What could be more certain than the fact that 2 plus 2 equals 4? Since the time of the ancient Greeks mathematicians have believed there is little---if anything---as unequivocal as a proved theorem. In fact, mathematical statements that can be proved true have often been regarded as a more solid foundation for a system of thought than any maxim about morals or even physical objects. The 17th-century German mathematician and philosopher Gottfried Wilhelm Leibniz even envisioned a ``calculus'' of reasoning such (...) that all disputes could one day be settled with the words ``Gentlemen, let us compute!'' By the beginning of this century symbolic logic had progressed to such an extent that the German mathematician David Hilbert declared that all mathematical questions are in principle decidable, and he confidently set out to codify once and for all the methods of mathematical reasoning. (shrink)

The use of computers and the role of women in radio astronomy and X-ray crystallography research at the Cavendish Laboratory between 1949 and 1975 have been investigated. We recorded examples of when computers were used, what they were used for and who used them from hundreds of papers published during these years. The use of the EDSAC, EDSAC 2 and TITAN computers was found to increase considerably over this time-scale and they were used for a diverse range of applications. The (...) majority of references to computer operators and programmers referred to women, 57% for astronomy and 62% for crystallography, in contrast to a very small proportion, 4% and 13% respectively, of female authors of papers. (shrink)

We examine two very different approaches to formalising real computation, commonly referred to as “Computable Analysis” and “the BSS approach”. The main models of computation underlying these approaches—bit computation and BSS, respectively—have also been put forward as appropriate foundations for scientific computing. The two frameworks offer useful computability and complexity results about problems whose underlying domain is an uncountable space. Since typically the problems dealt with in physical sciences, applied mathematics, economics, and engineering are also defined in uncountable (...) domains, it is fitting that we choose between these two approaches a foundational framework for scientific computing. However, the models are incompatible as to their results. What is more, the BSS model is highly idealised and unrealistic; yet, it is the de facto implicit model in various areas of computational mathematics, with virtually no problems for the everyday practice. This paper serves three purposes. First, we attempt to delineate what the goal of developing foundations for scientific computing exactly is. We distinguish between two very different interpretations of that goal, and on the separate basis of each one, we put forward answers about the appropriateness of each framework. Second, we provide an account of the fruitfulness and wide use of BSS, despite its unrealistic assumptions. Third, according to one of our proposed interpretations of the scope of foundations, the target domain of both models is a certain mathematical structure. In a clear sense, then, we are using idealised models to study a purely mathematical structure. The third purpose is to point out and explain this intriguing phenomenon and attempt to make connections with the typical case of idealised models of empirical domains. (shrink)

Quantum computing technologies have become a hot topic in academia and industry receiving much attention and financial support from all sides. Building a quantum computer that can be used practically is in itself an outstanding challenge that has become the ‘new race to the moon’. Next to researchers and vendors of future computing technologies, national authorities are showing strong interest in maturing this technology due to its known potential to break many of today’s encryption techniques, which would have (...) significant and potentially disruptive impact on our society. It is, however, quite likely that quantum computing has beneficial impact on many computational disciplines. In this article we describe our vision of future developments in scientific computing that would be enabled by the advent of software-programmable quantum computers. We thereby assume that quantum computers will form part of a hybrid accelerated computing platform like GPUs and co-processor cards do today. In particular, we address the potential of quantum algorithms to bring major breakthroughs in applied mathematics and its applications. Finally, we give several examples that demonstrate the possible impact of quantum-accelerated scientific computing on society. (shrink)

Computer simulations have conventionally been understood to be either extensions of formal methods such as mathematical models or as special cases of empirical practices such as experiments. Here, I argue that computer simulations are best understood as instruments. Understanding them as such can better elucidate their actual role as well as their potential epistemic standing in relation to science and other scientific methods, practices and devices.

Model checking, a prominent formal method used to predict and explain the behaviour of software and hardware systems, is examined on the basis of reflective work in the philosophy of science concerning the ontology of scientific theories and model-based reasoning. The empirical theories of computational systems that model checking techniques enable one to build are identified, in the light of the semantic conception of scientific theories, with families of models that are interconnected by simulation relations. And the mappings (...) between these scientific theories and computational systems in their scope are analyzed in terms of suitable specializations of the notions of model of experiment and model of data. Furthermore, the extensively mechanized character of model-based reasoning in model checking is highlighted by a comparison with proof procedures adopted by other formal methods in computer science. Finally, potential epistemic benefits flowing from the application of model checking in other areas of scientific inquiry are emphasized in the context of computer simulation studies of biological information processing. (shrink)

Scientific discovery is often regarded as romantic and creative - and hence unanalyzable - whereas the everyday process of verifying discoveries is sober and more suited to analysis. Yet this fascinating exploration of how scientific work proceeds argues that however sudden the moment of discovery may seem, the discovery process can be described and modeled. Using the methods and concepts of contemporary information-processing psychology (or cognitive science) the authors develop a series of artificial-intelligence programs that can simulate the (...) human thought processes used to discover scientific laws. The programs - BACON, DALTON, GLAUBER, and STAHL - are all largely data-driven, that is, when presented with series of chemical or physical measurements they search for uniformities and linking elements, generating and checking hypotheses and creating new concepts as they go along. "Scientific Discovery examines the nature of scientific research and reviews the arguments for and against a normative theory of discovery; describes the evolution of the BACON programs, which discover quantitative empirical laws and invent new concepts; presents programs that discover laws in qualitative and quantitative data; and ties the results together, suggesting how a combined and extended program might find research problems, invent new instruments, and invent appropriate problem representations. Numerous prominent historical examples of discoveries from physics and chemistry are used as tests for the programs and anchor the discussion concretely in the history of science. Pat Langley is an Associate Professor in the Department of Information and Computer Science at the University of California, Irvine.Herbert Simon is a Professor in the Departments of Psychology, Computer Science, and Philosophy at Carnegie-Mellon University. Gary L. Bradshaw is an Assistant Professor in the Department of Psychology and Institute of Cognitive Science at the University of Colorado, Boulder. Jan M. Zytkow is an Associate Professor in the Computer Science Department at Wichita State University. (shrink)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to (...) formalise algorithmic computation and to offer foundations for scientific computing. -/- The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. -/- In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. -/- In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (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)

This dissertation examines aspects of the interplay between computing and scientific practice. The appropriate foundational framework for such an endeavour is rather real computability than the classical computability theory. This is so because physical sciences, engineering, and applied mathematics mostly employ functions defined in continuous domains. But, contrary to the case of computation over natural numbers, there is no universally accepted framework for real computation; rather, there are two incompatible approaches --computable analysis and BSS model--, both claiming to (...) formalise algorithmic computation and to offer foundations for scientific computing. The dissertation consists of three parts. In the first part, we examine what notion of 'algorithmic computation' underlies each approach and how it is respectively formalised. It is argued that the very existence of the two rival frameworks indicates that 'algorithm' is not one unique concept in mathematics, but it is used in more than one way. We test this hypothesis for consistency with mathematical practice as well as with key foundational works that aim to define the term. As a result, new connections between certain subfields of mathematics and computer science are drawn, and a distinction between 'algorithms' and 'effective procedures' is proposed. In the second part, we focus on the second goal of the two rival approaches to real computation; namely, to provide foundations for scientific computing. We examine both frameworks in detail, what idealisations they employ, and how they relate to floating-point arithmetic systems used in real computers. We explore limitations and advantages of both frameworks, and answer questions about which one is preferable for computational modelling and which one for addressing general computability issues. In the third part, analog computing and its relation to analogue (physical) modelling in science are investigated. Based on some paradigmatic cases of the former, a certain view about the nature of computation is defended, and the indispensable role of representation in it is emphasized and accounted for. We also propose a novel account of the distinction between analog and digital computation and, based on it, we compare analog computational modelling to physical modelling. It is concluded that the two practices, despite their apparent similarities, are orthogonal. (shrink)

The question about the scientific nature of computing has been widely debated with no universal consensus reached about its disciplinary status. Positions vary from acknowledging computing as the science of computers to defining it as a synthetic engineering discipline. In this paper, we aim at discussing the nature of computing from a methodological perspective. We consider, in particular, the nature and role of experiments in this field, whether they can be considered close to the traditional experimental (...) scientific method or, instead, they possess peculiar and unique features. We argue that this experimental perspective should be taken into account when discussing the status of computing. We critically survey how the experimental method has been conceived and applied in computing, and some open issues that could be tackled with the aid of the history of science, the philosophy of science, and the philosophy of technology. (shrink)

This study is concerned with processes for discovering new theories in science. It considers a computational approach to scientific discovery, as applied to the discovery of theories in cognitive science. The approach combines two ideas. First, a process-based scientific theory can be represented as a computer program. Second, an evolutionary computational method, genetic programming, allows computer programs to be improved through a process of computational trialand-error. Putting these two ideas together leads to a system that can automatically generate (...) and improve scientific theories. The application of this method to the discovery of theories in cognitive science is examined. Theories are built up from primitive operators. These are contained in a theory language that defines the space of possible theories. An example of a theory generated by this method is described. These results support the idea that scientific discovery can be achieved through a heuristic search process, even for theories involving a sequence of steps. However, this computational approach to scientific discovery does not eliminate the need for human input. Human judgment is needed to make reasonable prior assumptions about the characteristics of operators used in the theory generation process, and to interpret and provide context for the computationally generated theories. (shrink)

Attempts by 20th century philosophers of science to define inductive concepts and methods concerning the support provided to scientific theories by empirical data have been unsuccessful. Although 20th century philosophers of science largely ignored statistical methods for testing theories, when they did address them they argued against rather than for their use. In contrast, this study demonstrates that traditional statistical methods used for validating computer simulation models provide tests of the scientific theories that those models may embody. This (...) study shows that these statistical methods are applicable regardless of whether the scientific theory or model is deterministic, stochastic, or chaos-based in nature. Traditional statistical methods, such as hypothesis testing, test theories by providing measures of their goodness-of-fit with the portion of the world the theories describe. Nothing more is needed to portray the agreement between theory and the world. Furthermore, the statistical measures of goodness-of-fit are not ampliative inductive measures. Therefore, the ultimate value and direction of the 20 th century ampliative inductive program within philosophy of science is thrown into question. This study also suggests that advanced statistical, visualization, and hybrid quantitative qualitative methods hold promise for offering scientists additional methods for testing scientific theories through validating their computer model representations. As a prerequisite to the above discussions, this study proves that scientific theories, when applied to concrete physical systems, can indeed be represented by computer models. (shrink)

The process of constructing mathematical models is examined and a case made that the construction process is an integral part of the justification for the model. The role of heuristics in testing and modifying models is described and some consequences for scientific methodology are drawn out. Three different ways of constructing the same model are detailed to demonstrate the claims made here.

This article aims to develop a new account of scientific explanation for computer simulations. To this end, two questions are answered: what is the explanatory relation for computer simulations? And what kind of epistemic gain should be expected? For several reasons tailored to the benefits and needs of computer simulations, these questions are better answered within the unificationist model of scientific explanation. Unlike previous efforts in the literature, I submit that the explanatory relation is between the simulation model (...) and the results of the simulation. I also argue that our epistemic gain goes beyond the unificationist account, encompassing a practical dimension as well. (shrink)

In this volume, scientists, historians, and philosophers join to examine computer simulations in scientific practice. One central aim of the volume is to provide a multiperspective view on the topic. Therefore, the text includes philosophical studies on computer simulations, as well as case studies from simulation practice, and historical studies of the evolution of simulations as a research method.

In this paper I examine Paul Thagard's computational approach to studying science, which is a contribution to the cognitive science of science. I present several criticisms of Thagard's approach and use them to motivate some suggestions for alternative approaches in cognitive science of science. I first argue that Thagard does not clearly establish the units of analysis of his study. Second, I argue that Thagard mistakenly applies the same model to both individual and group decision making. Finally, I argue that (...) in attempting to account for psychological and social processes as well as providing a philosophical model of successful reasoning Thagard attempts to explain too much with one model, thus straining the plausibility of his model. (shrink)

We propose a reflection on the construction of scientific knowledge and in so doing an image of this knowledge. This will allow us to develop a comparative analysis of some of the main principles underpinning the constitution of the different sciences. We will highlight the role of critical thought in science, or even “negative results,” which pose limits and hence open new trajectories. In particular, we will address a misleading point of view, based on some informal concepts taken from (...) computer science, which dominates the biological imaginary. An “ethics of knowledge” will follow, as a critical and open perspective, capable of taking on the well-intentioned responsibility of proposing universal, though not absolute, principles of knowledge. (shrink)

In many scientific fields, today’s practices of empirical enquiry rely heavily on the production of images that display the investigated phenomena. And while scientific images of phenomena have been important for a long time, what is striking now is that scientists have found ways to visualize such widely different types of phenomena. In the past twenty or thirty years, we have become accustomed to seeing images of galaxies, of cells, of the human brain but also of blood flow (...) or of turbulent fluids. This success in making images relies first on the set of imaging devices that have flourished in the twentieth century, instruments such as radio-telescopes, electronic microscopes, MRI and many more. Without these... (shrink)

I begin with a representative example of a contemporary scientific activity, observations using the Hubble Space Telescope, and ask what approaches within the cognitive sciences seem most fruitful as aids in developing an overall account of this sort of scientific activity. After presenting the Hubble Space Telescope System and a recent result, I consider applying a standard computational paradigm to this system. I find difficulties in identifying an appropriate cognitive agent and in making a suitable place for the (...) instrumentation that constitutes such a large part of the whole system. I next consider applying the notion of distributed cognition as developed by Hutchins (1995), and then return to the question whether The Hubble System, understood as a distributed cognitive system, should be regarded as a computational system. I find a large computational component, but also an important part, the Hubble Telescope itself, that seems better characterized as a dynamic system than as a computational system. Moreover, the group of scientists interpreting the images produced by the system seem best thought of as a human/cultural system along the lines advocated by those developing a cognitive (Lakoff, 1987) or usage-based (Tomasello, 2003) approach to language acquisition and language use. I argue next that, while cognition may be theorized as distributed among both humans and instruments, there is no need to introduce into cognitive science a notion of distributed knowledge beyond simple collective knowledge. Even less is there any need to introduce notions of distributed mind or distributed consciousness. The result is that the agency involved in distributed cognitive systems remains simply human agency as ordinarily conceived. I conclude that distributed cognitive systems like The Hubble System are hybrid systems composed partly of dynamic physical systems, partly of computational systems, and partly of human cultural systems. (shrink)

With increasing publication and data production, scientific knowledge presents not simply an achievement but also a challenge. Scientific publications and data are increasingly treated as resources that need to be digitally ‘managed.’ This gives rise to scientific Knowledge Management : second-order scientific work aiming to systematically collect, take care of and mobilise first-hand disciplinary knowledge and data in order to provide new first-order scientific knowledge. We follow the work of Leonelli, Efstathiou and Hislop in our (...) analysis of the use of KM in semantic systems biology. Through an empirical philosophical account of KM-enabled biological research, we argue that KM helps produce new first-order biological knowledge that did not exist before, and which could not have been produced by traditional means. KM work is enabled by conceiving of ‘knowledge’ as an object for computational science: as explicated in the text of biological articles and computable via appropriate data and metadata. However, these founded knowledge concepts enabling computational KM risk focusing on only computationally tractable data as knowledge, underestimating practice-based knowing and its significance in ensuring the validity of ‘manageable’ knowledge as knowledge. (shrink)

We have two theses about scientific knowledge in the age of computation. Our general claim is that scientific Knowledge Management practices emerge as second-order practices whose aim is to systematically collect, take care of and mobilise first-hand disciplinary knowledge and data. Our specific thesis is that knowledge management practices are transforming biological research in at least three ways. We argue that scientific Knowledge Management a. operates with founded concepts of biological knowledge as explicated and computable, b. enables (...) new outputs and ways of knowing within biology, and c. risks enforcing objectivist epistemologies of knowledge as some one objective thing. (shrink)

To explain why, in scientific problem solving, a diagram can be “worth ten thousand words,” Jill Larkin and Herbert Simon (1987) relied on a computer model: two representations can be “informationally” equivalent but differ “computationally,” just as the same data can be encoded in a computer in multiple ways, more or less suited to different kinds of processing. The roots of this proposal lay in cognitive psychology, more precisely in the “imagery debate” of the 1970s on whether there are (...) image-like mental representations. Simon (1972, 1978) hoped to solve this debate by thoroughly reducing the differences between forms of mental representations (e.g., between images and sentences) to differences in computational efficiency; to carry out this reduction, he borrowed from computer science the concepts of data type and of data structure. I argue that, in the end, his account amounted to nothing more than characterizing representations by the fast operations on them. This analysis then allows me to assess what Simon’s approach actually achieves when transported from psychology to the study of scientific representations, as in Larkin and Simon (1987): it allows comparing, not representations in and of themselves, but rather the computational roles they play in particular problem-solving processes—that is, representations together with a particular way of using them. (shrink)

Various errors can affect scientific code and detecting them is a central concern within computational science. Could formal verification methods, which are now available tools, be widely adopted to guarantee the general reliability of scientific code? After discussing their benefits and drawbacks, we claim that, absent significant changes as regards features like their user-friendliness and versatility, these methods are unlikely to be adopted throughout computational science, beyond certain specific contexts for which they are well-suited. This issue exemplifies the (...) epistemological heterogeneity of computational science: profoundly different practices can be appropriate to meet the reliability challenge that rises for scientific code. (shrink)

In this article, I develop three conceptual innovations within the area of formal metatheory, and present a computer program, called Reconstructor, that implements those developments. The first development consists in a methodology for testing formal reconstructions of scientific theories, which involves checking both whether translations of paradigmatically successful applications into models satisfy the formalisation of the laws, and also whether unsuccessful applications do not. I show how Reconstructor can help carry this out, since it allows the end-user to specify (...) a formal language, input axioms and models formulated in that language, and then ask if the models satisfy the axioms. The second innovation is the introduction of incomplete models (for which the denotation of some terms is missing) into scientific metatheory, in order to represent cases of missing information. I specify the paracomplete semantics built into Reconstructor to deal with sentences where denotation failures occur. The third development consists in a new way of explicating the structuralist notion of a determination method, by equating them with algorithms. This allows determination methods to be loaded into Reconstructor and then executed within a model to find out the value of a previously non-denoting term (i.e. it allows the formal reconstruction to make predictions). This, in turn, can help test the reconstruction in a different way. Finally, I conclude with some suggestions about additional uses the program may have. (shrink)

Computational philosophy (CP) aims at investigating many important concepts and problems of the philosophical and epistemological tradition in a new way by taking advantage of information-theoretic, cognitive, and artificial intelligence methodologies. I maintain that the results of computational philosophy meet the classical requirements of some Peircian pragmatic ambitions. Indeed, more than a 100 years ago, the American philosopher C.S. Peirce, when working on logical and philosophical problems, suggested the concept of pragmatism(pragmaticism, in his own words) as a logical criterion to (...) analyze what words and concepts express through their practical meaning. Many words have been spent on creative processes and reasoning, especially in the case of scientific practices. In fact, many philosophers have usually offered a number of ways of construing hypotheses generation, but they aim at demonstrating that the activity of generating hypotheses is paradoxical, obscure, and thus not analyzable. Those descriptions are often so far from Peircian pragmatic prescription and so abstract to result completely unknowable and obscure. To dismiss this tendency and gain interesting insight about the so-called logic of scientific discovery we need to build constructive procedures, which could play a role in moving the problem-solving process forward by implementing them in some actual models. The computational turn gives us a new way to understand creative processes in a strictly pragmatic sense. In fact, by exploiting artificial intelligence and cognitive science tools, computational philosophy allows us to test concepts and ideas previously conceived only in abstract terms. It is in the perspective of these actual computational models that I find the central role of abduction in the explanation of creative reasoning in science. I maintain that the computational philosophy analysis of model-based and manipulative abduction and of external and epistemic mediators is important not only to delineate the actual practice of abduction, but also to further enhance the development of programs computationally adequate in rediscovering, or discovering for the first time, for example, scientific hypotheses or mathematical theorems. The last part of the paper is devoted to illustrating the problem of the extra-theoretical dimension of reasoning and discovery from the perspective of some mathematical cases derived from calculus and geometry. (shrink)

The breadth-first search adopted by Bayesian researchers to map out the conceptual space and identify what the framework can do is beneficial for science and reflective of its collaborative and incremental nature. Theoretical pluralism among researchers facilitates refinement of models within various levels of analysis, which ultimately enables effective cross-talk between different levels of analysis.

Novel computational representations, such as simulation models of complex systems and video games for scientific discovery, are dramatically changing the way discoveries emerge in science and engineering. The cognitive roles played by such computational representations in discovery are not well understood. We present a theoretical analysis of the cognitive roles such representations play, based on an ethnographic study of the building of computational models in a systems biology laboratory. Specifically, we focus on a case of model-building by an engineer (...) that led to a remarkable discovery in basic bioscience. Accounting for such discoveries requires a distributed cognition analysis, as DC focuses on the roles played by external representations in cognitive processes. However, DC analyses by and large have not examined scientific discovery, and they mostly focus on memory offloading, particularly how the use of existing external representations changes the nature of cognitive tasks. In contrast, we study discovery processes and argue that discoveries emerge from the processes of building the computational representation. The building process integrates manipulations in imagination and in the representation, creating a coupled cognitive system of model and modeler, where the model is incorporated into the modeler's imagination. This account extends DC significantly, and we present some of the theoretical and application implications of this extended account. (shrink)