Serious study of Peirce began some fifty years ago, in 1931, with the publication of the first of six volumes of the Collected Papers of Charles Sanders Peirce, edited by Charles Hartshorne and Paul Weiss. Arthur Burks added two volumes to that collection in 1958. In the meantime there had appeared, and continued to appear, several one-volume editions, namely those by Morris R. Cohen, Justus Buchler, Vincent Tomas, Philip P. Wiener, and Edward C. Moore. A new era in Peirce scholarship (...) began in 1975 with the appearance of the first of three important multi-volume editions: Charles Sanders Peirce: Contributions to “The Nation,” edited by Kenneth L. Ketner and James E. Cook ; The New Elements of Mathematics by Charles S. Peirce, edited by Carolyn Eisele ; and Charles Sanders Peirce: Complete Published Works, Including Selected Secondary Materials, the 149-microfiche collection edited by members of the Texas Tech University Institute for Studies in Pragmaticism. (shrink)

In the philosophy of mathematical practice, the aim is to understand the various aspects of this practice. Even though definitions are a central element of mathematical practice, the study of this aspect of mathematical practice is still in its infancy. In particular, there is little empirical evidence to substantiate claims about definitions in practice. In this article, we address this gap by reporting on an empirical investigation on how mathematicians create definitions and which roles and properties they attribute to them. (...) On the basis of interviews with thirteen research mathematicians, we provide a broad range of relevant aspects of definitions. In particular, we address various roles of definitions and show that definitions are not just a product of mathematical factors, but also of social and contingent factors. Furthermore, we provide concrete examples of how mathematicians interact and think about definition. This broad empirical basis with a variety of examples provides an optimal starting point for future investigations into definitions in mathematical practice. (shrink)

The Many-Interacting-Worlds (MIW) approach to a quantum theory without wave functions proposed in [8] leads naturally to numerical integrators of the Schrödinger equation on comoving grids. As yet, little is known about concrete MIW models for more than one spatial dimension and/or more than one particle. In honour of Detlef Dürr, we report on a further development of the MIW approach to treat arbitrary degrees of freedom and provide a numerical proof of concept for ground states in 2d. The latter (...) is part of a systematic numerical study [22] that includes also 1d ground and excited states. With this step towards the treatment of higher degrees of freedom we hope to stimulate their further study. (shrink)

Bundel van vier voordrachten waarin de filosofische achtergronden van de grote politieke partijen worden belicht.

Individuals make decisions under uncertainty every day based on incomplete information concerning the potential outcome of the choice or chance levels. The choices individuals make often deviate from the rational or mathematically objective solution. Accordingly, the dynamics of human decision-making are difficult to capture using conventional, linear mathematical models. Here, we present data from a two-choice task with variable risk between sure loss and risky loss to illustrate how a simple nonlinear dynamical system can be employed to capture the dynamics (...) of human decision-making under uncertainty (i.e., multi-stability, bifurcations). We test the feasibility of this model quantitatively and demonstrate how the model can account for up to 86% of the observed choice behavior. The implications of using dynamical models for explaining the nonlinear complexities of human decision-making are discussed, as well as the degree to which nonlinear dynamical systems theory might offer an alternative framework for understanding human decision-making processes. (shrink)

The concepts of joint probability as implied by the Copenhagen and realist interpretations of quantum mechanics are examined in relation to (a) the rules for manipulation of probabilistic quantities, and (b) the role of the Bell inequalities in assessing the completeness of standard quantum theory. Proponents of completeness of the Copenhagen interpretation are required to accept a modification of the classical laws of probability to provide a mechanism for complementarity. A new formulation of the locality postulate is given, not involving (...) factorizability or conditional probabilities, which clarifies the role of locality in the derivation of the Bell inequalities. (shrink)

"Contemporary Mind - Some Modern Answers" is a fantastic collection of essays by English science writer John W. Sullivan. They deal with a range of subjects, ranging from mysticism and immortality to the relationship between science and art. John William Navin Sullivan (1886 - 1937) was a literary journalist and popular science writer most famous for his study of Beethoven. He is also responsible for having written some of the earliest non-technical accounts of Einstein's General Theory of Relativity, and he (...) was acquainted with many important writers in London in the 1920s, including John Middleton Murry, Aldous Huxley, Wyndham Lewis, Aleister Crowley and T. S. Eliot. Other notable works by this author include "Aspects of Science" (1923), "Aspects of Science: Second Series" (1926), and An Outline of Modern Knowledge (1931). Contents include: "The Balanced Life," "The Problem of Suffering," "The Necessity of Mysticism," "Human Immortality," "A Dissertation on Beethoven," "The Scientific Outlook," "A Dissertation on Maxwell," "New Principles," "A Dissertation on Newton," "Science and Art," "Mathematics and Culture," "Sir Josiah Stamp," "Mr. Aldous Huxley," etc. Many vintage books such as this are increasingly scarce and expensive. It is with this in mind that we are republishing this volume now in an affordable, modern, high-quality edition complete with the original text and artwork. (shrink)

In his book The Retreat to Commitment Professor Bartley raised an important problem: can rationalism can rationalism be held in a rational way, that is, in a way that complies with its own requirements? Or is there bound to be something irrational in the rationalist's position? Briefly, Hartley's answer was that an element of irrationalism is involved in extant versions of rationalism; however, Bartley proposed a new version of rationalism that can, he claimed, be held in a way that is (...) rational according to its own account of rationality. Bartley called this ‘Comprehensively Critical Rationalism’. (shrink)

Although the theory of definability had many important antecedents—such as the descriptive set theory initiated by the French semi-intuitionists in the early 1900s—the main ideas were first laid out in precise mathematical terms by Alfred Tarski beginning in 1929. We review here the basic notions of languages, explicit definability, and grammatical complexity, and emphasize common themes in the theories of definability for four important languages underlying, respectively, descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic. We review (...) the history of previous studies of the similarities and differences in the theories of definability of the first three of these four languages. A seminal role leading toward unification of the theories has been played by the separation principles introduced by Nikolai Luzin in 1927. Emphasizing analogies and driving toward further unification embracing finite-universe logic we concentrate on a simple example—the first and second separation principles for existential-universal first-order sentences . Using this as a test case for the fundamental problem of how to “finitize” arguments in classical pure logic to the finite-universe case, we are led to the analogous negative solution by using the theory of certain special graphs: a graph is - special for any positive integers m , n , p , q iff it is bipartite with m red points and n blue points and for every p -tuple of red points there is a blue point to which they are all connected . As an aside we introduce for further study a natural “Ramseyesque” increasing sequence A of positive integers, where A is the least positive integer n for which an -special graph exists. (shrink)

My reason for bringing up the familiar matter of phenomenalism is both critical and historical. Almost to a man those who have been interested in arguing for or against phenomenalism have assumed that Berkeley was a phenomenalist. Now if Berkeley's doctrine is appropriately named “phenomenalism,” then it is a phenomenalism of a quite different stripe from the twentieth century variety, though many who have described his doctrine as phenomenalism have not sufficiently stressed the difference.