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Articles 1 - 12 of 12
Full-Text Articles in Arts and Humanities
Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza
Lagrange's Theory Of Analytical Functions And His Ideal Of Purity Of Method, Giovanni Ferraro, Marco Panza
MPP Published Research
We reconstruct essential features of Lagrange’s theory of analytical functions by exhibiting its structure and basic assumptions, as well as its main shortcomings. We explain Lagrange’s notions of function and algebraic quantity, and we concentrate on power-series expansions, on the algorithm for derivative functions, and the remainder theorem—especially on the role this theorem has in solving geometric and mechanical problems. We thus aim to provide a better understanding of Enlightenment mathematics and to show that the foundations of mathematics did not, for Lagrange, concern the solidity of its ultimate bases, but rather purity of method—the generality and internal organization of …
Understanding Controversies And Ill-Structured Problems Through Argument Visualization. Curriculum And Learning Materials For Problem-Based Learning In Small Groups Of Students Who Work Autonomously On Projects With The Interactive Agora Software, Including An Exemplary Reader On Genetically Modified Plants, Michael H.G. Hoffmann
Michael H.G. Hoffmann
No abstract provided.
An Introduction To The P-Adic Numbers, Charles I. Harrington
An Introduction To The P-Adic Numbers, Charles I. Harrington
Honors Theses
One way to construct the real numbers involves creating equivalence classes of Cauchy sequences of rational numbers with respect to the usual absolute value. But, with a different absolute value we construct a completely different set of numbers called the p-adic numbers, and denoted Qp.
A General Look At Posets Rings And Lattices, Courtney A. Phillips
A General Look At Posets Rings And Lattices, Courtney A. Phillips
Honors Theses
A lattice is a type of structure that aims to organize certain relationships that exist between members of a set. This thesis seeks to define lattices, and demonstrate the different types. It will give examples of lattices, as well as various ways to describe and classify them.
The Quantum Dialectic, Logan Kelley
The Quantum Dialectic, Logan Kelley
Pitzer Senior Theses
A philosophic account of quantum physics. The thesis is divided into two parts. Part I is dedicated to laying the groundwork of quantum physics, and explaining some of the primary difficulties. Subjects of interest will include the principle of locality, the quantum uncertainty principle, and Einstein's criterion for reality. Quantum dilemmas discussed include the double-slit experiment, observations of spin and polarization, EPR, and Bell's theorem. The first part will argue that mathematical-physical descriptions of the world fall short of explaining the experimental observations of quantum phenomenon. The problem, as will be argued, is framework of the physical descriptive schema. Part …
Solving The Helmholtz Equation For The Neumann Boundary Condition For The Pseudosphere By The Galerkin Method, Jane Pleskunas
Solving The Helmholtz Equation For The Neumann Boundary Condition For The Pseudosphere By The Galerkin Method, Jane Pleskunas
Mathematics Theses
In this paper, the Helmholtz equation for the exterior Neumann boundary condition for the pseudosphere in three dimensions using the global Galerkin method is studied. The Galerkin method will be used to solve Jones’ modified integral equation approach (modified as a series of radiating waves will be added to the fundamental solution) for the Neumann problem for the Helmholtz equation, which uses a series of double sums to approximate the integral. A Fortran 77 program is used and some required subroutines from the Naval Warfare Center are called to help increase ouraccuracy since these boundary integrals are difficult to solve. …
Una Reflexión Entorno A “El Espíritu De La Ilustración” De Tzvetan Todorov., Mariado Hinojosa
Una Reflexión Entorno A “El Espíritu De La Ilustración” De Tzvetan Todorov., Mariado Hinojosa
Mariado Hinojosa
Tomando como referencia la obra de Tzvetan Todorov, el presente artículo reflexiona brevemente sobre algunos de los presupuestos heredados de la Ilustración y que marcaron profundamente el horizonte social, cultural y político del pasado siglo XX.
Powerful Arguments: Logical Argument Mapping, Michael H.G. Hoffmann
Powerful Arguments: Logical Argument Mapping, Michael H.G. Hoffmann
Michael H.G. Hoffmann
This paper argues that deductive arguments are "powerful" when the goal is to stimulate reflection on one's own reasoning. Powerful arguments are defined as arguments that leave only one choice for a potential opponent: either to accept the conclusion or to defeat one of its premises. In the first part, the paper presents an argument for the thesis that so defined powerful arguments are possible when we do not only provide reasons as premises of an argument, but also what is called an "enabler." An "enabler" is that premise in an argument that guarantees that the reason provided in this …
Cognitive Effects Of Argument Visualization Tools, Michael H.G. Hoffmann
Cognitive Effects Of Argument Visualization Tools, Michael H.G. Hoffmann
Michael H.G. Hoffmann
External representations play a crucial role in learning. At the same time, cognitive load theory suggests that the possibility of learning depends on limited resources of the working memory and on cognitive load imposed by instructional design and representation tools. Both these observations motivate a critical look at Computer-Supported Argument Visualization (CSAV) tools that are supposed to facilitate learning. This paper uses cognitive load theory to compare the cognitive efficacy of RationaleTM 2 and AGORA.
Analyzing Framing Processes In Conflicts And Communication By Means Of Logical Argument Mapping, Michael H.G. Hoffmann
Analyzing Framing Processes In Conflicts And Communication By Means Of Logical Argument Mapping, Michael H.G. Hoffmann
Michael H.G. Hoffmann
The primary goal of this chapter is to present a new method—called Logical Argument Mapping (LAM)—for the analysis of framing processes as they occur in any communication, but especially in conflicts. I start with a distinction between boundary setting, meaning construction, and sensemaking as three forms or aspects of framing, and argue that crucial for the resolution of frame-based controversies is our ability to deal with those “webs” of mutually supporting beliefs that determine sensemaking processes. Since any analysis of framing in conflicts and communication is itself influenced by sensemaking—there is no “frame-neutrality”—the main problem for an analyst is to …
Propositional Quantification, Ryan Christensen
Propositional Quantification, Ryan Christensen
Philosophy Faculty Publications
Ramsey deWned truth in the following way: xz is true if and only if 'pzz(xz = [zpz] & pz). This deWnition is ill-formed in standard Wrst-order logic, so it is normally interpreted using substitutional or some kind of higher-order quanti-Wer. I argue that these quantiWers fail to provide an adequate reading of the deWnition, but that, given certain adjustments, standard objectual quantiWcation does provide an adequate reading.
A Foundation For Arithmetic, Kevin Halasz
A Foundation For Arithmetic, Kevin Halasz
Summer Research
This paper contains a proof of Frege's Theorem: the statement, first discovered by George Boolos, that Gottlob Frege's failed proof of the analyticity of arithmetic could be slightly altered so as to provide an axiomitization of arithmetic with just one proposition. After an expository treatment of the mathematical work in Frege's 'Foundations of Arithmetic,' the work in which Frege presented his failed proof, a novel, and particularly succinct, proof of the Theorem is provided.