87 research outputs found
A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography
We analyze the developments in mathematical rigor from the viewpoint of a
Burgessian critique of nominalistic reconstructions. We apply such a critique
to the reconstruction of infinitesimal analysis accomplished through the
efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's
foundational work associated with the work of Boyer and Grabiner; and to
Bishop's constructivist reconstruction of classical analysis. We examine the
effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint
Variational Analysis Down Under Open Problem Session
© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We state the problems discussed in the open problem session at Variational Analysis Down Under conference held in honour of Prof. Asen Dontchev on 19â21 February 2018 at Federation University Australia
Ten Misconceptions from the History of Analysis and Their Debunking
The widespread idea that infinitesimals were "eliminated" by the "great
triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an
uninterrupted chain of work on infinitesimal-enriched number systems. The
elimination claim is an oversimplification created by triumvirate followers,
who tend to view the history of analysis as a pre-ordained march toward the
radiant future of Weierstrassian epsilontics. In the present text, we document
distortions of the history of analysis stemming from the triumvirate ideology
of ontological minimalism, which identified the continuum with a single number
system. Such anachronistic distortions characterize the received interpretation
of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note:
text overlap with arXiv:1108.2885 and arXiv:1110.545
Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond
Many historians of the calculus deny significant continuity between
infinitesimal calculus of the 17th century and 20th century developments such
as Robinson's theory. Robinson's hyperreals, while providing a consistent
theory of infinitesimals, require the resources of modern logic; thus many
commentators are comfortable denying a historical continuity. A notable
exception is Robinson himself, whose identification with the Leibnizian
tradition inspired Lakatos, Laugwitz, and others to consider the history of the
infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies,
Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly
demonstrating the inconsistency of reasoning with historical infinitesimal
magnitudes. We argue that Robinson, among others, overestimates the force of
Berkeley's criticisms, by underestimating the mathematical and philosophical
resources available to Leibniz. Leibniz's infinitesimals are fictions, not
logical fictions, as Ishiguro proposed, but rather pure fictions, like
imaginaries, which are not eliminable by some syncategorematic paraphrase. We
argue that Leibniz's defense of infinitesimals is more firmly grounded than
Berkeley's criticism thereof. We show, moreover, that Leibniz's system for
differential calculus was free of logical fallacies. Our argument strengthens
the conception of modern infinitesimals as a development of Leibniz's strategy
of relating inassignable to assignable quantities by means of his
transcendental law of homogeneity.Comment: 69 pages, 3 figure
Understanding (in) Newtonâs Argument for Universal Gravitation.
In this essay, I attempt to assess Henk De Regt and Dennis Dieks recent pragmatic and contextual account of scientific understanding on the basis of an important historical case-study: understanding in Newtonâs theory of universal gravitation and Huygensâ reception of universal gravitation. It will be shown that de Regt and Dieksâ CIT-criterion, which stipulates that the appropriate combination of scientistsâ skills and intelligibility-enhancing theoretical virtues is a condition for scientific understanding, is too strong. On the basis of this case-study, it will be shown that scientists can understand each othersâ positions qualitatively and quantitatively, despite their endorsement of different worldviews and despite their convictions as what counts as a proper explanation
Rickettsia felis from cat fleas: Isolation and culture in a tick-derived cell line
Rickettsia felis, the etiologic agent of spotted fever, is maintained in cat fleas by vertical transmission and resembles other tick-borne spotted fever group rickettsiae. In the present study, we utilized an Ixodes scapularis-derived tick cell line, ISE6, to achieve isolation and propagation of R. felis. A cytopathic effect of increased vacuolization was commonly observed in R. felis-infected cells, while lysis of host cells was not evident despite large numbers of rickettsiae. Electron microscopy identified rickettsia-like organisms in ISE6 cells, and sequence analyses of portions of the citrate synthase (gltA), 16S rRNA, Rickettsia genus-specific 17-kDa antigen, and spotted fever group-specific outer membrane protein A (ompA) genes and, notably, R. felis conjugative plasmids indicate that this cultivatable strain (LSU) was R. felis. Establishment of R. felis (LSU) in a tick-derived cell line provides an alternative and promising system for the expansion of studies investigating the interactions between R. felis and arthropod hosts. Copyright © 2006, American Society for Microbiology. All Rights Reserved
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