Representation

According to a still popular belief, science represents the world and is an image of reality. Certainly, the model-theoretic view of theories, according to which theories are foremost classes of models, makes such a view more plausible than the state­ment view, for which theories are sets of sentences or better, propositions (which are the semantic contents of sentences) which are asserted, i.e.

In the last decades, representation has become a trendy topic in the philosophy of science, due to the increasing influence of philosophers such as Bas van Fraassen who promoted the model-theoretic view of theories. Such a view is the heir of the representational conception of knowledge which accompanied the birth of modern science. We all know that both 17th century rationalists like Descartes and empiricists such as Locke construed knowledge as a faithful correspondence between our mental representations—our ideas—with reality. However, the rep­resentational conception of knowledge is confronted with a serious problem, called the “bridge problem” (Agazzi 2014, 29). Surely, we are immediately present to our ideas and we can safely investigate the properties of the idea of triangle without worrying about its possible correspondence with real entities. But how can we justify the belief that some of our ideas or representations faithfully mirror—at least in some respects—something external existing independently of our minds? This is the idealistic predicament which plagues the representational conception of knowledge.

The anti-psychological turn at the beginning of the 20th century did little towards the solution of the bridge problem. Extracting ideas^{[32] [33] out of the human mind and endowing them with flesh and blood in the external world does little to solve the problem. Granted, doing so localizes representations in representing artifacts—such as scientific models—which are accessible to a community of human subjects just as physical, as opposed to mental, images are. By this move, representations escape the privacy of our minds and do acquire an objective status, in the sense of intersubjectivity. Human subjects can immediately see a colored two-dimensional entity, and even come to an agreement in admitting that it is a portrait of someone in an appropriate context. But to resolve the bridge problem, we have first to muster arguments in favor of the belief that the person we aim at representing by the portrait is unambiguously identified and exists. In other words, we have to argue in favor of the existence of the particular target or the referent of the portrait. Furthermore, one must provide good reasons to believe that the portrait is faithful (or not) to its referent, always in some respects only (because a portrait is not a mere duplicate of its target). Such arguments and reasons cannot be gained from an examination of the internal properties of a possibly representing artifact, because the success in representing a target by means of a specific artifact depends upon factors which are external to it.}

As van Fraassen rightly stresses, to represent is to act. To represent involves someone who represents (a user or subject S), a representing artifact (representor) R, something that is represented (a target T) in some context C. As in any action, we can succeed (or fail) in representing the target that we intend to represent. Success (or failure) can obtain with respect to three distinct aims: identifying the target, representing it as such and such, and partially representing it in a correct way.^[34]

In representing, we must beforehand unambiguously identify our intended tar­get, provisionally bracketing at this first stage the issue of its existence. The entity which we decide to employ as a representational artifact has some properties that we can ascertain. But this fact alone does not provide any clue for identifying the target. Anything, whether natural or artificial, can be used by someone to represent any target. The user must initially stipulate which properties of the representor are relevant for his purpose. These are the properties which are meant to convey some information about the intended target. In general, the cultural context suffices to determine the relevant properties since it contains some specifications or conven­tions implicitly agreed upon by a community. Cultural contexts are of course external to the artifact itself. Moreover, these contexts widely vary in space and time. The physical characteristics of maritime maps for example considerably differ among cultures. To find their way at sea, Micronesians use sticks and shells bounded with ropes whereas we use sheets of papers covered with patches and lines of different colors, forms and widths. When an entity is used to represent, it becomes a construct, our artificially fabricated representor.

Identification of a target thus depends on the correspondence, established by the user, between some properties of the representor, which are considered to be per­tinent, and certain properties of the intended target. Such a correspondence fixes a code. The stipulated correspondence or the code is a matter of convention. How­ever, the actual possession of specific properties by the representor and the intended target, especially if the latter exists, is not conventional.

Arrived at this point, I wish to introduce a distinction between two ways of proceeding when we perform representing actions. First, we could start from a given perceived entity, which is immediately and unambiguously identified, such as a pipe, and attempt to represent it in a certain way. Or, and this is the second way, we can construct a representor, which functions as an unambiguous representation of an intended target, such as a unicorn, and inquire about the existence of unicorns. Surely, representation as such is directed: we use representors to represent targets, and not the other way around. In fact, within the representational conception of knowledge the users proceed by starting from their representors. Then, they ponder the reasons to believe that they represent some entities, which may or may not exist. Such a manner of proceeding is characteristic of modern times. Descartes asked himself if some ideas in his mind had internal characteristics which immediately pointed to a definite target and at the same time warranted its existence as well as the conformity of the idea with its target.

After representors have been expelled from human minds and became entities in the world, the success and adequacy of a representing action not only acquired the status of meaningful (and interesting) issues, but must be assessed on the basis of considerations which do not solely belong to the representors and their intended targets. In scientific theorizing about unobserved objects, at the beginning of the representational demarche, I (the user) have to start from a potential representor to identify its possible target, and not the other way around, in the same way as the modern thinkers started from their internal representations and not from things in the world. Thus, the identification of a target of a representation can only be achieved by taking my representor as an initial point of departure. Then, I select in it some relevant properties corresponding to some properties of the intended target, irrespective of its existence, as in the example of unicorns. After having tacitly or explicitly specified the code, in order to convince myself of the existence of the target, I must obviously somehow verify that there is something in the world which possesses some relevant properties.

Once the target has been identified, the second aim pursued when we perform representations is to represent the target as having certain properties, which are distinct from the properties used for its identification. For clarity, it is convenient to distinguish in the representing artifact the properties A relevant for the identification of its target from the properties B that we consider to be relevant to convey interesting information about the target. Again, success in this respect can be achieved whether the intended target exists or not and whether it possesses the properties B or not. Some codified internal properties of the representor, such as distortion of bodily features in a portrait, can be used to succeed in representing Bismarck as vainglorious. In Spott's caricature, its referent is identified by means of pictorial elements internal to the representor associated with some properties of the intended target such as having a moustache, being bald etc. Additionally, Bismarck is represented as vainglorious since in the caricature his body is partially distorted in such a way that some of its parts resemble certain features possessed by pea­cocks. In our culture, peacocks are conventional symbols of vanity. Success in representing Bismarck as vainglorious is thus achieved independently of his being actually so (of course, he was...).

So far, we remained confined to the domain of our representations. Evidently, some ingredients external to our representors, such as conventions and selection of relevant properties, had to be mobilized in order to achieve success in identifying an intended target and in representing it as such and such. But the goal of correctly representing a target has not been sufficiently addressed yet. Obviously, the issue of correctness only arises for existing targets which may have properties corre­sponding to some properties of our representors according to the established code. Thus, we must have good reasons to believe that the intended target exists before raising the faithfulness issue. Such reasons cannot be extracted from the representor and the conventions adopted by the users only.

In the case of perceptual entities, actual perception can do the trick. We see a pipe which we compare with its representor, which could be Magritte's famous painting La trahison des images http://collections.lacma.org/node/239578. The sentence written on the canvas Ceci n’est pas une pipe makes clear that the exis­tence of the pipe does not follow from the existence of the painting, since the word “ceci” refers to the painted pipe and not to a “real” pipe. But we can perceptually ascertain the existence of a pipe and verify that the brown area in the painting corresponds to a feature possessed by the real pipe which we see, e.g. the property of being brown.

In so doing we attribute a property to the pipe in an act of predication. In fact, acts of predication have been present, although tacitly, throughout the entire process which initiated with the identification of the referent and ended with the verification of the partial (i.e. in some respects) correctness of the representor to its target. To identify a target, I had to select or insert in the representing artifact some charac­teristics and assume that they do belong to the artifact. Further, I had to select or insert in the artifact elements which allow me to employ the artifact as a representor of the target in some of its respects. Given this, I (or another user) is able to represent the target as having certain properties. Irrespectively of its possible existence, those properties are predicated of the target or referent. Thereafter, an existing perceived entity is identified as a pipe, that is, as having the property of being a pipe. Finally, the faithfulness of the painting with respect to a specific feature of the target, its color for instance, is confirmed by observation and expressed in the act of predication of the property of being brown to both the real pipe and the painted pipe, provided we conventionally assume that the brown expanse in the painting corresponds to the property of being brown for the pipe (we could have decided that the brown expanse corresponds to being pink in reality...).

An act of predication consists in attributing a property to an entity. Such an act is equivalent to asserting that an entity possesses a property, by means of a judgement, a statement or an assertion. The word “judgement” has traditionally been associated with a judging subject. Nowadays, the terms “statement” and “assertion” are taken to be more neutral, or impersonal, in the sense that the truth of a statement or assertion transcends the particular idiosyncrasies of the judging subject. We will come back to the problem of objectivity below. As for now, it must be emphasized that the entire business of representing depends on the success of acts of predication and further, on the truth of statements.

As we saw, the user must specify at least implicitly a correspondence between some properties of the representor and some properties of the target. The faith­fulness of a representor to its target in some respects cannot be conveyed by some feature intrinsic to the representor. Suppose a specific mark, such as a cross or a green dot, in the representing artifact is to signify that it is faithful to its target in some respect. Here, we inserted a property of the representor which does not correspond to a property of its target, and which consequently does not play a representational role. Success in representing presupposes a correspondence, a matching, between the representor and its target. What is called a representative function (Da Costa and French 2003, 49) has to be constructed by the user. Such a function must be an isomorphism or a homomorphism^[36] which preserves the form, or the structure, common to the representor and its target. An established structural similarity is a necessary (not sufficient) condition for the success of representation. If we add a mark to the painting of the pipe to indicate that it correctly represents existing pipes in some respects, we have constructed another representing artifact and the problem of correctness has been pushed one step back (van Fraassen 2008, 31; Ghins 2010, 527).

In the example of the painting of a pipe (without Magritte’s sentence), it seems that the bridge problem has been solved. On the one hand, we have a representing entity, the painting, and on the other, a represented entity, the pipe. Both are immediately perceptible and we can compare them to assess the partial correctness of the painting to its referent. The idealistic predicament has been dissolved by objectifying mental ideas into real perceivable entities and thereby making repre­sentors and their targets inhabitants of the same perceptual world in which the relevant comparisons can be performed.

This is an illusion. The initial modern defenders of the representational con­ception of knowledge claimed that we have direct cognitive grasp of our mental ideas or representations only. Thus, they deny that representing artifacts and per­ceived targets can be immediately known. The replacement of mental ideas by worldly representing artifacts has not been achieved at all. The comparison between the representor and its target is nothing else than a comparison between two mental representations. There is no warrant whatsoever that we have hit upon external real entities.

Even if we avoid any recourse to mental representations and defend some ver­sion of direct realism about paintings, pipes etc., we must concede that the cognitive content does not belong to representing artifacts per se but pertains to facts which are extrinsic to them among which the truth of some predicative assertions certainly is the most important. Representors are not the primary vectors of knowledge. What we originally know is that some perceived entities, representors and targets, possess some properties because we are immediately perceptually present to them. Such knowledge provides the ground for the success of our representing activity. I insist that the predicative statements which express this knowledge do not trade on representation. To assert that an entity possesses a specific property is not to say that the property (adequately?) represents the entity albeit partially and much less that the predicate term represents that entity as having such property (Ghins 2010 533; van Fraassen 2010, 553).

In science we often deal with theoretical models which are meant to represent targets which lie beyond our possibility of perceiving them. In such instances, the perceptual comparison between the model and its purported target cannot be carried out. The epistemological debate of scientific realism hinges on the cogency of the reasons which the realist can adduce in favor of belief in the existence of unob­servable referents or targets. But before addressing this issue, a discussion of objectivity is in order.

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