According to the received view, reduction is a deductive relation between two formal theories. In this paper, I develop an alternative approach, according to which reduction is a representational relation between models, rather than a deductive relation between theories; more specifically, I maintain that this representational relation is the one of emulation. To support this thesis, I focus attention on mathematical dynamical systems and I argue that, as far as these systems are concerned, the emulation relation is sufficient for reduction. (...) I then extend this representational model-based view of reduction to the case of empirically interpreted dynamical systems, as well as to a treatment of partial, approximate, and asymptotic reduction. (shrink)

This paper aims to set forth Carnapian structuralism, i.e., a syntactic view of the structuralist approach which is deeply inspired by Carnap’s dual level conception of scientific theories. At its core is the axiomatisation of a metatheoretical concept AE(T) which characterises those extensions of an intended application that are admissible in the sense of being models of the theory-element T and that satisfy all links, constraints and specialisations. The union of axiom systems of AE(T) (where T is an element of (...) the theory-net N) will allow us to present scientific theories in an axiomatic fashion so that deductive reasoning in science can be formalised. Thereupon defeasible and paraconsistent means of reasoning will be introduced. The logical study of scientific reasoning is the key motivation of Carnapian structuralism. A further motivation is to help overcome the syntactic-semantic split in the philosophy of science. (shrink)

The many-faced relationship between chemistry and physics is one of the most discussed topics in the philosophy of chemistry. In his recent book Reducing Chemistry to Physics. Limits, Models, Consequences, Hinne Hettema conceives this relationship as a reduction link, and devotes his work to defend this position on the basis of a “naturalized” concept of reduction. In the present paper I critically review three kinds of issues stemming from Hettema’s argumentation: philosophical, scientific and methodological.

The distinction between the syntactic and the semantic approach to scientific theories emerged in formal philosophy of science. The semantic approach is commonly considered more advanced and more successful than the syntactic one, but the transition from the one approach to the other was not brought about without any loss. In essence, it is the formal analysis of atomic propositions and the analysis of deductive reasoning that dropped out of consideration in at least some of the elaborated versions of the (...) semantic approach. In structuralist theory of science, as founded by Sneed and Stegmüller, the focus is on global propositions concerning the question of whether or not certain empirical systems satisfy a set-theoretic predicate that encodes the axioms of a scientific theory. Hence, an analysis of deductive reasoning from atomic premisses with the help of a given theory is missing. The objective of the present paper is to develop a deductive system on the basis of the structuralist framework. This system comes with a novel formulation of empirical propositions in structuralism. (shrink)

Whether meaning is compositional has been a major issue in linguistics and formal philosophy of language for the last 2 decades. Semantic holism is widely and plausibly considered as an objection to the principle of semantic compositionality therein. It comes as a surprise that the holistic peculiarities of scientific language have been rarely addressed in formal accounts so far, given that semantic holism has its roots in the philosophy of science. For this reason, a model-theoretic approach to semantic holism in (...) the language of science is presented here. This approach preserves compositionality to a large extent. *Received September 2009; revised February 2010. †To contact the author, please write to: Seminar for Philosophy, Logic, and Theory of Science, Hauspostfach 49, Ludwig-Maximilians-Universität, Munich 80539, Germany; e-mail: [email protected]. (shrink)

Tarski’s conceptual analysis of the notion of logical consequence is one of the pinnacles of the process of defining the metamathematical foundations of mathematics in the tradition of his predecessors Euclid, Frege, Russell and Hilbert, and his contemporaries Carnap, Gödel, Gentzen and Turing. However, he also notes that in defining the concept of consequence “efforts were made to adhere to the common usage of the language of every day life.” This paper addresses the issue of what relationship Tarski’s analysis, and (...) Béziau’s further generalization of it in universal logic, have to reasoning in the everyday lives of ordinary people from the cognitive processes of children through to those of specialists in the empirical and deductive sciences. It surveys a selection of relevant research in a range of disciplines providing theoretical and empirical studies of human reasoning, discusses the value of adopting a universal logic perspective, answers the questions posed in the call for this special issue, and suggests some specific research challenges. (shrink)

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to every, inertial (...) or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (shrink)

In this article, we redefine classical notions of theory reduction in such a way that model-theoretic preferential semantics becomes part of a realist depiction of this aspect of science. We offer a model-theoretic reconstruction of science in which theory succession or reduction is often better - or at a finer level of analysis - interpreted as the result of model succession or reduction. This analysis leads to 'defeasible reduction', defined as follows: The conjunction of the assumptions of a reducing theory (...) T with the definitions translating the vocabulary of a reduced theory T' to the vocabulary of T, defeasibly entails the assumptions of reduced T'. This relation of defeasible reduction offers, in the context of additional knowledge becoming available, articulation of a more flexible kind of reduction in theory development than in the classical case. Also, defeasible reduction is shown to solve the problems of entailment that classical homogeneous reduction encounters. Reduction in the defeasible sense is a practical device for studying the processes of science, since it is about highlighting different aspects of the same theory at different times of application, rather than about naive dreams concerning a metaphysical unity of science. (shrink)

This paper aims to study the foundations of applied mathematics, using a formalized base theory for applied mathematics: ZFCAσ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \mathsf {ZFCA}_{\sigma }$$\end{document} with atoms, where the subscript used refers to a signature specific to the application. Examples are given, illustrating the following five features of applied mathematics: comprehension principles, application conditionals, representation hypotheses, transfer principles and abstract equivalents.

According to a seminal paper by Barsalou , frames are attribute-value-matrices for representing exemplars or concepts. Frames have been used as a tool for reconstructing scientific concepts as well as conceptual change within scientific revolutions . In the frame-based representations of scientific concepts developed so far the semantic content of concepts is determined by a set of attribute-specific values. This way of representing semantic content works best for prototype concepts and defined concepts of a conceptual taxonomy satisfying the no-overlap principle. (...) In addition to the semantic content of prototype concepts and defined concepts, frames can also contain empirical knowledge that is represented as constraints between the values of the frame. Beside prototype concepts and defined concepts, theoretical concepts that are multiply operationalized play an important role in science. However, so far no frame-based representation of theoretical concepts has been proposed. In this paper, it will be shown that theoretical concepts can be represented by frames and that frame-based representations of prototype concepts and defined concepts have another structure than frame-based representations of theoretical concepts. In order to explicate this difference, we will develop a frame-based method for representing all three kinds of concepts by means of mathematical graph-theory. One important consequence will be that the constraints of a frame representing a theoretical concept are entailed by the structure of the frame, as opposed to a frame representing defined or prototype concepts. (shrink)

Scientists of many disciplines use theoretical models to explain and predict the dynamics of the world. They often have to rely on digital computer simulations to draw predictions fromthe model. But to deliver phenomenologically adequate results, simulations deviate from the assumptions of the theoretical model. Therefore the role of simulations in scientific explanation demands itself an explanation. This paper analyzes the relation between real-world system, theoretical model, and simulation. It is argued that simulations do not explain processes in the real (...) world directly. The way in which simulations help explaining real-world processes is conceived as indirect, mediated by the theoretical model. Simulacra are characterized further, and turn out to be a priori measurable. This gives a clue to a better understanding of the epistemic role of computer simulations in scientific research. (shrink)

The continuity thesis of the Poznań school threshold model of the growth of scientific knowledge is considered in the light of the example of Van der Waals' and Boyle-Mariotte's laws. It is argued - using both traditional logical means and the structuralist reconstruction of the example - that the continuity thesis does not hold. A distinction between 'a historical and a systematic point of view' is introduced and it is argued that the continuity thesis of the threshold model presupposes the (...) systematic point of view. However, looking at matters from the systematic point of view need not yield the original theory, looked at from the historical point of view. Applied to the case of Van der Waals/Boyle-Mariotte laws, it turns out that the latter law is not a true idealizing special case of the former, contrary to the continuity thesis. The structuralist analysis of the example indicates that Boyle-Mariotte's law is a false factual law from the historical point of view. However, viewed from the systematic point of view, Boyle-Mariotte's law turns out to be a law which is expandable, adding the relevant new concepts, to an idealized version of Van der Waals' law. This idealizing version of Van der Waal's law in turn is a structuralist specialization of the (general) Van der Waals' law. (shrink)

The project of integrated HPS has occupied philosophers of science in one form or another since at least the 1960s. Yet, despite this substantial interest in bringing together philosophical and historical reflections on the nature of science, history of science and formal philosophy of science remain as divided as ever. In this paper, I will argue that the continuing separation between historical and formal philosophy of science is ill-founded. I will argue for this in both abstract and concrete terms. At (...) the abstract level, I reconstruct two possible arguments for the incompatibility of historical and formal philosophy of science and argue that they are both wanting. At the concrete level, I discuss how historical and formal philosophy of science have been brought together in practice, namely: in the form of a largely forgotten research tradition that I will refer to here as the study of formalized macro-units. After a brief exposition, I argue that this research tradition has been unduly overlooked by historically minded philosophers of science. Bringing together these observations, I argue that the divide between historical and formal philosophy of science is not grounded in any substantive arguments, but can be primarily attributed to disciplinary happenstance. (shrink)

The goal of this paper is to present and defend an empiricist, neo-Hempelian account of scientific explanation as ampliative, specialized embedding. The proposal aims to preserve what I take to be the core of Hempel’s empiricist account, by weakening it in some respects and strengthening it in others, introducing two new conditions that solve most of Hempel’s problems without abandoning his empiricist strictures. According to this proposal, to explain a phenomenon is to make it expectable by introducing new conceptual/ontological machinery (...) and using special, and non-ad hoc, non-accidental regularities. The new conditions are elaborated making essential use of two central structuralist ideas, namely T-theoreticity and specialization. I first introduce and qualify the project, then present the new account in detail and assess it vis-à-vis its rivals, and finally discuss some possible objections, concluding that the account fares better than its monistic rivals and well enough to qualify as a promising neo-Hempelian account. Even for those unpersuaded by its monistic goals, it has the merit of calling attention to two new necessary conditions not explicitly emphasized thus far and showing how they serve to answer many of the criticisms addressed against Hempel’s account. (shrink)

ABSTRACT:In response to criticism of empirical or “positive” approaches to corporate social responsibility (CSR), we defend the importance of these approaches for any CSR theory that seeks to have practical impact. Although we acknowledge limitations to positive approaches, we unpack the neglected but crucial relationships between positive knowledge on the one hand and normative knowledge on the other in the implementation of CSR principles. Using the structure of a practical syllogism, we construct a model that displays the key role of (...) empirical knowledge in fulfilling a firm’s responsibility to society, paying special attention to the implications of the “ought implies can” dictum. We also defend the importance of one particular class of empirical claims; namely, claims from the field of economics. Even positive economic theory, which is often criticized for endorsing profits rather than values, can cooperate in intriguing ways with non-economic concepts in the implementation of CSR goals. (shrink)

This paper offers a novel way of reconstructing conceptual change in empirical theories. Changes occur in terms of the structure of the dimensions—that is to say, the conceptual spaces—underlying the conceptual framework within which a given theory is formulated. Five types of changes are identified: (1) addition or deletion of special laws, (2) change in scale or metric, (3) change in the importance of dimensions, (4) change in the separability of dimensions, and (5) addition or deletion of dimensions. Given this (...) classification, the conceptual development of empirical theories becomes more gradual and rationalizable. Only the most extreme type—replacement of dimensions—comes close to a revolution. The five types are exemplified and applied in a case study on the development within physics from the original Newtonian mechanics to special relativity theory. (shrink)

The incommensurability thesis, as introduced by T.S. Kuhn and P.K. Feyerabend, states that incommensurable theories are conceptually incompatible theories which share a common domain of application. Such claim has often been regarded as incoherent, since it has been understood that the determination of a common domain of application at least requires a certain degree of conceptual compatibility between the theories. The purpose of this work is to contribute to the defense of the notion of local or gradual incommensurability, as proposed (...) by late Kuhn. The application of this notion would allow to render the incommensurability thesis coherent. To support this view, a typical example of incommensurability will be formally analyzed by applying the structuralist metatheory developed, among others by W. Balzer, C.U. Moulines and J.D. Sneed. The structural reconstruction of the relation between the phlogiston theory and the oxygen theory offered here will reveal that they are locally incommensurable, and will even make possible to determine the ontological reduction relation that they also exemplify. (shrink)

In this paper the structuralist approach of theory reconstruction is applied to International Trade Theory. In the basic element the universal laws of the theory are stated and the general concepts are defined in terms of three sets and seven functions. Ricardo’s Theory of Comparative Advantage and the Factor Proportions Theory by Heckscher and Ohlin are reconstructed as specialisations of the basic element. Two intratheoretical constraints are formulated in order to ensure the consistency of the theory. A number of empirical (...) studies are shown to be paradigmatic, successful or questionable applications of International Trade Theory. The reconstruction allows the assessment of the theory from a metatheoretical angle and illuminates the logical interdependencies of its components. (shrink)

Primarily addressed to readers unfamiliar with the structuralist approach in philosophy of science, we introduce the basic concepts that the contributions to this special issue presuppose. By means of examples, we briefly review set-theoretic structures and predicates, the potential and actual models of an empirical theory, intended applications, as well as links and specializations that are applied, among others, in reconstructing the empirical claim associated with a theory element.

The paper, as Part I of a two-part series, argues for a hybrid formulation of the semantic view of scientific theories. For stage-setting, it first reviews the elements of the model theory in mathematical logic (on whose foundation the semantic view rests), the syntactic and the semantic view, and the different notions of models used in the practice of science. The paper then argues for an integration of the notions into the semantic view, and thereby offers a hybrid semantic view, (...) which at once secures the view's logical foundations and enhances its applicability. The dilemma of either losing touch with the practice of science or yielding up the benefits of the model theory is thus avoided. (shrink)

The epistemic status of Natural Selection has seemed intriguing to biologists and philosophers since the very beginning of the theory to our present times. One prominent contemporary example is Elliott Sober, who claims that NS, and some other theories in biology, and maybe in economics, are peculiar in including explanatory models/conditionals that are a priori in a sense in which explanatory models/conditionals in Classical Mechanics and most other standard theories are not. Sober’s argument focuses on some “would promote” sentences that (...) according to him, play a central role in NS explanations and are both causal and a priori. Lange and Rosenberg criticize Sober arguing that, though there may be some unspecific a priori causal claims, there are not a priori causal claims that specify particular causal factors. Although we basically agree with Lange and Rosenberg’s criticism, we think it remains silent about a second important element in Sober’s dialectics, namely his claim that, contrary to what happens in mechanics, in NS explanatory conditionals are a priori, and that this is so in quite specific explanatory models. In this paper we criticize this second element of Sober’s argument by analyzing what we take to be the four possible interpretations of Sober’s claim, and argue that, terminological preferences aside, the possible senses in which explanatory models in NS can qualify, or include elements that can qualify, as a priori, also apply to CM and other standard, highly unified theories. We conclude that this second claim is unsound, or at least that more needs to be said in order to sustain that NS explanatory models are a priori in a sense in which CM models are not. (shrink)

The purpose of this paper is to defend, contra Fodor and Piattelli-Palmarini (F&PP), that the theory of natural selection (NS) is a perfectly bona fide empirical unified explanatory theory. F&PP claim there is nothing non-truistic, counterfactual-supporting, of an “adaptive” character and common to different explanations of trait evolution. In his debate with Fodor, and in other works, Sober defends NS but claims that, compared with classical mechanics (CM) and other standard theories, NS is peculiar in that its explanatory models are (...) a priori (a trait shared with few other theories). We argue that NS provides perfectly bona fide adaptive explanations of phenotype evolution, unified by a common natural-selection guiding principle. First, we introduce the debate and reply to F&PP’s main argument against NS. Then, by reviewing different examples and analyzing Fisher’s model in detail, we show that NS explanations of phenotypic evolution share a General Natural Selection Principle. Third, by elaborating an analogy with CM, we argue against F&PP’s claim that such a principle would be a mere truism and thus explanatorily useless, and against Sober’s thesis that NS models/explanations have a priori components that are not present in CM and other common empirical theories. Irrespective of differences in other respects, the NS guiding principle has the same epistemic status as other guiding principles in other highly unified theories such as CM. We argue that only by pointing to the guiding principle-driven nature that it shares with CM and other highly unified theories, something no-one has done yet in this debate, one can definitively show that NS is not defective in F&PP’s sense: in the respects relevant to the debate, Natural Selection is as defective and as epistemically peculiar as Classical Mechanics and other never questioned theories. (shrink)

The concept of Galilean Idealization is based on a pragmatically grounded relation between universes of so-called real and idealized entities. The concept was developed in the course of a critical discussion of different explications of the concept of idealization (e.g. by W. F. Barr, C. G. Hempel and L. Nowak), these being attempts to specify sufficient syntactic and semantic criterions for idealization. But this line of argument shall not be followed here. Instead, first the concept of Pragmatic Idealization, and as (...) its special case the Galilean one, is presented (1.) and certain aspects of the application of an idealized theory are discussed (2.). Then, working within the Strucuralist View of theories, definitions of the idealized variants of the diachronic theory-element and theory-net are presented (3.). (shrink)

Any advanced theory of physics contains modules defined as essential components that are themselves theories with different domains of application. Different kinds of modules can be distinguished according to the way in which they fit in the symbolic and interpretive apparatus of a theory. The number and kind of the modules of a given theory vary as the theory evolves in time. The relative stability of modules and the variability of their insertion in other theories play a vital role in (...) the application, comparison, construction, and communication of theories. Modularity conveys some global unity to physics through the sharing of modules by diverse theories. This alternative to rigid hierarchies and holistic totalities permits a dynamical, plastic, and symbiotic approach to physical theory. (shrink)

In this paper, a modest version of the Semantic View is motivated as both tenable and potentially fruitful for philosophy of science. An analysis is proposed in which the Semantic View is characterized by three main claims. For each of these claims, a distinction is made between stronger and more modest interpretations. It is argued that the criticisms recently leveled against the Semantic View hold only under the stronger interpretations of these claims. However, if one only commits to the modest (...) interpretation for all the claims, then the view obtained, the Modest Semantic View, is tenable and fruitful for the philosophy of science. (shrink)

This paper argues for the theoretical and practical validity of similarity as a useful epistemological tool in scientific knowledge generation, specifically in chemistry. Classical analyses of similarity in philosophy of science do not account for the concept’s practical significance in scientific activities. We recur to examples from chemistry to counter the claim of authors like Quine or Goodman to the effect that similarity must be excluded from scientific practices . In conclusion we argue that more recent conceptualizations of the notion (...) of similarity, particularly Giere’s one, are appropriate for a philosophical analysis that considers scientific practices on equal terms with scientific theory. (shrink)

The present paper aims at a synthesis of belief revision theory with the Sneed formalism known as the structuralist theory of science. This synthesis is brought about by a dynamisation of classical structuralism, with an abductive inference rule and base generated revisions in the style of Rott (2001). The formalism of prioritised default logic (PDL) serves as the medium of the synthesis. Why seek to integrate the Sneed formalism into belief revision theory? With the hybrid system of the present investigation, (...) a substantial simplification of the ranking information that is necessary to define revisions and contractions uniquely is achieved. This system is, furthermore, expressive enough to capture complex and non-trivial scientific examples. It is thus closely related to a novel research area within belief revision theory which addresses the dynamics of scientific knowledge. (shrink)

In the last two sections of Structure, Thomas Kuhn first develops his famous threefold conception of the incommensurability of scientific paradigms and, subsequently, a conception of scientific progress as growth of empirical strength. The latter conception seems to be at odds with the former in that semantic incommensurability appears to imply the existence of situations where scientific progress in Kuhns sense can no longer exist. In contrast to this seeming inconsistency of Kuhns conception, we will try to show in this (...) study that the semantic incommensurability of scientific terms appears to be fully compatible with scientific progress. Our argumentation is based on an improved version of the formalization of Kuhns conception as developed in the 1970s by Joseph Sneed and Wolfgang Stegmüller: In order to be comparable, incommensurable theories need the specification of relations that refer to the concrete ontologies of these theories and involve certain truth claims. The original structuralist account of reduction fails to provide such relations, because (1) it is too structural and (2) it is too wide. Moreover, the original structuralist account also fails to cover important cases of incommensurable theories in being too restrictive for them. In this paper, we develop an improved notion of “reduction” that allows us to avoid these shortcomings by means of a more flexible device for the formalization of (partially reductive) relations between theories. For that purpose, we use a framework of rigid logic, i.e., logic that is based on a fixed collection of objects. (shrink)

Our aim in this article is to show how the theory of conceptual spaces can be useful in describing diachronic changes to conceptual frameworks, and thus useful in understanding conceptual change in the empirical sciences. We also compare the conceptual space approach to Moulines’s typology of intertheoretical relations in the structuralist tradition. Unlike structuralist reconstructions, those based on conceptual spaces yield a natural way of modeling the changes of a conceptual framework, including noncumulative changes, by tracing the changes to the (...) dimensions that reconstitute a conceptual framework. As a consequence, the incommensurability of empirical theories need not be viewed as a matter of conceptual representation. (shrink)

In this paper, a new account of empirical claims in structuralism is developed. Its novelty derives from the use that is made of the linguistic approach to scientific theories despite the presumed incompatibility of structuralism with that approach. It is shown how the linguistic approach can be applied to the framework of structuralism if the semantic foundations of that approach are refined to do justice to the doctrine of indirect interpretation of theoretical terms. This doctrine goes back to Carnap but (...) has been advanced until the present day without a proper semantic explanation. (shrink)

This paper is the second of a two-part series on models and theories, the first of which appeared in International Studies in the Philosophy of Science, Vol. 11, No. 2, 1997. It further explores some of themes of the first paper and examines applications, including: the relations between “similarity” and “isomorphism”, and between “model” and “interpretation”, and the notion of structural explanation.

My main aim in this paper is to show that influential antireductionist arguments such as Fodor's, Kitcher's, and Dupré's state stronger conclusions than they actually succeed in establishing. By putting to the fore the role of metaphysical presuppositions in these arguments, I argue that they are convincing only as 'temporally qualified argument', and not as 'generally valid ones'. I also challenge the validity of the strategy consisting in drawing metaphysical lessons from the failure of reductionist programmes. What most of these (...) antireductionist standpoints have in common is a pretension to methodological imports. I conclude by explaining why, in order to remain relevant for scientific practice, antireductionist arguments should stay clear of metaphysics, for the latter, I argue, does not mix well with a taste for methodological prescriptions. (shrink)

Several case studies and theoretical reports indicate that the structuralist concept of a constraint has a central role in the reconstruction of physical theories. It is surprising that there is, in the literature, only little theoretical discussion on the relevance of constraints for the reconstruction of social scientific theories. Almost all structuralist reconstructions of social theorizing are vacuously constrained. Consequently, constraints are methodologically irrelevant.In this paper I try to show that there really exist constraint-type assumptions in mathematical modelling in the (...) social sciences. Methodologically constraints have exactly the same role in the context of social mathematical modelling as they have in physical theories. In typical cases of mathematical modelling in the social sciences, the related constraints work as empirical hypotheses and should be tested by statistical means. (shrink)

This paper develops the first parts of a logical framework for the empirical sciences, by means of a redefinition of theory structuralism as originally developed by Joseph Sneed, Wolfgang Stegmüller, and others, in the context of a ‘rigid’ logic as based on a fixed (therefore rigid) ontology. The paper defends a formal conception of the empirical sciences that has an irreducible ontological basis and is unable, in general, to provide purely structural characterizations of the domain of a theory. The extreme (...) rationalist utopia of a characterization of the real world ‘up to isomorphism’, therefore, is rejected. (shrink)

Scientific discourse leaves implicit a vast amount of knowledge, assumes that this background knowledge is taken into account – even taken for granted – and treated as undisputed. In particular, the terminology in the empirical sciences is treated as antecedently understood. The background knowledge surrounding a theory is usually assumed to be true or approximately true. This is in sharp contrast with logic, which explicitly ignores underlying presuppositions and assumes uninterpreted languages. We discuss the problems that background knowledge may cause (...) for the formalization of scientific theories. In particular, we will show how some of these problems can be addressed in the context of the computational representation of scientific theories. (shrink)