Online research in philosophy

The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources.

In science, models are used in many different ways: to test empirical hypotheses, to help in theory formation, to visualize data, and so on. Scientists construct and study the behavior of models, and compare this to observed behavior of a target system. We propose that for this to be possible models must carry information about their targets. When models are viewed as information carrying entities, this property can be used as a foundation for a representational theory of models. This account presents a way of avoiding the need to refer to modelers’ intentions (or their mental states) as constitutive of the semantics of scientific representations. Moreover, an information theory based account of scientific representations can provide a naturalistic account of models which can deal the problems of asymmetry, relevance and circularity that afflict currently popular proposals based on user intentions. From the information semantic perspective, models as scientific representations can be considered a special case of a larger problem of naturalistic representation. In this paper we will look at what we think is the most promising avenue of developing this information theoretic account of representational models. Traditionally, there has been a strong tendency towards a clear-cut division of labor between philosophers of science and philosophers of mind. We believe that there are some important philosophical insights about representation that are relevant for both camps.

Representation has been one of the main themes in the recent discussion of models. Several authors have argued for a pragmatic approach to representation that takes users and their interpretations into account. It appears to me, however, that this emphasis on representation places excessive limitations on our view of models and their epistemic value. Models should rather be thought of as epistemic artifacts through which we gain knowledge in diverse ways. Approaching models this way stresses their materiality and media-specificity. Focusing on models as multi-functional artifacts loosens them from any pre-established and fixed representational relationships and leads me to argue for a two-fold approach to representation.

Models are generally used by scientists to obtain predictions and to provide explanations about phenomena. Their predictive and explanatory power is generally thought of as depending on their representative power. It is still not clear, though, in virtue of which features models allow scientists to draw inferences about the system they stand for. In this paper, I focus on a special kind of models, namely imaginary models (I-models) such as the simple pendulum. The main question I address is: how do scientists use I-models in representing target systems? First, I propose a clarification of the very notion of representation, by emphasizing the importance of what I call the format of a representation to the inferences cognitive agents can draw from it. Then, I analyze the various representational relationships that are in play in the use of I-models. I finally conclude that there is no special semantics to be applied to I-models, and that the study of the representational power of models in general should instead focus on the variety of the formats that are used in scientific practice.

It is now part and parcel of the official philosophical wisdom that models are essential to the acquisition and organisation of scientific knowledge. It is also generally accepted that most models represent their target systems in one way or another. But what does it mean for a model to represent its target system? I begin by introducing three conundrums that a theory of scientific representation has to come to terms with and then address the question of whether the semantic view of theories, which is the currently most widely accepted account of theories and models, provides us with adequate answers to these questions. After having argued in some detail that it does not, I conclude by pointing out in what direction a tenable account of scientific representation might be sought.

In this paper I propose an account of representation for scientific models based on Kendall Walton’s ‘make-believe’ theory of representation in art. I first set out the problem of scientific representation and respond to a recent argument due to Craig Callender and Jonathan Cohen, which aims to show that the problem may be easily dismissed. I then introduce my account of models as props in games of make-believe and show how it offers a solution to the problem. Finally, I demonstrate an important advantage my account has over other theories of scientific representation. All existing theories analyse scientific representation in terms of relations, such as similarity or denotation. By contrast, my account does not take representation in modelling to be essentially relational. For this reason, it can accommodate a group of models often ignored in discussions of scientific representation, namely models which are representational but which represent no actual object.

In this paper, I show how some of the fundamental problems that face a structuralist conception of representation can be solved by (a) distinguishing between three relevant senses of ‘representation’ (i.e. denotation, epistemic representation, and faithful epistemic representation), (b) claiming that, properly understood, the structural conception of representation aims at providing us with an account of faithful epistemic representation not of epistemic representation simpliciter, and (c) adopting an interpretational conception of epistemic representation.

The main aim of this paper is to disentangle three senses in which we can say that a model represents a system—denotation epistemic representation, and successful epistemic representation--and to individuate what questions arise from each sense of the notion of representation as used in this context. Also, I argue that a model is an epistemic representation of a system only if a user adopts a general interpretation of the model in terms of a system. In the process, I hope to clarify where those who, following Craig Callander and Jonathan Cohen, claim that there is no special problem about scientific representation go wrong. In the terminology adopted here, even if scientific representation is only an instance of epistemic representation, scientific representation should not be confounded with denotation.

The recent discussion on scientific representation has focused on models and their relationship to the real world. It has been assumed that models give us knowledge because they represent their supposed real target systems. However, here agreement among philosophers of science has tended to end as they have presented widely different views on how representation should be understood. I will argue that the traditional representational approach is too limiting as regards the epistemic value of modelling given the focus on the relationship between a single model and its supposed target system, and the neglect of the actual representational means with which scientists construct models. I therefore suggest an alternative account of models as epistemic tools. This amounts to regarding them as concrete artefacts that are built by specific representational means and are constrained by their design in such a way that they facilitate the study of certain scientific questions, and learning from them by means of construction and manipulation.

In this paper, I develop Mauricio Suárez’s distinction between denotation, epistemic representation, and faithful epistemic representation. I then outline an interpretational account of epistemic representation, according to which a vehicle represents a target for a certain user if and only if the user adopts an interpretation of the vehicle in terms of the target, which would allow them to perform valid (but not necessarily sound) surrogative inferences from the model to the system. The main difference between the interpretational conception I defend here and Suárez’s inferential conception is that the interpretational account is a substantial account—interpretation is not just a “symptom” of representation; it is what makes something an epistemic representation of a something else.