This thesis starts with three challenges to the structuralist accounts of applied mathematics. Structuralism views applied mathematics as a matter of building mapping functions between mathematical and target-ended structures. The first challenge concerns how it is possible for a non-mathematical target to be represented mathematically when the mapping functions per se are mathematical objects. The second challenge arises out of inconsistent early calculus, which suggests that mathematical representation does not require rigorous mathematical structures. The third challenge comes from renormalisation group (...) (RG) explanations of universality. It is argued that the structural mapping between the world and a highly abstract minimal model adds little value to our understanding of how RG obtains its explanatory force. I will address the first and second challenges from the similarity perspective. The similarity account captures representations as similarity relations, providing a more flexible and broader conception of representation than structuralism. It is the specification of the respect and degree of similarity that forges mathematics into a context of representation and directs it to represent a specific system in reality. Structuralism is treatable as a tool for explicating similarity rela-tions set-theoretically. The similarity account, combined with other approaches (e.g., Nguyen and Frigg’s extensional abstraction account and van Fraassen’s pragmatic equivalence), can dissolve the first challenge. Additionally, I will make a structuralist response to the second challenge, and suggestions regarding the role of infinitesimals from the similarity perspective. In light of the similarity account, I will propose the “hotchpotch picture” as a method-ological reflection of our study of representation and explanation. Its central insight is to dissect a representation or an explanation into several aspects and use different theories (that are usually thought of competing) to appropriate each of them. Based on the hotchpotch picture, RG explanations can be dissected to the “indexing” and “inferential” conceptions of explanation, which are captured or characterised by structural mappings. Therefore, structuralism accommodates RG explanations, and the third challenge is resolved. (shrink)

In this essay, I examine the role of dissimilarity in scientific representation. After briefly reviewing some of the philosophical literature which places a strong emphasis on the role of similarity, I turn to examine some work from Carroll and Borges which demonstrates that perfect similarity is not valuable in the representational use of maps. Expanding on this insight, I go on to argue that this shows that dissimilarity is an important part of the representational use of maps—a point I then (...) extend to the case of scientific representation. Relying on some work from Latour, I argue that dissimilarity plays an essential role in representational practice, by providing novel forms of manipulation and use which affords the achievement of various epistemic and nonepistemic aims. After showing how this point connects to some other literature on scientific representation, I discuss some examples of the value of dissimilarity in the use of representational vehicles. Overall, I argue that to understand scientific representation, we will need to consider more than just similarity. We will need to explore dissimilarities as well. (shrink)

This paper argues for a representational semantic conception of scientific theories, which respects the bare claim of any semantic view, namely that theories can be characterised as sets of models. RSC must be sharply distinguished from structural versions that assume a further identity of ‘models’ and ‘structures’, which we reject. The practice-turn in the recent philosophical literature suggests instead that modelling must be understood in a deflationary spirit, in terms of the diverse representational practices in the sciences. These insights are (...) applied to some mathematical models, thus showing that the mathematical sciences are not in principle counterexamples to RSC. (shrink)

Scientific models are used to predict and understand the target phenomena in the reality. The kind of epistemic relationship between the model and the reality is always regarded by most of the philosophers as a representational one. I argue that, complementary to this representational role, some of the scientific models have a constructive role to play in altering and reconstructing the reality in a physical way. I hold that the idealized model assumptions and elements bestow the constructive force of a (...) model on the reality. By recognizing the physical constructive force of some scientific models, the merit of these models could be judged by how successful they are in the reality construction, rather than by the traditional criterion of model-world representation. (shrink)

How does mathematics apply to something non-mathematical? We distinguish between a general application problem and a special application problem. A critical examination of the answer that structural mapping accounts offer to the former problem leads us to identify a lacuna in these accounts: they have to presuppose that target systems are structured and yet leave this presupposition unexplained. We propose to fill this gap with an account that attributes structures to targets through structure generating descriptions. These descriptions are physical descriptions (...) and so there is no such thing as a solely mathematical account of a target system. (shrink)

Science provides us with representations of atoms, elementary particles, polymers, populations, genetic trees, economies, rational decisions, aeroplanes, earthquakes, forest fires, irrigation systems, and the world’s climate. It's through these representations that we learn about the world. This entry explores various different accounts of scientific representation, with a particular focus on how scientific models represent their target systems. As philosophers of science are increasingly acknowledging the importance, if not the primacy, of scientific models as representational units of science, it's important to (...) stress that how they represent plays a fundamental role in how we are to answer other questions in the philosophy of science. This entry begins by disentangling ‘the’ problem of scientific representation, before critically evaluating the current options available in the literature. (shrink)

The structuralist approach represents the relation between a model and physical system as a relation between two mathematical structures. However, since a physical system is _prima facie_ _not_ a mathematical structure, the structuralist approach seemingly fails to represent the fact that science is about concrete, physical reality. In this paper, I take up this _problem of lost reality_ and suggest how it may be solved in a purely structuralist fashion. I start by briefly introducing both the structuralist approach and the (...) problem of lost reality and discussing the various (non-structuralist) solutions that have been proposed in the literature. Following this, I decompose the problem into the _ontological mismatch_ and _specification_ problems. In response to the former, I present a _metascientific dissolution argument_, according to which the difference in kind between mathematical structures and physical systems poses no deep obstacle to the structuralist approach, and consider some upshots of this argument for our views on representation. By way of conclusion, I argue that the metascientific dissolution argument paves the way for a solution to the specification problem as well. (shrink)

Previously, I (Boesch 2017) described a notion called “representational licensing”—the set of activities of scientific practice by which scientists establish the intended representational use of a vehicle. In this essay, I expand and develop this concept of representational licensing. I begin by showing how the concept is of value for both pragmatic and substantive approaches to scientific representation. Then, through the examination of a case study of the Mississippi River Basin Model, I point out and explain some of the activities (...) of representational licensing that help to establish the representational nature of this model. Throughout the exploration of the case study, I pause to identify some important lessons which apply more generally about the nature of representational licensing in science. (shrink)