 

inferential conception.  

 



26	
  
	
  

 In particular, inferential capacity is minimally informative about the features of 

representation that are responsible for surrogate reasoning. For any representation to 

possess inferential power towards some target it is required that there be some rules of 

inference that connect source and target – yet note that on a deflationary account 

representation is not constituted by those connections in themselves, but by the rules 

that provide the source with the capacity to generate the inferences. Such rules are 

complex features of the practice that involve carrying out demonstrations or 

modifications of the source in order to guide our beliefs regarding the behaviour of the 

target. So there must be two types of inference rules involved. First of all there must be 

rules to the demonstration steps within the model which are consequently internal to the 

workings of the source. These are the rules that govern the process of demonstration in 

Hughes’ account and we may refer to them as vertical rules since demonstration appears 

as a vertical movement in his original diagram (Figure 3). For representation there must 

in addition be rules that cut across this process and connect source and target. These 

rules are set up, or constituted, by what Hughes refers to as the interpretation stage, and 

which we have found more accurately to refer to as application. We may call these the 

‘horizontal’ rules for the similar reasons to those above. The inferential capacity of a 

source is a product of vertical and horizontal rules. The idea that scientific 

representation minimally involves the inferential capacity of sources relative to targets 

is therefore tantamount to the requirement that in some representational practice that 

employs such sources there are established vertical and horizontal rules of inference.   

 

 Now, this is all relevant to the third sense of deflationism considered, namely 

‘use-based’ deflationism; for remember that, on this account, an account of a concept X 

is deflationary if it links it essentially – by definition or otherwise – to features of the 

use of this concept in practice. There is some ambiguity at this point regarding whether 

those features are normative, or merely descriptive. If the latter, there could be 

exceptional patterns of use, but given the widespread diversity of uses of any concept, it 

cannot be ruled out that the resulting account be incoherent. This problem is likely to be 

particularly acute with a concept as widely used as representation. Thus I will here opt 

for the normative option, and assume the mentioned features to be characteristics of the 

norms of use, rather than descriptive of the use itself. This allows for anomalous 

divergence from the norms, and for deviant uses of concepts, but it has the virtue that it 

renders the account internally consistent regardless of such divergence or deviance. On 



27	
  
	
  

this third deflationary approach, representational force and inferential capacities are 

general features that model sources must have in practice if they are to play a 

representational role at all. In other words, no object (model, graph, equation) may play 

a genuine representational role unless it is normatively ascribed both components within 

a representational practice. If and when particular uses of some sources deviate from 

these two basic norms we are, on this account, to judge them non-representational, at 

least with respect to the practice at hand. 

 

 But as a matter of fact very little will be ruled out by such minimal constraints 

on use. For as we saw in section 2, both representational force and inferential capacity 

are features of activities within a normative practice, and do not stand for relations 

between sources and targets. And the bare satisfaction of these two conditions does not 

impose stringent constraints upon use; on the contrary, there will a vast range of uses 

that satisfy them. Representational force only fails to obtain when a source stands for 

itself only, and allows no surrogate reasoning towards any (fictional or real) target. As 

for inferential capacity, it was noted that it essentially requires normative constraints on 

two types of inference – referred to as vertical and horizontal inferences – but these are 

constraints on the validity of inferences and not the truth of their conclusions. Many 

types of hypothetical reasoning – and any reasoning grounded on idealized assumptions 

– will ensue in conclusions that are false or incorrect. One important task of modelling 

is precisely to pull apart, amongst all those inferences permitted by the constraints, 

those that issue in conclusions that we may assume to be truthful or correct.  The leeway 

is therefore as large as desired in order to accommodate instances of distortion, 

idealized or fictional models. xxx 

 

 Finally, let me quickly consider the second deflationary strategy that I have 

discussed in this essay, namely ‘abstract minimalism’. The inferential conception also 

lends itself naturally to this deflationary strategy. xxxi For, let us suppose that we close 

the definition of representation in terms of the two conditions (representational force 

and inferential capacity) that we have so far taken to be merely necessary, but that we 

do so by turning the concept abstract in the way abstract minimalism requires. We then 

obtain a definition proper of the abstract notion, as follows: “A represents B if and only 

if i) the representational force of A points towards B and ii) A allows competent and 

informed agents to draw specific inferences regarding B” (Suárez and Solé, 2006, p. 



28	
  
	
  

29). Yet, on the abstract minimalism proposed here considered, to apply this notion to 

any given concrete case of representation requires that some additional relation obtains 

between A and B, or a property of A or B, or some other application condition. Without 

such an additional specification the notion above will remain empty – in the sense of 

lacking any precise application conditions. 

 

 Thus this ‘abstract minimalism’ regarding representation is perhaps best 

understood in terms of the distinction between the means and constituents of 

representation. xxxii The constituents are the necessary and sufficient conditions that 

define the concept. The means are whatever relations or properties of the sources and 

targets are employed by representation users – in the particular context of their 

representational practice – in order to draw conclusions regarding aspects of the target 

by means of some reasoning grounded on aspects or features of the source (what is 

known as ‘surrogate’ or ‘surrogative’ reasoning). On any of the two deflationary views 

first reviewed (the ‘no-theory’ and ‘use based’ version of the inferential conception) 

representation has no constituents, only means (in the case of the ‘use based’ version it 

even makes sense to say that ‘the constituents of representation are its means’). By 

contrast, on the ‘abstract minimalism’ version of the inferential conception, 

representation is constituted abstractly by the platitudes of representational force and 

inferential capacities. And, of course, there are also means of representation – those 

concrete relations and properties of sources and targets that are in fact employed by 

users in their particular context. Yet, this is not a substantive account of representation 

since on this account the constituents explicitly fail to explain the means.  That is, it is 

impossible to determine on account of the abstract definition of the concept what would 

be its conditions of application in any context, since the conditions of application are, 

on this account, underdetermined by its constituents. Thus on this view representation is 

a well-defined property, and moreover one that is not to be identified with any use or 

practice, but it is a property that cannot in any way explain any use or any practice.  

 

 The main insight of abstract minimalism is precisely the thought that there can 

be an abstract definition of the concept so minimal as to lay down virtually no 

constraints on the application of the concept. This does not render the concept empty if 

there are in addition concrete conditions of application – but abstract minimalism denies 

that the concrete constraints must be correspondingly minimal or thin. In other words 



29	
  
	
  

one can impose very stringent constraints on the application of the concept in every 

domain, without requiring an explanation in terms of the general abstract definition. In 

the case of representation this amounts to the view that the context of use may impose 

highly constrained conditions on the appropriate means of application in that context, 

while remaining virtually silent – e.g. minimal – on the constituents. The view is 

certainly compatible with the inferential conception and aptly reflects the extant 

pluralism and contextualism regarding the various means available in practice.  

 

5. Conclusions 

 

 In this largely theoretical paper I have aimed at an improved understanding of 

what is meant by the claim that an account of representation is “deflationary”. I have 

distinguished three different meanings of the term “deflationary” and applied them to 

two accounts of representation that have been claimed to be deflationary. In so doing I 

hope to have illustrated the concept of representation, as much as the relevant kinds of 

deflationism. If the analysis provided of the different options is sound, it certainly 

carries consequences for “philosophy of science in practice” (whether the “philosophy-

of-science in practice” or “philosophy of science-in-practice” varieties). The most 

important consequence is that – whatever sense of “deflationary” applied – the analysis 

of the concept of representation, even where feasible, cannot determine its conditions of 

application, and therefore cannot explain its use. These conditions concern the means of 

representation – and these are essentially plural and context-dependent. This strikes me 

as a novel consequence concerning ‘philosophy-of-science in practice’ which has not 

been fully explored yet, and deserves further discussion.  

 

 The second relevant consequence is related to ‘philosophy of science-in-

practice’ and is by now better known and established, namely that a study of the uses of 

a representation is indispensible in order to determine its content. In particular as 

regards scientific models it is a widely accepted view by now that we are not able to 

understand what and how they aim to represent unless we have an understanding of the 

function that these models play in the particular context in which they are employed. 

The discussion in this paper does not perhaps lend further support to this view, except to 

the extent that it provides some theoretical grounds for why it should be true. If the 

concept of representation is deflationary, regardless of how we understand the term, 



30	
  
	
  

then any understanding that we may possibly acquire of its nature is tied essentially to 

its use. This may be because the concept has no other nature of its own (‘no-theory’ 

theories), because it is too abstract to yield any explanation of its application (abstract 

minimalism), or because its nature is essentially given by its use (‘use-based’ theories). 

No matter what deflationary account, representation only acquires its functional role 

through a particular representational practice. All deflationary accounts have this much 

in common, and it follows that the study of scientific representation must always be 

carried out in explicit or implicit reference to a particular scientific practice.  

 

Acknowledgements 

 
I thank audiences at the Society for the Philosophy of Science in Practice (SPSP) 
conference in Toronto in 2013, the British Society for the Philosophy of Science 
(BSPS) 2013 conference and at the University of the Balearic Islands, and Open 
University (UNED) during the Madrid Inferentialism in Epistemology and Philosophy 
of Science conference in November 2013. Thanks in particular to my co-symposiaists, 
Chiara Ambrosio and Chris Pincock, at the SPSP conference. I also thank two referees 
of Studies for their substantial and helpful comments. Financial support is 
acknowledged from the Spanish Ministry of Economics and Competitiveness project 
FFI2011-29834-C03-01, and from the European Commission under the Marie Curie 
programme PEF-GA-2012-329430. Figures 1 and 3 are reprinted from Hughes (1997) 
with permission from University of Chicago Press. 
 

 

References 

 

Ayer, A. J. (1936), Language, Truth and Logic, London: Gollanz. 

Bartels, A. (2006), “Defending the Structural Concept of Representation”, Theoria 21 

(1), 7-21. 

Baxandall, M. (1985), Patterns of Intention: On the Historical Explanation of Pictures, 

New Haven: Yale University Press. 

Bolinska, A. (2013) “Epistemic representation, informativeness and the aim of faithful 

representation”, Synthese 190 (2), 219-234. 

Blackburn, S. and K. Simmons, Eds. (1999), Truth, Oxford University Press. 

Burke, T. (1994), Dewey’s New Logic, University of Chicago Press. 

Chang, C. and Kleiser, J. (1990), Model Theory, North-Holland, Amsterdam. 

Contessa, G. (2007), “Scientific Representation, Interpretation, and Surrogative 

Reasoning”, Philosophy of Science, 74 (1), pp. 48-68. 



31	
  
	
  

Callender, C. and J. Cohen (2006), “There is no Special Problem about Scientific 

Representation”, Theoria 21 (1), pp. 67-85. 

Elgin, C. (1996), Considered Judgement, Princeton: Princeton University Press. 

Elgin, C. (2009) “Exemplification, Idealization and Understanding”, in M. Suárez (Ed.), 

2009, pp. 77-90. 

French, S. (2003), “A Model-Theoretic Account of Representation”, Philosophy of 

Science, 70 (5), 1472-1483. 

Giere, R. (2004), “How Models are Used to Represent Reality”, Philosophy of Science, 

71, pp. 742-752. 

Goodman, N. (1976), Languages of Art, Indianapolis / Cambridge: Hackett Publishing 

Company.  

Hookway, C. (2000), Truth, Rationality and Pragmatism: Themes from Peirce, Oxford 

University Press. 

Hughes, RIG. (1997), “Models and Representation”, Philosophy of Science 

(Proceedings), S325-S336. 

Knuuttila, T. (2009), “Some Consequences of the Pragmatist Approach to 

Representation: Decoupling the Model-Target Dyad and Indirect Reasoning”, in EPSA: 

Epistemology and Methodology: Launch of the European Philosophy of Science 

Association, pp. 139-148. 

Maxwell, J. C. (1861), “On Physical Lines of Force”, Philosophical Magazine, vol 21 

and 23. 

Nersessian, N. (2008), Creating Scientific Concepts, MIT Press.  

Petroski, H. (1995), Engineers of Dreams, Vintage Books, Random House. 

Pincock, C. (2012), Mathematics and Scientific Representation, Oxford University 

Press. 

Ramsey, F. P. (1927), “Symposium: Facts and Propositions”, Proceedings of the 

Aristotelian Society Supplementary Volumes, vol. 7, pp. 153-206. 

Shipway, J. S. (1990), “The Forth Railway Bridge Centenary: 1890-1990: Some Notes 

on its Design”, Proceedings of the Institution of Civil Engineers, 88, pp. 1079-1107. 

Suárez, M. (2003), “Scientific Representation: Against Similarity and Isomorphism”, 

International Studies in the Philosophy of Science, 17 (3), pp. 225-244. 

Suárez, M. (2004), “An Inferential Conception of Scientific Representation”, 

Philosophy of Science, 71, pp. 767-79. 



32	
  
	
  

Suárez, M. and A. Solé (2006), “On the Analogy between Cognitive Representation and 

Truth”, Theoria, 21 (1), pp. 39-48. 

Suárez, M., Ed., (2009), Fictions in Science: Philosophical Essays on Modeling and 

Idealization, London: Routledge. 

Suárez, M. (2010), “Scientific Representation”, Philosophy Compass 5/1, pp. 91-101. 

Van Fraassen, B. (2008), Scientific Representation, Oxford University Press.  

Weisberg, M. (2013), Simulation and Similarity: Using Models to Understand the 

World, Oxford University Press. 

Williamson, T. (2000), Knowledge and its Limits, Oxford University Press. 

Woods, J. (Ed.), Fictions and Models: New Essays, 2011, Munich: Philosophia Verlag. 

Wright, C. (1992), Truth and Objectivity, Harvard University Press. 



33	
  
	
  

Figures 

 
Figure 1: Galileo’s geometrical model 

 

 
Figure 2: B. Baker’s representation of the Forth Rail Bridge 

 

 
Figure 3: The DDI model 

 



34	
  
	
  

	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
i	
  There	
  have	
  also	
  been	
  claims	
  to	
  the	
  effect	
  that	
  these	
  questions	
  are	
  themselves	
  irrelevant	
  and	
  /	
  or	
  ill	
  
posed.	
  For	
  instance,	
  Callender	
  and	
  Cohen	
  (2006)	
  argue	
  that	
  the	
  notion	
  of	
  representation	
  that	
  plays	
  
a	
  role	
  in	
  the	
  sciences	
  is	
  essentially	
  the	
  Gricean	
  one	
  discussed	
  in	
  philosophy	
  of	
  mind,	
  and	
  there	
  are	
  
no	
  particular	
  issues	
  to	
  be	
  broached	
  in	
  the	
  scientific	
  context.	
  There	
  is	
  no	
  space	
  to	
  deal	
  with	
  this	
  view	
  
here	
  -­‐	
  although	
  it	
  is	
  an	
  interesting	
  question	
  whether	
  the	
  view	
  genuinely	
  bypasses	
  the	
  present	
  
debate,	
  or	
  rather	
  reduces	
  to	
  some	
  form	
  of	
  deflatonism	
  (in	
  analogy	
  with	
  redundancy	
  theories	
  of	
  
truth,	
  as	
  discussed	
  later	
  on	
  in	
  the	
  text).	
  At	
  any	
  rate	
  the	
  term	
  “representation”	
  and	
  its	
  cognates	
  such	
  
as	
  “model”	
  do	
  appear	
  prominently	
  in	
  the	
  scientific	
  literature,	
  so	
  there	
  is	
  prima	
  facie	
  a	
  legitimate	
  
philosophical	
  question	
  to	
  address	
  regarding	
  its	
  nature	
  and	
  /	
  or	
  function	
  in	
  science.	
  
ii	
  I	
  will	
  therefore	
  ignore	
  the	
  ‘primitivism’	
  option	
  in	
  the	
  rest	
  of	
  the	
  paper,	
  reserving	
  the	
  term	
  
“substantive”	
  for	
  those	
  accounts	
  that	
  are	
  both	
  substantive	
  and	
  reductive	
  in	
  the	
  ways	
  described.	
  
iii	
  Both	
  Pincock	
  and	
  Weisberg	
  accept	
  this	
  descriptive	
  requirement,	
  and	
  there	
  is	
  no	
  doubt	
  that	
  it	
  may	
  
be	
  best	
  for	
  a	
  substantive	
  account	
  of	
  representation	
  to	
  dovetail	
  with	
  representational	
  practice;	
  my	
  
point	
  is	
  that	
  there	
  is	
  nothing	
  in	
  substantialism	
  per	
  se	
  that	
  conceptually	
  or	
  logically	
  requires	
  any	
  
degree	
  of	
  fit.	
  	
  
iv	
  The	
  norms	
  involved	
  here	
  exclude	
  those	
  pertaining	
  to	
  the	
  accuracy	
  or	
  faithfulness	
  of	
  the	
  model,	
  
and	
  can	
  be	
  seen	
  to	
  be	
  restricted	
  only	
  to	
  those	
  norms	
  that	
  prescribe	
  the	
  selection	
  of	
  appropriate	
  
targets	
  and	
  sources	
  and	
  their	
  inferential	
  connections	
  (what	
  I	
  will	
  later	
  refer	
  to	
  as	
  representational	
  
force	
  and	
  inferential	
  capacities).	
  At	
  any	
  rate,	
  the	
  basic	
  point	
  is	
  that	
  while	
  individual	
  modellers	
  may	
  
fail	
  on	
  occasion	
  to	
  follow	
  the	
  appropriate	
  norms	
  of	
  their	
  representational	
  practice,	
  the	
  concept	
  of	
  
representation	
  that	
  they	
  employ	
  cannot	
  –	
  on	
  a	
  deflationary	
  view	
  –	
  fail	
  to	
  conform	
  to	
  the	
  norms	
  of	
  
their	
  representational	
  practice.	
  
v	
  The	
  careful	
  formulation	
  above	
  attempts	
  to	
  make	
  it	
  clear	
  that	
  while	
  there	
  can	
  be,	
  in	
  a	
  particular	
  
context,	
  a	
  relation	
  between	
  model	
  sources	
  and	
  targets	
  which,	
  in	
  that	
  context,	
  may	
  be	
  said	
  to	
  
instantiate	
  representation	
  or	
  to	
  constitute	
  its	
  end	
  product,	
  it	
  would	
  be	
  a	
  mistake,	
  even	
  in	
  that	
  
context,	
  to	
  identify	
  representation	
  with	
  that	
  or	
  any	
  other	
  relation.	
  Representation	
  is	
  rather	
  an	
  
activity.	
  
vi	
  Hence,	
  on	
  any	
  deflationary	
  account,	
  a	
  practical	
  inquiry	
  into	
  representation	
  is	
  primary,	
  while	
  any	
  
analytical	
  inquiry	
  is	
  secondary.	
  (For	
  more	
  on	
  these	
  terms,	
  see	
  Suárez,	
  2010).	
  That	
  is,	
  a	
  full	
  
description	
  of	
  the	
  means	
  of	
  representation	
  used	
  in	
  some	
  practice	
  enables	
  an	
  inquiry	
  into	
  its	
  nature.	
  
Substantive	
  accounts	
  will	
  typically	
  order	
  things	
  the	
  other	
  way	
  round	
  –	
  they	
  will	
  assume	
  that	
  an	
  
analytical	
  inquiry	
  is	
  prior	
  to	
  any	
  practical	
  inquiry.	
  
vii	
  In	
  this	
  paper	
  I	
  only	
  address	
  representation,	
  but	
  I	
  believe	
  that	
  a	
  similar	
  distinction	
  between	
  
practical	
  and	
  analytical	
  inquiries	
  may	
  be	
  applied	
  to	
  discussions	
  over	
  the	
  nature	
  of	
  ‘scientific	
  theory’.	
  	
  
At	
  any	
  rate	
  one	
  of	
  the	
  interesting	
  consequences	
  of	
  the	
  contemporary	
  deflationary	
  zeitgeist	
  is	
  that	
  
discussions	
  of	
  representation	
  no	
  longer	
  hinge	
  on	
  any	
  particular	
  account	
  of	
  the	
  nature	
  of	
  scientific	
  
theory.	
  More	
  colloquially,	
  we	
  could	
  say	
  that	
  ‘deflationism	
  has	
  emancipated	
  representation	
  (from	
  
theory)’.	
  
viii	
  I	
  will	
  throughout	
  gloss	
  over	
  the	
  distinction	
  between	
  sentences	
  and	
  propositions	
  since	
  it	
  does	
  not	
  
matter	
  to	
  any	
  of	
  my	
  purposes	
  here.	
  There	
  are	
  deflationary	
  theories	
  such	
  as	
  Quine’s,	
  and	
  arguably	
  
Ayer’s,	
  where	
  truth	
  is	
  predicated	
  of	
  sentences;	
  other	
  deflationary	
  theories	
  such	
  as	
  Horwich’s,	
  and	
  
arguably	
  Ramsey’s,	
  appeal	
  to	
  propositions	
  instead.	
  
ix	
  It	
  is	
  in	
  fact	
  an	
  issue	
  to	
  what	
  extent	
  the	
  (DS)	
  is	
  compatible	
  with	
  the	
  different	
  theories	
  here	
  
reviewed,	
  but	
  many	
  of	
  their	
  champions	
  claim	
  them	
  to	
  be	
  so	
  compatible,	
  and	
  for	
  the	
  sake	
  of	
  
argument	
  I	
  shall	
  assume	
  that	
  this	
  is	
  generally	
  the	
  case.	
  See	
  Blackburn	
  and	
  Simmons	
  (1999)	
  for	
  
extended	
  discussion.	
  
x	
  Since	
  theories	
  of	
  truth	
  differ	
  greatly	
  as	
  to	
  what	
  they	
  consider	
  to	
  be	
  the	
  fundamental	
  conditions	
  of	
  
truth,	
  it	
  may	
  be	
  more	
  appropriate	
  to	
  refer	
  to	
  a	
  more	
  general	
  principle	
  such	
  as:	
  ‘P’	
  is	
  T	
  if	
  and	
  only	
  if	
  
P.	
  It	
  then	
  remains	
  open	
  whether	
  T	
  is	
  ascribed	
  the	
  right	
  features	
  for	
  truth.	
  I	
  gloss	
  over	
  the	
  issue,	
  
since	
  it	
  goes	
  well	
  beyond	
  what	
  is	
  needed	
  for	
  our	
  present	
  purposes,	
  but	
  see	
  Wright	
  (2001,	
  pp.	
  13-­‐
14)	
  for	
  discussion.	
  
xi	
  It	
  bears	
  mentioning	
  that	
  this	
  crude	
  theory	
  was	
  not	
  actually	
  defended	
  by	
  any	
  of	
  the	
  traditional	
  
pragmatists,	
  save	
  the	
  possible	
  exception	
  of	
  James	
  in	
  one	
  of	
  his	
  most	
  radical	
  moments,	
  and	
  thus	
  
hardly	
  deserves	
  the	
  name.	
  (For	
  discussions	
  of	
  Peirce’s	
  rejection	
  of	
  such	
  a	
  crude	
  ‘pragmatist’	
  theory	
  
see	
  Hookway,	
  2000.	
  For	
  an	
  equivalent	
  discussion	
  regarding	
  Dewey,	
  see	
  Burke,	
  1994).	
  
xii	
  I	
  claim	
  this	
  is	
  a	
  legitimate	
  way	
  to	
  partition	
  broadly	
  ‘deflationary’	
  approaches	
  to	
  truth,	
  but	
  I	
  do	
  not	
  
insist	
  this	
  is	
  the	
  only	
  way	
  to	
  classify	
  such	
  approaches.	
  The	
  distinctions	
  I	
  draw	
  are	
  certainly	
  driven	
  
in	
  part	
  by	
  the	
  uses	
  I	
  want	
  to	
  put	
  them	
  to	
  in	
  the	
  discussion	
  regarding	
  scientific	
  representation.	
  Of	
  



35	
  
	
  

	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
course,	
  even	
  if	
  the	
  distinctions	
  were	
  illegitimate	
  regarding	
  deflationary	
  approaches	
  to	
  truth,	
  their	
  
application	
  to	
  scientific	
  representation	
  may	
  still	
  be	
  legitimate,	
  and	
  enlightening.	
  However,	
  the	
  
analogy	
  seems	
  to	
  me	
  to	
  add	
  strength	
  to	
  deflationary	
  approaches	
  to	
  representation	
  to	
  the	
  extent	
  
that	
  the	
  same	
  classification	
  obtains	
  in	
  the	
  case	
  of	
  truth	
  –	
  hence	
  the	
  extended	
  discussion	
  of	
  
deflationary	
  theories	
  of	
  truth	
  in	
  this	
  section.	
  
xiii	
  The	
  use	
  of	
  the	
  predicate	
  may	
  have	
  other	
  functions	
  –	
  for	
  instance	
  it	
  helps	
  in	
  generalization	
  and	
  
quotation	
  –	
  as	
  in	
  “everything	
  Ed	
  says	
  is	
  true”	
  –	
  but	
  even	
  then	
  it	
  does	
  not	
  express	
  any	
  substantive	
  
property	
  –	
  it	
  does	
  not	
  establish	
  that	
  everything	
  Ed	
  says	
  is	
  true	
  in	
  virtue	
  of	
  any	
  substantial	
  property	
  
that	
  all	
  the	
  propositions	
  that	
  he	
  utters	
  share.	
  	
  	
  
xiv	
  The	
  distinction	
  between	
  redundant	
  and	
  substantial	
  properties	
  is	
  subtle	
  but	
  it	
  does	
  not	
  need	
  
detain	
  us	
  here	
  –	
  it	
  is	
  enough	
  for	
  our	
  purposes	
  to	
  mark	
  the	
  difference	
  as	
  one	
  between	
  a	
  nominal	
  and	
  
a	
  real	
  property.	
  A	
  nominal	
  property	
  relies	
  entirely	
  on	
  features	
  of	
  the	
  symbol	
  system	
  employed	
  to	
  
describe	
  or	
  denote	
  it,	
  while	
  a	
  real	
  property	
  depends	
  on	
  the	
  constitutive	
  nature	
  of	
  those	
  objects	
  that	
  
share	
  it	
  –	
  independently	
  of	
  how	
  we	
  choose	
  to	
  describe	
  them.	
  Thus	
  ‘weighting	
  less	
  than	
  70	
  kg.’	
  
expresses	
  a	
  characteristically	
  real	
  property,	
  while	
  ‘having	
  a	
  name	
  that	
  begins	
  with	
  M’	
  is	
  nominal.	
  
The	
  distinction	
  only	
  becomes	
  blurry	
  for	
  those	
  properties	
  of	
  the	
  symbol	
  systems	
  we	
  employ	
  (e.g.	
  
properties	
  of	
  sentences	
  or	
  any	
  other	
  entities	
  in	
  our	
  natural	
  languages	
  –	
  such	
  as	
  ‘being	
  seven	
  letters	
  
long’),	
  but	
  these	
  properties	
  do	
  not	
  play	
  a	
  role	
  in	
  the	
  analogy	
  presented	
  here	
  (and	
  their	
  analogues	
  
for	
  scientific	
  models	
  are	
  in	
  fact	
  expressively	
  ruled	
  out	
  by	
  the	
  inferential	
  conception	
  to	
  be	
  later	
  
reviewed).	
  
xv	
  In	
  other	
  words,	
  we	
  focus	
  on	
  those	
  aspects	
  of	
  Ramsey’s	
  redundancy	
  account	
  that	
  led	
  Ayer	
  to	
  what	
  
is	
  sometimes	
  known	
  as	
  the	
  ‘no-­‐theory	
  theory’	
  of	
  truth	
  (Ayer,	
  1936,	
  p.117).	
  On	
  this	
  account	
  the	
  
redundancy	
  view	
  claims	
  that	
  ‘truth’	
  is	
  a	
  tool	
  –	
  for	
  disquotation,	
  generalization,	
  etc	
  –,	
  which	
  does	
  not	
  
deserve	
  any	
  analysis	
  beyond	
  whatever	
  concerns	
  its	
  use	
  in	
  practice	
  as	
  a	
  ‘vehicle	
  of	
  semantic	
  
descent’.	
  There	
  is	
  no	
  point	
  looking	
  for	
  necessary	
  and	
  sufficient	
  conditions	
  for	
  ‘truth’	
  since	
  ‘truth’	
  is	
  
not	
  a	
  genuine	
  concept	
  and	
  requires	
  no	
  such	
  conditions.	
  
xvi	
  The	
  full	
  list	
  is	
  as	
  follows	
  (Wright,	
  1992,	
  pp.	
  34	
  and	
  72):	
  i)	
  to	
  assert	
  is	
  to	
  present	
  as	
  true;	
  ii)	
  any	
  
truth-­‐apt	
  content	
  has	
  a	
  significant	
  negation	
  which	
  is	
  likewise	
  truth-­‐apt;	
  iii)	
  to	
  be	
  true	
  is	
  to	
  
correspond	
  to	
  the	
  facts;	
  iv)	
  a	
  statement	
  may	
  be	
  justified	
  without	
  being	
  true,	
  and	
  vice-­‐versa;	
  v)	
  truth	
  
is	
  absolute	
  (there	
  is,	
  strictly,	
  no	
  being	
  more	
  or	
  less	
  true)	
  and	
  vi)	
  it	
  is	
  stable	
  (if	
  a	
  content	
  is	
  ever	
  true,	
  
it	
  always	
  is).	
  Wright	
  makes	
  it	
  clear	
  (ibid,	
  pp.	
  72-­‐74)	
  that	
  all	
  these	
  platitudes	
  of	
  truth	
  must	
  be	
  
understood	
  in	
  a	
  suitable	
  deflationary	
  spirit,	
  and	
  in	
  particular	
  iii)	
  does	
  not	
  entail	
  the	
  metaphysical	
  
relation	
  between	
  propositions	
  and	
  facts	
  characteristic	
  of	
  correspondence	
  theories	
  of	
  truth.	
  	
  
xvii	
  This	
  crucially	
  does	
  not	
  amount	
  to	
  the	
  view	
  that	
  ‘truth’	
  has	
  no	
  sufficient	
  conditions,	
  or	
  that	
  its	
  
necessary	
  and	
  sufficient	
  conditions	
  are	
  given	
  by	
  an	
  extremely	
  long,	
  perhaps	
  infinite,	
  or	
  
indeterminate,	
  list	
  of	
  conjunctive	
  properties,	
  each	
  corresponding	
  to	
  a	
  particular	
  domain.	
  Any	
  of	
  
these	
  alternatives	
  would	
  be	
  entail	
  a	
  radical	
  relativism	
  according	
  to	
  which	
  there	
  is	
  no	
  unique	
  or	
  
unified	
  truth	
  concept.	
  The	
  whole	
  point	
  of	
  abstract	
  minimalism	
  is	
  precisely	
  to	
  argue	
  that	
  there	
  is	
  one	
  
unique	
  truth	
  concept,	
  it	
  just	
  so	
  happens	
  to	
  be	
  an	
  abstract	
  one.	
  
xviii	
  I	
  am	
  not	
  claiming	
  that	
  every	
  concept	
  necessarily	
  is	
  susceptible	
  to	
  one	
  of	
  these	
  strategies	
  for	
  
deflation.	
  There	
  are	
  successful	
  substantial	
  accounts	
  of	
  a	
  range	
  of	
  different	
  concepts,	
  both	
  across	
  the	
  
sciences	
  (formal	
  and	
  empirical)	
  and	
  in	
  ordinary	
  life,	
  and	
  philosophers	
  have	
  often	
  excelled	
  at	
  
bringing	
  out	
  their	
  details.	
  I	
  merely	
  claim	
  that	
  some	
  concepts	
  are	
  deflationary	
  in	
  that	
  they	
  resist	
  any	
  
substantial	
  or	
  explanatory	
  analysis,	
  and	
  for	
  those	
  concepts	
  any	
  of	
  these	
  strategies	
  for	
  deflation	
  is	
  
available.	
  They	
  each	
  provides	
  a	
  hermeneutics:	
  A	
  complex	
  interpretative	
  framework	
  which	
  allows	
  a	
  
better	
  understanding	
  of	
  the	
  concept.	
  Other	
  deflationary	
  strategies	
  or	
  hermeneutics	
  may	
  be	
  
appropriate	
  for	
  some	
  of	
  these	
  concepts;	
  and	
  often	
  more	
  than	
  one	
  strategy	
  will	
  suit.	
  For	
  instance,	
  in	
  
the	
  case	
  of	
  truth,	
  each	
  of	
  the	
  three	
  strategies	
  has	
  something	
  going	
  for	
  it,	
  and	
  illuminates	
  –	
  at	
  least	
  in	
  
part	
  –	
  the	
  nature	
  of	
  truth’s	
  resistance	
  to	
  substantial	
  analysis.	
  Similarly,	
  I	
  argue,	
  for	
  scientific	
  
representation:	
  Each	
  of	
  the	
  three	
  deflationary	
  strategies	
  has	
  something	
  going	
  for	
  it	
  there	
  too,	
  and	
  
each	
  sheds	
  some	
  light	
  on	
  why	
  scientific	
  representation	
  resists	
  a	
  substantial	
  analysis.	
  	
  	
  
xix	
  I	
  am	
  therefore	
  assuming	
  that	
  any	
  account	
  on	
  which	
  representation	
  can	
  be	
  understood	
  as	
  
denoting	
  a	
  substantive	
  property	
  or	
  relation	
  of	
  sources	
  and	
  targets,	
  will	
  thereby	
  be	
  able	
  to	
  provide	
  a	
  
reductive	
  analysis	
  in	
  terms	
  of	
  the	
  application	
  conditions	
  of	
  this	
  property	
  or	
  relation.	
  
xx	
  A	
  standard	
  way	
  to	
  put	
  this	
  would	
  be	
  to	
  say	
  that	
  the	
  truth	
  conditions	
  of	
  statements	
  involving	
  
representation	
  are	
  in	
  the	
  practice	
  itself,	
  and	
  in	
  no	
  way	
  depend	
  essentially	
  on	
  the	
  obtaining	
  of	
  any	
  
relation	
  between	
  source	
  and	
  target.	
  There	
  is	
  to	
  my	
  mind	
  nothing	
  in	
  this	
  standard	
  expression	
  that	
  is	
  



36	
  
	
  

	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  	
  
objectionable,	
  but	
  I	
  avoid	
  the	
  expression	
  ‘truth-­‐conditions’	
  in	
  order	
  to	
  avoid	
  any	
  appearance	
  of	
  
conflation	
  or	
  collision	
  with	
  the	
  analogy	
  I	
  develop	
  with	
  theories	
  of	
  truth	
  in	
  section	
  3.	
  	
  	
  
xxi	
  In	
  what	
  follows	
  I	
  am	
  indebted	
  to	
  Baxandall	
  (1985),	
  as	
  well	
  as	
  further	
  documents	
  on	
  the	
  Forth	
  
Rail	
  Bridge	
  from	
  a	
  more	
  straightforward	
  engineering	
  point	
  of	
  view,	
  such	
  as	
  Petroski	
  (1995,	
  
particularly	
  Ch.	
  III),	
  and	
  Shipway	
  (1990).	
  	
  
xxii	
  At	
  the	
  point	
  at	
  which	
  it	
  had	
  been	
  decided	
  to	
  bridge	
  it,	
  the	
  Forth	
  required	
  two	
  bridge	
  spans	
  each	
  
500	
  m.	
  long,	
  with	
  a	
  central	
  pier	
  at	
  Inchgarvie	
  Island,	
  which	
  happened	
  to	
  conveniently	
  lie	
  in	
  the	
  
middle.	
  Still	
  this	
  was	
  an	
  unprecedented	
  length	
  over	
  which	
  to	
  build	
  a	
  cantilever.	
  Petroski	
  (1995,	
  p.	
  
87)	
  points	
  out	
  that	
  cantilever	
  bridges	
  had	
  been	
  built	
  in	
  North	
  America	
  already,	
  but	
  Baxandall	
  
documents	
  Baker’s	
  inspiration	
  in	
  oriental	
  bridge	
  designs	
  which,	
  applying	
  the	
  same	
  principles,	
  were	
  
able	
  to	
  respect	
  symmetry.	
  This	
  observation	
  is	
  not	
  entirely	
  inconsequential	
  for	
  the	
  inferential	
  
capacities	
  of	
  Baker’s	
  representations	
  of	
  the	
  bridge,	
  but	
  we	
  may	
  leave	
  it	
  aside	
  for	
  now.	
  	
  
xxiii	
  I	
  believe	
  the	
  DDI	
  model	
  may	
  also	
  be	
  extended	
  in	
  order	
  to	
  comply	
  with	
  abstract	
  minimalism,	
  but	
  
for	
  reasons	
  of	
  space	
  I	
  leave	
  that	
  strategy	
  for	
  another	
  occasion.	
  
xxiv	
  Goodman	
  (1976);	
  see	
  also	
  Elgin	
  (1996,	
  2009).	
  
xxv	
  For	
  instance	
  see	
  Chang	
  and	
  Kleiser	
  (1990,	
  p.	
  20)	
  which	
  informs	
  my	
  discussion.	
  
xxvi	
  Hence	
  the	
  source	
  and	
  the	
  target	
  are	
  both	
  regarded	
  as	
  ‘structures’	
  under	
  some	
  abstract	
  
description	
  suitable	
  on	
  pragmatic	
  grounds	
  –	
  and	
  there	
  is	
  no	
  direct	
  application	
  to	
  the	
  target	
  
conceived	
  as	
  a	
  bare	
  system.	
  See	
  e.g.	
  Van	
  Fraassen	
  (2008,	
  p.	
  X)	
  and	
  Suárez	
  (1999)	
  for	
  discussion.	
  
xxvii	
  See	
  the	
  various	
  essays	
  contained	
  in	
  Suárez	
  (2009)	
  and	
  Woods	
  (2011).	
  
xxviii	
  Maxwell	
  (1861);	
  for	
  discussion	
  see	
  e.g.	
  Nersessian	
  (2008).	
  
xxix	
  A	
  commitment	
  that	
  I	
  wish	
  to	
  move	
  away	
  from,	
  as	
  will	
  hopefully	
  become	
  clearer	
  in	
  the	
  discussion	
  
of	
  the	
  inferential	
  conception.	
  
xxx	
  If	
  anything,	
  the	
  inferential	
  conception	
  has	
  been	
  criticized	
  for	
  affording	
  too	
  much	
  leeway	
  at	
  this	
  
point	
  –	
  see	
  e.g.	
  Bolinska	
  (2013).	
  
xxxi	
  As	
  has	
  been	
  argued	
  more	
  extensively	
  in	
  Suárez	
  and	
  Solé	
  (2006)	
  of	
  which	
  the	
  text	
  above	
  is	
  a	
  
development	
  and	
  summary.	
  
xxxii	
  These	
  notions	
  were	
  first	
  introduced	
  in	
  Suárez	
  (2003,	
  pp.	
  229-­‐230).