Switch to: References

Citations of:

Hilbert's

The Monist 13 (2):303-309 (1903)

Add citations

You must login to add citations.

An Okapi Hypothesis: Non-Euclidean Geometry and the Professional Expert in American Mathematics.Jemma Lorenat - 2022 - Isis 113 (1):85-107.details Open Court began publishingThe Monistin 1890 as a journal“devotedto the philosophy of science”that regularly included mathematics. The audiencewas understood to be“cultured people who have not a technical mathematicaltraining”but nevertheless“have a mathematical penchant.”With these constraints,the mathematical content varied from recreations to logical foundations, but every-one had something to say about non-Euclidean geometry, in debates that rangedfrom psychology to semantics. The focus in this essay is on the contested value ofmathematical expertise in legitimating what should be considered as mathematics.While some mathematicians urgedThe (...) Download Export citation Bookmark
A note on the introduction of Hilbert’s Grundlagen der Geometrie.Giorgio Venturi - 2017 - Manuscrito 40 (2):5-17.details ABSTRACT We present and discuss a change in the introduction of Hilbert’s Grundlagen der Geometrie between the first and the subsequent editions: the disappearance of the reference to the independence of the axioms. We briefly outline the theoretical relevance of the notion of independence in Hilbert’s work and we suggest that a possible reason for this disappearance is the discovery that Hilbert’s axioms were not, in fact, independent. In the end we show how this change gives textual evidence for the (...) Download Export citation Bookmark
Jean van Heijenoort’s Contributions to Proof Theory and Its History.Irving H. Anellis - 2012 - Logica Universalis 6 (3-4):411-458.details Jean van Heijenoort was best known for his editorial work in the history of mathematical logic. I survey his contributions to model-theoretic proof theory, and in particular to the falsifiability tree method. This work of van Heijenoort’s is not widely known, and much of it remains unpublished. A complete list of van Heijenoort’s unpublished writings on tableaux methods and related work in proof theory is appended. Download Export citation Bookmark
Annual meeting of the association for symbolic logic: Philadelphia 1981.Simon Kochen, Hugues Leblanc & Charles D. Parsons - 1983 - Journal of Symbolic Logic 48 (3):898-910.details Download Export citation Bookmark 2 citations
Who were the American Postulate Theorists?Michael Scanlan - 1991 - Journal of Symbolic Logic 56 (3):981-1002.details Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency. Download Export citation Bookmark 41 citations
Sheffer's Criticism of Royce's Theory of Order.J. Brent Crouch, Michael Scanlan, Scott L. Pratt, Robert W. Burch & Phillip Deen - 2010 - Transactions of the Charles S. Peirce Society 46 (2):178-201.details Henry Sheffer’s 1908 Harvard Ph.D. thesis contains an interesting appendix on a central feature of the logical work of his thesis advisor, Josiah Royce. This is the claim in Royce’s 1905 article “The Relations of the Principles of Logic to the Foundations of Geometry” that an unsymmetric ordering relation can be defined on the single symmetric O-relation for which he gives postulates in that paper. Sheffer criticizes Royce’s specific definition from the point of view of the evolving twentieth century conception (...) Download Export citation Bookmark

1