Lukas M. Verburgt

By focusing on the nineteenth-century debate between William Whewell and Augustus De Morgan on the nature and scope of scientific method and induction, this article captures an important episode in the history of Baconianism. More specifically, it sheds new light on the social and intellectual construction of Francis Bacon as an emblem of modern science and on British Baconianism as part of the creation of a vision of the modern enterprise. A critic of Whewell’s renovated Baconianism and an advocate of an alternative anti-Baconian (or pro-Newtonian) view of science, De Morgan is presented for the first time as a philosopher of science (or metascientist), one who pioneered the application of probability theory to scientific reasoning.

The Spedding-Ellis-Heath edition of The Works of Francis Bacon appeared in seven volumes between 1857 and 1859. Both a monument to Victorian scholarship and a staple of the history of science, this classic and historically significant work has been the authoritative edition of Bacon’s oeuvre ever since. This essay tells part of the story of its creation, reception, and influence. It describes the origin of and plan for the edition and, focusing on the three philosophical volumes, examines in detail the collaboration between James Spedding and Robert Leslie Ellis. On the basis of fresh archival research, it is shown that Spedding and Ellis disagreed fundamentally about the very thing their new edition was meant to settle: the correct interpretation of Bacon’s philosophical writings and of the role of his famous inductive method in the development of modern science from the time of Newton. With the Works, Spedding and Ellis did more than furnish what was long believed to be the Baconian canon; they also (at least in part unwittingly) produced a valuable primary source for the history of nineteenth-century Baconianism.

John Venn is remembered today as the inventor of the famous "Venn diagram." The postmortem fame of the namesake diagram has until now eclipsed Venn's own status as one of the most accomplished logicians in his day. Praised by John Stuart Mill as a "highly successful thinker" with much "power of original thought," Venn profoundly influenced nineteenth-century philosophers, ranging from Mill and Henry Sidgwick to Charles Sanders Peirce. Venn was heir to a clerical, Evangelical dynasty but religious doubts led him to resign Holy Orders and instead turn to an academic life, writing influential textbooks on probability theory and logic and advocating for education reform, including for women's education. Venn also collaborated with Francis Galton in the unofficial Anthropometrical Laboratory, and, through his writing and teaching, a direct line can be traced from Venn and his circle to the development of analytic philosophy in the work of W. E. Johnson, G. E. Moore, Bertrand Russell, and C. D. Broad. Through family descent, Venn was connected to eminent Victorians like Leslie Stephen and Virginia Woolf. This essential book explores Venn's life and work in context, taking readers on his journey from Evangelical son to Cambridge don. The picture that emerges of Venn, the person, is of a man with many sympathies-sometimes mutually reinforcing and at other times outwardly contradictory.

During 1881, the British logicians John Venn and Hugh MacColl engaged in a brief dispute in Nature about ‘symbolical logic’. The letters to the editor shed interesting light on the early reception of MacColl’s contributions to logic and his position in the logical community of the Victorian era. Drawing on the correspondence between Venn and William Stanley Jevons, this paper analyzes the background and context of these letters, adding to the recent interest in the social dimensions of the development of British algebraic logic in the confusing intermediary period between the 1870s and 1890s.

Although it has become a common place to refer to the ׳sixth problem׳ of Hilbert׳s (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert׳s project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a ׳vague׳ mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the ׳sixth problem׳ of 1900.

The goal of this paper is to provide a detailed reading of John Venn's Logic of Chance as a work of logic or, more specifically, as a specific portion of the general system of so-called ‘material’ logic developed in his Principles of Empirical or Inductive Logic and to discuss it against the background of his Boolean-inspired views on the connection between logic and mathematics. It is by means of this situating of Venn 1866 [The Logic of Chance. An Essay on the Foundations and Province of the Theory of Probability. With Especial Reference to Its Application to Moral and Social Science, London: Macmillan] within the entirety of his oeuvre that it becomes both possible to revisit and necessary to re-articulate its place in the history of the frequency interpretation of probability. For it is clear that if Venn's approach to logic not only allowed him to establish its foundations on the basis of a process of idealization and define it as consisting of so-called hypothetical infinite series, bu..

Reverend H.F.C. Logan is put forward as the formerly unidentified figure to which Robert Leslie Ellis referred in a journal entry of 1840 in which he wrote that it was due to his influence that William Whewell came to uphold particular Kantian views on time and space. The historical evidence of Ellis’s early familiarity with, and later commitment to Kant is noteworthy for at least two reasons. Firstly, it puts into doubt the accepted view of the second generation of reformers of British algebra as non-philosophical, practice-oriented mathematicians. Secondly, in so far as Logan was the correspondent of William Rowan Hamilton, it re-emphasizes that the role of Kantianism in the transition from ‘symbolical’ to ‘abstract’ algebra in nineteenth-century British algebra requires closer scrutiny.

ABSTRACTThis paper provides a detailed account of the period of the complex history of British algebra and geometry between the publication of George Peacock's Treatise on Algebra in 1830 and William Rowan Hamilton's paper on quaternions of 1843. During these years, Duncan Farquharson Gregory and William Walton published several contributions on ‘algebraical geometry’ and ‘geometrical algebra’ in the Cambridge Mathematical Journal. These contributions enabled them not only to generalize Peacock's symbolical algebra on the basis of geometrical considerations, but also to initiate the attempts to question the status of Euclidean space as the arbiter of valid geometrical interpretations. At the same time, Gregory and Walton were bound by the limits of symbolical algebra that they themselves made explicit; their work was not and could not be the ‘abstract algebra’ and ‘abstract geometry’ of figures such as Hamilton and Cayley. The central argument of the paper is that an understanding of the contributions to ‘algebraical geometry’ and ‘geometrical algebra’ of the second generation of ‘scientific’ symbolical algebraists is essential for a satisfactory explanation of the radical transition from symbolical to abstract algebra that took place in British mathematics in the 1830s–1840s.