Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a (...) scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics. (shrink)

Science is popularly understood as being an ideal of impartial algorithmic objectivity that provides us with a realistic description of the world down to the last detail. The essays collected in this book—written by some of the leading experts in the field—challenge this popular image right at its heart, taking as their starting point that science trades not only in truth, but in fiction, too. With case studies that range from physics to economics and to biology, _Fictions in Science_ reveals (...) that fictions are as ubiquitous in scientific narratives and practice as they are in any other human endeavor, including literature and art. Of course scientific activity, most prominently in the formal sciences, employs logically precise algorithmic thinking. However, the key to the predictive and technological success of the empirical sciences might well lie elsewhere—perhaps even in scientists’ extraordinary creative imagination instead. As these essays demonstrate, within the bounds of what is empirically possible, a scientist’s capacity for invention and creative thinking matches that of any writer or artist. (shrink)

Computational methods such as computer simulations, Monte Carlo methods, and agent-based modeling have become the dominant techniques in many areas of science. Extending Ourselves contains the first systematic philosophical account of these new methods, and how they require a different approach to scientific method. Paul Humphreys draws a parallel between the ways in which such computational methods have enhanced our abilities to mathematically model the world, and the more familiar ways in which scientific instruments have expanded our access to the (...) empirical world. This expansion forms the basis for a new kind of empiricism, better suited to the needs of science than the older anthropocentric forms of empiricism. Human abilities are no longer the ultimate standard of epistemological correctness.Humphreys also includes arguments for the primacy of properties rather than objects, the need to consider technological constraints when appraising scientific methods, and a detailed account of how the path from computational template to scientific application is constructed. This last feature allows us to hold a form of selective realism in which anti-realist arguments based on formal reconstructions of theories can be avoided. One important consequence of the rise of computational methods is that the traditional organization of the sciences is being replaced by an organization founded on computational templates.Extending Ourselves will be of interest to philosophers of science, epistemologists, and to anyone interested in the role played by computers in modern science. (shrink)

Non-actual model systems discussed in scientific theories are compared to fictions in literature. This comparison may help with the understanding of similarity relations between models and real-world target systems. The ontological problems surrounding fictions in science may be particularly difficult, however. A comparison is also made to ontological problems that arise in the philosophy of mathematics.

The picture of synthetic biology as a kind of engineering science has largely created the public understanding of this novel field, covering both its promises and risks. In this paper, we will argue that the actual situation is more nuanced and complex. Synthetic biology is a highly interdisciplinary field of research located at the interface of physics, chemistry, biology, and computational science. All of these fields provide concepts, metaphors, mathematical tools, and models, which are typically utilized by synthetic biologists by (...) drawing analogies between the different fields of inquiry. We will study analogical reasoning in synthetic biology through the emergence of the functional meaning of noise, which marks an important shift in how engineering concepts are employed in this field. The notion of noise serves also to highlight the differences between the two branches of synthetic biology: the basic science-oriented branch and the engineering-oriented branch, which differ from each other in the way they draw analogies to various other fields of study. Moreover, we show that fixing the mapping between a source domain and the target domain seems not to be the goal of analogical reasoning in actual scientific practice. (shrink)

Synthetic biology is often understood in terms of the pursuit for well-characterized biological parts to create synthetic wholes. Accordingly, it has typically been conceived of as an engineering dominated and application oriented field. We argue that the relationship of synthetic biology to engineering is far more nuanced than that and involves a sophisticated epistemic dimension, as shown by the recent practice of synthetic modeling. Synthetic models are engineered genetic networks that are implanted in a natural cell environment. Their construction is (...) typically combined with experiments on model organisms as well as mathematical modeling and simulation. What is especially interesting about this combinational modeling practice is that, apart from greater integration between these different epistemic activities, it has also led to the questioning of some central assumptions and notions on which synthetic biology is based. As a result synthetic biology is in the process of becoming more “biology inspired.”. (shrink)

This book not only outlines the indispensability argument in considerable detail but also defends it against various challenges.

Suppose we are asked to draw up a list of things we take to exist. Certain items seem unproblematic choices, while others (such as God) are likely to spark controversy. The book sets the grand theological theme aside and asks a less dramatic question: should mathematical objects (numbers, sets, functions, etc.) be on this list? In philosophical jargon this is the ‘ontological’ question for mathematics; it asks whether we ought to include mathematicalia in our ontology. The goal of this work (...) is to answer this question in the affirmative, by drawing on considerations on the the applicability of mathematics to natural science. (shrink)

The question is discussed how noise gained a functional meaning in the context of biology. According to the common view, noise is considered a disturbance or perturbation. I analyze how this understanding changed and what kind of developments during the last 10 years contributed to the emergence of a new understanding of noise. Results gained during a field study in a synthetic biology laboratory show that the emergence of this new research discipline—its highly interdisciplinary character, its new technologies and novel (...) modeling strategies—provided essential impulses, which led to the observed change in the concept of noise. The laboratory study is combined with a historical analysis, which explores the general question as to how concepts travel between disciplines and, specifically, how noise was transferred from engineering and physics into biology. In the past, scientists, such as Lotka and Goodwin, tried to introduce a statistical mechanics into biology and discussed the problem of “unfitting” concepts. The change in the meaning of the concept can be interpreted as a way of making it fit to the novel context in which it is applied. (shrink)

The goal of the present article is to contribute to the epistemology and methodology of computer simulations. The central thesis is that the process of simulation modeling takes the form of an explorative cooperation between experimenting and modeling. This characteristic mode of modeling turns simulations into autonomous mediators in a specific way; namely, it makes it possible for the phenomena and the data to exert a direct influence on the model. The argumentation will be illustrated by a case study of (...) the general circulation models of meteorology, the major simulation models in climate research. (shrink)

Synthetic biology is often understood in terms of the pursuit for well-characterized biological parts to create synthetic wholes. Accordingly, it has typically been conceived of as an engineering dominated and application oriented field. We argue that the relationship of synthetic biology to engineering is far more nuanced than that and involves a sophisticated epistemic dimension, as shown by the recent practice of synthetic modeling. Synthetic models are engineered genetic networks that are implanted in a natural cell environment. Their construction is (...) typically combined with experiments on model organisms as well as mathematical modeling and simulation. What is especially interesting about this combinational modeling practice is that, apart from greater integration between these different epistemic activities, it has also led to the questioning of some central assumptions and notions on which synthetic biology is based. As a result synthetic biology is in the process of becoming more “biology inspired.”. (shrink)