title={THE INFINITE},
  author={Katrina Relief},
Until the 19th century the study of the in nite was an exclusive domain of philosophers and theologians. For mathematicians, while the concept of in nity was crucial in applications of calculus and in nite series, the in nite itself was (to paraphrase Gauss) just \the manner of speaking." Indeed, 18th century mathematics, even with its frequent use of in nite sequences and in nitesimals, had no real need to study the concept of in nity itself. The increasing use of abstract functions of real… Expand
Executing Gödel’s programme in set theory
The study of set theory (a mathematical theory of infinite collections) has garnered a great deal of philosophical interest since its development. There are several reasons for this, not leastExpand
Computational finitism and concrete foundations of mathematics
  • 2014
Contemporary mathematics makes significant use of notions which belong to ideal mathematics (in Hilbert’s sense [Hil02]). The latter is expressed in language essentially employing the concept ofExpand
Creating mathematical infinities: Metaphor, blending, and the beauty of transfinite cardinals
Abstract The infinite is one of the most intriguing, controversial, and elusive ideas in which the human mind has ever engaged. In mathematics, a particularly interesting form of infinity—actualExpand
On the Origin of Symbolic Mathematics and Its Significance for Wittgenstein’s Thought
The main topic of this essay is symbolic mathematics or the method of symbolic construction, which I trace to the end of the sixteenth century when Franciscus Vieta invented the algebraic symbolismExpand
Foundations of Mathematics without Actual Infinity
Contemporary mathematics significantly uses notions which belong to ideal mathematics (in Hilbert’s sense) – which is expressed in language which essentially uses actual infinity. However, we do notExpand
The Sense of Finitude and the Finitude of Sense
For Martin Heidegger in Being and Time, human existence (Dasein) is essentially finite in its directedness toward death as a final and unavoidable individuating possibility. In Kant and the ProblemExpand
Poincaré against foundationalists old and new
The early 20th century witnessed concerted research in foundationalism in mathematics. Those pursuing a basis for mathematics included Hilbert, Russell, Zermelo, Frege, and Dedekind. They found aExpand
Paradoxes of Transfinite Cosmology
The starting point of this paper is the question whether the modern cosmology has solved the first Kant's antinomy, i.e., whether the universe is finite or infinite in space and time. In thisExpand
  • P. Mancosu
  • Computer Science, Mathematics
  • The Review of Symbolic Logic
  • 2009
This article reviewing the contributions of some thinkers who argued in favor of the assignment of different sizes to infinite collections of natural numbers and some recent mathematical developments that generalize the part–whole principle to infinite sets in a coherent fashion show how these new developments are important for a proper evaluation of a number of positions in philosophy of mathematics. Expand
Varieties of Finitism
We consider here several versions of finitism or conceptions that try to work around postulating sets of infinite size. Restricting oneself to the so-called potential infinite seems to rest either onExpand


The generation of waves in infinite structures by moving harmonic loads
Abstract The theory of convolution is extended to account for time-varying loads moving over infinite systems. Fourier transforms are used to simplify the convolution, reducing it to a multiplicationExpand
Finite Element Procedures
  • K. Bathe
  • Mathematics, Materials Science
  • 1995
1. An Introduction to the Use of Finite Element Procedures. 2. Vectors, Matrices and Tensors. 3. Some Basic Concepts of Engineering Analysis and an Introduction to the Finite Element Methods. 4.Expand
Finite element procedures for nonlinear structures in moving coordinates. Part II: Infinite beam under moving harmonic loads
This paper presents a numerical approach to the stationary solution of infinite Euler-Bernoulli beams posed on Winkler foundations under moving harmonic loads. The procedure proposed in Part 1Expand
On a composite implicit time integration procedure for nonlinear dynamics
Transient analysis of nonlinear problems in structural and solid mechanics is mainly carried out using direct time integration of the equations of motion. For reliable solutions, a stable andExpand
A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
A new family of time integration algorithms is presented for solving structural dynamics problems. The new method, denoted as the generalized-α method, possesses numerical dissipation that can beExpand
This book analyzes the effects of moving loads on elastic and inelastic solids, elements and parts of structures and on elastic media, namely beams, continuous beams, beams on elastic foundations,Expand
Discretization considerations in moving load finite element beam models
Abstract This paper investigates continuum discretization for finite element models analyzing a moving load on an elastic beam. Moving load analysis is shown to require accurate evaluation of beamExpand
Comportement dynamique de structures non-linéaires soumises à des charges mobiles
Ce travail a pour but l'etude de la dynamique de structures non-lineaires soumises a des passages de vehicules. Le cas d'un demi-espace multi-couche visco-elastique soumis a une charge mobile estExpand
Improved numerical dissipation for time integration algorithms in structural dynamics
A new family of unconditionally stable one-step methods for the direct integration of the equations of structural dynamics is introduced and is shown to possess improved algorithmic dampingExpand
Conserving energy and momentum in nonlinear dynamics: A simple implicit time integration scheme
We focus on a simple implicit time integration scheme for the transient response solution of structures when large deformations and long time durations are considered. Our aim is to have a practicalExpand