• Corpus ID: 39474807

The Crisis in the Foundations of Mathematics

  title={The Crisis in the Foundations of Mathematics},
  author={Jos{\'e} Ferreir{\'o}s},
The foundational crisis is a celebrated affair among mathematicians and it has also reached a large nonmathematical audience. A well-trained mathematician is supposed to know something about the three viewpoints called “logicism,” “formalism,” and “intuitionism” (to be explained below), and about what Gödels incompleteness results tell us about the status of mathematical knowledge. Professional mathematicians tend to be rather opinionated about such topics, either dismissing the foundational… 
  • Simon B. Duffy
  • Philosophy
    Problems in Twentieth Century French Philosophy
  • 2020
Abstract Albert Lautman (1908–44) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical
Theological Underpinnings of the Modern Philosophy of Mathematics.
Abstract The study is focused on the relation between theology and mathematics in the situation of increasing secularization. My main concern is nineteenth-century mathematics. Theology was present
Number Concepts Are Constructed through Material Engagement: A Reply to Sutliff, Read, and Everett
I respond to three responses to my 2015 Current Anthropology article, “Numerosity Structures the Expression of Quantity in Lexical Numbers and Grammatical Number.” This study examined the categorical
The surface and the abyss/Rethinking topology
Through a critical deployment of the surface/depth metaphor, this article explores the catalytic potential of topological thinking to establish points of articulation between apparently opposed
Quantum computation beyond the unitary circuit model
This thesis considers various paradigms of quantum computation in an attempt to understand the nature of the underlying physics, and introduces Measurement-Based Classical Computing, an essentially classical model of computation, wherein the complexity hard wired into probability distributions generated via quantum means yields surprising non classical results.
Dis-locating innovation: amphibious geographies of creative reuse and alternative value production
Through a critical deployment of the surface/depth metaphor, this article explores the catalytic potential of topological thinking to establish points of articulation between apparently opposed
Metaphorical reactions in 1932: from the mathematical ‘crisis of intuition’ to ‘reconstruction in the exact sciences’
  • M. Friedman
  • Philosophy
    British Journal for the History of Mathematics
  • 2022
In 1932, the mathematician Hans Hahn delivered a lecture titled ‘The crisis of intuition’, held within a lecture series called ‘Crisis and Reconstruction in the Exact Sciences’, organized by Karl


Hilbert's Programs: 1917–1922
  • W. Sieg
  • Philosophy
    Bulletin of Symbolic Logic
  • 1999
The connection of Hilbert's considerations to issues in the foundations of mathematics during the second half of the 19th century is sketched, the work that laid the basis of modern mathematical logic is described, and the first steps in the new subject of proof theory are analyzed.
The Practice of Finitism: Epsilon Calculus and Consistency Proofs in Hilbert's Program
The paper traces the development of the ``simultaneous development of logic and mathematics'' through the ∈-notation and provides an analysis of Ackermann's consistency proofs for primitive recursive arithmetic and for the first comprehensive mathematical system, the latter using thesubstitution method.
David Hilbert and his mathematical work
A great master of mathematics passed away when David Hilbert died in Gottingen on February the 14th, 1943, at the age of eighty-one. In retrospect it seems to us that the era of mathematics upon
Logical dilemmas - the life and work of Kurt Gödel
Kurt Goedel's seminal achievements that changed the perception and foundations of mathematics are explained in the context of his life from the turn of the century Austria to the Institute for Advanced Study in Princeton.
Gnomes in the Fog: The Reception of Brouwer's Intuitionism in the 1920s
1 Kronecker, the semi-intuitionists, Poincare.- 1.1 Introduction.- 1.1.1 Mathematical prerequisites.- 1.2 Kronecker.- 1.2.1 Kronecker's conflicts.- 1.2.2 Kronecker's views.- 1.3 The French
Between Vienna and Berlin: The Immediate Reception of Godel's Incompleteness Theorems
What were the earliest reactions to Godel's incompleteness theorems? After a brief summary of previous work in this area I analyse, by means of unpublished archival material, the first reactions in
The War of the frogs and the mice, or the crisis of themathematische annalen
On 27 October 1928, a curious telegram was delivered to L. E. J. Brouwer, a telegram that was to plunge him into a conflict that for some months threatened to split the German mathematical community.
Sur l'histoire du théorème fondamental de l'algèbre: théorie des équations et calcul intégral
2. La theorie generale des equations au XVIIe siecle 3. Leibniz, l'integration des differentielles rationnelles et le probleme du theoreme fondamental de l'algebre 4. Integration en termes finis et
Natur und mathematisches Erkennen
:From Kant to Hilbert: A Source Book in the Foundations of Mathematics