The concept of representation has gained momentum in the philosophy of science. The simplest concept of representation conceivable is expressed by the following dyadic predicate: structure S(HeB) represents HeB. Steven French defended that to represent something in science is the same as to have a model for it, where models are set-structures; then ‘representation’ and ‘model’ become synonyms and so do ‘to represent’ and ‘to model’. Nevertheless, this simplest conception was quickly thrown overboard as too simple by amongst others Ronald Giere, who replaced this dyadic predicate with a quadratic predicate to express a more involved concept of representation:
Scientist S uses model S to represent being B for purpose P,
where ‘model’ can here be identified with ‘structure’. Another step was set by Bas van Fraassen. As early as 1994, in his contribution to J. Hilgevoord’s Physics and our View of the World, Van Fraassen brought Nelson Goodman’s distinction between representation-of and representation-as — drawn in his seminal Languages of Art – to bear on science; he went on to argue that all representation in science is representation-as. We represent a Helium atom in a uniform magnetic field as a set-theoretical wave-mechanical structure S(HeB). In his new tome Scientific Representation, Van Fraassen has moved essentially to a hexadic predicate to express the most fundamental and most involved concept of representation to date:
Repr(S, V, S, B, F, P) ,
which reads: subject or scientist S is V -ing artefact S to represent B as an F for purpose P. Example: In the 1920ies, Heisenberg (S) constructed (V) a mathematical object (S) to represent a Helium atom (B) as a wave-mechanical structure (F) to calculate its electro-magnetic spectrum (P). We concentrate on the following triadic predicate, which is derived from the fundamental hexadic one:
ReprAs(S, B, F) iff ∃S, ∃V, ∃P : Repr(S, V, A, B, F, P)
which reads: abstract object S represents being B as an F, so that F(S).
Giere, Van Fraassen and contemporaries are not the first to include manifestations of human agency in their analysis of models and representation in science. A little more than most half a century ago, Peter Achinstein expounded the following as a characteristic of models in science:
A theoretical model is treated as an approximation useful for certain purposes. (…) The value of a given model, therefore, can be judged from different though related viewpoints: how well it serves the purposes for which it is eimployed, and the completeness and accuracy of the representation it proposes. (…) To propose something as a model of X is to suggest it as way of representing X which provides at least some approximation of the actual situation; moreover, it is to admit the possibility of alternative representations useful for different purposes.
One year later, M.W. Wartofsky explicitly proposed, during the Annual Meeting of the American Philosophical Association, Western Division, Philadelphia, 1966, to consider a model as a genus of representation, to take in that representation involves “relevant respects for relevant for purposes”, and to consider “the modelling relation triadically in this way: M(S,x,y), where S takes x as a model of y”.20 Two years later, in 1968, Wartofsky wrote in his essay ‘Telos and Technique: Models as Modes of Action’ the following:
In this sense, models are embodiments of purpose and, at the same time, instruments for carrying out such purposes. Let me attempt to clarify this idea. No entity is a model of anything simply by virtue of looking like, or being like, that thing. Anything is like anything else in an infinite number of respects and certainly in some specifiable respect; thus, if I like, I may take anything as a model of anything else, as long as I can specify the respect in which I take it. There is no restriction on this. Thus an array of teacups, for example, may be take as a model for the employment of infantry battalions, and matchsticks as models of mu-mesons, there being some properties that any of these things share with the others. But when we choose something to be a model, we choose it with some end in view, even when that end in view is simply to aid the imagination or the understanding. In the most trivial cases, then, the model is already normative and telic. It is normative in that is chosen to represent abstractly only certain features of the thing we model, not everything all at once, but those features we take to be important or significant or valuable. The model is telic in that significance and value can exist only with respect to some end in view or purpose that the model serves.
Further, during the 1950ies and 1960ies the role of analogies, besides that of models, was much discussed among philosophers of science (Hesse, Achinstein, Girill, Nagel, Braithwaite, Wartofsky).
On the basis of the general concept of representation, we can echo Wartofsky by asserting that almost anything can represent everything for someone for some purpose. In scientific representations, representans and representandum will share some features, but not all features, because to represent is neither to mirror nor to copy. Realists, a-realists and anti-realists will all agree that ReprAs(S, B, F) is true only if on the basis of F(S) one can save all phenomena that being B gives rise to, i.e. one can calculate or accommodate all measurement results obtained from observing B or experimenting with B. Whilst for structural empiricists like Van Fraassen this is also sufficient, for StrR it is not. StrR will want to add that structure S of type F ‘is realised’, that S of type F truly is the structure of being B or refers to B, so that also F(B). StrR will want to order the representations of being B that scientists have constructed during the course of history as approaching the one and only true structure of B, its structure an sich, the Kantian regulative ideal of StrR. But this talk of truth and reference, of beings and structures an sich, is in dissonance with the concept of representation-as.
Some being B can be represented as many other things and all the ensuing representations are all hunky-dory if each one serves some purpose of some subject. When the concept of representation-as is taken as pivotal to make sense of science, then the sort of ‘perspectivalism’ that Giere advocates is more in consonance with the ensuing view of science than realism is. Giere attempts to hammer a weak variety of realism into his ‘perspectivalism’: all perspectives are perspectives on one and the same reality and from every perspective something is said that can be interpreted realistically: in certain respects the representans resembles its representandum to certain degrees. A single unified picture of the world is however not to be had. Nancy Cartwright’s dappled world seems more near to Giere’s residence of patchwork realism. A unified picture of the physical world that realists dream of is completely out of the picture here. With friends like that, realism needs no enemies.
There is prima facie a way, however, for realists to express themselves in terms of representation, as follows. First, fix the purpose P to be: to describe the world as it is. When this fixed purpose leaves a variety of representations on the table, then choose the representation that is empirically superior, that is, that performs best in terms of describing the phenomena, because the phenomena are part of the world. This can be established objectively. When this still leaves more than one representation on the table, which thus save the phenomena equally well, choose the one that best explains the phenomena. In this context, Van Fraassen mentions the many interpretations of QM: each one constitutes a different representation of the same beings, or of only the same observable beings (phenomena), their similarities notwithstanding. Do all these interpre- tations provide equally good explanations? This can be established objectively too, but every judgment here will depend on which view of explanation is employed. Suppose we are left with a single structure A, of type G. Then we assert that ‘G(B)’ is true. When this ‘G’ predicates structure to B, we still need to know what ‘structure’ literally means in order to know what it is that we attribute to B, of what A is that B instantiates, and, even more important, we need to know this for our descriptivist account of reference, which realists need in order to be realists. Yes, we now have arrived where we were at the end of the previous two Sections. We conclude that this way for realists, to express themselves in terms of representation, is a dead end. The concept of representation is not going to help them.
The need for substantive accounts of truth and reference fade away as soon as one adopts a view of science that takes the concept of representation-as as its pivotal concept. Fundamentally different kinds of mathematical structure, set-theoretical and category-theoretical, can then easily be accommodated. They are ‘only representations’. That is moving away from realism, StrR included, dissolving rather than solving the problem for StrR of clarifying its Central Claim of what it means to say that being B is or has structure S — ‘dissolved’, because ‘is or has’ is replaced with ‘is represented-as’. Realism wants to know what B is, not only how it can be represented for someone who wants to do something for some purpose. When we take it for granted that StrR needs substantive accounts of truth and reference, more specifically a descriptivist account of reference and then an account of truth by means of reference, then a characterisation of structure as directly as possible, without committing one to a profusion of abstract objects, is mandatory.