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Representation, Ontology, and Heuristics: Regulating Trade Between the Philosophy of Art and Philoso
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Steven French

One way of approaching the relationship between science and art is via the way we characterize and represent science and art at the level of philosophical enquiry (indeed, some would say there is no other way!). My interest in particular is in the way that certain devices, approaches and manoeuvres from one field of enquiry might be brought over into the other. Elsewhere (French and McKenzie 2012) I have referred (tongue in cheek) to the ‘Viking approach’ that a philosopher of science might adopt towards metaphysics, grabbing and appropriating what she needs to help her in the effort to understand science. But as we all now know, taking the Vikings to be nothing but a bunch of looters is to do them an injustice and given the more sedate atmosphere of aesthetical enquiry (!), perhaps it is better to refer to a ‘trading’ approach when it comes to the relationship between the philosophy of science and the philosophy of art. For the most part I shall be considering trade that runs from the latter to the former, but examples of the reverse movement can also be given. And in particular I am interested in those factors that might constrain or limit that trade.

The trading zone I wish to focus on is that which deals in theories and artworks, and the core question I wish to examine is: to what extent are these two kinds of ‘things’ similar? The constraints on trade I shall briefly look at are the role of intentions and the nature of heuristics, and the conclusion I shall sketch is that to the extent that theories are like paintings, but also not, and like musical works, but also are not, perhaps we should drop the assumption that theories are kinds of objects to begin with.

Theories as Representations

In recent years the question of the relationship between scientific theories and the world, or the phenomena (depending on one’s realist inclinations) has been reframed in terms of representation, with philosophers of science explicitly drawing on accounts and examples in the philosophy of art (see Bueno and French 2011; Suarez 2003, van Fraassen 2008). Van Fraassen, in particular, has identified at least two central features of this relationship where the philosophy of science can learn from the philosophy of art: the first is that representation has to be acknowledged as representation as, giving his ‘Hauptsatz’: “There is no representation except in the sense that some things are used, made or taken, to represent some things as thus or so” (2008, p. 23). Thus theory T represents phenomenon P only for a user A in an appropriate context C. Here the role of the user’s intentions may become manifest, something I will return to shortly. The second concerns the significance of perspective and invariance, something which greatly interests me as a structural realist but which I shall not discuss here.

Now this shift in interest towards representation arose in part as a result of the shift in characterization of scientific theories within the philosophy of science from closed sets of logico-linguistic sentences to families of set-theoretic models (this forming the heart of the so-called semantic or ‘model-theoretic’ approach). In terms of the former, the relationship between theories and the world is captured by the notion of reference, holding between linguistic terms and objects; whereas for the latter, the relationship is best captured in terms of representation, holding between a model and the relevant system. In these terms the idea of a representational mapping can then be formally captured via the notion of an isomorphism--even if only partial (Bueno and French op. cit.)--holding between the model and the system, allowing us to say that the representation consists in the preservation of selected relations.

This works well (I would claim) for many examples from the philosophy of science and some (e.g., Budd 1993) have attempted to articulate something similar in the philosophy of art (less successfully perhaps). However, it has been objected that isomorphism-based accounts are neither necessary nor sufficient for representation (Suarez 2003). They are not necessary, it is claimed, because one can give examples of representations for which isomorphism is inappropriate to capture the relationship. Thus consider Picasso’s Guernica; here, it is argued, there lies a crucial ambiguity: on the one hand the painting represents the concrete pain of the inhabitants of the Basque town; on the other, it represents the abstract threat of the rise of fascism. Hence it cannot be placed in a 1-1 mapping with the things it represents. But of course, an obvious move that the philosopher of science can make is to insist that such apparent counter-examples cannot be traded over from the philosophy of art, not least because it is hard to come up with similar cases of ambiguity in science. And of course, even remaining within the domain of aesthetics, one might be inclined to say that although elements of Picasso’s composition do represent, for example, a dying horse, a bereaved mother and child and so on, the intent here is not is not so much to represent but to express the horror of war, the injustice of the attack and so on. Furthermore, to say that scientific theories express rather than represent would be a radical move that all but the most extreme anti-realists would be reluctant to endorse! The point here is that already we can see that trade between the philosophy of art and the philosophy of science needs some regulation--an obvious point perhaps but one that not all contributors to the relevant debate have appreciated.

Isomorphism is also argued to be insufficient for representation because of the latter’s directionality--the classic portrait of van Gogh represents van Gogh but not vice versa (at least not on most accounts) and hence something further is needed. Appealing to intentions--whether of the artist or the observer--is an obvious option, although it still leaves isomorphism as the underlying mechanism of representation. Here intentions function so as to transform a given object from non-art to art. Consider the classic case of Damien Hirst’s pile of apparent detritus, intended to represent the chaos of the artist’s studio, which was inadvertently swept away by a cleaner unaware of this intention. Or imagine that you are walking out in the forest and you come across a rock formation with caves that looks just like a human skull. Typically it would be insisted that without the relevant intention this could not be called a representation and this matches our intuitions. But now imagine that you walk out of the forest and into the desert and there you encounter Einstein’s famous equation E = mc2, apparently carved by the wind and rain out of the sand and rock. Here it is not so clear that our intuition supports the claim that without the relevant intention behind it, this edifice cannot represent relativistic phenomena. After all, who cares how this manifestation of Einstein’s equation came about? The provenance seems less important in this case and I would suggest that our discomfort with the claim that it cannot be said to represent relativistic phenomena without the appropriate representation has something to do with our unease over the presumption that theories are the sorts of objects that can be transformed from non-scientific to scientific in the way that artworks apparently can; indeed, I shall suggest that we should not consider theories as objects at all.

The Ontology of Theories

What kinds of things are theories? I’ve already mentioned two characterizations of theories: one in terms of logico-linguistic statements, the other in terms of families of set-theoretic models. One way of answering our question is to appeal to one or other of these characterizations and insist that that is what a theory is: either a closed set of statements on the former view, or a family of models on the latter. Indeed, with the rise of the latter, it has been suggested that models, and hence theories, should be seen as abstract entities (Giere 1988). Of course, this raises concerns regarding the second of my trade constraints above: how are we to understand the heuristics of scientific discovery and pursuit as applied to abstract entities?

Now, there is a sense in which we have been here before. Popper famously took theories to be inhabitants of his ‘world 3’--distinct from both world 1 of concrete, material entities and world 2 of the mind – along with works of literature and music: “Examples of world 3 objects are: the American Constitution; or Shakespeare’s The Tempest; or his Hamlet; or Beethoven’s Fifth Symphony; or Newton’s theory of gravitation” (Popper 1978, p. 145). And he continued, “One can, if one wishes, say that the world 3 objects themselves are abstract objects, and that their physical embodiments or realizations are concrete objects” (ibid.). Of course Popper was equally famously dismissive of scientific discovery, relegating it to psychology at best, but he did allow the inhabitants of his world 3 to be causally interactive, in the sense of being both subject to change and affecting us.

His justification for placing theories and artworks in world 3 were different in each kind of case. When it came to Beethoven’s Fifth, for example, he argued that this should be regarded as real and as living in world 3 because we can objectively judge good and bad performances. This is obviously inappropriate for scientific theories, and here he appeals to the element of surprise: “… it must have been a surprise for Einstein when he found, shortly after writing his first paper on Special Relativity, that the now-famous formula E = mc2 could be deduced from it as a theorem” (Tanner Lectures, p. 162). Thus Einstein’s Theory of Relativity is real (and lives in world 3) because it has surprising consequences, just as, for example, material objects do (they have hidden ‘sides’ to them, or hidden properties or they behave in unexpected ways and so on). This is not an uncommon way of distinguishing the ‘real’ from the not-real, of course. However, it’s not a good criterion in this case. As Wittgenstein famously noted, the reasons why people are surprised by certain deductive consequences has to do with their limitations and even Einstein could not have been expected to have been logically omniscient!

However, Popper also had what he called a “fundamental argument” for including theories in world 3 and this was that “… scientific conjectures or theories can exert a causal or an instrumental effect upon physical things; far more so than, say, screwdrivers or scissors” (ibid., p. 154). Indeed, he took world 3 objects to be causally interactive in that not only can they affect us, but we can change them. This is obviously reminiscent of Thomasson’s more recent view of artworks as abstract artifacts, which are created by and depend for their continued existence on certain human intentional states but are not to be identified with either the imaginary creations of individual minds or physical objects (Thomasson 2006).

Two questions obviously arise at this point: first, in what sense can world 3 objects causally affect us? Of course, a copy of Newton’s Principia may certainly affect us (if its thrown at us …), as may a performance of Beethoven’s Fifth, but that’s not the same thing as saying that the theory/musical work qua object living in world 3 can affect us. Here the advocate of world 3 ontology obviously owes us an account of that causal relationship, just as the Platonist does with, say, mathematical objects. The second question concerns how we, or our intentional states, can create, sustain and generally interact with these world 3 entities, and again some account is owed. In particular, the claim that theories qua world 3 entities are subject to change requires an appropriate account of how the heuristic moves embedded in the practices of world 1 affect such objects in world 3. Likewise, the claims that musical works are created and subject to change require a similarly appropriate account of the way in which intentions are constrained.

So, at one extreme, one might consider that any heuristic move, however ‘slight’ or minor, or any relevant intention to produce a theory or musical work in world 1 creates the corresponding abstract artifact in world 3. But then a quick scan through the bulky pages of Physical Review, or even worse, a review of the notes, presentations, work in progress seminars, blogs etc. of the world’s scientists will immediately establish just how vast the ontological inflation involved in such a suggestion would be. Alternatively, one might take the sub-set of the resultant plethora of such artifacts that meet the relevant heuristic criteria to count as (bone fide) musical works or ‘theories’ respectively. But obviously some account is needed of these heuristic effects. In some cases, this seems comparatively straightforward. So, one well-known heuristic move in the philosophy of science concerns what is sometimes called the General Correspondence Principle, which comes in various formulations but is often expressed as ‘keep the best (i.e., the empirically successful parts) of what you have.’ Applying this suggests that new theories are built upon the ‘best’/empirically successful/most well confirmed parts of their predecessors. It raises obvious concerns as to how one is to account for scientific revolutions (and, relatedly, runs counter to Kuhn’s controversial thesis that in some cases the ‘best’/empirically successful/most well confirmed parts of certain theories are lost through revolutionary change) but let’s leave that to one side. Then one might see how certain practices involving the construction of a new theory via building on the successful parts of an old theory in world 1 might be paralleled by a similar relationship between artifacts in world 3. But it is less clear what story one might tell about other heuristic moves, such as the exportation of certain symmetry principles from one domain of physics to another, to considerable heuristic effect. Are such principles effectively picking out artifacts already present in some sense in world 3? Or is it the case that their application in world 1 is again paralleled by something similar in world 3, leading to the coming into existence of an artifact in that world?

Of course, different moves can be identified in art. Consider Picasso’s sketches of dying horses and bulls in the bullring and the way they informed various features of Guernica. Or take the famous motif of Beethoven’s Fifth and the song of the yellowhammer. Is the latter ‘there’ in world 3, bearing the same relationship to the former as in world 1? Or is it the case that when Beethoven heard that birdsong in world 1, his intention to incorporate it into his symphony generated the corresponding artifact in world 3? The point is that the relationship between the moves in worlds 1 and 3 needs to be spelled out somehow.

Similar concerns arise with regard to the further question: in what sense do world 3 objects/abstract artifacts depend for their continued existence on certain intentional states? To answer this requires the articulation of an appropriate notion of world-spanning dependence and this can still be filed under ‘forthcoming.’ Now, I think that the notion of dependence in general is sufficiently elastic that some such account can surely be given, but the point is that once one considers the relevant heuristic moves the relationship between world 1 practices and world 3 artifacts becomes quite complex!

However, there is a way of cutting through that complexity, Alexandrian style, at least when it comes to scientific theories. This is to deny that theories are objects at all, whether ‘living’ in world 1 or 3. On this eliminativist line, there are no theories (qua objects) in science, merely elements or features of practice that make true certain statements, such as ‘Einstein’s theory of relativity is empirically successful’ or ‘Einstein’s theory of relativity is beautiful’, that are ostensibly but only apparently about theories (see French and Vickers 2011). We are multiply misled, I think, into viewing theories as objects: by the supposed element of surprise, when it comes to Popper’s world 3 entities, by their apparent representational character, where discussions draw extensively on concrete artworks such as certain paintings and by the comparison with musical works and the latter’s relationship with scores, for example. But if we drop the object-oriented ontology and simply focus on the relevant features of scientific practice, we have no need to find a world for these objects to live in, or to articulate the relevant dependence between entities of that world and this, and, I would argue (not here though) we will obtain a more perspicuous view of that practice itself. Can we say the same about artworks? This way of cutting the knot in science draws explicitly on a similar and earlier move made by Cameron with regard to musical works (Cameron 2008) and here we have a nice example of a two stage Viking raid: from the philosophy of art into metaphysics and from the philosophy of science into the philosophy of art! Alternatively, thinking in terms of the idea of a trading zone, here we have multiple trades going on. And, of course, there are other, different trades to be had – there are other ways of articulating the nature of theories and artworks than eliminativism, obviously--but such trading will have to be appropriately constrained, as I have sketched here, by considerations of the role of intentions when it comes to theories as representational devices and the role of heuristic factors with regard to their discovery.


Budd, M. (1993), “How Pictures Look,” in D. Knowles and J. Skorupski (eds.), Virtue and Taste, Blackwell, pp. 154-175.
Cameron, R. (2008), “There Are No Things That Are Musical Works,” British Journal of Aesthetics 48: 295-314.
French, S. and Vickers, P. (2011), “Are There No Things That are Scientific Theories?” British Journal of the Philosophy of Science 62: 771-804.
Popper, K.R. (1978), Tanner Lectures.
Suárez, M. (2003), “Scientific Representation: Similarity and Isomorphism”, International Studies in the Philosophy of Science, 17: 225 – 244.
Thomasson, A. (2006), “Debates about the Ontology of Art,” Philosophy Compass 1/3: 245 – 255.

2013 © Steven French

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