Abduction, tomography, and other inverse problems

Charles S. Peirce introduced in the late 19^th century the notion of abduction as inference from effects to causes, or from observational data to explanatory theories. Abductive reasoning has become a major theme in contemporary logic, philosophy of science, and artificial intelligence. This paper argues that the new growing branch of applied mathematics called inverse problems deals successfully with various kinds of abductive inference within a variety of scientific disciplines. The fundamental theorem about the inverse reconstruction of plane functions from their line integrals was proved by Johann Radon already in 1917. The practical applications of Radon’s theorem and its generalizations include computerized tomography which became a routine imaging technique of diagnostic medicine in the 1970s.     

Unwarranted assumptions: Claude Bernard and the growth of the vera causa standard

The physiologist Claude Bernard was an important nineteenth-century methodologist of the life sciences. Here I place his thought in the context of the history of the vera causa standard, arguably the dominant epistemology of science in the eighteenth and early nineteenth centuries. Its proponents held that in order for a cause to be legitimately invoked in a scientific explanation, the cause must be shown by direct evidence to exist and to be competent to produce the effects ascribed to it. Historians of scientific method have argued that in the course of the nineteenth century the vera causa standard was superseded by a more powerful consequentialist epistemology, which also admitted indirect evidence for the existence and competence of causes. The prime example of this is the luminiferous ether, which was widely accepted, in the absence of direct evidence, because it entailed verified observational consequences and, in particular, successful novel predictions. According to the received view, the vera causa standard's demand for direct evidence of existence and competence came to be seen as an impracticable and needless restriction on the scope of legitimate inquiry into the fine structure of nature. The Mill-Whewell debate has been taken to exemplify this shift in scientific epistemology, with Whewell's consequentialism prevailing over Mill's defense of the older standard. However, Bernard's reflections on biological practice challenge the received view. His methodology marked a significant extension of the vera causa standard that made it both powerful and practicable. In particular, Bernard emphasized the importance of detection procedures in establishing the existence of unobservable entities. Moreover, his sophisticated notion of controlled experimentation permitted inferences about competence even in complex biological systems. In the life sciences, the vera causa standard began to flourish precisely around the time of its alleged abandonment.     

Incredulity towards Lyotard: a critique of a postmodernist account of science and knowledge

Philosophers of science have paid little attention, positive or negative, to Lyotard’s book The postmodern condition, even though it has been popular in other fields. We set out some of the reasons for this neglect. Lyotard thought that sciences could be justified by non-scientific narratives (a position he later abandoned). We show why this is unacceptable, and why many of Lyotard’s characterisations of science are either implausible or are narrowly positivist. One of Lyotard’s themes is that the nature of knowledge has changed and thereby so has society itself. However much of what Lyotard says muddles epistemological matters about the definition of ‘knowledge’ with sociological claims about how information circulates in modern society. We distinguish two kinds of legitimation of science: epistemic and socio-political. In proclaiming ‘incredulity towards metanarratives’ Lyotard has nothing to say about how epistemic and methodological principles are to be justified (legitimated). He also gives a bad argument as to why there can be no epistemic legitimation, which is based on an act/content confusion, and a confusion between making an agreement and the content of what is agreed to. As for socio-political legitimation, Lyotard’s discussion remains at the abstract level of science as a whole rather than at the level of the particular applications of sciences. Moreover his positive points can be accepted without taking on board any of his postmodernist account of science. Finally we argue that Lyotard’s account of paralogy, which is meant to provide a ‘postmodern’ style of justification, is a failure.     

The intelligibility of motion and construction: Descartes’ early mathematics and metaphysics, 1619-1637

I argue for an interpretation of the connection between Descartes’ early mathematics and metaphysics that centers on the standard of geometrical intelligibility that characterizes Descartes’ mathematical work during the period 1619 to 1637. This approach remains sensitive to the innovations of Descartes’ system of geometry and, I claim, sheds important light on the relationship between his landmark Geometry (1637) and his first metaphysics of nature, which is presented in Le monde (1633). In particular, I argue that the same standard of clear and distinct motions for construction that allows Descartes to distinguish ‘geometric’ from ‘imaginary’ curves in the domain of mathematics is adopted in Le monde as Descartes details God’s construction of nature. I also show how, on this interpretation, the metaphysics of Le monde can fruitfully be brought to bear on Descartes’ attempted solution to the Pappus problem, which he presents in Book I of the Geometry. My general goal is to show that attention to the standard of intelligibility Descartes invokes in these different areas of inquiry grants us a richer view of the connection between his early mathematics and philosophy than an approach that assumes a common method is what binds his work in these domains together.     

Public scientific testimony in the scientific image

In this paper, I draw on philosophy of science to address a challenge for science communication. Empirical research indicates that some people who trust a meteorologist's report that they are in the path of a storm do not trust a climate scientist's report that we are on a path to global warming. Such selective skepticism about climate science exemplifies a more general challenge:

The Challenge of Selective UptakeLaypersons who generally accept public scientific testimony nevertheless fail to accept public scientific testimony concerning select, equally well warranted, scientific hypotheses.

A prominent response arising from the novel interdisciplinary science of science communication is a principle called Consensus Reporting. According to this principle, science reporters should, whenever feasible, report the scientific consensus or lack thereof for a reported scientific view.However, philosophy of science may offer a different perspective on the issue. This perspective is critical insofar as it indicates some inadequacies of Consensus Reporting. But it is also constructive insofar as it guides the development of an alternative principle, Justification Reporting, according to which science reporters should, whenever feasible, report aspects of the nature and strength of scientific justification or lack thereof for a reported scientific view. A central difference between these proposals is that Consensus Reporting appeals to the authority of the scientists whereas Justification Reporting appeals to the authority of scientific justification. As such, Justification Reporting reflects the image of science.The paper considers the philosophical and empirical motivation for Justification Reporting and its limitations. This includes prospects and problems for implementing it in a way that addresses The Challenge of Selective Uptake. From a methodological point of view, the paper illustrates how empirically informed philosophy of science may help address challenges for science communication.     

Physics,metaphysics, dispositions,and symmetries – À la French

Recent philosophy has paid increasing attention to the nature of the relationship between the philosophy of science and metaphysics. In The Structure of the World: Metaphysics and Representation, Steven French offers many insights into this relationship (primarily) in the context of fundamental physics, and claims that a specific, structuralist conception of the ontology of the world exemplifies an optimal understanding of it. In this paper I contend that his messages regarding how best to think about the relationship are mixed, and in tension with one another. The tension is resolvable but at a cost: a weakening of the argument for French's structuralist ontology. I elaborate this claim in a specific case: his assertion of the superiority of a structuralist account of de re modality in terms of realism about laws and symmetries (conceived ontologically) over an account in terms of realism about dispositional properties. I suggest that these two accounts stem from different stances regarding how to theorize about scientific ontology, each of which is motivated by important aspects of physics.     

Cicero's demarcation of science: A report of shared criteria

The problem of establishing intensional criteria to demarcate science from non-science, and in particular science from pseudoscience, received a great amount of attention in the 20th century philosophy of science. It remains unsolved. This article compares demarcation criteria found in Marcus Tullius Cicero’s rejection of genethliac astrology and other pseudo-divinatory techniques in his De divinatione (44 BCE) with criteria advocated by a broad selection of modern philosophers of science and other specialists in science studies. Remarkable coincidences across two millennia are found on five basic criteria, which hints at a certain historical stability of some of the most fundamental features of a concept of “science” broadly construed.     

Helmholtz's early empiricism and the Erhaltung der Kraft

Hermann Helmholtz has often been understood to have started research under the influence of Kant, and then to have made a transition to a later mature empiricist phase. Without claiming that in 1847 Helmholtz held the same positions that he later espoused, I suggest that already in his 1847 ‘Über die Erhaltung der Kraft’ one may find important aspects of his later empiricism. I highlight the ways in which, from early on, Helmholtz turned Kant to use in developing an empirical program of inquiry into possible basic natural causes. To that end, I indicate how, throughout his arguments, Helmholtz employed, sometimes explicitly, but often tacitly, an empiricist logic, one that ran contrary to any form of transcendental deduction, and even to all a priori knowledge. Instead of deriving aspects about the ultimate constituents of nature, Helmholtz aimed to define the proper project for physical natural science. The first part of the paper describes the context of discussion in which Helmholtz entered. The bulk of the paper then analyzes Helmholtz's arguments in order to make space between (1) Kantian, and other, deductions of characteristics that must be true of nature and (2) Helmholtz's delineation of empirically determinable characteristics of presumed ultimate elements of nature, ones that he meant to be specified and delimited through future experimental research. The paper highlights that throughout his discussion Helmholtz meant to define the proper project for physical natural science, a project rife with empiricist aspects.     

Why did Kuhn’s Structure of scientific revolutions cause a fuss?

After the publication of The structure of scientific revolutions, Kuhn attempted to fend off accusations of extremism by explaining that his allegedly “relativist” theory is little more than the mundane analytical apparatus common to most historians. The appearance of radicalism is due to the novelty of applying this machinery to the history of science. This defence fails, but it provides an important clue. The claim of this paper is that Kuhn inadvertently allowed features of his procedure and experience as an historian to pass over into his general account of science. Kuhn’s familiar claims, that science is directed in part by extra-scientific influences; that the history of science is divided by revolutionary breaks into periods that cannot be easily compared; that there is no ahistorical standard of rationality by which past episodes may be judged; and that science cannot be shown to be heading towards the Truth—these now appear as methodological commitments rather than historico-philosophical theses.     

Incommensurabilities in the work of Thomas Kuhn

I distinguish between two ways in which Kuhn employs the concept of incommensurability based on for whom it presents a problem. First, I argue that Kuhn’s early work focuses on the comparison and underdetermination problems scientists encounter during revolutionary periods (actors’ incommensurability) whilst his later work focuses on the translation and interpretation problems analysts face when they engage in the representation of science from earlier periods (analysts’ incommensurability). Secondly, I offer a new interpretation of actors’ incommensurability. I challenge Kuhn’s account of incommensurability which is based on the compartmentalisation of the problems of both underdetermination and non-additivity to revolutionary periods. Through employing a finitist perspective, I demonstrate that in principle these are also problems scientists face during normal science. I argue that the reason why in certain circumstances scientists have little difficulty in concurring over their judgements of scientific findings and claims while in others they disagree needs to be explained sociologically rather than by reference to underdetermination or non-additivity. Thirdly, I claim that disagreements between scientists should not be couched in terms of translation or linguistic problems (aspects of analysts’ incommensurability), but should be understood as arising out of scientists’ differing judgments about how to take scientific inquiry further.     

Conventionalism,structuralism and neo-Kantianism in Poincaré׳s philosophy of science

Poincaré is well known for his conventionalism and structuralism. However, the relationship between these two theses and their place in Poincaré׳s epistemology of science remain puzzling. In this paper I show the scope of Poincaré׳s conventionalism and its position in Poincaré׳s hierarchical approach to scientific theories. I argue that for Poincaré scientific knowledge is relational and made possible by synthetic a priori, empirical and conventional elements, which, however, are not chosen arbitrarily. By examining his geometric conventionalism, his hierarchical account of science and defence of continuity in theory change, I argue that Poincaré defends a complex structuralist position based on synthetic a priori and conventional elements, the mind-dependence of which precludes epistemic access to mind-independent structures.     

From Helmholtz to Schlick: The evolution of the sign-theory of perception

Efforts to trace the influence of fin de siècle neo-Kantianism on early 20th Century philosophy of science have led scholars to recognize the powerful influence on Moritz Schlick of Hermann von Helmholtz, the doyen of 19th Century physics and a leader of the zur?ck zu Kant movement. But Michael Friedman thinks that Schlick misunderstood Helmholtz' signature philosophical doctrine, the sign-theory of perception. Indeed, Friedman has argued that Schlick transformed Helmholtz' Kantian view of spatial intuition into an empiricist version of the causal theory of perception. However, it will be argued that, despite the key role the sign-theory played in his epistemology, Schlick thought the Kantianism in Helmholtz' thought was deeply flawed, rendered obsolete by philosophical insights which emerged from recent scientific developments. So even though Schlick embraced the sign-theory, he rejected Helmholtz' ideas about spatial intuition. In fact, like his teacher, Max Planck, Schlick generalized the sign-theory into a form of structural realism. At the same time, Schlick borrowed the method of concept-formation developed by the formalist mathematicians, Moritz Pasch and David Hilbert, and combined it with the conventionalism of Henri Poincaré. Then, to link formally defined concepts with experience, Schlick's introduced his ‘method of coincidences’, similar to the ‘point-coincidences’ featured in Einstein's physics. The result was an original scientific philosophy, which owed much to contemporary scientific thinkers, but little to Kant or Kantianism.     

Zweideutigkeit about “Zweideutigkeit”: Sommerfeld,Pauli, and the methodological origins of quantum mechanics

In early 1925, Wolfgang Pauli (1900–1958) published the paper for which he is now most famous and for which he received the Nobel Prize in 1945. The paper detailed what we now know as his “exclusion principle.” This essay situates the work leading up to Pauli's principle within the traditions of the “Sommerfeld School,” led by Munich University's renowned theorist and teacher, Arnold Sommerfeld (1868–1951). Offering a substantial corrective to previous accounts of the birth of quantum mechanics, which have tended to sideline Sommerfeld's work, it is suggested here that both the method and the content of Pauli's paper drew substantially on the work of the Sommerfeld School in the early 1920s. Part One describes Sommerfeld's turn away from a faith in the power of model-based (modellmässig) methods in his early career towards the use of a more phenomenological emphasis on empirical regularities (Gesetzmässigkeiten) during precisely the period that both Pauli and Werner Heisenberg (1901–1976), among others, were his students. Part two delineates the importance of Sommerfeld's phenomenology to Pauli's methods in the exclusion principle paper, a paper that also eschewed modellmässig approaches in favour of a stress on Gesetzmässigkeiten. In terms of content, a focus on Sommerfeld's work reveals the roots of Pauli's understanding of the fundamental Zweideutigkeit (ambiguity) involving the quantum number of electrons within the atom. The conclusion points to the significance of these results to an improved historical understanding of the origin of aspects of Heisenberg's 1925 paper on the “Quantum-theoretical Reformulation (Umdeutung) of Kinematical and Mechanical Relations.”     

Hilbert's axiomatic method and Carnap's general axiomatics

This paper compares the axiomatic method of David Hilbert and his school with Rudolf Carnap's general axiomatics that was developed in the late 1920s, and that influenced his understanding of logic of science throughout the 1930s, when his logical pluralism developed. The distinct perspectives become visible most clearly in how Richard Baldus, along the lines of Hilbert, and Carnap and Friedrich Bachmann analyzed the axiom system of Hilbert's Foundations of Geometry—the paradigmatic example for the axiomatization of science. Whereas Hilbert's axiomatic method started from a local analysis of individual axiom systems in which the foundations of mathematics as a whole entered only when establishing the system's consistency, Carnap and his Vienna Circle colleague Hans Hahn instead advocated a global analysis of axiom systems in general. A primary goal was to evade, or formalize ex post, mathematicians' ‘material’ talk about axiom systems for such talk was held to be error-prone and susceptible to metaphysics.     

Norton's material theory of analogy

In his book, The Material Theory of Induction, Norton argues that the quest for a universal formal theory or ‘schema’ for analogical inference should be abandoned. In its place, he offers the “material theory of analogy”: each analogical inference is “powered” by a local fact of analogy rather than by any formal schema. His minimalist model promises a straightforward, fact-based approach to the evaluation and justification of analogical inferences. This paper argues that although the rejection of universal schemas is justified, Norton's positive theory is limited in scope: it works well only for a restricted class of analogical inferences. Both facts and quasi-formal criteria have roles to play in a theory of analogical reasoning.     

Descartes’s changing mind

Descartes is always concerned about knowledge. However, the Galileo affair in 1633, the reactions to his Discourse on method, and later his need to reply to objections to his Meditations provoked crises in Descartes’s intellectual development the import of which has not been sufficiently recognized. These events are the major reasons why Descartes’s philosophical position concerning how we know and what we may know is radically different at the end of his life from what it was when he began. We call this later position Descartes’s epistemic stance and contrast it with his earlier methodological, metaphysical realism. Yet Descartes’s epistemic views cannot be separated from other aspects of his work, for example, his views concerning God, causality, metaphysics, and the nature of science. A further meta-implication is that serious errors await any scholar who cites early Cartesian texts in support of late Cartesian positions, or who uses later texts in conjunction with early ones to support a reading of Descartes’s philosophy.     

The methodological origins of Newton’s queries

This paper analyses the different ways in which Isaac Newton employed queries in his writings on natural philosophy. It is argued that queries were used in three different ways by Newton and that each of these uses is best understood against the background of the role that queries played in the Baconian method that was adopted by the leading experimenters of the early Royal Society. After a discussion of the role of queries in Francis Bacon’s natural historical method, Newton’s queries in his Trinity Notebook are shown to reveal the influence of his early reading in the new experimental philosophy. Then after a discussion of Robert Hooke’s view of the role of queries, the paper turns to an assessment of Newton’s correspondence and Opticks. It is argued that the queries in his correspondence with Oldenburg on his early optical experiments are closely tied to an experimental program, whereas the queries in the Opticks are more discursive and speculative, but that each of these uses of queries represents a significant Baconian legacy in his natural philosophical methodology.     

The early Kant’s (anti-) Newtonianism

It is well known that during his pre-Critical period, Kant was a major proponent of Newtonian physics, for the project of the Universal Natural History explicitly uses “Newtonian principles” to explain the formation of the various bodies that constitute our solar system as well as those that lie beyond. What has not been widely noted, however, is that the early Kant also developed a major criticism of Newton, one that is based on subtle metaphysical issues pertaining to God, which are most at home in philosophical theology. Interestingly, this criticism is neither an inchoate precursor of his later criticisms of Newton’s account of absolute space, nor isolated to the abstract realm of metaphysics, but has a wide range of implications for the way in which a scientific account of the formation and constitution of the heavenly bodies ought to be developed, that is, for the kind of argument Newton offered in the Principia. That Kant remained interested in this set of issues later in his Critical period suggests that, alongside the revolutionary changes that comprise transcendental idealism, there are deep continuities not only in his Newtonian commitments, but in his anti-Newtonian tendencies as well.     

The professor and the pea: Lives and afterlives of William Bateson’s campaign for the utility of Mendelism

As a defender of the fundamental importance of Mendel’s experiments for understanding heredity, the English biologist William Bateson (1861–1926) did much to publicize the usefulness of Mendelian science for practical breeders. In the course of his campaigning, he not only secured a reputation among breeders as a scientific expert worth listening to but articulated a vision of the ideal relations between pure and applied science in the modern state. Yet historical writing about Bateson has tended to underplay these utilitarian elements of his program, to the extent of portraying him, notably in still-influential work from the 1960s and 1970s, as a type specimen of the scientist who could not care less about application. This paper offers a corrective view of Bateson himself—including the first detailed account of his role as an expert witness in a courtroom dispute over the identity of a commercial pea variety—and an inquiry into the historiographic fate of his efforts in support of Mendelism’s productivity. For all that a Marxian perspective classically brings applied science to the fore, in Bateson’s case, and for a range of reasons, it did the opposite during the Cold War.