The semantic conception and the structuralist view of theories: A critique of Suppe’s criticisms

Different conceptions of scientific theories, such as the state spaces approach of Bas van Fraassen, the phase spaces approach of Frederick Suppe, the set-theoretical approach of Patrick Suppes, and the structuralist view of Joseph Sneed et al. are usually put together into one big family. In addition, the definite article is normally used, and thus we speak of the semantic conception (view or approach) of theories and of its different approaches (variants or versions). However, in The Semantic Conception of Theories and Scientific Realism (Urban and Chicago: University of Illinois Press, 1989), starting from certain remarks already made in “Theory Structure” (in P. Asquith and H. Kyburg (Eds.), Current Research in Philosophy of Science, East Lansing: Philosophy of Science Association, 1979, pp. 317–338), Frederick Suppe excludes the structuralist view as well as other “European” versions from the semantic conception of theories. In this paper I will critically examine the reasons put forward by Suppe for this decision and, later, I will provide a general characterization of the semantic family and of the structuralist view of theories in such a way as to justify the inclusion of the structuralist view (as well as other “European” versions) as a member of this family.     

The eagle and the starlings: Galileo’s argument for the autonomy of science—how pertinent is it today?

After Galileo’s argument for the autonomy of science is analysed and adapted to take into account later developments of scientific practices, we conclude that, in the final analysis, it is not compelling. Nevertheless, Galileo’s argument still provides a useful point of reference, for aspects of it can be interpreted to anticipate central components of the often acclaimed ideal of science as value free, so that appraising it contributes to the larger purpose of exploring how well that ideal stands up today. Finally, we will argue that residue from Galileo’s struggle with the Church remains with us, making it difficult to identify the conditions that would need to be put into place today for any robust sense of the autonomy of science to be defensible.     

On the equivalence of Goodman’s and Hempel’s paradoxes

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other.     

The law of refraction and Kepler’s heuristics

Archive for History of Exact Sciences - Johannes Kepler dedicated much of his work to discover a law for the refraction of light. Unfortunately, he formulated an incorrect law. Nevertheless, it was...     

Babbage’s guidelines for the design of mathematical notations

The design of good notation is a cause that was dear to Charles Babbage’s heart throughout his career. He was convinced of the “immense power of signs” (1864, 364), both to rigorously express complex ideas and to facilitate the discovery of new ones. As a young man, he promoted the Leibnizian notation for the calculus in England, and later he developed a Mechanical Notation for designing his computational engines. In addition, he reflected on the principles that underlie the design of good mathematical notations. In this paper, we discuss these reflections, which can be found somewhat scattered in Babbage’s writings, for the first time in a systematic way. Babbage’s desiderata for mathematical notations are presented as ten guidelines pertinent to notational design and its application to both individual symbols and complex expressions. To illustrate the applicability of these guidelines in non-mathematical domains, some aspects of his Mechanical Notation are also discussed.     

The potter’s wheel: the host’s role in sculpting its microbiota

Animals, ranging from basal metazoans to primates, are host to complex microbial ecosystems; engaged in a symbiotic relationship that is essential for host physiology and homeostasis. Epithelial surfaces vary in the composition of colonizing microbiota as one compares anatomic sites, developmental stages and species origin. Alterations of microbial composition likely contribute to susceptibility to several distinct diseases. The forces that shape the colonizing microbial composition are the focus of much current investigation, and it is evident that there are pressures exerted both by the host and the external environment to mold these ecosystems. The focus of this review is to discuss recent studies that demonstrate the critical importance of host factors in selecting for its microbiome. Greater insight into host–microbiome interactions will be essential for understanding homeostasis at mucosal surfaces, and developing useful interventions when homeostasis is disrupted.     

Anti-amyloidogenic therapies: strategies for prevention and treatment of Alzheimer’s disease

Deposition of amyloid β-protein (Aβ) in the brain is an early and invariant neuropathological feature of Alzheimer’s disease (AD). The current search for anti-AD drugs is mainly focused on modification of the process of accumulation of Aβ in the brain. Here, we review four anti-amyloidogenic strategies: (i) reduction of Aβ production, which has mainly been approached with secretase inhibition, (ii) promotion of the Aβ degrading catabolic pathway, including an Aβ degrading enzyme, neprilysin, (iii) immunotherapy for Aβ and (iv) inhibition of Aβ aggregation. We have reported that AD patients have a favorable molecular environment for Aβ aggregation and that various compounds, such as polyphenols, interfere with Aβ aggregation and destabilize preformed Aβ fibrils. Received 21 December 2005; received after revision 14 February 2006; accepted 29 March 2006     

The natures of numbers in and around Bombelli’s L’algebra

The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.     

Thomas Harriot’s optics,between experiment and imagination: the case of Mr Bulkeley’s glass

Some time in the late 1590s, the Welsh amateur mathematician John Bulkeley wrote to Thomas Harriot asking his opinion about the properties of a truly gargantuan (but totally imaginary) plano-spherical convex lens, 48 feet in diameter. While Bulkeley’s original letter is lost, Harriot devoted several pages to the optical properties of “Mr Bulkeley his Glasse” in his optical papers (now in British Library MS Add. 6789), paying particular attention to the place of its burning point. Harriot’s calculational methods in these papers are almost unique in Harriot’s optical remains, in that he uses both the sine law of refraction and interpolation from Witelo’s refraction tables in order to analyze the passage of light through the glass. For this and other reasons, it is very likely that Harriot wrote his papers on Bulkeley’s glass very shortly after his discovery of the law and while still working closely with Witelo’s great Optics; the papers represent, perhaps, his very first application of the law. His and Bulkeley’s interest in this giant glass conform to a long English tradition of curiosity about the optical and burning properties of large glasses, which grew more intense in late sixteenth-century England. In particular, Thomas Digges’s bold and widely known assertions about his father’s glasses that could see things several miles distant and could burn objects a half-mile or further away may have attracted Harriot and Bulkeley’s skeptical attention; for Harriot’s analysis of the burning distance and the intensity of Bulkeley’s fantastic lens, it shows that Digges’s claims could never have been true about any real lens (and this, I propose, was what Bulkeley had asked about in his original letter to Harriot). There was also a deeper, mathematical relevance to the problem that may have caught Harriot’s attention. His most recent source on refraction—Giambattista della Porta’s De refractione of 1593—identified a mathematical flaw in Witelo’s cursory suggestion about the optics of a lens (the only place that lenses appear, however fleetingly, in the writings of the thirteenth-century Perspectivist authors). In his early notes on optics, in a copy of Witelo’s optics, Harriot highlighted Witelo’s remarks on the lens and della Porta’s criticism (which he found unsatisfactory). The most significant problem with Witelo’s theorem would disappear as the radius of curvature of the lens approached infinity. Bulkeley’s gigantic glass, then, may have provided Harriot an opportunity to test out Witelo’s claims about a plano-spherical glass, at a time when he was still intensely concerned with the problems and methods of the Perspectivist school.     

The coming-to-be of Hansen’s method

This article by Curtis Wilson is an account of the origin of Hansen’s powerful systematic method for finding contributions of higher order perturbations in celestial mechanics. Hansen’s method was developed in the course of improving on Laplace’s treatment of the mutual perturbations of Jupiter and Saturn. This method, an entirely new way of doing celestial mechanics when it first appeared, later made possible the successful treatment of the complicated motions of our moon (see Wilson 2010). In this paper Wilson gives a brief historical introduction followed by an account of relevant technical details of the Laplacian background, an account illustrating technical details in Hansen’s initial development in his Disquisitions of 1829, and a treatment illustrating details contributing to the achievement of Hansen’s more refined development in his Untersuchung of 1831. These details include conditional equations Hansen provides for checking the accuracy of calculations. Wilson also includes a detailed assessment showing the extraordinary improvement in empirical accuracy of Hansen’s treatment over the best earlier treatment of the Jupiter-Saturn  interactions.     

The evolution of X chromosome inactivation in mammals: the demise of Ohno’s hypothesis?

Ohno’s hypothesis states that dosage compensation in mammals evolved in two steps: a twofold hyperactivation of the X chromosome in both sexes to compensate for gene losses on the Y chromosome, and silencing of one X (X-chromosome inactivation, XCI) in females to restore optimal dosage. Recent tests of this hypothesis have returned contradictory results. In this review, we explain this ongoing controversy and argue that a novel view on dosage compensation evolution in mammals is starting to emerge. Ohno’s hypothesis may be true for a few, dosage-sensitive genes only. If so few genes are compensated, then why has XCI evolved as a chromosome-wide mechanism? This and several other questions raised by the new data in mammals are discussed, and future research directions are proposed.     

The foundational aspects of Gauss’s work on the hypergeometric,factorial and digamma functions

In his writings about hypergeometric functions Gauss succeeded in moving beyond the restricted domain of eighteenth-century functions by changing several basic notions of analysis. He rejected formal methodology and the traditional notions of functions, complex numbers, infinite numbers, integration, and the sum of a series. Indeed, he thought that analysis derived from a few, intuitively given notions by means of other well-defined concepts which were reducible to intuitive ones. Gauss considered functions to be relations between continuous variable quantities while he regarded integration and summation as appropriate operations with limits. He also regarded infinite and infinitesimal numbers as a façon de parler and used inequalities in order to prove the existence of certain limits. He took complex numbers to have the same legitimacy as real quantities. However, Gauss’s continuum was linked to a revised form of the eighteenth-century notion of continuous quantity: it was not reducible to a set of numbers but was immediately given.     

The role of inflammation in sporadic and familial Parkinson’s disease

The etiology of Parkinson’s disease (PD) is complex and most likely involves numerous environmental and heritable risk factors. Interestingly, many genetic variants, which have been linked to familial forms of PD or identified as strong risk factors, also play a critical role in modulating inflammatory responses. There has been considerable debate in the field as to whether inflammation is a driving force in neurodegeneration or simply represents a response to neuronal death. One emerging hypothesis is that inflammation plays a critical role in the early phases of neurodegeneration. In this review, we will discuss emerging aspects of both innate and adaptive immunity in the context of the pathogenesis of PD. We will highlight recent data from genetic and functional studies that strongly support the theory that genetic susceptibility plays an important role in modulating immune pathways and inflammatory reactions, which may precede and initiate neuronal dysfunction and subsequent neurodegeneration. A detailed understanding of such cellular and molecular inflammatory pathways is crucial to uncover pathogenic mechanisms linking sporadic and hereditary PD and devise tailored neuroprotective interventions.     

Boyle’s teleological mechanism and the myth of immanent teleology

According to recent commentators, medieval natural philosophers endorsed immanent teleology, the view that natural agents possess immanent active powers to achieve certain ends. Moreover, some scholars have argued that Robert Boyle, despite his intentions, failed to eliminate immanent teleology from his natural philosophy. I argue in this paper that it is not at all clear that immanent teleology was widely endorsed in the medieval period. Moreover, I argue that a proper understanding of immanent teleology, and why it was rejected by mainstream medieval natural philosophers, reveals that Boyle did not fail to eliminate immanent teleology from his natural philosophy. I conclude that any attempt to describe the break between medieval and early modern natural philosophy in terms of a break with immanent teleology is likely not on target.