There was a methodological revolution in the mathematics of the nineteenth century, and philosophers have, for the most part, failed to notice.2 My objective in this chapter is to convince you of this, and further to convince you of the following points. The philosophy of mathematics has been informed by an inaccurately narrow picture of the emergence of rigour and logical foundations in the nineteenth century. This blinkered vision encourages a picture of philosophical and logical foundations as essentially disengaged from (...) ongoing mathematical practice. Frege is a telling example: we have misunderstood much of what Frege was trying to do, and missed the intended significance of much of what he wrote, because our received stories underestimate the complexity of nineteenth-century mathematics and mislocate Frege’s work within that context. Given Frege’s perceived status as a paradigmatic analytic philosopher, this mislocation translates into an unduly narrow vision of the relation between mathematics and philosophy. This chapter surveys one part of a larger project that takes Frege as a benchmark to fix some of the broader interest and philosophical significance of nineteenth-century developments. To keep this contribution to a manageable.. (shrink)

With this treatise, an insightful exploration of the probabilistic connection between philosophy and the history of science, the famous economist breathed new life into studies of both disciplines. Originally published in 1921, this important mathematical work represented a significant contribution to the theory regarding the logical probability of propositions. Keynes effectively dismantled the classical theory of probability, launching what has since been termed the “logical-relationist” theory. In so doing, he explored the logical relationships between classifying a proposition as “highly probable” (...) and as a “justifiable induction.” Unabridged republication of the classic 1921 edition. (shrink)

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and (...) made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps, and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may (...) freely copy and distribute this work, as no entity has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

Gottlob Frege (1848-1925) und Ludwig Wittgenstein gelten als die geistigen Väter der analytischen Philosophie. Das wissenschaftliche Schaffen Gottlob Freges hat wie kein anderes nach Aristoteles die Logik in ihrer theoretischen Erscheinungsform und in ihrer praktischen Relevanz grundlegend verändert. Seine logisch-semantischen Untersuchungen haben noch immer auf Philosophie und Sprachwissenschaft großen Einfluß. Doch wer war dieser Mann, der die Geistesgeschichte des 20. Jahrhunderts mitgestaltete, dessen Rückführung logischen Schließens auf mechanisch kontrollierte Elementarschritte den Weg zur Logik der elektronischen Datenverarbeitung eröffnete? Zwar gibt es (...) Arbeiten, die sich mit besonderen Seiten oder speziellen Zeiten von Freges Leben beschäftigen, eine umfassende Biographie über ihn gab es jedoch bislang nicht. Diese Lücke schließt Lothar Kreisers Buch. Freges Leben wird biographisch zunächst in dem Kontext der Stadt und Stadtschule Wismar, dann in dem der Stadt und der Universität Jena eingebettet rekonstruiert. Regional übergreifende politische und wissenschaftliche Vorgänge werden einbezogen, um verbürgten konkreten Ereignissen aus Freges Leben einen für das Verstehen tieferen und festeren Rahmen zu geben. Seine Mitwirkung in Kommisionen und Gesellschaften kommt ebenso zur Sprache wie die Wurzeln seines wissenschaftlichen Lebenswerkes, seine Beziehungen zu anderen Persönlichkeiten und deren Bestrebungen, aber auch der Wandel in seinen politischen Überzeugungen. Die Biographie setzt keine speziellen Fachkenntnisse, nur Interesse an einem spannenden Abschnitt der Wissenschaftsgeschichte, fokussiert auf die Person Gottlob Frege, voraus. "Gottlob Frege: Leben - Werk - Zeit" ist Biographie und Millieustudie zugleich. (shrink)

No mathematical background is necessary to appreciate this classic of probability theory, which remains unsurpassed in its clarity, readability, and sheer charm. Its author, British logician John Venn (1834-1923), popularized the famous Venn Diagrams that are commonly used in teaching elementary mathematics.

This paper develops some respects in which the philosophy of mathematics can fruitfully be informed by mathematical practice, through examining Frege's Grundlagen in its historical setting. The first sections of the paper are devoted to elaborating some aspects of nineteenth century mathematics which informed Frege's early work. (These events are of considerable philosophical significance even apart from the connection with Frege.) In the middle sections, some minor themes of Grundlagen are developed: the relationship Frege envisions between arithmetic and geometry and (...) the way in which the study of reasoning is to illuminate this. In the final section, it is argued that the sorts of issues Frege attempted to address concerning the character of mathematical reasoning are still in need of a satisfying answer. (shrink)

This work is the long awaited sequel to the author’s classic Frege: Philosophy of Language. But it is not exactly what the author originally planned. He tells us that when he resumed work on the book in the summer of 1989, after a long interruption, he decided to start afresh. The resulting work followed a different plan from the original drafts. The reader does not know what was lost by their abandonment, but clearly much was gained: The present work may (...) be the most compactly organized of Dummett’s philosophical books, and its value as commentary on Frege is enhanced by its being organized as a study of Die Grundlagen der Arithmetik and selected parts of Grundgesetze. Moreover, since Dummett has been thinking and writing about Frege for forty years, we have a single, mature chronological stage of his thought. (shrink)

Why was Hensen unsuccesful in the quantification of ecological sampling? No aspect of plankton research itself seems to have hindered quantification; both collecting methods and taxonomy were sufficiently advanced. The reason is probably that at the time he began sampling, Hensen had to devise his own statistical methods for expressing the reproducibility and validity of samples. Hensen might have succeeded in this if he had overcome prevalent nineteenth-century attitudes toward randomness.The statistical literature of medicine and physics with which Hensen was (...) probably familiar gave methods for expressing reproducibility and for comparing differences between means of different sets of observations. For example, a student of Poisson writing on medical statistics advocated using Poisson's limit (standard error 2√2) to test the difference between two means56. Other authors suggested that differences between means were most meaningful if very large numbers of observations were used.57 In his laboratory subsampling, Hensen used the propable error as a limit about means. In this and other ways, he seems most indebted to the physicist Ernst Abbe for statistical methods.58 However, all the methodology available to Hensen had been developed for situations in which errors are a property of the measurement or sampling process, and not of the phenomena themselves. The available methods for measuring reproducibility were based on the assumption that differences from the average were small and that they tended to accumulate about the mean in a bell-shaped pattern. Hensen constantly reinvestigated the distribution of plankton numbers about the average using a different method each time. Westergaard points out that medical statisticians did not make such investigations with their biological data.59To a considerable extent, biological sampling problems forced development of theory because samples afforded the only information on a pattern in water or soil which could not be directly observed. The sampling methods of Laplace and the late nineteenth-century government statisticians contrasted strongly with Hensen's because, either through subjective knowledge of the population sampled or through censuses, they attempted to choose representative or typical samples.60 The high reproducibility and validity of representative sampling is attained by knowing more about a population than a biologist can ordinarily know. The uncertain reproducibility and validity of biological sampling spurred the development of formal sampling theory.A formal sampling theory developed only after change in the general intellectual attitude toward randomness, which was reflected in nineteenth-century statistics.61 The ninteenth-century attitude that randomness is not part of nature changed in the twentieth century to a view of randomness as a property of nature.62 The physicist's incorporation of randomness into physical models in response to this intellectual change late in the nineteenth-century is discussed by Bork.63 In biology, the change was initiated by the attention Darwin focused on morphological variation. The English biometricians — Francis Galton and W. F. R. Weldon, for example — were prominent in developing methods for the analysis of biological variation.64 Most pertinent to the development of sampling theory was Karl Pearson's use of frequency distributions as models of biological variation. In ecology, quantification was brought about by Ronald Fisher more than by anyone else; he incorporated randomness into sampling plans and built upon the methods developed earlier for analysis of individual variation. Fisher's use of random sampling allowed comparison between the sample collections and the collections expected from a model population of known patterning (calculated with a frequency distribution). This is a much more efficient method of determining the validity of a sample than Hensen's comparison of collections with a model uniform collection. Intellectual background and accumulated biological information caused Fisher to find variability where Hensen had seen uniformity.In summary, Victor Hensen became interested in fisheries research because of the economic importance of fishing to Germany. Hensen had considerable understanding of the prerequisites for valid sampling, but the value of his quantitative approach was limited by the general preconceptions shared by most nineteenth-century biologists. Through Hensen's efforts many other biologists were stimulated to undertake quantitative samples, even though the statistical methods for analyzing variation among populations developed only after methods for analyzing variation among individuals had been developed. *** DIRECT SUPPORT *** A8402011 00003. (shrink)

Emphasizing the debt of science to nonspecialist intellectuals, Theodore Porter describes in detail the nineteenth-century background that produced the burst of modern statistical innovation of the early 1900s. Statistics arose as a study of society--the science of the statist--and the pioneering statistical physicists and biologists, Maxwell, Boltzmann, and Galton, each introduced statistical models by pointing to analogies between his discipline and social science.

In this important new study Ian Hacking continues the enquiry into the origins and development of certain characteristic modes of contemporary thought undertaken in such previous works as his best selling Emergence of Probability. Professor Hacking shows how by the late nineteenth century it became possible to think of statistical patterns as explanatory in themselves, and to regard the world as not necessarily deterministic in character. Combining detailed scientific historical research with characteristic philosophic breath and verve, The Taming of Chance (...) brings out the relations among philosophy, the physical sciences, mathematics and the development of social institutions, and provides a unique and authoritative analysis of the "probabilization" of the Western world. (shrink)

In recent years, it has been acknowledged increasingly that the relationship between analytic and continental philosophy is one of complementarity rather than opposition, as previously often assumed. In this essay I will argue that, in fact, early analytic philosophy has its roots in the tradition of continental philosophy. The essay will focus on Hermann Lotze's influence on Frege and on Frege's relationship to the Neo‐Kantians Otto Liebmann and Wilhelm Windelband. It will provide new evidence for the claim that Frege's philosophy (...) should be seen as belonging to the tradition of Neo‐Kantianism and, along the way, exhibit the continental roots of Frege's context principle. (shrink)