In this paper, I argue that Imre Lakatos’s account on the relation between the history and the philosophy of science, if properly understood and also if properly modified, can be valuable for the philosophical comprehension of the relation between the history and the philosophy of science. The paper is divided into three main parts. In the first part, I provide a charitable exegesis of the Lakatosian conception of the history of science in order to show that Lakatos’s history cannot be (...) a caricature. In the second part, I describe what I believe are the real problems of Lakatos’s account on a metaphysical and on a methodological level. In order to address these problems, I take advantage of the recent critique of the so-called “confrontation model”. Finally, in the third part, I suggest that a proper modification of Lakatos’s perspective can resolve the aforementioned problems without distorting Lakatos’s central aspiration, which is that the philosophical theories of scientific rationality can be assessed with the help of the history of science without losing their normative content. (shrink)

An agent exercises instrumental rationality to the degree that she adopts appropriate means to achieving her ends. Adopting appropriate means to achieving one’s ends can, in turn, involve overcoming one’s strongest desires, that is, it can involve exercising synchronic self-control. However, contra prominent approaches, I deny that synchronic self-control is possible. Specifically, I draw on computational models and empirical evidence from cognitive neuroscience to describe a naturalistic, multi-system model of the mind. On this model, synchronic self-control is impossible. Must we, (...) then, give up on a meaningful conception of instrumental rationality? No. A multi-system view still permits something like synchronic self-control: an agent can control her very strong desires. Adopting a multi-system model of the mind thus places limitations on our conceptions of instrumental rationality, without requiring that we abandon the notion altogether. (shrink)

According to the "confrontation model," integrated history and philosophy of science operates like an empirical science. It tests philosophical accounts of science against historical case studies much like other sciences test theory against data. However, the confrontation model's critics object that historical facts can neither support generalizations nor genuinely test philosophical theories. Here I argue that most of the model's defects trace to its usual framing in terms of two problematic accounts of empirical inference: the hypothetico-deductive method and enumerative induction. (...) This framing can be taken to suggest an unprofitable one-off confrontation between particular historical facts and general philosophical theories. I outline more recent accounts of empirical inquiry, which describe an iterative back-and-forth movement between concrete empirical exemplars to their abstract descriptions. Reframed along similar lines, the confrontation model continues to offer both conceptual insight and practical guidance for a naturalized philosophy of science. (shrink)

Philosophers of science discuss whether theory selection depends on aesthetic judgments or criteria, and whether these putatively aesthetic features are genuinely extra-epistemic. As examples, judgments involving criteria such as simplicity and symmetry are often cited. However, other theory selection criteria, such as fecundity, coherence, internal consistency, and fertility, more closely match those criteria used in art contexts and by scholars working in aesthetics. Paying closer attention to the way these criteria are used in art contexts allows us to understand some (...) evaluative and developmental practices in scientific theory selection as genuinely aesthetic, enlarging the scope of the goals of science. (shrink)

We show how faceted search using a combination of traditional classification systems and mixed-membership topic models can go beyond keyword search to inform resource discovery, hypothesis formulation, and argument extraction for interdisciplinary research. Our test domain is the history and philosophy of scientific work on animal mind and cognition. The methods can be generalized to other research areas and ultimately support a system for semi-automatic identification of argument structures. We provide a case study for the application of the methods to (...) the problem of identifying and extracting arguments about anthropomorphism during a critical period in the development of comparative psychology. We show how a combination of classification systems and mixed-membership models trained over large digital libraries can inform resource discovery in this domain. Through a novel approach of “drill-down” topic modeling—simultaneously reducing both the size of the corpus and the unit of analysis—we are able to reduce a large collection of fulltext volumes to a much smaller set of pages within six focal volumes containing arguments of interest to historians and philosophers of comparative psychology. The volumes identified in this way did not appear among the first ten results of the keyword search in the HathiTrust digital library and the pages bear the kind of “close reading” needed to generate original interpretations that is the heart of scholarly work in the humanities. Zooming back out, we provide a way to place the books onto a map of science originally constructed from very different data and for different purposes. The multilevel approach advances understanding of the intellectual and societal contexts in which writings are interpreted. (shrink)

Today, Larry Laudan is known predominantly for his work on the pessimistic metainduction and for his discussion of science and values. This essay examines a less familiar part of Laudan’s work, his typology of historical methodologies from the late 1970s. My aim is to elucidate Laudan’s typology and to examine one of the types in more depth, namely, the “pragmatic, symbiotic” model of historical methodology. Laudan expounded the model in the essays that eventually became his 1981 book Science and Hypothesis. (...) Laudan himself characterized this approach to methodology as “history of philosophy of science” and described a number of historiographical guidelines for this history. Several of Laudan’s questions about past scientific methodologies are still worth pursuing, although—and in part because—the concept of scientific methodology changed dramatically as philosophers turned to experimentation in the late twentieth century. Moreover, the study of Laudan’s work in the historical context in which it was devised can shed light on the historical turn in philosophy of science. (shrink)

William Bateson vigorously objected to the assumptions within the chromosome theory of heredity proposed by T. H. Morgan because he perceived inadequate experimental data that could substantiate the theory. Those objections were largely resolved by 1921, and Bateson reluctantly accepted the basic assumption that chromosomes carried the genetic factors from one generation to the next. Bateson's own research at that time on developmental genetics seemed out of touch with the general tone of the genetics field, and the chromosome theory did (...) not provide illuminating mechanisms that elucidated phenomena such as plant variegations or chimeras. Bateson imagined a general theory of heredity and development based on vortices and waves, concepts he borrowed from contemporary physics. For decades he sought to devise an intellectually and aesthetically satisfying theory to eventually explain evolution in genetic terms, but his aspirations remained unfulfilled when he died in 1926. (shrink)

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the (...) field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. -/- The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. -/- The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. Each chapter engages in an assessment of the strengths and weakness of the research addressed, and suggests potentially fruitful avenues of future research. A key element of the handbook’s broader analytical framework is its identification and examination of unnoticed philosophical assumptions in science and mathematics research. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. (shrink)

This essay offers some reflections on the recent history of the disputes about the relation between history and philosophy of science (HPS) and the merits and prospects of HPS as an intellectual endeavor. As everyone knows, the issue was hotly debated in the 1960s and 1970s. That was the hey-day of the slogan "history without philosophy of science is blind, philosophy without history of science is empty" as well as of the many variations on the theme of HPS as a (...) "marriage of convenience," "intimate relation," or "marriage for the sake of reason." There was a flurry of interest in the early 1990s, as evidenced by sections in the 1992 and 1994 issues of PSA, entitled: "Do the History of Science and the Philosophy of .. (shrink)

As made manifest by Clower's comments on their “science fiction” nature, general equilibrium theories present such peculiar and puzzling features that the methodologist must perforce seek some specific methodological accommodation for this part of economic theory. The role played by such theories in contemporary economics is so fundamental that the impossibility of appraising them by means of any version of falsificationism, and their patent lack of empirical content if approached with the conceptual devices of the methodology of scientific research programs, (...) have prompted several scholars interested in the methodology of economics to search for a reasonable way out. (shrink)

A close scrutiny of the psychological literature reveals that many psychologists favor a 'segregative' approach to theory development. One theory is pitted against another, and the one that accounts for the data most successfully is deemed the theory of choice. However, an examination of the theoretical debates in which the segregative approach has been pursued reveals a variety of weaknesses to the approach, namely, masking an underlying theoretical indistinguishability of theoretical predictions, causing psychologists to focus unknowingly on different aspects of (...) the same phenomemon, and locking the theorist into a particular way of looking at a phenomemon. Although recent work in the philosophy of science has sought to develop a more satisfactory approach to theory development, this work also suffers from a variety of shortcomings. Work on intentionality and constructionism by philosophers of mind suggests an alternative to the segregative approach to theory development. We call this alternative the 'integrative' approach. In this approach one integrates the best aspects of a set of given theories with one's own ideas regarding the domain under investigation. Instead of emphasising those features that discriminate among theories, this approach seeks to identify those facets of competing theories that can provide a unified explanation of a given problem area. (shrink)

In a 1993 paper, I argued that empirical treatments of the epistemologyused by scientists in experimental work are too abstract in practice tocounter relativist efforts to explain the outcome of scientificcontroversies by reference to sociological forces. This was because, atthe rarefied level at which the methodology of scientists is treated byphilosophers, multiple mutually inconsistent instantiations of theprinciples described by philosophers are employed by contestingscientists. These multiple construals change within a scientificcommunity over short time frames, and these different versions ofscientific methodology (...) can determine the outcome of a controversy. Iillustrated with a comparatively detailed analysis of the methodologyused by biologists debating the existence of an entity called thebacterial mesosome between the mid-1950s and the mid-1970s. This 1993piece has drawn several critiques in the philosophical literature. Inthis present piece I respond to these critiques and argue that they failto address the core argument of the original paper, and I reflectfurther on the methodologies of philosophers of science pursuingempirical or `naturalistic' epistemology. (shrink)

Of the Merits of History for Philosophy of Science. This essay is inspired by some of the contributions to the two special issues “History of Science and Philosophy of Science” of the journal Berichte zur Wissenschaftsgeschichte. I consider possible roles of historical study for philosophy of science. The first part of the essay discusses contributions to the Anglo‐American debate about history and philosophy of science in the 1960s and 1970s. I present two approaches. According to Larry Laudan and others, philosophy (...) of science should be regarded as an empirical theory of science, which has to be tested against historical episodes. I show why this conception of philosophy of science is problematic. According to Dudley Shapere and others, by contrast, philosophical analysis of science requires hermeneutic understanding and should include the study of the development of scientific knowledge. I agree that the method of philosophy of science is best described as hermeneutic. To defend a genuine historical‐hermeneutic philosophy of science, however, one would have to demonstrate the privilege of historical analysis over other forms of science studies, such as sociology of science or studies of science communication. I do not think that such a demonstration can be made. (shrink)

Although there is universal consensus both in the science education literature and in the science standards documents to the effect that students should learn not only the content of science but also its nature, there is little agreement about what that nature is. This led many science educators to adopt what is sometimes called “the consensus view” about the nature of science (NOS), whose goal is to teach students only those characteristics of science on which there is wide consensus. This (...) is an attractive view, but it has some shortcomings and weaknesses. In this article we present and defend an alternative approach based on the notion of family resemblance. We argue that the family resemblance approach is superior to the consensus view in several ways, which we discuss in some detail. (shrink)

In this paper I explore possibilities of bringing post-positivist philosophies of empirical science to bear on the dynamics of mathematical development. This is done by way of a convergent accommodation of a mathematical version of Lakatos's methodology of research programmes, and a version of Kuhn's account of scientific change that is made applicable to mathematics by cleansing it of all references to the psychology of perception. The resulting view is argued in the light of two case histories of radical conceptual (...) innovations. (shrink)

Publics trust experts for personal and pro-social reasons. Scientists are among the experts publics trust most, and so, epistemic trust is routinely afforded to them. The call for epistemic trust to be more socially situated in order to account for the impact of science on society and public welfare is at the forefront of enhanced epistemic trust. I argue that the value-free ideal for science challenges establishing enhanced epistemic trust by preventing the inclusion of non-epistemic values throughout the evaluation of (...) evidence and communication of these values. By selectively silencing non-epistemic values, the ideal cannot take into account publics’ social and moral responses to inductive risk, which are instrumental for defining and determining public welfare. Furthermore, by emphasising epistemic values almost exclusively in science education and communication, the value-free ideal is presented to publics in such a way that it becomes a social indicator of trust. I show this through examination of the importance of values in decisions to trust, and conclude that values (and restrictions on them) can be used by lay publics to help decide which experts to trust. (shrink)

A longstanding philosophical premise perceives simplicity as a desirable attribute of scientific theories. One of several raised justifications for this notion is that simple theories are more likely to indicate the true makeup of natural systems. Qualitatively parsimonious hypotheses and theories keep to a minimum the number of different postulated entities within a system. Formulation of such ontologically simple working hypotheses proved to be useful in the experimental probing of narrowly defined bio systems. It is less certain, however, whether qualitatively (...) parsimonious theories are effective indicators of the true nature of complex biological systems. This paper assesses the success of ontologically simple theories in envisaging the makeup of three complex systems in bacteriology, immunology, and molecular biology. Evidence shows that parsimonious theories completely misconstrued the actual ontologically complex constitutions of the three examined systems. Since evolution and selective pressures typically produce ontologically intricate rather than simple bio systems, qualitatively parsimonious theories are mostly inapt indicators of the true nature of complex biological systems. (shrink)

History of science and philosophy of science have experienced a somewhat turbulent relationship over the last century. At times it has been said that philosophy needs history, or that history needs philosophy. Very occasionally, something entirely new is said to need them both. Often, however, their relationship is seen as little more than a marriage of convenience. This article explores that marriage by analyzing the citations of over 7,000 historians, philosophers, and sociologists of science. The data reveal that a small (...) but tightly-knit bridge does exist between the disciplines, and raises suggestions about how to understand that bridge in a more nuanced fashion. (shrink)

The cosmic singularity provides negligible evidence for creation in the finite past, and hence theism. A physical theory might have no metric or multiple metrics, so a ‘beginning’ must involve a first moment, not just finite age. Whether one dismisses singularities or takes them seriously, physics licenses no first moment. The analogy between the Big Bang and stellar gravitational collapse indicates that a Creator is required in the first case only if a Destroyer is needed in the second. The need (...) for and progress in quantum gravity and the underdetermination of theories by data make it difficult to take singularities seriously. The singularity exemplifies the sort of gap that is likely to be closed by scientific progress, obviating special divine action. The apparent irrelevance of cardinality to practices of counting infinite sets in classical field theory and Fourier analysis is noted. Introduction The Doctrine of Creation and Its Warrant Cardinality and Sizes of Infinity Modern Cosmology and Creation Tolerance or Intolerance toward Singularities? Leibniz against Incompetent Watchmaker? Induction from Earlier Theories' Breakdown? Stellar Collapse Implies Theistic Destroyer Stacking the Deck for GTR Quantum Gravity Tends to Resolve Singularities Vicious God-of-the-Gaps Character Fluctuating or Inaccessible Warrant Big Bang Cosmology Not Especially Congenial to Faith CiteULike Connotea Del.icio.us What's this? (shrink)

That Piagetian epistemology has the dynamics of knowledge growth as its core consideration predetermines a need to consider it as potentially applicable to teaching. This paper addresses that need by first outlining the Piagetian theory of equilibration and then applying it to the construction of methods of teaching science.

Since the publication of Science and Values in which Laudan unveiled his “reticulated model of scientific change” (Laudan (1984)), he has published a series of articles emphasizing the naturalistic axiology inherent in this model. (Laudan (1986), (1987a), (1987b), (1989), and (forthcoming)). His epistemic naturalism makes the business of fixing rational beliefs about facts, theories, methodologies, and aims all together “cut from the same piece of empirical cloth.” Laudan’s position has numerous attractive qualities: It allows one to accept a great deal (...) of the wisdom in historicism without caving in to relativism. It allows one to accept the seemingly inevitable annexation of the theory of knowledge by the sciences and yet still maintain a normative epistemology. Finally, it awakens philosophers of science’s dogmatic slumbers regarding the axiology of scientific inquiry, and stimulates historical research into the relation between practiced means and professed ends in the sciences. (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)

More powerful methods for studying and integrating the historical track record of scientific episodes and scientific judgment, or what Faust and Meehl describe as a program of meta‐science and meta‐scientific studies, can supplement and extend more commonly used case study methods. We describe the basic premises of meta‐science, overview methodological considerations, and provide examples of meta‐scientific studies. Meta‐science can help to clarify or resolve long‐standing questions in the history and philosophy of science and provide practical help to the working scientist.

In this paper, I present the problem of scientific change as an explanatory problem, that is, as a philosophical problem concerning what logical forms of explanation we should employ in order to un...

Philosophers use historical case studies to support wide-ranging claims about science. This practice is often criticized as problematic. In this paper we suggest that the function of case studies can be understood and justified by analogy to a well-established practice in biology: the investigation of model organisms. We argue that inferences based on case studies are no more problematic than inferences from model organisms to larger classes of organisms in biology. We demonstrate our view in detail by reference to a (...) case study with a long history: Semmelweis’s discovery of the cause of childbed fever. (shrink)

Evo-Devo exhibits a plurality of scientific “cultures” of practice and theory. When are the cultures acting—individually or collectively—in ways that actually move research forward, empirically, theoretically, and ethically? When do they become imperialistic, in the sense of excluding and subordinating other cultures? This chapter identifies six cultures – three /styles/ (mathematical modeling, mechanism, and history) and three /paradigms/ (adaptationism, structuralism, and cladism). The key assumptions standing behind, under, or within each of these cultures are explored. Characterizing the internal structure of (...) the cultures is necessary for understanding how they collaborate or compete, and how they are fragmented or integrated, in the rich interdisciplinary /trading zone/ (Galison 1997) of Evo-Devo. Evo-Devo is an important example of how science can progress through a radical plurality of perspectives and cultures. (shrink)

Nearly thirty years after the first stirrings of the Kuhnian revolution, history and philosophy of science continues to galvanize methodological discussions in all corners of the academy except its own. Evidence for this domestic stagnation appears in Warren Schmaus's thoughtful review of Social Epistemology in which Schmaus takes for granted that history of science is the ultimate court of appeal for disputes between philosophers and sociologists. As against this, this essay argues that such disputes may be better treated by experimental (...) psychology. Humanistic methods typically (though not always) blind the historian to cognitive biases and limitations that make it difficult for philosophers and sociologists to mobilize historical research for settling their differences. It is also observed that the failure of philosophers to incorporate the methods and findings of experiemental psychology is symptomatic of an artificially restrictive understanding of the normative dimension of their enterprise. (shrink)

Steve Fuller has replied to my critique of his endorsement of a post-truth epistemology. I trace the divergence in our approach to social epistemology by examining our distinct responses to the principle of symmetry in the sociology of scientific knowledge. Fuller has extended the concept of symmetry and challenged the field to embrace a post-truth condition that flattens the difference between experts and the public. By contrast, I have criticized the concept of symmetry for policing the field to rule ideology (...) critique out of court. I argue that a focus on post-truth populism obscures the role of counter-elites and ideologies that restrict political choice. A better way to promote democracy would be to support minority positions within science that promise to open up suppressed political possibilities and to seek the coordinated use of different disciplines to address significant public problems. (shrink)

The usual account of Auguste Comte, thinker of the “positive” science, overshadows his attention to the “spectacle of destruction”, to which the metaphysical state of human knowledge and humanity offers the stage. I first illustrate the understanding of this Comtian metaphysical state as both a progressive and self-destructive transformation of “theology”, using an example drawn from the history of astronomy. The broader relevance of this conception is then assessed in the field of social philosophy, so that the realm of natural (...) sciences is finally re-examined with the analysis of Comte’s criticisms of the theory of chemical affinity. (shrink)

Understanding the nature of science has long been a desired outcome of science education, despite ongoing disagreements about the content, structure, and focus of NOS expectations. Addressing the concern that teachers likely focus only on student learning expectations appearing in standards documents, this study examines the current state of NOS in science education standards documents from nine diverse countries to determine the overt NOS learning expectations that appeared, NOS statements provided near those learning expectations, but not identified as learning outcomes, (...) and NOS statements found in ancillary text. Findings indicate that NOS ideas rarely occur as expectations for student learning and are far more commonly found in ancillary material. Moreover, consensus was not apparent in the overt learning outcomes for students. Given the well-documented poor state of NOS instruction and the consistent lack of NOS appearing in published curriculum materials, the NOS standards appearing in nearly all documents analyzed are unlikely to provide sufficient conceptual or pedagogical support for NOS to be accurately interpreted or translated into meaningful experiences for students. (shrink)

Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)

Normative naturalism is a view about the status of epistemology and philosophy of science; it is a meta-epistemology. It maintains that epistemology can both discharge its traditional normative role and nonetheless claim a sensitivity to empirical evidence. The first sections of this essay set out the central tenets of normative naturalism, both in its epistemic and its axiological dimensions; later sections respond to criticisms of that species of naturalism from Gerald Doppelt, Jarrett Leplin and Alex Rosenberg.

_ Source: _Page Count 19 In this paper, we tackle the contribution that history of science can make to the _problem of rule-choice_, i.e., the choice from among competing methodological rules. Taking our cue from Larry Laudan’s writings, we extensively discuss what we call _historicist naturalism_, i.e., the view that history of science plays a pivotal role in the justification of rules, since it is one source of the evidence required to settle methodological controversies. As we illustrate, there are cases (...) of rule-choice that depend on conceptual considerations alone, and in which history of science does not factor. Moreover, there are cases in which methodological change is prompted – and explained – by empirical information that is not historical in nature: as suggested by what we call _scientific naturalism_, the justification of methodological choices comes from our knowledge of the structure of the world, as expressed by our currently accepted scientific theories. As we argue, due to its backward-looking character, historicist naturalism does not satisfactorily deal with the case of newly introduced rules, for which no evidence concerning their past performance is available. In sum, we conclude, the contribution that history of science can make to rule-choice is more modest than Laudan suggests. (shrink)

We argue that abduction does not work in isolation from other inference mechanisms and illustrate this through an inference scheme designed to evaluate multiple hypotheses. We use game theory to relate the abductive system to actions that produce new information. To enable evaluation of the implications of this approach we have implemented the procedures used to calculate the impact of new information in a computer model. Experiments with this model display a number of features of collective belief-revision leading to consensus-formation, (...) such as the influence of bias and prejudice. The scheme of inferential calculations invokes a Peircian concept of ‘belief’ as the propensity to choose a particular course of action. (shrink)

This paper argues against the view that the standard explanation of phase transitions in statistical mechanics may be considered a causal explanation, a distortion that can nevertheless successfully represent causal relations.

The paper presents an example of unified theory bearing interest from both a historical and systematic point of view. The example is chosen from evolutionary population genetics (neo-Darwinian synthetic theory). It exhibits various aspects of theoretical change in science that have been shown in Part I (Geiger, 1988) to be characteristic of syntheses of theories.

Cases where analogy has played a significant role in the formation of a new scientific concept are well-documented. Yet, how is it that genuinely new representations can be constructed from existing representations? It is argued that the process of ‘generic modeling’ enables abstraction of features common to both the domain of the source of the analogy and of the target phenomena. The analysis focuses on James Clerk Maxwell's construction of the electromagnetic field concept. The mathematical representation Maxwell constructed turned out (...) to be a system of abstract laws that when applied to electromagnetic systems yield laws of a dynamical system that will not map back onto the mechanicals domains used in their construction. (shrink)